:: QUATERN2 semantic presentation

REAL is set
NAT is non zero epsilon-transitive epsilon-connected ordinal Element of K6(REAL)
K6(REAL) is set
COMPLEX is set
QUATERNION is non zero set
omega is non zero epsilon-transitive epsilon-connected ordinal set
K6(omega) is set
K6(NAT) is set
0 is zero epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V16() non-empty empty-yielding set
1 is non zero epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real Element of NAT
0 is zero epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V16() non-empty empty-yielding Element of NAT
1q is quaternion set
1q *' is quaternion Element of QUATERNION
Rea 1q is complex ext-real real Element of REAL
Im1 1q is complex ext-real real Element of REAL
- (Im1 1q) is complex ext-real real Element of REAL
<i> is quaternion set
K119(REAL,0,1,0,1) is V16() Function-like V30({0,1}, REAL ) Element of K6(K7({0,1},REAL))
{0,1} is non zero set
K7({0,1},REAL) is V16() set
K6(K7({0,1},REAL)) is set
(- (Im1 1q)) * <i> is quaternion set
(Rea 1q) + ((- (Im1 1q)) * <i>) is quaternion set
Im2 1q is complex ext-real real Element of REAL
- (Im2 1q) is complex ext-real real Element of REAL
<j> is quaternion Element of QUATERNION
2 is non zero epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real Element of NAT
3 is non zero epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real Element of NAT
K147(NAT,0,1,2,3,0,0,1,0) is V16() Function-like V30(K138(0,1,2,3), NAT ) Element of K6(K7(K138(0,1,2,3),NAT))
K138(0,1,2,3) is set
K7(K138(0,1,2,3),NAT) is V16() set
K6(K7(K138(0,1,2,3),NAT)) is set
K118(0,1,0,0) is set
K118(2,3,1,0) is set
K115(K118(0,1,0,0),K118(2,3,1,0)) is V16() Function-like set
[*0,0,1,0*] is quaternion Element of QUATERNION
(- (Im2 1q)) * <j> is quaternion set
((Rea 1q) + ((- (Im1 1q)) * <i>)) + ((- (Im2 1q)) * <j>) is quaternion Element of QUATERNION
Im3 1q is complex ext-real real Element of REAL
- (Im3 1q) is complex ext-real real Element of REAL
<k> is quaternion Element of QUATERNION
K147(NAT,0,1,2,3,0,0,0,1) is V16() Function-like V30(K138(0,1,2,3), NAT ) Element of K6(K7(K138(0,1,2,3),NAT))
K118(2,3,0,1) is set
K115(K118(0,1,0,0),K118(2,3,0,1)) is V16() Function-like set
[*0,0,0,1*] is quaternion Element of QUATERNION
(- (Im3 1q)) * <k> is quaternion set
(((Rea 1q) + ((- (Im1 1q)) * <i>)) + ((- (Im2 1q)) * <j>)) + ((- (Im3 1q)) * <k>) is quaternion Element of QUATERNION
0q is quaternion set
|.0q.| is complex ext-real real set
Rea 0q is complex ext-real real Element of REAL
(Rea 0q) ^2 is complex ext-real real Element of REAL
(Rea 0q) * (Rea 0q) is complex ext-real real set
Im1 0q is complex ext-real real Element of REAL
(Im1 0q) ^2 is complex ext-real real Element of REAL
(Im1 0q) * (Im1 0q) is complex ext-real real set
((Rea 0q) ^2) + ((Im1 0q) ^2) is complex ext-real real Element of REAL
Im2 0q is complex ext-real real Element of REAL
(Im2 0q) ^2 is complex ext-real real Element of REAL
(Im2 0q) * (Im2 0q) is complex ext-real real set
(((Rea 0q) ^2) + ((Im1 0q) ^2)) + ((Im2 0q) ^2) is complex ext-real real Element of REAL
Im3 0q is complex ext-real real Element of REAL
(Im3 0q) ^2 is complex ext-real real Element of REAL
(Im3 0q) * (Im3 0q) is complex ext-real real set
((((Rea 0q) ^2) + ((Im1 0q) ^2)) + ((Im2 0q) ^2)) + ((Im3 0q) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea 0q) ^2) + ((Im1 0q) ^2)) + ((Im2 0q) ^2)) + ((Im3 0q) ^2)) is complex ext-real real Element of REAL
|.1q.| is complex ext-real real set
(Rea 1q) ^2 is complex ext-real real Element of REAL
(Rea 1q) * (Rea 1q) is complex ext-real real set
(Im1 1q) ^2 is complex ext-real real Element of REAL
(Im1 1q) * (Im1 1q) is complex ext-real real set
((Rea 1q) ^2) + ((Im1 1q) ^2) is complex ext-real real Element of REAL
(Im2 1q) ^2 is complex ext-real real Element of REAL
(Im2 1q) * (Im2 1q) is complex ext-real real set
(((Rea 1q) ^2) + ((Im1 1q) ^2)) + ((Im2 1q) ^2) is complex ext-real real Element of REAL
(Im3 1q) ^2 is complex ext-real real Element of REAL
(Im3 1q) * (Im3 1q) is complex ext-real real set
((((Rea 1q) ^2) + ((Im1 1q) ^2)) + ((Im2 1q) ^2)) + ((Im3 1q) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea 1q) ^2) + ((Im1 1q) ^2)) + ((Im2 1q) ^2)) + ((Im3 1q) ^2)) is complex ext-real real Element of REAL
c1 is quaternion set
c1 is complex ext-real real set
c1 ^2 is complex ext-real real set
c1 * c1 is complex ext-real real set
c2 is complex ext-real real set
c2 ^2 is complex ext-real real set
c2 * c2 is complex ext-real real set
(c1 ^2) + (c2 ^2) is complex ext-real real set
c3 is complex ext-real real set
c3 ^2 is complex ext-real real set
c3 * c3 is complex ext-real real set
((c1 ^2) + (c2 ^2)) + (c3 ^2) is complex ext-real real set
y1 is complex ext-real real set
y1 ^2 is complex ext-real real set
y1 * y1 is complex ext-real real set
(((c1 ^2) + (c2 ^2)) + (c3 ^2)) + (y1 ^2) is complex ext-real real set
c1 is complex ext-real real set
c1 ^2 is complex ext-real real set
c1 * c1 is complex ext-real real set
c2 is complex ext-real real set
c2 ^2 is complex ext-real real set
c2 * c2 is complex ext-real real set
(c1 ^2) + (c2 ^2) is complex ext-real real set
c3 is complex ext-real real set
c3 ^2 is complex ext-real real set
c3 * c3 is complex ext-real real set
((c1 ^2) + (c2 ^2)) + (c3 ^2) is complex ext-real real set
y1 is complex ext-real real set
y1 ^2 is complex ext-real real set
y1 * y1 is complex ext-real real set
(((c1 ^2) + (c2 ^2)) + (c3 ^2)) + (y1 ^2) is complex ext-real real set
c1 is complex ext-real real Element of REAL
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
[*c1,c2,c3,y1*] is quaternion Element of QUATERNION
c2 * <i> is quaternion set
c1 + (c2 * <i>) is quaternion set
c3 * <j> is quaternion set
(c1 + (c2 * <i>)) + (c3 * <j>) is quaternion Element of QUATERNION
y1 * <k> is quaternion set
((c1 + (c2 * <i>)) + (c3 * <j>)) + (y1 * <k>) is quaternion Element of QUATERNION
[*0,1*] is Element of COMPLEX
[*0,1,0,0*] is quaternion Element of QUATERNION
c2 * 0 is complex ext-real real Element of REAL
c2 * 1 is complex ext-real real Element of REAL
[*(c2 * 0),(c2 * 1),(c2 * 0),(c2 * 0)*] is quaternion Element of QUATERNION
[*0,c2,0,0*] is quaternion Element of QUATERNION
c3 * 0 is complex ext-real real Element of REAL
c3 * 1 is complex ext-real real Element of REAL
[*(c3 * 0),(c3 * 0),(c3 * 1),(c2 * 0)*] is quaternion Element of QUATERNION
[*0,0,c3,0*] is quaternion Element of QUATERNION
y1 * 0 is complex ext-real real Element of REAL
y1 * 1 is complex ext-real real Element of REAL
[*(y1 * 0),(y1 * 0),(y1 * 0),(y1 * 1)*] is quaternion Element of QUATERNION
[*0,0,0,y1*] is quaternion Element of QUATERNION
c1 + 0 is complex ext-real real Element of REAL
[*(c1 + 0),c2,0,0*] is quaternion Element of QUATERNION
[*c1,c2,0,0*] is quaternion Element of QUATERNION
c2 + 0 is complex ext-real real Element of REAL
0 + c3 is complex ext-real real Element of REAL
0 + 0 is zero epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V16() non-empty empty-yielding Element of REAL
[*(c1 + 0),(c2 + 0),(0 + c3),(0 + 0)*] is quaternion Element of QUATERNION
[*c1,c2,c3,0*] is quaternion Element of QUATERNION
0 + y1 is complex ext-real real Element of REAL
[*(c1 + 0),(c2 + 0),(0 + c3),(0 + y1)*] is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
c1 + c2 is quaternion Element of QUATERNION
c3 is quaternion set
(c1 + c2) + c3 is quaternion Element of QUATERNION
c2 + c3 is quaternion Element of QUATERNION
c1 + (c2 + c3) is quaternion Element of QUATERNION
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
z1 is complex ext-real real Element of REAL
x2 is complex ext-real real Element of REAL
[*y1,w1,z1,x2*] is quaternion Element of QUATERNION
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
z2 is complex ext-real real Element of REAL
c1 is complex ext-real real Element of REAL
[*y2,w2,z2,c1*] is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
q0 is complex ext-real real Element of REAL
q1 is complex ext-real real Element of REAL
q2 is complex ext-real real Element of REAL
[*c2,q0,q1,q2*] is quaternion Element of QUATERNION
y2 + c2 is complex ext-real real Element of REAL
w2 + q0 is complex ext-real real Element of REAL
z2 + q1 is complex ext-real real Element of REAL
c1 + q2 is complex ext-real real Element of REAL
[*(y2 + c2),(w2 + q0),(z2 + q1),(c1 + q2)*] is quaternion Element of QUATERNION
y1 + y2 is complex ext-real real Element of REAL
w1 + w2 is complex ext-real real Element of REAL
z1 + z2 is complex ext-real real Element of REAL
x2 + c1 is complex ext-real real Element of REAL
[*(y1 + y2),(w1 + w2),(z1 + z2),(x2 + c1)*] is quaternion Element of QUATERNION
[*(y1 + y2),(w1 + w2),(z1 + z2),(x2 + c1)*] + [*c2,q0,q1,q2*] is quaternion Element of QUATERNION
(y1 + y2) + c2 is complex ext-real real Element of REAL
(w1 + w2) + q0 is complex ext-real real Element of REAL
(z1 + z2) + q1 is complex ext-real real Element of REAL
(x2 + c1) + q2 is complex ext-real real Element of REAL
[*((y1 + y2) + c2),((w1 + w2) + q0),((z1 + z2) + q1),((x2 + c1) + q2)*] is quaternion Element of QUATERNION
y1 + (y2 + c2) is complex ext-real real Element of REAL
w1 + (w2 + q0) is complex ext-real real Element of REAL
z1 + (z2 + q1) is complex ext-real real Element of REAL
x2 + (c1 + q2) is complex ext-real real Element of REAL
[*(y1 + (y2 + c2)),(w1 + (w2 + q0)),(z1 + (z2 + q1)),(x2 + (c1 + q2))*] is quaternion Element of QUATERNION
() is quaternion Element of QUATERNION
c1 is quaternion set
c1 + () is quaternion Element of QUATERNION
[*0,0*] is Element of COMPLEX
[*0,0,0,0*] is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
[*c2,c3,y1,w1*] is quaternion Element of QUATERNION
c2 + 0 is complex ext-real real Element of REAL
c3 + 0 is complex ext-real real Element of REAL
y1 + 0 is complex ext-real real Element of REAL
w1 + 0 is complex ext-real real Element of REAL
[*(c2 + 0),(c3 + 0),(y1 + 0),(w1 + 0)*] is quaternion Element of QUATERNION
c1 is complex ext-real real Element of REAL
- c1 is complex ext-real real Element of REAL
c2 is complex ext-real real Element of REAL
- c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
- c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
[*c1,c2,c3,y1*] is quaternion Element of QUATERNION
- [*c1,c2,c3,y1*] is quaternion Element of QUATERNION
- y1 is complex ext-real real Element of REAL
[*(- c1),(- c2),(- c3),(- y1)*] is quaternion Element of QUATERNION
[*c1,c2,c3,y1*] + [*(- c1),(- c2),(- c3),(- y1)*] is quaternion Element of QUATERNION
c1 - c1 is complex ext-real real Element of REAL
- c1 is complex ext-real real set
c1 + (- c1) is complex ext-real real set
c2 - c2 is complex ext-real real Element of REAL
- c2 is complex ext-real real set
c2 + (- c2) is complex ext-real real set
c3 - c3 is complex ext-real real Element of REAL
- c3 is complex ext-real real set
c3 + (- c3) is complex ext-real real set
y1 - y1 is complex ext-real real Element of REAL
- y1 is complex ext-real real set
y1 + (- y1) is complex ext-real real set
[*(c1 - c1),(c2 - c2),(c3 - c3),(y1 - y1)*] is quaternion Element of QUATERNION
[*0,0*] is Element of COMPLEX
c1 is complex ext-real real Element of REAL
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
[*c1,c2,c3,y1*] is quaternion Element of QUATERNION
w1 is complex ext-real real Element of REAL
c1 - w1 is complex ext-real real Element of REAL
- w1 is complex ext-real real set
c1 + (- w1) is complex ext-real real set
z1 is complex ext-real real Element of REAL
c2 - z1 is complex ext-real real Element of REAL
- z1 is complex ext-real real set
c2 + (- z1) is complex ext-real real set
x2 is complex ext-real real Element of REAL
c3 - x2 is complex ext-real real Element of REAL
- x2 is complex ext-real real set
c3 + (- x2) is complex ext-real real set
y2 is complex ext-real real Element of REAL
[*w1,z1,x2,y2*] is quaternion Element of QUATERNION
[*c1,c2,c3,y1*] - [*w1,z1,x2,y2*] is quaternion Element of QUATERNION
- [*w1,z1,x2,y2*] is quaternion set
[*c1,c2,c3,y1*] + (- [*w1,z1,x2,y2*]) is quaternion set
y1 - y2 is complex ext-real real Element of REAL
- y2 is complex ext-real real set
y1 + (- y2) is complex ext-real real set
[*(c1 - w1),(c2 - z1),(c3 - x2),(y1 - y2)*] is quaternion Element of QUATERNION
- w1 is complex ext-real real Element of REAL
- z1 is complex ext-real real Element of REAL
- x2 is complex ext-real real Element of REAL
- y2 is complex ext-real real Element of REAL
[*(- w1),(- z1),(- x2),(- y2)*] is quaternion Element of QUATERNION
[*c1,c2,c3,y1*] + [*(- w1),(- z1),(- x2),(- y2)*] is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
c1 - c2 is quaternion Element of QUATERNION
- c2 is quaternion set
c1 + (- c2) is quaternion set
c3 is quaternion set
(c1 - c2) + c3 is quaternion Element of QUATERNION
c1 + c3 is quaternion Element of QUATERNION
(c1 + c3) - c2 is quaternion Element of QUATERNION
(c1 + c3) + (- c2) is quaternion set
c1 is quaternion set
c2 is quaternion set
c1 + c2 is quaternion Element of QUATERNION
(c1 + c2) - c2 is quaternion Element of QUATERNION
- c2 is quaternion set
(c1 + c2) + (- c2) is quaternion set
c2 - c2 is quaternion Element of QUATERNION
c2 + (- c2) is quaternion set
c1 + (c2 - c2) is quaternion Element of QUATERNION
c1 + () is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
c1 - c2 is quaternion Element of QUATERNION
- c2 is quaternion set
c1 + (- c2) is quaternion set
(c1 - c2) + c2 is quaternion Element of QUATERNION
c1 + c2 is quaternion Element of QUATERNION
(c1 + c2) - c2 is quaternion Element of QUATERNION
(c1 + c2) + (- c2) is quaternion set
c1 is quaternion set
c2 is complex ext-real real Element of REAL
- c2 is complex ext-real real Element of REAL
(- c2) * c1 is quaternion set
c2 * c1 is quaternion set
- (c2 * c1) is quaternion Element of QUATERNION
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
z1 is complex ext-real real Element of REAL
[*c3,y1,w1,z1*] is quaternion Element of QUATERNION
(- c2) * c3 is complex ext-real real Element of REAL
(- c2) * y1 is complex ext-real real Element of REAL
(- c2) * w1 is complex ext-real real Element of REAL
(- c2) * z1 is complex ext-real real Element of REAL
[*((- c2) * c3),((- c2) * y1),((- c2) * w1),((- c2) * z1)*] is quaternion Element of QUATERNION
c2 * c3 is complex ext-real real Element of REAL
- (c2 * c3) is complex ext-real real Element of REAL
c2 * y1 is complex ext-real real Element of REAL
- (c2 * y1) is complex ext-real real Element of REAL
c2 * w1 is complex ext-real real Element of REAL
- (c2 * w1) is complex ext-real real Element of REAL
c2 * z1 is complex ext-real real Element of REAL
- (c2 * z1) is complex ext-real real Element of REAL
[*(- (c2 * c3)),(- (c2 * y1)),(- (c2 * w1)),(- (c2 * z1))*] is quaternion Element of QUATERNION
[*(c2 * c3),(c2 * y1),(c2 * w1),(c2 * z1)*] is quaternion Element of QUATERNION
- [*(c2 * c3),(c2 * y1),(c2 * w1),(c2 * z1)*] is quaternion Element of QUATERNION
[*(c2 * c3),(c2 * y1),(c2 * w1),(c2 * z1)*] + [*(- (c2 * c3)),(- (c2 * y1)),(- (c2 * w1)),(- (c2 * z1))*] is quaternion Element of QUATERNION
(c2 * c3) + (- (c2 * c3)) is complex ext-real real Element of REAL
(c2 * y1) + (- (c2 * y1)) is complex ext-real real Element of REAL
(c2 * w1) + (- (c2 * w1)) is complex ext-real real Element of REAL
(c2 * z1) + (- (c2 * z1)) is complex ext-real real Element of REAL
[*((c2 * c3) + (- (c2 * c3))),((c2 * y1) + (- (c2 * y1))),((c2 * w1) + (- (c2 * w1))),((c2 * z1) + (- (c2 * z1)))*] is quaternion Element of QUATERNION
[*0,0*] is Element of COMPLEX
c1 is quaternion set
|.c1.| is complex ext-real real set
Rea c1 is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
Im1 c1 is complex ext-real real Element of REAL
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
c1 is quaternion set
(c1) is complex ext-real real Element of REAL
Rea c1 is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
Im1 c1 is complex ext-real real Element of REAL
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
c1 is quaternion set
(c1) is complex ext-real real Element of REAL
Rea c1 is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
Im1 c1 is complex ext-real real Element of REAL
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
[*0,0,0,0*] is quaternion Element of QUATERNION
[*0,0*] is Element of COMPLEX
c1 is quaternion set
() * c1 is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
[*c2,c3,y1,w1*] is quaternion Element of QUATERNION
z1 is complex ext-real real Element of REAL
x2 is complex ext-real real Element of REAL
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
[*z1,x2,y2,w2*] is quaternion Element of QUATERNION
c2 * z1 is complex ext-real real Element of REAL
c3 * x2 is complex ext-real real Element of REAL
(c2 * z1) - (c3 * x2) is complex ext-real real Element of REAL
- (c3 * x2) is complex ext-real real set
(c2 * z1) + (- (c3 * x2)) is complex ext-real real set
y1 * y2 is complex ext-real real Element of REAL
((c2 * z1) - (c3 * x2)) - (y1 * y2) is complex ext-real real Element of REAL
- (y1 * y2) is complex ext-real real set
((c2 * z1) - (c3 * x2)) + (- (y1 * y2)) is complex ext-real real set
w1 * w2 is complex ext-real real Element of REAL
(((c2 * z1) - (c3 * x2)) - (y1 * y2)) - (w1 * w2) is complex ext-real real Element of REAL
- (w1 * w2) is complex ext-real real set
(((c2 * z1) - (c3 * x2)) - (y1 * y2)) + (- (w1 * w2)) is complex ext-real real set
c2 * x2 is complex ext-real real Element of REAL
c3 * z1 is complex ext-real real Element of REAL
(c2 * x2) + (c3 * z1) is complex ext-real real Element of REAL
y1 * w2 is complex ext-real real Element of REAL
((c2 * x2) + (c3 * z1)) + (y1 * w2) is complex ext-real real Element of REAL
w1 * y2 is complex ext-real real Element of REAL
(((c2 * x2) + (c3 * z1)) + (y1 * w2)) - (w1 * y2) is complex ext-real real Element of REAL
- (w1 * y2) is complex ext-real real set
(((c2 * x2) + (c3 * z1)) + (y1 * w2)) + (- (w1 * y2)) is complex ext-real real set
c2 * y2 is complex ext-real real Element of REAL
z1 * y1 is complex ext-real real Element of REAL
(c2 * y2) + (z1 * y1) is complex ext-real real Element of REAL
x2 * w1 is complex ext-real real Element of REAL
((c2 * y2) + (z1 * y1)) + (x2 * w1) is complex ext-real real Element of REAL
w2 * c3 is complex ext-real real Element of REAL
(((c2 * y2) + (z1 * y1)) + (x2 * w1)) - (w2 * c3) is complex ext-real real Element of REAL
- (w2 * c3) is complex ext-real real set
(((c2 * y2) + (z1 * y1)) + (x2 * w1)) + (- (w2 * c3)) is complex ext-real real set
c2 * w2 is complex ext-real real Element of REAL
w1 * z1 is complex ext-real real Element of REAL
(c2 * w2) + (w1 * z1) is complex ext-real real Element of REAL
c3 * y2 is complex ext-real real Element of REAL
((c2 * w2) + (w1 * z1)) + (c3 * y2) is complex ext-real real Element of REAL
y1 * x2 is complex ext-real real Element of REAL
(((c2 * w2) + (w1 * z1)) + (c3 * y2)) - (y1 * x2) is complex ext-real real Element of REAL
- (y1 * x2) is complex ext-real real set
(((c2 * w2) + (w1 * z1)) + (c3 * y2)) + (- (y1 * x2)) is complex ext-real real set
[*((((c2 * z1) - (c3 * x2)) - (y1 * y2)) - (w1 * w2)),((((c2 * x2) + (c3 * z1)) + (y1 * w2)) - (w1 * y2)),((((c2 * y2) + (z1 * y1)) + (x2 * w1)) - (w2 * c3)),((((c2 * w2) + (w1 * z1)) + (c3 * y2)) - (y1 * x2))*] is quaternion Element of QUATERNION
c1 is quaternion set
c1 * () is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
[*c2,c3,y1,w1*] is quaternion Element of QUATERNION
z1 is complex ext-real real Element of REAL
x2 is complex ext-real real Element of REAL
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
[*z1,x2,y2,w2*] is quaternion Element of QUATERNION
c2 * z1 is complex ext-real real Element of REAL
c3 * x2 is complex ext-real real Element of REAL
(c2 * z1) - (c3 * x2) is complex ext-real real Element of REAL
- (c3 * x2) is complex ext-real real set
(c2 * z1) + (- (c3 * x2)) is complex ext-real real set
y1 * y2 is complex ext-real real Element of REAL
((c2 * z1) - (c3 * x2)) - (y1 * y2) is complex ext-real real Element of REAL
- (y1 * y2) is complex ext-real real set
((c2 * z1) - (c3 * x2)) + (- (y1 * y2)) is complex ext-real real set
w1 * w2 is complex ext-real real Element of REAL
(((c2 * z1) - (c3 * x2)) - (y1 * y2)) - (w1 * w2) is complex ext-real real Element of REAL
- (w1 * w2) is complex ext-real real set
(((c2 * z1) - (c3 * x2)) - (y1 * y2)) + (- (w1 * w2)) is complex ext-real real set
c2 * x2 is complex ext-real real Element of REAL
c3 * z1 is complex ext-real real Element of REAL
(c2 * x2) + (c3 * z1) is complex ext-real real Element of REAL
y1 * w2 is complex ext-real real Element of REAL
((c2 * x2) + (c3 * z1)) + (y1 * w2) is complex ext-real real Element of REAL
w1 * y2 is complex ext-real real Element of REAL
(((c2 * x2) + (c3 * z1)) + (y1 * w2)) - (w1 * y2) is complex ext-real real Element of REAL
- (w1 * y2) is complex ext-real real set
(((c2 * x2) + (c3 * z1)) + (y1 * w2)) + (- (w1 * y2)) is complex ext-real real set
c2 * y2 is complex ext-real real Element of REAL
z1 * y1 is complex ext-real real Element of REAL
(c2 * y2) + (z1 * y1) is complex ext-real real Element of REAL
x2 * w1 is complex ext-real real Element of REAL
((c2 * y2) + (z1 * y1)) + (x2 * w1) is complex ext-real real Element of REAL
w2 * c3 is complex ext-real real Element of REAL
(((c2 * y2) + (z1 * y1)) + (x2 * w1)) - (w2 * c3) is complex ext-real real Element of REAL
- (w2 * c3) is complex ext-real real set
(((c2 * y2) + (z1 * y1)) + (x2 * w1)) + (- (w2 * c3)) is complex ext-real real set
c2 * w2 is complex ext-real real Element of REAL
w1 * z1 is complex ext-real real Element of REAL
(c2 * w2) + (w1 * z1) is complex ext-real real Element of REAL
c3 * y2 is complex ext-real real Element of REAL
((c2 * w2) + (w1 * z1)) + (c3 * y2) is complex ext-real real Element of REAL
y1 * x2 is complex ext-real real Element of REAL
(((c2 * w2) + (w1 * z1)) + (c3 * y2)) - (y1 * x2) is complex ext-real real Element of REAL
- (y1 * x2) is complex ext-real real set
(((c2 * w2) + (w1 * z1)) + (c3 * y2)) + (- (y1 * x2)) is complex ext-real real set
[*((((c2 * z1) - (c3 * x2)) - (y1 * y2)) - (w1 * w2)),((((c2 * x2) + (c3 * z1)) + (y1 * w2)) - (w1 * y2)),((((c2 * y2) + (z1 * y1)) + (x2 * w1)) - (w2 * c3)),((((c2 * w2) + (w1 * z1)) + (c3 * y2)) - (y1 * x2))*] is quaternion Element of QUATERNION
() is quaternion Element of QUATERNION
c1 is quaternion set
c1 * () is quaternion Element of QUATERNION
[*1,0*] is Element of COMPLEX
[*1,0,0,0*] is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
[*c2,c3,y1,w1*] is quaternion Element of QUATERNION
c2 * 1 is complex ext-real real Element of REAL
c3 * 0 is complex ext-real real Element of REAL
(c2 * 1) - (c3 * 0) is complex ext-real real Element of REAL
- (c3 * 0) is complex ext-real real set
(c2 * 1) + (- (c3 * 0)) is complex ext-real real set
y1 * 0 is complex ext-real real Element of REAL
((c2 * 1) - (c3 * 0)) - (y1 * 0) is complex ext-real real Element of REAL
- (y1 * 0) is complex ext-real real set
((c2 * 1) - (c3 * 0)) + (- (y1 * 0)) is complex ext-real real set
w1 * 0 is complex ext-real real Element of REAL
(((c2 * 1) - (c3 * 0)) - (y1 * 0)) - (w1 * 0) is complex ext-real real Element of REAL
- (w1 * 0) is complex ext-real real set
(((c2 * 1) - (c3 * 0)) - (y1 * 0)) + (- (w1 * 0)) is complex ext-real real set
c2 * 0 is complex ext-real real Element of REAL
c3 * 1 is complex ext-real real Element of REAL
(c2 * 0) + (c3 * 1) is complex ext-real real Element of REAL
((c2 * 0) + (c3 * 1)) + (y1 * 0) is complex ext-real real Element of REAL
(((c2 * 0) + (c3 * 1)) + (y1 * 0)) - (w1 * 0) is complex ext-real real Element of REAL
(((c2 * 0) + (c3 * 1)) + (y1 * 0)) + (- (w1 * 0)) is complex ext-real real set
1 * y1 is complex ext-real real Element of REAL
(c2 * 0) + (1 * y1) is complex ext-real real Element of REAL
0 * w1 is complex ext-real real Element of REAL
((c2 * 0) + (1 * y1)) + (0 * w1) is complex ext-real real Element of REAL
0 * c3 is complex ext-real real Element of REAL
(((c2 * 0) + (1 * y1)) + (0 * w1)) - (0 * c3) is complex ext-real real Element of REAL
- (0 * c3) is complex ext-real real set
(((c2 * 0) + (1 * y1)) + (0 * w1)) + (- (0 * c3)) is complex ext-real real set
w1 * 1 is complex ext-real real Element of REAL
(c2 * 0) + (w1 * 1) is complex ext-real real Element of REAL
((c2 * 0) + (w1 * 1)) + (c3 * 0) is complex ext-real real Element of REAL
(((c2 * 0) + (w1 * 1)) + (c3 * 0)) - (y1 * 0) is complex ext-real real Element of REAL
(((c2 * 0) + (w1 * 1)) + (c3 * 0)) + (- (y1 * 0)) is complex ext-real real set
[*((((c2 * 1) - (c3 * 0)) - (y1 * 0)) - (w1 * 0)),((((c2 * 0) + (c3 * 1)) + (y1 * 0)) - (w1 * 0)),((((c2 * 0) + (1 * y1)) + (0 * w1)) - (0 * c3)),((((c2 * 0) + (w1 * 1)) + (c3 * 0)) - (y1 * 0))*] is quaternion Element of QUATERNION
c1 is quaternion set
() * c1 is quaternion Element of QUATERNION
[*1,0*] is Element of COMPLEX
[*1,0,0,0*] is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
[*c2,c3,y1,w1*] is quaternion Element of QUATERNION
c2 * 1 is complex ext-real real Element of REAL
c3 * 0 is complex ext-real real Element of REAL
(c2 * 1) - (c3 * 0) is complex ext-real real Element of REAL
- (c3 * 0) is complex ext-real real set
(c2 * 1) + (- (c3 * 0)) is complex ext-real real set
y1 * 0 is complex ext-real real Element of REAL
((c2 * 1) - (c3 * 0)) - (y1 * 0) is complex ext-real real Element of REAL
- (y1 * 0) is complex ext-real real set
((c2 * 1) - (c3 * 0)) + (- (y1 * 0)) is complex ext-real real set
w1 * 0 is complex ext-real real Element of REAL
(((c2 * 1) - (c3 * 0)) - (y1 * 0)) - (w1 * 0) is complex ext-real real Element of REAL
- (w1 * 0) is complex ext-real real set
(((c2 * 1) - (c3 * 0)) - (y1 * 0)) + (- (w1 * 0)) is complex ext-real real set
c2 * 0 is complex ext-real real Element of REAL
c3 * 1 is complex ext-real real Element of REAL
(c2 * 0) + (c3 * 1) is complex ext-real real Element of REAL
((c2 * 0) + (c3 * 1)) + (y1 * 0) is complex ext-real real Element of REAL
(((c2 * 0) + (c3 * 1)) + (y1 * 0)) - (w1 * 0) is complex ext-real real Element of REAL
(((c2 * 0) + (c3 * 1)) + (y1 * 0)) + (- (w1 * 0)) is complex ext-real real set
1 * y1 is complex ext-real real Element of REAL
(c2 * 0) + (1 * y1) is complex ext-real real Element of REAL
0 * w1 is complex ext-real real Element of REAL
((c2 * 0) + (1 * y1)) + (0 * w1) is complex ext-real real Element of REAL
0 * c3 is complex ext-real real Element of REAL
(((c2 * 0) + (1 * y1)) + (0 * w1)) - (0 * c3) is complex ext-real real Element of REAL
- (0 * c3) is complex ext-real real set
(((c2 * 0) + (1 * y1)) + (0 * w1)) + (- (0 * c3)) is complex ext-real real set
w1 * 1 is complex ext-real real Element of REAL
(c2 * 0) + (w1 * 1) is complex ext-real real Element of REAL
((c2 * 0) + (w1 * 1)) + (c3 * 0) is complex ext-real real Element of REAL
(((c2 * 0) + (w1 * 1)) + (c3 * 0)) - (y1 * 0) is complex ext-real real Element of REAL
(((c2 * 0) + (w1 * 1)) + (c3 * 0)) + (- (y1 * 0)) is complex ext-real real set
[*((((c2 * 1) - (c3 * 0)) - (y1 * 0)) - (w1 * 0)),((((c2 * 0) + (c3 * 1)) + (y1 * 0)) - (w1 * 0)),((((c2 * 0) + (1 * y1)) + (0 * w1)) - (0 * c3)),((((c2 * 0) + (w1 * 1)) + (c3 * 0)) - (y1 * 0))*] is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
c1 * c2 is quaternion Element of QUATERNION
c3 is quaternion set
(c1 * c2) * c3 is quaternion Element of QUATERNION
c2 * c3 is quaternion Element of QUATERNION
c1 * (c2 * c3) is quaternion Element of QUATERNION
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
z1 is complex ext-real real Element of REAL
x2 is complex ext-real real Element of REAL
[*y1,w1,z1,x2*] is quaternion Element of QUATERNION
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
z2 is complex ext-real real Element of REAL
c1 is complex ext-real real Element of REAL
[*y2,w2,z2,c1*] is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
q0 is complex ext-real real Element of REAL
q1 is complex ext-real real Element of REAL
q2 is complex ext-real real Element of REAL
[*c2,q0,q1,q2*] is quaternion Element of QUATERNION
y1 * y2 is complex ext-real real Element of REAL
w1 * w2 is complex ext-real real Element of REAL
(y1 * y2) - (w1 * w2) is complex ext-real real Element of REAL
- (w1 * w2) is complex ext-real real set
(y1 * y2) + (- (w1 * w2)) is complex ext-real real set
z1 * z2 is complex ext-real real Element of REAL
((y1 * y2) - (w1 * w2)) - (z1 * z2) is complex ext-real real Element of REAL
- (z1 * z2) is complex ext-real real set
((y1 * y2) - (w1 * w2)) + (- (z1 * z2)) is complex ext-real real set
x2 * c1 is complex ext-real real Element of REAL
(((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1) is complex ext-real real Element of REAL
- (x2 * c1) is complex ext-real real set
(((y1 * y2) - (w1 * w2)) - (z1 * z2)) + (- (x2 * c1)) is complex ext-real real set
y1 * w2 is complex ext-real real Element of REAL
w1 * y2 is complex ext-real real Element of REAL
(y1 * w2) + (w1 * y2) is complex ext-real real Element of REAL
z1 * c1 is complex ext-real real Element of REAL
((y1 * w2) + (w1 * y2)) + (z1 * c1) is complex ext-real real Element of REAL
x2 * z2 is complex ext-real real Element of REAL
(((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2) is complex ext-real real Element of REAL
- (x2 * z2) is complex ext-real real set
(((y1 * w2) + (w1 * y2)) + (z1 * c1)) + (- (x2 * z2)) is complex ext-real real set
y1 * z2 is complex ext-real real Element of REAL
y2 * z1 is complex ext-real real Element of REAL
(y1 * z2) + (y2 * z1) is complex ext-real real Element of REAL
w2 * x2 is complex ext-real real Element of REAL
((y1 * z2) + (y2 * z1)) + (w2 * x2) is complex ext-real real Element of REAL
c1 * w1 is complex ext-real real Element of REAL
(((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1) is complex ext-real real Element of REAL
- (c1 * w1) is complex ext-real real set
(((y1 * z2) + (y2 * z1)) + (w2 * x2)) + (- (c1 * w1)) is complex ext-real real set
y1 * c1 is complex ext-real real Element of REAL
x2 * y2 is complex ext-real real Element of REAL
(y1 * c1) + (x2 * y2) is complex ext-real real Element of REAL
w1 * z2 is complex ext-real real Element of REAL
((y1 * c1) + (x2 * y2)) + (w1 * z2) is complex ext-real real Element of REAL
z1 * w2 is complex ext-real real Element of REAL
(((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2) is complex ext-real real Element of REAL
- (z1 * w2) is complex ext-real real set
(((y1 * c1) + (x2 * y2)) + (w1 * z2)) + (- (z1 * w2)) is complex ext-real real set
[*((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)),((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)),((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)),((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2))*] is quaternion Element of QUATERNION
[*((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)),((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)),((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)),((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2))*] * c3 is quaternion Element of QUATERNION
((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * c2 is complex ext-real real Element of REAL
((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q0 is complex ext-real real Element of REAL
(((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * c2) - (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q0) is complex ext-real real Element of REAL
- (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q0) is complex ext-real real set
(((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * c2) + (- (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q0)) is complex ext-real real set
((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q1 is complex ext-real real Element of REAL
((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * c2) - (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q0)) - (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q1) is complex ext-real real Element of REAL
- (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q1) is complex ext-real real set
((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * c2) - (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q0)) + (- (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q1)) is complex ext-real real set
((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * q2 is complex ext-real real Element of REAL
(((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * c2) - (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q0)) - (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q1)) - (((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * q2) is complex ext-real real Element of REAL
- (((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * q2) is complex ext-real real set
(((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * c2) - (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q0)) - (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q1)) + (- (((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * q2)) is complex ext-real real set
((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q0 is complex ext-real real Element of REAL
((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * c2 is complex ext-real real Element of REAL
(((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q0) + (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * c2) is complex ext-real real Element of REAL
((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q2 is complex ext-real real Element of REAL
((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q0) + (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * c2)) + (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q2) is complex ext-real real Element of REAL
((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * q1 is complex ext-real real Element of REAL
(((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q0) + (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * c2)) + (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q2)) - (((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * q1) is complex ext-real real Element of REAL
- (((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * q1) is complex ext-real real set
(((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q0) + (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * c2)) + (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q2)) + (- (((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * q1)) is complex ext-real real set
((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q1 is complex ext-real real Element of REAL
c2 * ((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) is complex ext-real real Element of REAL
(((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q1) + (c2 * ((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1))) is complex ext-real real Element of REAL
q0 * ((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) is complex ext-real real Element of REAL
((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q1) + (c2 * ((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)))) + (q0 * ((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2))) is complex ext-real real Element of REAL
q2 * ((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) is complex ext-real real Element of REAL
(((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q1) + (c2 * ((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)))) + (q0 * ((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)))) - (q2 * ((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2))) is complex ext-real real Element of REAL
- (q2 * ((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2))) is complex ext-real real set
(((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q1) + (c2 * ((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)))) + (q0 * ((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)))) + (- (q2 * ((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)))) is complex ext-real real set
((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q2 is complex ext-real real Element of REAL
((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * c2 is complex ext-real real Element of REAL
(((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q2) + (((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * c2) is complex ext-real real Element of REAL
((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q1 is complex ext-real real Element of REAL
((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q2) + (((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * c2)) + (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q1) is complex ext-real real Element of REAL
((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q0 is complex ext-real real Element of REAL
(((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q2) + (((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * c2)) + (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q1)) - (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q0) is complex ext-real real Element of REAL
- (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q0) is complex ext-real real set
(((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q2) + (((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * c2)) + (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q1)) + (- (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q0)) is complex ext-real real set
[*((((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * c2) - (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q0)) - (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q1)) - (((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * q2)),((((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q0) + (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * c2)) + (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q2)) - (((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * q1)),((((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q1) + (c2 * ((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)))) + (q0 * ((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)))) - (q2 * ((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)))),((((((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) * q2) + (((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) * c2)) + (((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) * q1)) - (((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) * q0))*] is quaternion Element of QUATERNION
(y1 * y2) * c2 is complex ext-real real Element of REAL
(w1 * w2) * c2 is complex ext-real real Element of REAL
((y1 * y2) * c2) - ((w1 * w2) * c2) is complex ext-real real Element of REAL
- ((w1 * w2) * c2) is complex ext-real real set
((y1 * y2) * c2) + (- ((w1 * w2) * c2)) is complex ext-real real set
(z1 * z2) * c2 is complex ext-real real Element of REAL
(((y1 * y2) * c2) - ((w1 * w2) * c2)) - ((z1 * z2) * c2) is complex ext-real real Element of REAL
- ((z1 * z2) * c2) is complex ext-real real set
(((y1 * y2) * c2) - ((w1 * w2) * c2)) + (- ((z1 * z2) * c2)) is complex ext-real real set
(x2 * c1) * c2 is complex ext-real real Element of REAL
((((y1 * y2) * c2) - ((w1 * w2) * c2)) - ((z1 * z2) * c2)) - ((x2 * c1) * c2) is complex ext-real real Element of REAL
- ((x2 * c1) * c2) is complex ext-real real set
((((y1 * y2) * c2) - ((w1 * w2) * c2)) - ((z1 * z2) * c2)) + (- ((x2 * c1) * c2)) is complex ext-real real set
(y1 * w2) * q0 is complex ext-real real Element of REAL
(w1 * y2) * q0 is complex ext-real real Element of REAL
((y1 * w2) * q0) + ((w1 * y2) * q0) is complex ext-real real Element of REAL
(z1 * c1) * q0 is complex ext-real real Element of REAL
(((y1 * w2) * q0) + ((w1 * y2) * q0)) + ((z1 * c1) * q0) is complex ext-real real Element of REAL
(x2 * z2) * q0 is complex ext-real real Element of REAL
((((y1 * w2) * q0) + ((w1 * y2) * q0)) + ((z1 * c1) * q0)) - ((x2 * z2) * q0) is complex ext-real real Element of REAL
- ((x2 * z2) * q0) is complex ext-real real set
((((y1 * w2) * q0) + ((w1 * y2) * q0)) + ((z1 * c1) * q0)) + (- ((x2 * z2) * q0)) is complex ext-real real set
(((((y1 * y2) * c2) - ((w1 * w2) * c2)) - ((z1 * z2) * c2)) - ((x2 * c1) * c2)) - (((((y1 * w2) * q0) + ((w1 * y2) * q0)) + ((z1 * c1) * q0)) - ((x2 * z2) * q0)) is complex ext-real real Element of REAL
- (((((y1 * w2) * q0) + ((w1 * y2) * q0)) + ((z1 * c1) * q0)) - ((x2 * z2) * q0)) is complex ext-real real set
(((((y1 * y2) * c2) - ((w1 * w2) * c2)) - ((z1 * z2) * c2)) - ((x2 * c1) * c2)) + (- (((((y1 * w2) * q0) + ((w1 * y2) * q0)) + ((z1 * c1) * q0)) - ((x2 * z2) * q0))) is complex ext-real real set
(y1 * z2) * q1 is complex ext-real real Element of REAL
(y2 * z1) * q1 is complex ext-real real Element of REAL
((y1 * z2) * q1) + ((y2 * z1) * q1) is complex ext-real real Element of REAL
(w2 * x2) * q1 is complex ext-real real Element of REAL
(((y1 * z2) * q1) + ((y2 * z1) * q1)) + ((w2 * x2) * q1) is complex ext-real real Element of REAL
(c1 * w1) * q1 is complex ext-real real Element of REAL
((((y1 * z2) * q1) + ((y2 * z1) * q1)) + ((w2 * x2) * q1)) - ((c1 * w1) * q1) is complex ext-real real Element of REAL
- ((c1 * w1) * q1) is complex ext-real real set
((((y1 * z2) * q1) + ((y2 * z1) * q1)) + ((w2 * x2) * q1)) + (- ((c1 * w1) * q1)) is complex ext-real real set
((((((y1 * y2) * c2) - ((w1 * w2) * c2)) - ((z1 * z2) * c2)) - ((x2 * c1) * c2)) - (((((y1 * w2) * q0) + ((w1 * y2) * q0)) + ((z1 * c1) * q0)) - ((x2 * z2) * q0))) - (((((y1 * z2) * q1) + ((y2 * z1) * q1)) + ((w2 * x2) * q1)) - ((c1 * w1) * q1)) is complex ext-real real Element of REAL
- (((((y1 * z2) * q1) + ((y2 * z1) * q1)) + ((w2 * x2) * q1)) - ((c1 * w1) * q1)) is complex ext-real real set
((((((y1 * y2) * c2) - ((w1 * w2) * c2)) - ((z1 * z2) * c2)) - ((x2 * c1) * c2)) - (((((y1 * w2) * q0) + ((w1 * y2) * q0)) + ((z1 * c1) * q0)) - ((x2 * z2) * q0))) + (- (((((y1 * z2) * q1) + ((y2 * z1) * q1)) + ((w2 * x2) * q1)) - ((c1 * w1) * q1))) is complex ext-real real set
(y1 * c1) * q2 is complex ext-real real Element of REAL
(x2 * y2) * q2 is complex ext-real real Element of REAL
((y1 * c1) * q2) + ((x2 * y2) * q2) is complex ext-real real Element of REAL
(w1 * z2) * q2 is complex ext-real real Element of REAL
(((y1 * c1) * q2) + ((x2 * y2) * q2)) + ((w1 * z2) * q2) is complex ext-real real Element of REAL
(z1 * w2) * q2 is complex ext-real real Element of REAL
((((y1 * c1) * q2) + ((x2 * y2) * q2)) + ((w1 * z2) * q2)) - ((z1 * w2) * q2) is complex ext-real real Element of REAL
- ((z1 * w2) * q2) is complex ext-real real set
((((y1 * c1) * q2) + ((x2 * y2) * q2)) + ((w1 * z2) * q2)) + (- ((z1 * w2) * q2)) is complex ext-real real set
(((((((y1 * y2) * c2) - ((w1 * w2) * c2)) - ((z1 * z2) * c2)) - ((x2 * c1) * c2)) - (((((y1 * w2) * q0) + ((w1 * y2) * q0)) + ((z1 * c1) * q0)) - ((x2 * z2) * q0))) - (((((y1 * z2) * q1) + ((y2 * z1) * q1)) + ((w2 * x2) * q1)) - ((c1 * w1) * q1))) - (((((y1 * c1) * q2) + ((x2 * y2) * q2)) + ((w1 * z2) * q2)) - ((z1 * w2) * q2)) is complex ext-real real Element of REAL
- (((((y1 * c1) * q2) + ((x2 * y2) * q2)) + ((w1 * z2) * q2)) - ((z1 * w2) * q2)) is complex ext-real real set
(((((((y1 * y2) * c2) - ((w1 * w2) * c2)) - ((z1 * z2) * c2)) - ((x2 * c1) * c2)) - (((((y1 * w2) * q0) + ((w1 * y2) * q0)) + ((z1 * c1) * q0)) - ((x2 * z2) * q0))) - (((((y1 * z2) * q1) + ((y2 * z1) * q1)) + ((w2 * x2) * q1)) - ((c1 * w1) * q1))) + (- (((((y1 * c1) * q2) + ((x2 * y2) * q2)) + ((w1 * z2) * q2)) - ((z1 * w2) * q2))) is complex ext-real real set
(y1 * y2) * q0 is complex ext-real real Element of REAL
(w1 * w2) * q0 is complex ext-real real Element of REAL
((y1 * y2) * q0) - ((w1 * w2) * q0) is complex ext-real real Element of REAL
- ((w1 * w2) * q0) is complex ext-real real set
((y1 * y2) * q0) + (- ((w1 * w2) * q0)) is complex ext-real real set
(z1 * z2) * q0 is complex ext-real real Element of REAL
(((y1 * y2) * q0) - ((w1 * w2) * q0)) - ((z1 * z2) * q0) is complex ext-real real Element of REAL
- ((z1 * z2) * q0) is complex ext-real real set
(((y1 * y2) * q0) - ((w1 * w2) * q0)) + (- ((z1 * z2) * q0)) is complex ext-real real set
(x2 * c1) * q0 is complex ext-real real Element of REAL
((((y1 * y2) * q0) - ((w1 * w2) * q0)) - ((z1 * z2) * q0)) - ((x2 * c1) * q0) is complex ext-real real Element of REAL
- ((x2 * c1) * q0) is complex ext-real real set
((((y1 * y2) * q0) - ((w1 * w2) * q0)) - ((z1 * z2) * q0)) + (- ((x2 * c1) * q0)) is complex ext-real real set
(y1 * w2) * c2 is complex ext-real real Element of REAL
(w1 * y2) * c2 is complex ext-real real Element of REAL
((y1 * w2) * c2) + ((w1 * y2) * c2) is complex ext-real real Element of REAL
(z1 * c1) * c2 is complex ext-real real Element of REAL
(((y1 * w2) * c2) + ((w1 * y2) * c2)) + ((z1 * c1) * c2) is complex ext-real real Element of REAL
(x2 * z2) * c2 is complex ext-real real Element of REAL
((((y1 * w2) * c2) + ((w1 * y2) * c2)) + ((z1 * c1) * c2)) - ((x2 * z2) * c2) is complex ext-real real Element of REAL
- ((x2 * z2) * c2) is complex ext-real real set
((((y1 * w2) * c2) + ((w1 * y2) * c2)) + ((z1 * c1) * c2)) + (- ((x2 * z2) * c2)) is complex ext-real real set
(((((y1 * y2) * q0) - ((w1 * w2) * q0)) - ((z1 * z2) * q0)) - ((x2 * c1) * q0)) + (((((y1 * w2) * c2) + ((w1 * y2) * c2)) + ((z1 * c1) * c2)) - ((x2 * z2) * c2)) is complex ext-real real Element of REAL
(y1 * z2) * q2 is complex ext-real real Element of REAL
(y2 * z1) * q2 is complex ext-real real Element of REAL
((y1 * z2) * q2) + ((y2 * z1) * q2) is complex ext-real real Element of REAL
(w2 * x2) * q2 is complex ext-real real Element of REAL
(((y1 * z2) * q2) + ((y2 * z1) * q2)) + ((w2 * x2) * q2) is complex ext-real real Element of REAL
(c1 * w1) * q2 is complex ext-real real Element of REAL
((((y1 * z2) * q2) + ((y2 * z1) * q2)) + ((w2 * x2) * q2)) - ((c1 * w1) * q2) is complex ext-real real Element of REAL
- ((c1 * w1) * q2) is complex ext-real real set
((((y1 * z2) * q2) + ((y2 * z1) * q2)) + ((w2 * x2) * q2)) + (- ((c1 * w1) * q2)) is complex ext-real real set
((((((y1 * y2) * q0) - ((w1 * w2) * q0)) - ((z1 * z2) * q0)) - ((x2 * c1) * q0)) + (((((y1 * w2) * c2) + ((w1 * y2) * c2)) + ((z1 * c1) * c2)) - ((x2 * z2) * c2))) + (((((y1 * z2) * q2) + ((y2 * z1) * q2)) + ((w2 * x2) * q2)) - ((c1 * w1) * q2)) is complex ext-real real Element of REAL
(y1 * c1) * q1 is complex ext-real real Element of REAL
(x2 * y2) * q1 is complex ext-real real Element of REAL
((y1 * c1) * q1) + ((x2 * y2) * q1) is complex ext-real real Element of REAL
(w1 * z2) * q1 is complex ext-real real Element of REAL
(((y1 * c1) * q1) + ((x2 * y2) * q1)) + ((w1 * z2) * q1) is complex ext-real real Element of REAL
(z1 * w2) * q1 is complex ext-real real Element of REAL
((((y1 * c1) * q1) + ((x2 * y2) * q1)) + ((w1 * z2) * q1)) - ((z1 * w2) * q1) is complex ext-real real Element of REAL
- ((z1 * w2) * q1) is complex ext-real real set
((((y1 * c1) * q1) + ((x2 * y2) * q1)) + ((w1 * z2) * q1)) + (- ((z1 * w2) * q1)) is complex ext-real real set
(((((((y1 * y2) * q0) - ((w1 * w2) * q0)) - ((z1 * z2) * q0)) - ((x2 * c1) * q0)) + (((((y1 * w2) * c2) + ((w1 * y2) * c2)) + ((z1 * c1) * c2)) - ((x2 * z2) * c2))) + (((((y1 * z2) * q2) + ((y2 * z1) * q2)) + ((w2 * x2) * q2)) - ((c1 * w1) * q2))) - (((((y1 * c1) * q1) + ((x2 * y2) * q1)) + ((w1 * z2) * q1)) - ((z1 * w2) * q1)) is complex ext-real real Element of REAL
- (((((y1 * c1) * q1) + ((x2 * y2) * q1)) + ((w1 * z2) * q1)) - ((z1 * w2) * q1)) is complex ext-real real set
(((((((y1 * y2) * q0) - ((w1 * w2) * q0)) - ((z1 * z2) * q0)) - ((x2 * c1) * q0)) + (((((y1 * w2) * c2) + ((w1 * y2) * c2)) + ((z1 * c1) * c2)) - ((x2 * z2) * c2))) + (((((y1 * z2) * q2) + ((y2 * z1) * q2)) + ((w2 * x2) * q2)) - ((c1 * w1) * q2))) + (- (((((y1 * c1) * q1) + ((x2 * y2) * q1)) + ((w1 * z2) * q1)) - ((z1 * w2) * q1))) is complex ext-real real set
(y1 * y2) * q1 is complex ext-real real Element of REAL
(w1 * w2) * q1 is complex ext-real real Element of REAL
((y1 * y2) * q1) - ((w1 * w2) * q1) is complex ext-real real Element of REAL
- ((w1 * w2) * q1) is complex ext-real real set
((y1 * y2) * q1) + (- ((w1 * w2) * q1)) is complex ext-real real set
(z1 * z2) * q1 is complex ext-real real Element of REAL
(((y1 * y2) * q1) - ((w1 * w2) * q1)) - ((z1 * z2) * q1) is complex ext-real real Element of REAL
- ((z1 * z2) * q1) is complex ext-real real set
(((y1 * y2) * q1) - ((w1 * w2) * q1)) + (- ((z1 * z2) * q1)) is complex ext-real real set
(x2 * c1) * q1 is complex ext-real real Element of REAL
((((y1 * y2) * q1) - ((w1 * w2) * q1)) - ((z1 * z2) * q1)) - ((x2 * c1) * q1) is complex ext-real real Element of REAL
- ((x2 * c1) * q1) is complex ext-real real set
((((y1 * y2) * q1) - ((w1 * w2) * q1)) - ((z1 * z2) * q1)) + (- ((x2 * c1) * q1)) is complex ext-real real set
c2 * y1 is complex ext-real real Element of REAL
(c2 * y1) * z2 is complex ext-real real Element of REAL
c2 * y2 is complex ext-real real Element of REAL
(c2 * y2) * z1 is complex ext-real real Element of REAL
((c2 * y1) * z2) + ((c2 * y2) * z1) is complex ext-real real Element of REAL
c2 * w2 is complex ext-real real Element of REAL
(c2 * w2) * x2 is complex ext-real real Element of REAL
(((c2 * y1) * z2) + ((c2 * y2) * z1)) + ((c2 * w2) * x2) is complex ext-real real Element of REAL
c2 * c1 is complex ext-real real Element of REAL
(c2 * c1) * w1 is complex ext-real real Element of REAL
((((c2 * y1) * z2) + ((c2 * y2) * z1)) + ((c2 * w2) * x2)) - ((c2 * c1) * w1) is complex ext-real real Element of REAL
- ((c2 * c1) * w1) is complex ext-real real set
((((c2 * y1) * z2) + ((c2 * y2) * z1)) + ((c2 * w2) * x2)) + (- ((c2 * c1) * w1)) is complex ext-real real set
(((((y1 * y2) * q1) - ((w1 * w2) * q1)) - ((z1 * z2) * q1)) - ((x2 * c1) * q1)) + (((((c2 * y1) * z2) + ((c2 * y2) * z1)) + ((c2 * w2) * x2)) - ((c2 * c1) * w1)) is complex ext-real real Element of REAL
q0 * y1 is complex ext-real real Element of REAL
(q0 * y1) * c1 is complex ext-real real Element of REAL
q0 * x2 is complex ext-real real Element of REAL
(q0 * x2) * y2 is complex ext-real real Element of REAL
((q0 * y1) * c1) + ((q0 * x2) * y2) is complex ext-real real Element of REAL
q0 * w1 is complex ext-real real Element of REAL
(q0 * w1) * z2 is complex ext-real real Element of REAL
(((q0 * y1) * c1) + ((q0 * x2) * y2)) + ((q0 * w1) * z2) is complex ext-real real Element of REAL
q0 * z1 is complex ext-real real Element of REAL
(q0 * z1) * w2 is complex ext-real real Element of REAL
((((q0 * y1) * c1) + ((q0 * x2) * y2)) + ((q0 * w1) * z2)) - ((q0 * z1) * w2) is complex ext-real real Element of REAL
- ((q0 * z1) * w2) is complex ext-real real set
((((q0 * y1) * c1) + ((q0 * x2) * y2)) + ((q0 * w1) * z2)) + (- ((q0 * z1) * w2)) is complex ext-real real set
((((((y1 * y2) * q1) - ((w1 * w2) * q1)) - ((z1 * z2) * q1)) - ((x2 * c1) * q1)) + (((((c2 * y1) * z2) + ((c2 * y2) * z1)) + ((c2 * w2) * x2)) - ((c2 * c1) * w1))) + (((((q0 * y1) * c1) + ((q0 * x2) * y2)) + ((q0 * w1) * z2)) - ((q0 * z1) * w2)) is complex ext-real real Element of REAL
q2 * y1 is complex ext-real real Element of REAL
(q2 * y1) * w2 is complex ext-real real Element of REAL
q2 * w1 is complex ext-real real Element of REAL
(q2 * w1) * y2 is complex ext-real real Element of REAL
((q2 * y1) * w2) + ((q2 * w1) * y2) is complex ext-real real Element of REAL
q2 * z1 is complex ext-real real Element of REAL
(q2 * z1) * c1 is complex ext-real real Element of REAL
(((q2 * y1) * w2) + ((q2 * w1) * y2)) + ((q2 * z1) * c1) is complex ext-real real Element of REAL
q2 * x2 is complex ext-real real Element of REAL
(q2 * x2) * z2 is complex ext-real real Element of REAL
((((q2 * y1) * w2) + ((q2 * w1) * y2)) + ((q2 * z1) * c1)) - ((q2 * x2) * z2) is complex ext-real real Element of REAL
- ((q2 * x2) * z2) is complex ext-real real set
((((q2 * y1) * w2) + ((q2 * w1) * y2)) + ((q2 * z1) * c1)) + (- ((q2 * x2) * z2)) is complex ext-real real set
(((((((y1 * y2) * q1) - ((w1 * w2) * q1)) - ((z1 * z2) * q1)) - ((x2 * c1) * q1)) + (((((c2 * y1) * z2) + ((c2 * y2) * z1)) + ((c2 * w2) * x2)) - ((c2 * c1) * w1))) + (((((q0 * y1) * c1) + ((q0 * x2) * y2)) + ((q0 * w1) * z2)) - ((q0 * z1) * w2))) - (((((q2 * y1) * w2) + ((q2 * w1) * y2)) + ((q2 * z1) * c1)) - ((q2 * x2) * z2)) is complex ext-real real Element of REAL
- (((((q2 * y1) * w2) + ((q2 * w1) * y2)) + ((q2 * z1) * c1)) - ((q2 * x2) * z2)) is complex ext-real real set
(((((((y1 * y2) * q1) - ((w1 * w2) * q1)) - ((z1 * z2) * q1)) - ((x2 * c1) * q1)) + (((((c2 * y1) * z2) + ((c2 * y2) * z1)) + ((c2 * w2) * x2)) - ((c2 * c1) * w1))) + (((((q0 * y1) * c1) + ((q0 * x2) * y2)) + ((q0 * w1) * z2)) - ((q0 * z1) * w2))) + (- (((((q2 * y1) * w2) + ((q2 * w1) * y2)) + ((q2 * z1) * c1)) - ((q2 * x2) * z2))) is complex ext-real real set
(y1 * y2) * q2 is complex ext-real real Element of REAL
(w1 * w2) * q2 is complex ext-real real Element of REAL
((y1 * y2) * q2) - ((w1 * w2) * q2) is complex ext-real real Element of REAL
- ((w1 * w2) * q2) is complex ext-real real set
((y1 * y2) * q2) + (- ((w1 * w2) * q2)) is complex ext-real real set
(z1 * z2) * q2 is complex ext-real real Element of REAL
(((y1 * y2) * q2) - ((w1 * w2) * q2)) - ((z1 * z2) * q2) is complex ext-real real Element of REAL
- ((z1 * z2) * q2) is complex ext-real real set
(((y1 * y2) * q2) - ((w1 * w2) * q2)) + (- ((z1 * z2) * q2)) is complex ext-real real set
(x2 * c1) * q2 is complex ext-real real Element of REAL
((((y1 * y2) * q2) - ((w1 * w2) * q2)) - ((z1 * z2) * q2)) - ((x2 * c1) * q2) is complex ext-real real Element of REAL
- ((x2 * c1) * q2) is complex ext-real real set
((((y1 * y2) * q2) - ((w1 * w2) * q2)) - ((z1 * z2) * q2)) + (- ((x2 * c1) * q2)) is complex ext-real real set
(y1 * c1) * c2 is complex ext-real real Element of REAL
(x2 * y2) * c2 is complex ext-real real Element of REAL
((y1 * c1) * c2) + ((x2 * y2) * c2) is complex ext-real real Element of REAL
(w1 * z2) * c2 is complex ext-real real Element of REAL
(((y1 * c1) * c2) + ((x2 * y2) * c2)) + ((w1 * z2) * c2) is complex ext-real real Element of REAL
(z1 * w2) * c2 is complex ext-real real Element of REAL
((((y1 * c1) * c2) + ((x2 * y2) * c2)) + ((w1 * z2) * c2)) - ((z1 * w2) * c2) is complex ext-real real Element of REAL
- ((z1 * w2) * c2) is complex ext-real real set
((((y1 * c1) * c2) + ((x2 * y2) * c2)) + ((w1 * z2) * c2)) + (- ((z1 * w2) * c2)) is complex ext-real real set
(((((y1 * y2) * q2) - ((w1 * w2) * q2)) - ((z1 * z2) * q2)) - ((x2 * c1) * q2)) + (((((y1 * c1) * c2) + ((x2 * y2) * c2)) + ((w1 * z2) * c2)) - ((z1 * w2) * c2)) is complex ext-real real Element of REAL
(y1 * w2) * q1 is complex ext-real real Element of REAL
(w1 * y2) * q1 is complex ext-real real Element of REAL
((y1 * w2) * q1) + ((w1 * y2) * q1) is complex ext-real real Element of REAL
(z1 * c1) * q1 is complex ext-real real Element of REAL
(((y1 * w2) * q1) + ((w1 * y2) * q1)) + ((z1 * c1) * q1) is complex ext-real real Element of REAL
(x2 * z2) * q1 is complex ext-real real Element of REAL
((((y1 * w2) * q1) + ((w1 * y2) * q1)) + ((z1 * c1) * q1)) - ((x2 * z2) * q1) is complex ext-real real Element of REAL
- ((x2 * z2) * q1) is complex ext-real real set
((((y1 * w2) * q1) + ((w1 * y2) * q1)) + ((z1 * c1) * q1)) + (- ((x2 * z2) * q1)) is complex ext-real real set
((((((y1 * y2) * q2) - ((w1 * w2) * q2)) - ((z1 * z2) * q2)) - ((x2 * c1) * q2)) + (((((y1 * c1) * c2) + ((x2 * y2) * c2)) + ((w1 * z2) * c2)) - ((z1 * w2) * c2))) + (((((y1 * w2) * q1) + ((w1 * y2) * q1)) + ((z1 * c1) * q1)) - ((x2 * z2) * q1)) is complex ext-real real Element of REAL
(y1 * z2) * q0 is complex ext-real real Element of REAL
(y2 * z1) * q0 is complex ext-real real Element of REAL
((y1 * z2) * q0) + ((y2 * z1) * q0) is complex ext-real real Element of REAL
(w2 * x2) * q0 is complex ext-real real Element of REAL
(((y1 * z2) * q0) + ((y2 * z1) * q0)) + ((w2 * x2) * q0) is complex ext-real real Element of REAL
(c1 * w1) * q0 is complex ext-real real Element of REAL
((((y1 * z2) * q0) + ((y2 * z1) * q0)) + ((w2 * x2) * q0)) - ((c1 * w1) * q0) is complex ext-real real Element of REAL
- ((c1 * w1) * q0) is complex ext-real real set
((((y1 * z2) * q0) + ((y2 * z1) * q0)) + ((w2 * x2) * q0)) + (- ((c1 * w1) * q0)) is complex ext-real real set
(((((((y1 * y2) * q2) - ((w1 * w2) * q2)) - ((z1 * z2) * q2)) - ((x2 * c1) * q2)) + (((((y1 * c1) * c2) + ((x2 * y2) * c2)) + ((w1 * z2) * c2)) - ((z1 * w2) * c2))) + (((((y1 * w2) * q1) + ((w1 * y2) * q1)) + ((z1 * c1) * q1)) - ((x2 * z2) * q1))) - (((((y1 * z2) * q0) + ((y2 * z1) * q0)) + ((w2 * x2) * q0)) - ((c1 * w1) * q0)) is complex ext-real real Element of REAL
- (((((y1 * z2) * q0) + ((y2 * z1) * q0)) + ((w2 * x2) * q0)) - ((c1 * w1) * q0)) is complex ext-real real set
(((((((y1 * y2) * q2) - ((w1 * w2) * q2)) - ((z1 * z2) * q2)) - ((x2 * c1) * q2)) + (((((y1 * c1) * c2) + ((x2 * y2) * c2)) + ((w1 * z2) * c2)) - ((z1 * w2) * c2))) + (((((y1 * w2) * q1) + ((w1 * y2) * q1)) + ((z1 * c1) * q1)) - ((x2 * z2) * q1))) + (- (((((y1 * z2) * q0) + ((y2 * z1) * q0)) + ((w2 * x2) * q0)) - ((c1 * w1) * q0))) is complex ext-real real set
[*((((((((y1 * y2) * c2) - ((w1 * w2) * c2)) - ((z1 * z2) * c2)) - ((x2 * c1) * c2)) - (((((y1 * w2) * q0) + ((w1 * y2) * q0)) + ((z1 * c1) * q0)) - ((x2 * z2) * q0))) - (((((y1 * z2) * q1) + ((y2 * z1) * q1)) + ((w2 * x2) * q1)) - ((c1 * w1) * q1))) - (((((y1 * c1) * q2) + ((x2 * y2) * q2)) + ((w1 * z2) * q2)) - ((z1 * w2) * q2))),((((((((y1 * y2) * q0) - ((w1 * w2) * q0)) - ((z1 * z2) * q0)) - ((x2 * c1) * q0)) + (((((y1 * w2) * c2) + ((w1 * y2) * c2)) + ((z1 * c1) * c2)) - ((x2 * z2) * c2))) + (((((y1 * z2) * q2) + ((y2 * z1) * q2)) + ((w2 * x2) * q2)) - ((c1 * w1) * q2))) - (((((y1 * c1) * q1) + ((x2 * y2) * q1)) + ((w1 * z2) * q1)) - ((z1 * w2) * q1))),((((((((y1 * y2) * q1) - ((w1 * w2) * q1)) - ((z1 * z2) * q1)) - ((x2 * c1) * q1)) + (((((c2 * y1) * z2) + ((c2 * y2) * z1)) + ((c2 * w2) * x2)) - ((c2 * c1) * w1))) + (((((q0 * y1) * c1) + ((q0 * x2) * y2)) + ((q0 * w1) * z2)) - ((q0 * z1) * w2))) - (((((q2 * y1) * w2) + ((q2 * w1) * y2)) + ((q2 * z1) * c1)) - ((q2 * x2) * z2))),((((((((y1 * y2) * q2) - ((w1 * w2) * q2)) - ((z1 * z2) * q2)) - ((x2 * c1) * q2)) + (((((y1 * c1) * c2) + ((x2 * y2) * c2)) + ((w1 * z2) * c2)) - ((z1 * w2) * c2))) + (((((y1 * w2) * q1) + ((w1 * y2) * q1)) + ((z1 * c1) * q1)) - ((x2 * z2) * q1))) - (((((y1 * z2) * q0) + ((y2 * z1) * q0)) + ((w2 * x2) * q0)) - ((c1 * w1) * q0)))*] is quaternion Element of QUATERNION
y2 * c2 is complex ext-real real Element of REAL
w2 * q0 is complex ext-real real Element of REAL
(y2 * c2) - (w2 * q0) is complex ext-real real Element of REAL
- (w2 * q0) is complex ext-real real set
(y2 * c2) + (- (w2 * q0)) is complex ext-real real set
z2 * q1 is complex ext-real real Element of REAL
((y2 * c2) - (w2 * q0)) - (z2 * q1) is complex ext-real real Element of REAL
- (z2 * q1) is complex ext-real real set
((y2 * c2) - (w2 * q0)) + (- (z2 * q1)) is complex ext-real real set
c1 * q2 is complex ext-real real Element of REAL
(((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2) is complex ext-real real Element of REAL
- (c1 * q2) is complex ext-real real set
(((y2 * c2) - (w2 * q0)) - (z2 * q1)) + (- (c1 * q2)) is complex ext-real real set
y2 * q0 is complex ext-real real Element of REAL
w2 * c2 is complex ext-real real Element of REAL
(y2 * q0) + (w2 * c2) is complex ext-real real Element of REAL
z2 * q2 is complex ext-real real Element of REAL
((y2 * q0) + (w2 * c2)) + (z2 * q2) is complex ext-real real Element of REAL
c1 * q1 is complex ext-real real Element of REAL
(((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1) is complex ext-real real Element of REAL
- (c1 * q1) is complex ext-real real set
(((y2 * q0) + (w2 * c2)) + (z2 * q2)) + (- (c1 * q1)) is complex ext-real real set
y2 * q1 is complex ext-real real Element of REAL
c2 * z2 is complex ext-real real Element of REAL
(y2 * q1) + (c2 * z2) is complex ext-real real Element of REAL
q0 * c1 is complex ext-real real Element of REAL
((y2 * q1) + (c2 * z2)) + (q0 * c1) is complex ext-real real Element of REAL
q2 * w2 is complex ext-real real Element of REAL
(((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2) is complex ext-real real Element of REAL
- (q2 * w2) is complex ext-real real set
(((y2 * q1) + (c2 * z2)) + (q0 * c1)) + (- (q2 * w2)) is complex ext-real real set
y2 * q2 is complex ext-real real Element of REAL
c1 * c2 is complex ext-real real Element of REAL
(y2 * q2) + (c1 * c2) is complex ext-real real Element of REAL
w2 * q1 is complex ext-real real Element of REAL
((y2 * q2) + (c1 * c2)) + (w2 * q1) is complex ext-real real Element of REAL
z2 * q0 is complex ext-real real Element of REAL
(((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0) is complex ext-real real Element of REAL
- (z2 * q0) is complex ext-real real set
(((y2 * q2) + (c1 * c2)) + (w2 * q1)) + (- (z2 * q0)) is complex ext-real real set
[*((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)),((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)),((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)),((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0))*] is quaternion Element of QUATERNION
c1 * [*((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)),((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)),((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)),((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0))*] is quaternion Element of QUATERNION
y1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)) is complex ext-real real Element of REAL
w1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)) is complex ext-real real Element of REAL
(y1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2))) - (w1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1))) is complex ext-real real Element of REAL
- (w1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1))) is complex ext-real real set
(y1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2))) + (- (w1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)))) is complex ext-real real set
z1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)) is complex ext-real real Element of REAL
((y1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2))) - (w1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)))) - (z1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2))) is complex ext-real real Element of REAL
- (z1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2))) is complex ext-real real set
((y1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2))) - (w1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)))) + (- (z1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)))) is complex ext-real real set
x2 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)) is complex ext-real real Element of REAL
(((y1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2))) - (w1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)))) - (z1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)))) - (x2 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0))) is complex ext-real real Element of REAL
- (x2 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0))) is complex ext-real real set
(((y1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2))) - (w1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)))) - (z1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)))) + (- (x2 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)))) is complex ext-real real set
y1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)) is complex ext-real real Element of REAL
w1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)) is complex ext-real real Element of REAL
(y1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1))) + (w1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2))) is complex ext-real real Element of REAL
z1 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)) is complex ext-real real Element of REAL
((y1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1))) + (w1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)))) + (z1 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0))) is complex ext-real real Element of REAL
x2 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)) is complex ext-real real Element of REAL
(((y1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1))) + (w1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)))) + (z1 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)))) - (x2 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2))) is complex ext-real real Element of REAL
- (x2 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2))) is complex ext-real real set
(((y1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1))) + (w1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)))) + (z1 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)))) + (- (x2 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)))) is complex ext-real real set
y1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)) is complex ext-real real Element of REAL
((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)) * z1 is complex ext-real real Element of REAL
(y1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2))) + (((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)) * z1) is complex ext-real real Element of REAL
((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)) * x2 is complex ext-real real Element of REAL
((y1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2))) + (((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)) * z1)) + (((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)) * x2) is complex ext-real real Element of REAL
((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)) * w1 is complex ext-real real Element of REAL
(((y1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2))) + (((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)) * z1)) + (((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)) * x2)) - (((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)) * w1) is complex ext-real real Element of REAL
- (((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)) * w1) is complex ext-real real set
(((y1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2))) + (((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)) * z1)) + (((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)) * x2)) + (- (((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)) * w1)) is complex ext-real real set
y1 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)) is complex ext-real real Element of REAL
x2 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)) is complex ext-real real Element of REAL
(y1 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0))) + (x2 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2))) is complex ext-real real Element of REAL
w1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)) is complex ext-real real Element of REAL
((y1 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0))) + (x2 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)))) + (w1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2))) is complex ext-real real Element of REAL
z1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)) is complex ext-real real Element of REAL
(((y1 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0))) + (x2 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)))) + (w1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)))) - (z1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1))) is complex ext-real real Element of REAL
- (z1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1))) is complex ext-real real set
(((y1 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0))) + (x2 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)))) + (w1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)))) + (- (z1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)))) is complex ext-real real set
[*((((y1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2))) - (w1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)))) - (z1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)))) - (x2 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)))),((((y1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1))) + (w1 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)))) + (z1 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)))) - (x2 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)))),((((y1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2))) + (((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)) * z1)) + (((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)) * x2)) - (((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)) * w1)),((((y1 * ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0))) + (x2 * ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)))) + (w1 * ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)))) - (z1 * ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1))))*] is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
c1 * c2 is quaternion Element of QUATERNION
c3 is quaternion set
c2 + c3 is quaternion Element of QUATERNION
c1 * (c2 + c3) is quaternion Element of QUATERNION
c1 * c3 is quaternion Element of QUATERNION
(c1 * c2) + (c1 * c3) is quaternion Element of QUATERNION
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
z1 is complex ext-real real Element of REAL
x2 is complex ext-real real Element of REAL
[*y1,w1,z1,x2*] is quaternion Element of QUATERNION
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
z2 is complex ext-real real Element of REAL
c1 is complex ext-real real Element of REAL
[*y2,w2,z2,c1*] is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
q0 is complex ext-real real Element of REAL
q1 is complex ext-real real Element of REAL
q2 is complex ext-real real Element of REAL
[*c2,q0,q1,q2*] is quaternion Element of QUATERNION
y2 + c2 is complex ext-real real Element of REAL
w2 + q0 is complex ext-real real Element of REAL
z2 + q1 is complex ext-real real Element of REAL
c1 + q2 is complex ext-real real Element of REAL
[*(y2 + c2),(w2 + q0),(z2 + q1),(c1 + q2)*] is quaternion Element of QUATERNION
c1 * [*(y2 + c2),(w2 + q0),(z2 + q1),(c1 + q2)*] is quaternion Element of QUATERNION
y1 * (y2 + c2) is complex ext-real real Element of REAL
w1 * (w2 + q0) is complex ext-real real Element of REAL
(y1 * (y2 + c2)) - (w1 * (w2 + q0)) is complex ext-real real Element of REAL
- (w1 * (w2 + q0)) is complex ext-real real set
(y1 * (y2 + c2)) + (- (w1 * (w2 + q0))) is complex ext-real real set
z1 * (z2 + q1) is complex ext-real real Element of REAL
((y1 * (y2 + c2)) - (w1 * (w2 + q0))) - (z1 * (z2 + q1)) is complex ext-real real Element of REAL
- (z1 * (z2 + q1)) is complex ext-real real set
((y1 * (y2 + c2)) - (w1 * (w2 + q0))) + (- (z1 * (z2 + q1))) is complex ext-real real set
x2 * (c1 + q2) is complex ext-real real Element of REAL
(((y1 * (y2 + c2)) - (w1 * (w2 + q0))) - (z1 * (z2 + q1))) - (x2 * (c1 + q2)) is complex ext-real real Element of REAL
- (x2 * (c1 + q2)) is complex ext-real real set
(((y1 * (y2 + c2)) - (w1 * (w2 + q0))) - (z1 * (z2 + q1))) + (- (x2 * (c1 + q2))) is complex ext-real real set
y1 * (w2 + q0) is complex ext-real real Element of REAL
w1 * (y2 + c2) is complex ext-real real Element of REAL
(y1 * (w2 + q0)) + (w1 * (y2 + c2)) is complex ext-real real Element of REAL
z1 * (c1 + q2) is complex ext-real real Element of REAL
((y1 * (w2 + q0)) + (w1 * (y2 + c2))) + (z1 * (c1 + q2)) is complex ext-real real Element of REAL
x2 * (z2 + q1) is complex ext-real real Element of REAL
(((y1 * (w2 + q0)) + (w1 * (y2 + c2))) + (z1 * (c1 + q2))) - (x2 * (z2 + q1)) is complex ext-real real Element of REAL
- (x2 * (z2 + q1)) is complex ext-real real set
(((y1 * (w2 + q0)) + (w1 * (y2 + c2))) + (z1 * (c1 + q2))) + (- (x2 * (z2 + q1))) is complex ext-real real set
y1 * (z2 + q1) is complex ext-real real Element of REAL
(y2 + c2) * z1 is complex ext-real real Element of REAL
(y1 * (z2 + q1)) + ((y2 + c2) * z1) is complex ext-real real Element of REAL
(w2 + q0) * x2 is complex ext-real real Element of REAL
((y1 * (z2 + q1)) + ((y2 + c2) * z1)) + ((w2 + q0) * x2) is complex ext-real real Element of REAL
(c1 + q2) * w1 is complex ext-real real Element of REAL
(((y1 * (z2 + q1)) + ((y2 + c2) * z1)) + ((w2 + q0) * x2)) - ((c1 + q2) * w1) is complex ext-real real Element of REAL
- ((c1 + q2) * w1) is complex ext-real real set
(((y1 * (z2 + q1)) + ((y2 + c2) * z1)) + ((w2 + q0) * x2)) + (- ((c1 + q2) * w1)) is complex ext-real real set
y1 * (c1 + q2) is complex ext-real real Element of REAL
x2 * (y2 + c2) is complex ext-real real Element of REAL
(y1 * (c1 + q2)) + (x2 * (y2 + c2)) is complex ext-real real Element of REAL
w1 * (z2 + q1) is complex ext-real real Element of REAL
((y1 * (c1 + q2)) + (x2 * (y2 + c2))) + (w1 * (z2 + q1)) is complex ext-real real Element of REAL
z1 * (w2 + q0) is complex ext-real real Element of REAL
(((y1 * (c1 + q2)) + (x2 * (y2 + c2))) + (w1 * (z2 + q1))) - (z1 * (w2 + q0)) is complex ext-real real Element of REAL
- (z1 * (w2 + q0)) is complex ext-real real set
(((y1 * (c1 + q2)) + (x2 * (y2 + c2))) + (w1 * (z2 + q1))) + (- (z1 * (w2 + q0))) is complex ext-real real set
[*((((y1 * (y2 + c2)) - (w1 * (w2 + q0))) - (z1 * (z2 + q1))) - (x2 * (c1 + q2))),((((y1 * (w2 + q0)) + (w1 * (y2 + c2))) + (z1 * (c1 + q2))) - (x2 * (z2 + q1))),((((y1 * (z2 + q1)) + ((y2 + c2) * z1)) + ((w2 + q0) * x2)) - ((c1 + q2) * w1)),((((y1 * (c1 + q2)) + (x2 * (y2 + c2))) + (w1 * (z2 + q1))) - (z1 * (w2 + q0)))*] is quaternion Element of QUATERNION
y1 * y2 is complex ext-real real Element of REAL
y1 * c2 is complex ext-real real Element of REAL
(y1 * y2) + (y1 * c2) is complex ext-real real Element of REAL
w1 * w2 is complex ext-real real Element of REAL
w1 * q0 is complex ext-real real Element of REAL
(w1 * w2) + (w1 * q0) is complex ext-real real Element of REAL
((y1 * y2) + (y1 * c2)) - ((w1 * w2) + (w1 * q0)) is complex ext-real real Element of REAL
- ((w1 * w2) + (w1 * q0)) is complex ext-real real set
((y1 * y2) + (y1 * c2)) + (- ((w1 * w2) + (w1 * q0))) is complex ext-real real set
z1 * z2 is complex ext-real real Element of REAL
z1 * q1 is complex ext-real real Element of REAL
(z1 * z2) + (z1 * q1) is complex ext-real real Element of REAL
(((y1 * y2) + (y1 * c2)) - ((w1 * w2) + (w1 * q0))) - ((z1 * z2) + (z1 * q1)) is complex ext-real real Element of REAL
- ((z1 * z2) + (z1 * q1)) is complex ext-real real set
(((y1 * y2) + (y1 * c2)) - ((w1 * w2) + (w1 * q0))) + (- ((z1 * z2) + (z1 * q1))) is complex ext-real real set
x2 * c1 is complex ext-real real Element of REAL
x2 * q2 is complex ext-real real Element of REAL
(x2 * c1) + (x2 * q2) is complex ext-real real Element of REAL
((((y1 * y2) + (y1 * c2)) - ((w1 * w2) + (w1 * q0))) - ((z1 * z2) + (z1 * q1))) - ((x2 * c1) + (x2 * q2)) is complex ext-real real Element of REAL
- ((x2 * c1) + (x2 * q2)) is complex ext-real real set
((((y1 * y2) + (y1 * c2)) - ((w1 * w2) + (w1 * q0))) - ((z1 * z2) + (z1 * q1))) + (- ((x2 * c1) + (x2 * q2))) is complex ext-real real set
y1 * w2 is complex ext-real real Element of REAL
y1 * q0 is complex ext-real real Element of REAL
(y1 * w2) + (y1 * q0) is complex ext-real real Element of REAL
w1 * y2 is complex ext-real real Element of REAL
w1 * c2 is complex ext-real real Element of REAL
(w1 * y2) + (w1 * c2) is complex ext-real real Element of REAL
((y1 * w2) + (y1 * q0)) + ((w1 * y2) + (w1 * c2)) is complex ext-real real Element of REAL
z1 * c1 is complex ext-real real Element of REAL
z1 * q2 is complex ext-real real Element of REAL
(z1 * c1) + (z1 * q2) is complex ext-real real Element of REAL
(((y1 * w2) + (y1 * q0)) + ((w1 * y2) + (w1 * c2))) + ((z1 * c1) + (z1 * q2)) is complex ext-real real Element of REAL
x2 * z2 is complex ext-real real Element of REAL
x2 * q1 is complex ext-real real Element of REAL
(x2 * z2) + (x2 * q1) is complex ext-real real Element of REAL
((((y1 * w2) + (y1 * q0)) + ((w1 * y2) + (w1 * c2))) + ((z1 * c1) + (z1 * q2))) - ((x2 * z2) + (x2 * q1)) is complex ext-real real Element of REAL
- ((x2 * z2) + (x2 * q1)) is complex ext-real real set
((((y1 * w2) + (y1 * q0)) + ((w1 * y2) + (w1 * c2))) + ((z1 * c1) + (z1 * q2))) + (- ((x2 * z2) + (x2 * q1))) is complex ext-real real set
y1 * z2 is complex ext-real real Element of REAL
y1 * q1 is complex ext-real real Element of REAL
(y1 * z2) + (y1 * q1) is complex ext-real real Element of REAL
y2 * z1 is complex ext-real real Element of REAL
c2 * z1 is complex ext-real real Element of REAL
(y2 * z1) + (c2 * z1) is complex ext-real real Element of REAL
((y1 * z2) + (y1 * q1)) + ((y2 * z1) + (c2 * z1)) is complex ext-real real Element of REAL
w2 * x2 is complex ext-real real Element of REAL
q0 * x2 is complex ext-real real Element of REAL
(w2 * x2) + (q0 * x2) is complex ext-real real Element of REAL
(((y1 * z2) + (y1 * q1)) + ((y2 * z1) + (c2 * z1))) + ((w2 * x2) + (q0 * x2)) is complex ext-real real Element of REAL
c1 * w1 is complex ext-real real Element of REAL
q2 * w1 is complex ext-real real Element of REAL
(c1 * w1) + (q2 * w1) is complex ext-real real Element of REAL
((((y1 * z2) + (y1 * q1)) + ((y2 * z1) + (c2 * z1))) + ((w2 * x2) + (q0 * x2))) - ((c1 * w1) + (q2 * w1)) is complex ext-real real Element of REAL
- ((c1 * w1) + (q2 * w1)) is complex ext-real real set
((((y1 * z2) + (y1 * q1)) + ((y2 * z1) + (c2 * z1))) + ((w2 * x2) + (q0 * x2))) + (- ((c1 * w1) + (q2 * w1))) is complex ext-real real set
y1 * c1 is complex ext-real real Element of REAL
y1 * q2 is complex ext-real real Element of REAL
(y1 * c1) + (y1 * q2) is complex ext-real real Element of REAL
x2 * y2 is complex ext-real real Element of REAL
x2 * c2 is complex ext-real real Element of REAL
(x2 * y2) + (x2 * c2) is complex ext-real real Element of REAL
((y1 * c1) + (y1 * q2)) + ((x2 * y2) + (x2 * c2)) is complex ext-real real Element of REAL
w1 * z2 is complex ext-real real Element of REAL
w1 * q1 is complex ext-real real Element of REAL
(w1 * z2) + (w1 * q1) is complex ext-real real Element of REAL
(((y1 * c1) + (y1 * q2)) + ((x2 * y2) + (x2 * c2))) + ((w1 * z2) + (w1 * q1)) is complex ext-real real Element of REAL
z1 * w2 is complex ext-real real Element of REAL
z1 * q0 is complex ext-real real Element of REAL
(z1 * w2) + (z1 * q0) is complex ext-real real Element of REAL
((((y1 * c1) + (y1 * q2)) + ((x2 * y2) + (x2 * c2))) + ((w1 * z2) + (w1 * q1))) - ((z1 * w2) + (z1 * q0)) is complex ext-real real Element of REAL
- ((z1 * w2) + (z1 * q0)) is complex ext-real real set
((((y1 * c1) + (y1 * q2)) + ((x2 * y2) + (x2 * c2))) + ((w1 * z2) + (w1 * q1))) + (- ((z1 * w2) + (z1 * q0))) is complex ext-real real set
[*(((((y1 * y2) + (y1 * c2)) - ((w1 * w2) + (w1 * q0))) - ((z1 * z2) + (z1 * q1))) - ((x2 * c1) + (x2 * q2))),(((((y1 * w2) + (y1 * q0)) + ((w1 * y2) + (w1 * c2))) + ((z1 * c1) + (z1 * q2))) - ((x2 * z2) + (x2 * q1))),(((((y1 * z2) + (y1 * q1)) + ((y2 * z1) + (c2 * z1))) + ((w2 * x2) + (q0 * x2))) - ((c1 * w1) + (q2 * w1))),(((((y1 * c1) + (y1 * q2)) + ((x2 * y2) + (x2 * c2))) + ((w1 * z2) + (w1 * q1))) - ((z1 * w2) + (z1 * q0)))*] is quaternion Element of QUATERNION
(y1 * y2) - (w1 * w2) is complex ext-real real Element of REAL
- (w1 * w2) is complex ext-real real set
(y1 * y2) + (- (w1 * w2)) is complex ext-real real set
((y1 * y2) - (w1 * w2)) - (z1 * z2) is complex ext-real real Element of REAL
- (z1 * z2) is complex ext-real real set
((y1 * y2) - (w1 * w2)) + (- (z1 * z2)) is complex ext-real real set
(((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1) is complex ext-real real Element of REAL
- (x2 * c1) is complex ext-real real set
(((y1 * y2) - (w1 * w2)) - (z1 * z2)) + (- (x2 * c1)) is complex ext-real real set
(y1 * w2) + (w1 * y2) is complex ext-real real Element of REAL
((y1 * w2) + (w1 * y2)) + (z1 * c1) is complex ext-real real Element of REAL
(((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2) is complex ext-real real Element of REAL
- (x2 * z2) is complex ext-real real set
(((y1 * w2) + (w1 * y2)) + (z1 * c1)) + (- (x2 * z2)) is complex ext-real real set
(y1 * z2) + (y2 * z1) is complex ext-real real Element of REAL
((y1 * z2) + (y2 * z1)) + (w2 * x2) is complex ext-real real Element of REAL
(((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1) is complex ext-real real Element of REAL
- (c1 * w1) is complex ext-real real set
(((y1 * z2) + (y2 * z1)) + (w2 * x2)) + (- (c1 * w1)) is complex ext-real real set
(y1 * c1) + (x2 * y2) is complex ext-real real Element of REAL
((y1 * c1) + (x2 * y2)) + (w1 * z2) is complex ext-real real Element of REAL
(((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2) is complex ext-real real Element of REAL
- (z1 * w2) is complex ext-real real set
(((y1 * c1) + (x2 * y2)) + (w1 * z2)) + (- (z1 * w2)) is complex ext-real real set
[*((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)),((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)),((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)),((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2))*] is quaternion Element of QUATERNION
[*((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)),((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)),((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)),((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2))*] + (c1 * c3) is quaternion Element of QUATERNION
(y1 * c2) - (w1 * q0) is complex ext-real real Element of REAL
- (w1 * q0) is complex ext-real real set
(y1 * c2) + (- (w1 * q0)) is complex ext-real real set
((y1 * c2) - (w1 * q0)) - (z1 * q1) is complex ext-real real Element of REAL
- (z1 * q1) is complex ext-real real set
((y1 * c2) - (w1 * q0)) + (- (z1 * q1)) is complex ext-real real set
(((y1 * c2) - (w1 * q0)) - (z1 * q1)) - (x2 * q2) is complex ext-real real Element of REAL
- (x2 * q2) is complex ext-real real set
(((y1 * c2) - (w1 * q0)) - (z1 * q1)) + (- (x2 * q2)) is complex ext-real real set
(y1 * q0) + (w1 * c2) is complex ext-real real Element of REAL
((y1 * q0) + (w1 * c2)) + (z1 * q2) is complex ext-real real Element of REAL
(((y1 * q0) + (w1 * c2)) + (z1 * q2)) - (x2 * q1) is complex ext-real real Element of REAL
- (x2 * q1) is complex ext-real real set
(((y1 * q0) + (w1 * c2)) + (z1 * q2)) + (- (x2 * q1)) is complex ext-real real set
(y1 * q1) + (c2 * z1) is complex ext-real real Element of REAL
((y1 * q1) + (c2 * z1)) + (q0 * x2) is complex ext-real real Element of REAL
(((y1 * q1) + (c2 * z1)) + (q0 * x2)) - (q2 * w1) is complex ext-real real Element of REAL
- (q2 * w1) is complex ext-real real set
(((y1 * q1) + (c2 * z1)) + (q0 * x2)) + (- (q2 * w1)) is complex ext-real real set
(y1 * q2) + (x2 * c2) is complex ext-real real Element of REAL
((y1 * q2) + (x2 * c2)) + (w1 * q1) is complex ext-real real Element of REAL
(((y1 * q2) + (x2 * c2)) + (w1 * q1)) - (z1 * q0) is complex ext-real real Element of REAL
- (z1 * q0) is complex ext-real real set
(((y1 * q2) + (x2 * c2)) + (w1 * q1)) + (- (z1 * q0)) is complex ext-real real set
[*((((y1 * c2) - (w1 * q0)) - (z1 * q1)) - (x2 * q2)),((((y1 * q0) + (w1 * c2)) + (z1 * q2)) - (x2 * q1)),((((y1 * q1) + (c2 * z1)) + (q0 * x2)) - (q2 * w1)),((((y1 * q2) + (x2 * c2)) + (w1 * q1)) - (z1 * q0))*] is quaternion Element of QUATERNION
[*((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)),((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)),((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)),((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2))*] + [*((((y1 * c2) - (w1 * q0)) - (z1 * q1)) - (x2 * q2)),((((y1 * q0) + (w1 * c2)) + (z1 * q2)) - (x2 * q1)),((((y1 * q1) + (c2 * z1)) + (q0 * x2)) - (q2 * w1)),((((y1 * q2) + (x2 * c2)) + (w1 * q1)) - (z1 * q0))*] is quaternion Element of QUATERNION
((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) + ((((y1 * c2) - (w1 * q0)) - (z1 * q1)) - (x2 * q2)) is complex ext-real real Element of REAL
((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) + ((((y1 * q0) + (w1 * c2)) + (z1 * q2)) - (x2 * q1)) is complex ext-real real Element of REAL
((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) + ((((y1 * q1) + (c2 * z1)) + (q0 * x2)) - (q2 * w1)) is complex ext-real real Element of REAL
((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) + ((((y1 * q2) + (x2 * c2)) + (w1 * q1)) - (z1 * q0)) is complex ext-real real Element of REAL
[*(((((y1 * y2) - (w1 * w2)) - (z1 * z2)) - (x2 * c1)) + ((((y1 * c2) - (w1 * q0)) - (z1 * q1)) - (x2 * q2))),(((((y1 * w2) + (w1 * y2)) + (z1 * c1)) - (x2 * z2)) + ((((y1 * q0) + (w1 * c2)) + (z1 * q2)) - (x2 * q1))),(((((y1 * z2) + (y2 * z1)) + (w2 * x2)) - (c1 * w1)) + ((((y1 * q1) + (c2 * z1)) + (q0 * x2)) - (q2 * w1))),(((((y1 * c1) + (x2 * y2)) + (w1 * z2)) - (z1 * w2)) + ((((y1 * q2) + (x2 * c2)) + (w1 * q1)) - (z1 * q0)))*] is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
c1 + c2 is quaternion Element of QUATERNION
c3 is quaternion set
(c1 + c2) * c3 is quaternion Element of QUATERNION
c1 * c3 is quaternion Element of QUATERNION
c2 * c3 is quaternion Element of QUATERNION
(c1 * c3) + (c2 * c3) is quaternion Element of QUATERNION
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
z1 is complex ext-real real Element of REAL
x2 is complex ext-real real Element of REAL
[*y1,w1,z1,x2*] is quaternion Element of QUATERNION
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
z2 is complex ext-real real Element of REAL
c1 is complex ext-real real Element of REAL
[*y2,w2,z2,c1*] is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
q0 is complex ext-real real Element of REAL
q1 is complex ext-real real Element of REAL
q2 is complex ext-real real Element of REAL
[*c2,q0,q1,q2*] is quaternion Element of QUATERNION
y1 + y2 is complex ext-real real Element of REAL
w1 + w2 is complex ext-real real Element of REAL
z1 + z2 is complex ext-real real Element of REAL
x2 + c1 is complex ext-real real Element of REAL
[*(y1 + y2),(w1 + w2),(z1 + z2),(x2 + c1)*] is quaternion Element of QUATERNION
[*(y1 + y2),(w1 + w2),(z1 + z2),(x2 + c1)*] * c3 is quaternion Element of QUATERNION
(y1 + y2) * c2 is complex ext-real real Element of REAL
(w1 + w2) * q0 is complex ext-real real Element of REAL
((y1 + y2) * c2) - ((w1 + w2) * q0) is complex ext-real real Element of REAL
- ((w1 + w2) * q0) is complex ext-real real set
((y1 + y2) * c2) + (- ((w1 + w2) * q0)) is complex ext-real real set
(z1 + z2) * q1 is complex ext-real real Element of REAL
(((y1 + y2) * c2) - ((w1 + w2) * q0)) - ((z1 + z2) * q1) is complex ext-real real Element of REAL
- ((z1 + z2) * q1) is complex ext-real real set
(((y1 + y2) * c2) - ((w1 + w2) * q0)) + (- ((z1 + z2) * q1)) is complex ext-real real set
(x2 + c1) * q2 is complex ext-real real Element of REAL
((((y1 + y2) * c2) - ((w1 + w2) * q0)) - ((z1 + z2) * q1)) - ((x2 + c1) * q2) is complex ext-real real Element of REAL
- ((x2 + c1) * q2) is complex ext-real real set
((((y1 + y2) * c2) - ((w1 + w2) * q0)) - ((z1 + z2) * q1)) + (- ((x2 + c1) * q2)) is complex ext-real real set
(y1 + y2) * q0 is complex ext-real real Element of REAL
(w1 + w2) * c2 is complex ext-real real Element of REAL
((y1 + y2) * q0) + ((w1 + w2) * c2) is complex ext-real real Element of REAL
(z1 + z2) * q2 is complex ext-real real Element of REAL
(((y1 + y2) * q0) + ((w1 + w2) * c2)) + ((z1 + z2) * q2) is complex ext-real real Element of REAL
(x2 + c1) * q1 is complex ext-real real Element of REAL
((((y1 + y2) * q0) + ((w1 + w2) * c2)) + ((z1 + z2) * q2)) - ((x2 + c1) * q1) is complex ext-real real Element of REAL
- ((x2 + c1) * q1) is complex ext-real real set
((((y1 + y2) * q0) + ((w1 + w2) * c2)) + ((z1 + z2) * q2)) + (- ((x2 + c1) * q1)) is complex ext-real real set
(y1 + y2) * q1 is complex ext-real real Element of REAL
c2 * (z1 + z2) is complex ext-real real Element of REAL
((y1 + y2) * q1) + (c2 * (z1 + z2)) is complex ext-real real Element of REAL
q0 * (x2 + c1) is complex ext-real real Element of REAL
(((y1 + y2) * q1) + (c2 * (z1 + z2))) + (q0 * (x2 + c1)) is complex ext-real real Element of REAL
q2 * (w1 + w2) is complex ext-real real Element of REAL
((((y1 + y2) * q1) + (c2 * (z1 + z2))) + (q0 * (x2 + c1))) - (q2 * (w1 + w2)) is complex ext-real real Element of REAL
- (q2 * (w1 + w2)) is complex ext-real real set
((((y1 + y2) * q1) + (c2 * (z1 + z2))) + (q0 * (x2 + c1))) + (- (q2 * (w1 + w2))) is complex ext-real real set
(y1 + y2) * q2 is complex ext-real real Element of REAL
(x2 + c1) * c2 is complex ext-real real Element of REAL
((y1 + y2) * q2) + ((x2 + c1) * c2) is complex ext-real real Element of REAL
(w1 + w2) * q1 is complex ext-real real Element of REAL
(((y1 + y2) * q2) + ((x2 + c1) * c2)) + ((w1 + w2) * q1) is complex ext-real real Element of REAL
(z1 + z2) * q0 is complex ext-real real Element of REAL
((((y1 + y2) * q2) + ((x2 + c1) * c2)) + ((w1 + w2) * q1)) - ((z1 + z2) * q0) is complex ext-real real Element of REAL
- ((z1 + z2) * q0) is complex ext-real real set
((((y1 + y2) * q2) + ((x2 + c1) * c2)) + ((w1 + w2) * q1)) + (- ((z1 + z2) * q0)) is complex ext-real real set
[*(((((y1 + y2) * c2) - ((w1 + w2) * q0)) - ((z1 + z2) * q1)) - ((x2 + c1) * q2)),(((((y1 + y2) * q0) + ((w1 + w2) * c2)) + ((z1 + z2) * q2)) - ((x2 + c1) * q1)),(((((y1 + y2) * q1) + (c2 * (z1 + z2))) + (q0 * (x2 + c1))) - (q2 * (w1 + w2))),(((((y1 + y2) * q2) + ((x2 + c1) * c2)) + ((w1 + w2) * q1)) - ((z1 + z2) * q0))*] is quaternion Element of QUATERNION
y1 * c2 is complex ext-real real Element of REAL
y2 * c2 is complex ext-real real Element of REAL
(y1 * c2) + (y2 * c2) is complex ext-real real Element of REAL
w1 * q0 is complex ext-real real Element of REAL
w2 * q0 is complex ext-real real Element of REAL
(w1 * q0) + (w2 * q0) is complex ext-real real Element of REAL
((y1 * c2) + (y2 * c2)) - ((w1 * q0) + (w2 * q0)) is complex ext-real real Element of REAL
- ((w1 * q0) + (w2 * q0)) is complex ext-real real set
((y1 * c2) + (y2 * c2)) + (- ((w1 * q0) + (w2 * q0))) is complex ext-real real set
z1 * q1 is complex ext-real real Element of REAL
z2 * q1 is complex ext-real real Element of REAL
(z1 * q1) + (z2 * q1) is complex ext-real real Element of REAL
(((y1 * c2) + (y2 * c2)) - ((w1 * q0) + (w2 * q0))) - ((z1 * q1) + (z2 * q1)) is complex ext-real real Element of REAL
- ((z1 * q1) + (z2 * q1)) is complex ext-real real set
(((y1 * c2) + (y2 * c2)) - ((w1 * q0) + (w2 * q0))) + (- ((z1 * q1) + (z2 * q1))) is complex ext-real real set
x2 * q2 is complex ext-real real Element of REAL
c1 * q2 is complex ext-real real Element of REAL
(x2 * q2) + (c1 * q2) is complex ext-real real Element of REAL
((((y1 * c2) + (y2 * c2)) - ((w1 * q0) + (w2 * q0))) - ((z1 * q1) + (z2 * q1))) - ((x2 * q2) + (c1 * q2)) is complex ext-real real Element of REAL
- ((x2 * q2) + (c1 * q2)) is complex ext-real real set
((((y1 * c2) + (y2 * c2)) - ((w1 * q0) + (w2 * q0))) - ((z1 * q1) + (z2 * q1))) + (- ((x2 * q2) + (c1 * q2))) is complex ext-real real set
y1 * q0 is complex ext-real real Element of REAL
y2 * q0 is complex ext-real real Element of REAL
(y1 * q0) + (y2 * q0) is complex ext-real real Element of REAL
w1 * c2 is complex ext-real real Element of REAL
w2 * c2 is complex ext-real real Element of REAL
(w1 * c2) + (w2 * c2) is complex ext-real real Element of REAL
((y1 * q0) + (y2 * q0)) + ((w1 * c2) + (w2 * c2)) is complex ext-real real Element of REAL
z1 * q2 is complex ext-real real Element of REAL
z2 * q2 is complex ext-real real Element of REAL
(z1 * q2) + (z2 * q2) is complex ext-real real Element of REAL
(((y1 * q0) + (y2 * q0)) + ((w1 * c2) + (w2 * c2))) + ((z1 * q2) + (z2 * q2)) is complex ext-real real Element of REAL
x2 * q1 is complex ext-real real Element of REAL
c1 * q1 is complex ext-real real Element of REAL
(x2 * q1) + (c1 * q1) is complex ext-real real Element of REAL
((((y1 * q0) + (y2 * q0)) + ((w1 * c2) + (w2 * c2))) + ((z1 * q2) + (z2 * q2))) - ((x2 * q1) + (c1 * q1)) is complex ext-real real Element of REAL
- ((x2 * q1) + (c1 * q1)) is complex ext-real real set
((((y1 * q0) + (y2 * q0)) + ((w1 * c2) + (w2 * c2))) + ((z1 * q2) + (z2 * q2))) + (- ((x2 * q1) + (c1 * q1))) is complex ext-real real set
y1 * q1 is complex ext-real real Element of REAL
y2 * q1 is complex ext-real real Element of REAL
(y1 * q1) + (y2 * q1) is complex ext-real real Element of REAL
c2 * z1 is complex ext-real real Element of REAL
c2 * z2 is complex ext-real real Element of REAL
(c2 * z1) + (c2 * z2) is complex ext-real real Element of REAL
((y1 * q1) + (y2 * q1)) + ((c2 * z1) + (c2 * z2)) is complex ext-real real Element of REAL
q0 * x2 is complex ext-real real Element of REAL
q0 * c1 is complex ext-real real Element of REAL
(q0 * x2) + (q0 * c1) is complex ext-real real Element of REAL
(((y1 * q1) + (y2 * q1)) + ((c2 * z1) + (c2 * z2))) + ((q0 * x2) + (q0 * c1)) is complex ext-real real Element of REAL
q2 * w1 is complex ext-real real Element of REAL
q2 * w2 is complex ext-real real Element of REAL
(q2 * w1) + (q2 * w2) is complex ext-real real Element of REAL
((((y1 * q1) + (y2 * q1)) + ((c2 * z1) + (c2 * z2))) + ((q0 * x2) + (q0 * c1))) - ((q2 * w1) + (q2 * w2)) is complex ext-real real Element of REAL
- ((q2 * w1) + (q2 * w2)) is complex ext-real real set
((((y1 * q1) + (y2 * q1)) + ((c2 * z1) + (c2 * z2))) + ((q0 * x2) + (q0 * c1))) + (- ((q2 * w1) + (q2 * w2))) is complex ext-real real set
y1 * q2 is complex ext-real real Element of REAL
y2 * q2 is complex ext-real real Element of REAL
(y1 * q2) + (y2 * q2) is complex ext-real real Element of REAL
x2 * c2 is complex ext-real real Element of REAL
c1 * c2 is complex ext-real real Element of REAL
(x2 * c2) + (c1 * c2) is complex ext-real real Element of REAL
((y1 * q2) + (y2 * q2)) + ((x2 * c2) + (c1 * c2)) is complex ext-real real Element of REAL
w1 * q1 is complex ext-real real Element of REAL
w2 * q1 is complex ext-real real Element of REAL
(w1 * q1) + (w2 * q1) is complex ext-real real Element of REAL
(((y1 * q2) + (y2 * q2)) + ((x2 * c2) + (c1 * c2))) + ((w1 * q1) + (w2 * q1)) is complex ext-real real Element of REAL
z1 * q0 is complex ext-real real Element of REAL
z2 * q0 is complex ext-real real Element of REAL
(z1 * q0) + (z2 * q0) is complex ext-real real Element of REAL
((((y1 * q2) + (y2 * q2)) + ((x2 * c2) + (c1 * c2))) + ((w1 * q1) + (w2 * q1))) - ((z1 * q0) + (z2 * q0)) is complex ext-real real Element of REAL
- ((z1 * q0) + (z2 * q0)) is complex ext-real real set
((((y1 * q2) + (y2 * q2)) + ((x2 * c2) + (c1 * c2))) + ((w1 * q1) + (w2 * q1))) + (- ((z1 * q0) + (z2 * q0))) is complex ext-real real set
[*(((((y1 * c2) + (y2 * c2)) - ((w1 * q0) + (w2 * q0))) - ((z1 * q1) + (z2 * q1))) - ((x2 * q2) + (c1 * q2))),(((((y1 * q0) + (y2 * q0)) + ((w1 * c2) + (w2 * c2))) + ((z1 * q2) + (z2 * q2))) - ((x2 * q1) + (c1 * q1))),(((((y1 * q1) + (y2 * q1)) + ((c2 * z1) + (c2 * z2))) + ((q0 * x2) + (q0 * c1))) - ((q2 * w1) + (q2 * w2))),(((((y1 * q2) + (y2 * q2)) + ((x2 * c2) + (c1 * c2))) + ((w1 * q1) + (w2 * q1))) - ((z1 * q0) + (z2 * q0)))*] is quaternion Element of QUATERNION
(y1 * c2) - (w1 * q0) is complex ext-real real Element of REAL
- (w1 * q0) is complex ext-real real set
(y1 * c2) + (- (w1 * q0)) is complex ext-real real set
((y1 * c2) - (w1 * q0)) - (z1 * q1) is complex ext-real real Element of REAL
- (z1 * q1) is complex ext-real real set
((y1 * c2) - (w1 * q0)) + (- (z1 * q1)) is complex ext-real real set
(((y1 * c2) - (w1 * q0)) - (z1 * q1)) - (x2 * q2) is complex ext-real real Element of REAL
- (x2 * q2) is complex ext-real real set
(((y1 * c2) - (w1 * q0)) - (z1 * q1)) + (- (x2 * q2)) is complex ext-real real set
(y1 * q0) + (w1 * c2) is complex ext-real real Element of REAL
((y1 * q0) + (w1 * c2)) + (z1 * q2) is complex ext-real real Element of REAL
(((y1 * q0) + (w1 * c2)) + (z1 * q2)) - (x2 * q1) is complex ext-real real Element of REAL
- (x2 * q1) is complex ext-real real set
(((y1 * q0) + (w1 * c2)) + (z1 * q2)) + (- (x2 * q1)) is complex ext-real real set
(y1 * q1) + (c2 * z1) is complex ext-real real Element of REAL
((y1 * q1) + (c2 * z1)) + (q0 * x2) is complex ext-real real Element of REAL
(((y1 * q1) + (c2 * z1)) + (q0 * x2)) - (q2 * w1) is complex ext-real real Element of REAL
- (q2 * w1) is complex ext-real real set
(((y1 * q1) + (c2 * z1)) + (q0 * x2)) + (- (q2 * w1)) is complex ext-real real set
(y1 * q2) + (x2 * c2) is complex ext-real real Element of REAL
((y1 * q2) + (x2 * c2)) + (w1 * q1) is complex ext-real real Element of REAL
(((y1 * q2) + (x2 * c2)) + (w1 * q1)) - (z1 * q0) is complex ext-real real Element of REAL
- (z1 * q0) is complex ext-real real set
(((y1 * q2) + (x2 * c2)) + (w1 * q1)) + (- (z1 * q0)) is complex ext-real real set
[*((((y1 * c2) - (w1 * q0)) - (z1 * q1)) - (x2 * q2)),((((y1 * q0) + (w1 * c2)) + (z1 * q2)) - (x2 * q1)),((((y1 * q1) + (c2 * z1)) + (q0 * x2)) - (q2 * w1)),((((y1 * q2) + (x2 * c2)) + (w1 * q1)) - (z1 * q0))*] is quaternion Element of QUATERNION
[*((((y1 * c2) - (w1 * q0)) - (z1 * q1)) - (x2 * q2)),((((y1 * q0) + (w1 * c2)) + (z1 * q2)) - (x2 * q1)),((((y1 * q1) + (c2 * z1)) + (q0 * x2)) - (q2 * w1)),((((y1 * q2) + (x2 * c2)) + (w1 * q1)) - (z1 * q0))*] + (c2 * c3) is quaternion Element of QUATERNION
(y2 * c2) - (w2 * q0) is complex ext-real real Element of REAL
- (w2 * q0) is complex ext-real real set
(y2 * c2) + (- (w2 * q0)) is complex ext-real real set
((y2 * c2) - (w2 * q0)) - (z2 * q1) is complex ext-real real Element of REAL
- (z2 * q1) is complex ext-real real set
((y2 * c2) - (w2 * q0)) + (- (z2 * q1)) is complex ext-real real set
(((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2) is complex ext-real real Element of REAL
- (c1 * q2) is complex ext-real real set
(((y2 * c2) - (w2 * q0)) - (z2 * q1)) + (- (c1 * q2)) is complex ext-real real set
(y2 * q0) + (w2 * c2) is complex ext-real real Element of REAL
((y2 * q0) + (w2 * c2)) + (z2 * q2) is complex ext-real real Element of REAL
(((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1) is complex ext-real real Element of REAL
- (c1 * q1) is complex ext-real real set
(((y2 * q0) + (w2 * c2)) + (z2 * q2)) + (- (c1 * q1)) is complex ext-real real set
(y2 * q1) + (c2 * z2) is complex ext-real real Element of REAL
((y2 * q1) + (c2 * z2)) + (q0 * c1) is complex ext-real real Element of REAL
(((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2) is complex ext-real real Element of REAL
- (q2 * w2) is complex ext-real real set
(((y2 * q1) + (c2 * z2)) + (q0 * c1)) + (- (q2 * w2)) is complex ext-real real set
(y2 * q2) + (c1 * c2) is complex ext-real real Element of REAL
((y2 * q2) + (c1 * c2)) + (w2 * q1) is complex ext-real real Element of REAL
(((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0) is complex ext-real real Element of REAL
- (z2 * q0) is complex ext-real real set
(((y2 * q2) + (c1 * c2)) + (w2 * q1)) + (- (z2 * q0)) is complex ext-real real set
[*((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)),((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)),((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)),((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0))*] is quaternion Element of QUATERNION
[*((((y1 * c2) - (w1 * q0)) - (z1 * q1)) - (x2 * q2)),((((y1 * q0) + (w1 * c2)) + (z1 * q2)) - (x2 * q1)),((((y1 * q1) + (c2 * z1)) + (q0 * x2)) - (q2 * w1)),((((y1 * q2) + (x2 * c2)) + (w1 * q1)) - (z1 * q0))*] + [*((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)),((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)),((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)),((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0))*] is quaternion Element of QUATERNION
((((y1 * c2) - (w1 * q0)) - (z1 * q1)) - (x2 * q2)) + ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2)) is complex ext-real real Element of REAL
((((y1 * q0) + (w1 * c2)) + (z1 * q2)) - (x2 * q1)) + ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1)) is complex ext-real real Element of REAL
((((y1 * q1) + (c2 * z1)) + (q0 * x2)) - (q2 * w1)) + ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2)) is complex ext-real real Element of REAL
((((y1 * q2) + (x2 * c2)) + (w1 * q1)) - (z1 * q0)) + ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)) is complex ext-real real Element of REAL
[*(((((y1 * c2) - (w1 * q0)) - (z1 * q1)) - (x2 * q2)) + ((((y2 * c2) - (w2 * q0)) - (z2 * q1)) - (c1 * q2))),(((((y1 * q0) + (w1 * c2)) + (z1 * q2)) - (x2 * q1)) + ((((y2 * q0) + (w2 * c2)) + (z2 * q2)) - (c1 * q1))),(((((y1 * q1) + (c2 * z1)) + (q0 * x2)) - (q2 * w1)) + ((((y2 * q1) + (c2 * z2)) + (q0 * c1)) - (q2 * w2))),(((((y1 * q2) + (x2 * c2)) + (w1 * q1)) - (z1 * q0)) + ((((y2 * q2) + (c1 * c2)) + (w2 * q1)) - (z2 * q0)))*] is quaternion Element of QUATERNION
- () is quaternion Element of QUATERNION
c1 is quaternion set
- c1 is quaternion Element of QUATERNION
(- ()) * c1 is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
[*c2,c3,y1,w1*] is quaternion Element of QUATERNION
- c2 is complex ext-real real Element of REAL
- c3 is complex ext-real real Element of REAL
- y1 is complex ext-real real Element of REAL
- w1 is complex ext-real real Element of REAL
[*(- c2),(- c3),(- y1),(- w1)*] is quaternion Element of QUATERNION
c1 + [*(- c2),(- c3),(- y1),(- w1)*] is quaternion Element of QUATERNION
c2 + (- c2) is complex ext-real real Element of REAL
c3 + (- c3) is complex ext-real real Element of REAL
y1 + (- y1) is complex ext-real real Element of REAL
w1 + (- w1) is complex ext-real real Element of REAL
[*(c2 + (- c2)),(c3 + (- c3)),(y1 + (- y1)),(w1 + (- w1))*] is quaternion Element of QUATERNION
[*0,0*] is Element of COMPLEX
[*1,0*] is Element of COMPLEX
[*1,0,0,0*] is quaternion Element of QUATERNION
- 1 is complex ext-real non positive real Element of REAL
[*(- 1),0,0,0*] is quaternion Element of QUATERNION
() + [*(- 1),0,0,0*] is quaternion Element of QUATERNION
1 + (- 1) is complex ext-real real Element of REAL
0 + 0 is zero epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V16() non-empty empty-yielding Element of REAL
[*(1 + (- 1)),(0 + 0),(0 + 0),(0 + 0)*] is quaternion Element of QUATERNION
[*(- 1),0,0,0*] * [*c2,c3,y1,w1*] is quaternion Element of QUATERNION
(- 1) * c2 is complex ext-real real Element of REAL
0 * c3 is complex ext-real real Element of REAL
((- 1) * c2) - (0 * c3) is complex ext-real real Element of REAL
- (0 * c3) is complex ext-real real set
((- 1) * c2) + (- (0 * c3)) is complex ext-real real set
0 * y1 is complex ext-real real Element of REAL
(((- 1) * c2) - (0 * c3)) - (0 * y1) is complex ext-real real Element of REAL
- (0 * y1) is complex ext-real real set
(((- 1) * c2) - (0 * c3)) + (- (0 * y1)) is complex ext-real real set
0 * w1 is complex ext-real real Element of REAL
((((- 1) * c2) - (0 * c3)) - (0 * y1)) - (0 * w1) is complex ext-real real Element of REAL
- (0 * w1) is complex ext-real real set
((((- 1) * c2) - (0 * c3)) - (0 * y1)) + (- (0 * w1)) is complex ext-real real set
(- 1) * c3 is complex ext-real real Element of REAL
0 * c2 is complex ext-real real Element of REAL
((- 1) * c3) + (0 * c2) is complex ext-real real Element of REAL
(((- 1) * c3) + (0 * c2)) + (0 * w1) is complex ext-real real Element of REAL
((((- 1) * c3) + (0 * c2)) + (0 * w1)) - (0 * y1) is complex ext-real real Element of REAL
((((- 1) * c3) + (0 * c2)) + (0 * w1)) + (- (0 * y1)) is complex ext-real real set
(- 1) * y1 is complex ext-real real Element of REAL
c2 * 0 is complex ext-real real Element of REAL
((- 1) * y1) + (c2 * 0) is complex ext-real real Element of REAL
c3 * 0 is complex ext-real real Element of REAL
(((- 1) * y1) + (c2 * 0)) + (c3 * 0) is complex ext-real real Element of REAL
w1 * 0 is complex ext-real real Element of REAL
((((- 1) * y1) + (c2 * 0)) + (c3 * 0)) - (w1 * 0) is complex ext-real real Element of REAL
- (w1 * 0) is complex ext-real real set
((((- 1) * y1) + (c2 * 0)) + (c3 * 0)) + (- (w1 * 0)) is complex ext-real real set
(- 1) * w1 is complex ext-real real Element of REAL
((- 1) * w1) + (0 * c2) is complex ext-real real Element of REAL
(((- 1) * w1) + (0 * c2)) + (0 * y1) is complex ext-real real Element of REAL
((((- 1) * w1) + (0 * c2)) + (0 * y1)) - (0 * c3) is complex ext-real real Element of REAL
((((- 1) * w1) + (0 * c2)) + (0 * y1)) + (- (0 * c3)) is complex ext-real real set
[*(((((- 1) * c2) - (0 * c3)) - (0 * y1)) - (0 * w1)),(((((- 1) * c3) + (0 * c2)) + (0 * w1)) - (0 * y1)),(((((- 1) * y1) + (c2 * 0)) + (c3 * 0)) - (w1 * 0)),(((((- 1) * w1) + (0 * c2)) + (0 * y1)) - (0 * c3))*] is quaternion Element of QUATERNION
c1 is quaternion set
- c1 is quaternion Element of QUATERNION
c2 is quaternion set
(- c1) * c2 is quaternion Element of QUATERNION
c1 * c2 is quaternion Element of QUATERNION
- (c1 * c2) is quaternion Element of QUATERNION
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
z1 is complex ext-real real Element of REAL
[*c3,y1,w1,z1*] is quaternion Element of QUATERNION
x2 is complex ext-real real Element of REAL
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
z2 is complex ext-real real Element of REAL
[*x2,y2,w2,z2*] is quaternion Element of QUATERNION
- c3 is complex ext-real real Element of REAL
- y1 is complex ext-real real Element of REAL
- w1 is complex ext-real real Element of REAL
- z1 is complex ext-real real Element of REAL
[*(- c3),(- y1),(- w1),(- z1)*] is quaternion Element of QUATERNION
[*(- c3),(- y1),(- w1),(- z1)*] * [*x2,y2,w2,z2*] is quaternion Element of QUATERNION
(- c3) * x2 is complex ext-real real Element of REAL
(- y1) * y2 is complex ext-real real Element of REAL
((- c3) * x2) - ((- y1) * y2) is complex ext-real real Element of REAL
- ((- y1) * y2) is complex ext-real real set
((- c3) * x2) + (- ((- y1) * y2)) is complex ext-real real set
(- w1) * w2 is complex ext-real real Element of REAL
(((- c3) * x2) - ((- y1) * y2)) - ((- w1) * w2) is complex ext-real real Element of REAL
- ((- w1) * w2) is complex ext-real real set
(((- c3) * x2) - ((- y1) * y2)) + (- ((- w1) * w2)) is complex ext-real real set
(- z1) * z2 is complex ext-real real Element of REAL
((((- c3) * x2) - ((- y1) * y2)) - ((- w1) * w2)) - ((- z1) * z2) is complex ext-real real Element of REAL
- ((- z1) * z2) is complex ext-real real set
((((- c3) * x2) - ((- y1) * y2)) - ((- w1) * w2)) + (- ((- z1) * z2)) is complex ext-real real set
(- c3) * y2 is complex ext-real real Element of REAL
(- y1) * x2 is complex ext-real real Element of REAL
((- c3) * y2) + ((- y1) * x2) is complex ext-real real Element of REAL
(- w1) * z2 is complex ext-real real Element of REAL
(((- c3) * y2) + ((- y1) * x2)) + ((- w1) * z2) is complex ext-real real Element of REAL
(- z1) * w2 is complex ext-real real Element of REAL
((((- c3) * y2) + ((- y1) * x2)) + ((- w1) * z2)) - ((- z1) * w2) is complex ext-real real Element of REAL
- ((- z1) * w2) is complex ext-real real set
((((- c3) * y2) + ((- y1) * x2)) + ((- w1) * z2)) + (- ((- z1) * w2)) is complex ext-real real set
(- c3) * w2 is complex ext-real real Element of REAL
x2 * (- w1) is complex ext-real real Element of REAL
((- c3) * w2) + (x2 * (- w1)) is complex ext-real real Element of REAL
y2 * (- z1) is complex ext-real real Element of REAL
(((- c3) * w2) + (x2 * (- w1))) + (y2 * (- z1)) is complex ext-real real Element of REAL
z2 * (- y1) is complex ext-real real Element of REAL
((((- c3) * w2) + (x2 * (- w1))) + (y2 * (- z1))) - (z2 * (- y1)) is complex ext-real real Element of REAL
- (z2 * (- y1)) is complex ext-real real set
((((- c3) * w2) + (x2 * (- w1))) + (y2 * (- z1))) + (- (z2 * (- y1))) is complex ext-real real set
(- c3) * z2 is complex ext-real real Element of REAL
(- z1) * x2 is complex ext-real real Element of REAL
((- c3) * z2) + ((- z1) * x2) is complex ext-real real Element of REAL
(- y1) * w2 is complex ext-real real Element of REAL
(((- c3) * z2) + ((- z1) * x2)) + ((- y1) * w2) is complex ext-real real Element of REAL
(- w1) * y2 is complex ext-real real Element of REAL
((((- c3) * z2) + ((- z1) * x2)) + ((- y1) * w2)) - ((- w1) * y2) is complex ext-real real Element of REAL
- ((- w1) * y2) is complex ext-real real set
((((- c3) * z2) + ((- z1) * x2)) + ((- y1) * w2)) + (- ((- w1) * y2)) is complex ext-real real set
[*(((((- c3) * x2) - ((- y1) * y2)) - ((- w1) * w2)) - ((- z1) * z2)),(((((- c3) * y2) + ((- y1) * x2)) + ((- w1) * z2)) - ((- z1) * w2)),(((((- c3) * w2) + (x2 * (- w1))) + (y2 * (- z1))) - (z2 * (- y1))),(((((- c3) * z2) + ((- z1) * x2)) + ((- y1) * w2)) - ((- w1) * y2))*] is quaternion Element of QUATERNION
c3 * x2 is complex ext-real real Element of REAL
- (c3 * x2) is complex ext-real real Element of REAL
y1 * y2 is complex ext-real real Element of REAL
(- (c3 * x2)) + (y1 * y2) is complex ext-real real Element of REAL
w1 * w2 is complex ext-real real Element of REAL
((- (c3 * x2)) + (y1 * y2)) + (w1 * w2) is complex ext-real real Element of REAL
z1 * z2 is complex ext-real real Element of REAL
(((- (c3 * x2)) + (y1 * y2)) + (w1 * w2)) + (z1 * z2) is complex ext-real real Element of REAL
c3 * y2 is complex ext-real real Element of REAL
- (c3 * y2) is complex ext-real real Element of REAL
y1 * x2 is complex ext-real real Element of REAL
(- (c3 * y2)) - (y1 * x2) is complex ext-real real Element of REAL
- (y1 * x2) is complex ext-real real set
(- (c3 * y2)) + (- (y1 * x2)) is complex ext-real real set
w1 * z2 is complex ext-real real Element of REAL
((- (c3 * y2)) - (y1 * x2)) - (w1 * z2) is complex ext-real real Element of REAL
- (w1 * z2) is complex ext-real real set
((- (c3 * y2)) - (y1 * x2)) + (- (w1 * z2)) is complex ext-real real set
z1 * w2 is complex ext-real real Element of REAL
(((- (c3 * y2)) - (y1 * x2)) - (w1 * z2)) + (z1 * w2) is complex ext-real real Element of REAL
c3 * w2 is complex ext-real real Element of REAL
- (c3 * w2) is complex ext-real real Element of REAL
x2 * w1 is complex ext-real real Element of REAL
(- (c3 * w2)) - (x2 * w1) is complex ext-real real Element of REAL
- (x2 * w1) is complex ext-real real set
(- (c3 * w2)) + (- (x2 * w1)) is complex ext-real real set
y2 * z1 is complex ext-real real Element of REAL
((- (c3 * w2)) - (x2 * w1)) - (y2 * z1) is complex ext-real real Element of REAL
- (y2 * z1) is complex ext-real real set
((- (c3 * w2)) - (x2 * w1)) + (- (y2 * z1)) is complex ext-real real set
z2 * y1 is complex ext-real real Element of REAL
(((- (c3 * w2)) - (x2 * w1)) - (y2 * z1)) + (z2 * y1) is complex ext-real real Element of REAL
c3 * z2 is complex ext-real real Element of REAL
- (c3 * z2) is complex ext-real real Element of REAL
z1 * x2 is complex ext-real real Element of REAL
(- (c3 * z2)) - (z1 * x2) is complex ext-real real Element of REAL
- (z1 * x2) is complex ext-real real set
(- (c3 * z2)) + (- (z1 * x2)) is complex ext-real real set
y1 * w2 is complex ext-real real Element of REAL
((- (c3 * z2)) - (z1 * x2)) - (y1 * w2) is complex ext-real real Element of REAL
- (y1 * w2) is complex ext-real real set
((- (c3 * z2)) - (z1 * x2)) + (- (y1 * w2)) is complex ext-real real set
w1 * y2 is complex ext-real real Element of REAL
(((- (c3 * z2)) - (z1 * x2)) - (y1 * w2)) + (w1 * y2) is complex ext-real real Element of REAL
[*((((- (c3 * x2)) + (y1 * y2)) + (w1 * w2)) + (z1 * z2)),((((- (c3 * y2)) - (y1 * x2)) - (w1 * z2)) + (z1 * w2)),((((- (c3 * w2)) - (x2 * w1)) - (y2 * z1)) + (z2 * y1)),((((- (c3 * z2)) - (z1 * x2)) - (y1 * w2)) + (w1 * y2))*] is quaternion Element of QUATERNION
(c3 * x2) - (y1 * y2) is complex ext-real real Element of REAL
- (y1 * y2) is complex ext-real real set
(c3 * x2) + (- (y1 * y2)) is complex ext-real real set
((c3 * x2) - (y1 * y2)) - (w1 * w2) is complex ext-real real Element of REAL
- (w1 * w2) is complex ext-real real set
((c3 * x2) - (y1 * y2)) + (- (w1 * w2)) is complex ext-real real set
(((c3 * x2) - (y1 * y2)) - (w1 * w2)) - (z1 * z2) is complex ext-real real Element of REAL
- (z1 * z2) is complex ext-real real set
(((c3 * x2) - (y1 * y2)) - (w1 * w2)) + (- (z1 * z2)) is complex ext-real real set
(c3 * y2) + (y1 * x2) is complex ext-real real Element of REAL
((c3 * y2) + (y1 * x2)) + (w1 * z2) is complex ext-real real Element of REAL
(((c3 * y2) + (y1 * x2)) + (w1 * z2)) - (z1 * w2) is complex ext-real real Element of REAL
- (z1 * w2) is complex ext-real real set
(((c3 * y2) + (y1 * x2)) + (w1 * z2)) + (- (z1 * w2)) is complex ext-real real set
(c3 * w2) + (x2 * w1) is complex ext-real real Element of REAL
((c3 * w2) + (x2 * w1)) + (y2 * z1) is complex ext-real real Element of REAL
(((c3 * w2) + (x2 * w1)) + (y2 * z1)) - (z2 * y1) is complex ext-real real Element of REAL
- (z2 * y1) is complex ext-real real set
(((c3 * w2) + (x2 * w1)) + (y2 * z1)) + (- (z2 * y1)) is complex ext-real real set
(c3 * z2) + (z1 * x2) is complex ext-real real Element of REAL
((c3 * z2) + (z1 * x2)) + (y1 * w2) is complex ext-real real Element of REAL
(((c3 * z2) + (z1 * x2)) + (y1 * w2)) - (w1 * y2) is complex ext-real real Element of REAL
- (w1 * y2) is complex ext-real real set
(((c3 * z2) + (z1 * x2)) + (y1 * w2)) + (- (w1 * y2)) is complex ext-real real set
[*((((c3 * x2) - (y1 * y2)) - (w1 * w2)) - (z1 * z2)),((((c3 * y2) + (y1 * x2)) + (w1 * z2)) - (z1 * w2)),((((c3 * w2) + (x2 * w1)) + (y2 * z1)) - (z2 * y1)),((((c3 * z2) + (z1 * x2)) + (y1 * w2)) - (w1 * y2))*] is quaternion Element of QUATERNION
((- c1) * c2) + (c1 * c2) is quaternion Element of QUATERNION
((((- (c3 * x2)) + (y1 * y2)) + (w1 * w2)) + (z1 * z2)) + ((((c3 * x2) - (y1 * y2)) - (w1 * w2)) - (z1 * z2)) is complex ext-real real Element of REAL
((((- (c3 * y2)) - (y1 * x2)) - (w1 * z2)) + (z1 * w2)) + ((((c3 * y2) + (y1 * x2)) + (w1 * z2)) - (z1 * w2)) is complex ext-real real Element of REAL
((((- (c3 * w2)) - (x2 * w1)) - (y2 * z1)) + (z2 * y1)) + ((((c3 * w2) + (x2 * w1)) + (y2 * z1)) - (z2 * y1)) is complex ext-real real Element of REAL
((((- (c3 * z2)) - (z1 * x2)) - (y1 * w2)) + (w1 * y2)) + ((((c3 * z2) + (z1 * x2)) + (y1 * w2)) - (w1 * y2)) is complex ext-real real Element of REAL
[*(((((- (c3 * x2)) + (y1 * y2)) + (w1 * w2)) + (z1 * z2)) + ((((c3 * x2) - (y1 * y2)) - (w1 * w2)) - (z1 * z2))),(((((- (c3 * y2)) - (y1 * x2)) - (w1 * z2)) + (z1 * w2)) + ((((c3 * y2) + (y1 * x2)) + (w1 * z2)) - (z1 * w2))),(((((- (c3 * w2)) - (x2 * w1)) - (y2 * z1)) + (z2 * y1)) + ((((c3 * w2) + (x2 * w1)) + (y2 * z1)) - (z2 * y1))),(((((- (c3 * z2)) - (z1 * x2)) - (y1 * w2)) + (w1 * y2)) + ((((c3 * z2) + (z1 * x2)) + (y1 * w2)) - (w1 * y2)))*] is quaternion Element of QUATERNION
[*0,0*] is Element of COMPLEX
c1 is quaternion set
c2 is quaternion set
- c2 is quaternion Element of QUATERNION
c1 * (- c2) is quaternion Element of QUATERNION
c1 * c2 is quaternion Element of QUATERNION
- (c1 * c2) is quaternion Element of QUATERNION
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
z1 is complex ext-real real Element of REAL
[*c3,y1,w1,z1*] is quaternion Element of QUATERNION
x2 is complex ext-real real Element of REAL
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
z2 is complex ext-real real Element of REAL
[*x2,y2,w2,z2*] is quaternion Element of QUATERNION
- x2 is complex ext-real real Element of REAL
- y2 is complex ext-real real Element of REAL
- w2 is complex ext-real real Element of REAL
- z2 is complex ext-real real Element of REAL
[*(- x2),(- y2),(- w2),(- z2)*] is quaternion Element of QUATERNION
[*c3,y1,w1,z1*] * [*(- x2),(- y2),(- w2),(- z2)*] is quaternion Element of QUATERNION
c3 * (- x2) is complex ext-real real Element of REAL
y1 * (- y2) is complex ext-real real Element of REAL
(c3 * (- x2)) - (y1 * (- y2)) is complex ext-real real Element of REAL
- (y1 * (- y2)) is complex ext-real real set
(c3 * (- x2)) + (- (y1 * (- y2))) is complex ext-real real set
w1 * (- w2) is complex ext-real real Element of REAL
((c3 * (- x2)) - (y1 * (- y2))) - (w1 * (- w2)) is complex ext-real real Element of REAL
- (w1 * (- w2)) is complex ext-real real set
((c3 * (- x2)) - (y1 * (- y2))) + (- (w1 * (- w2))) is complex ext-real real set
z1 * (- z2) is complex ext-real real Element of REAL
(((c3 * (- x2)) - (y1 * (- y2))) - (w1 * (- w2))) - (z1 * (- z2)) is complex ext-real real Element of REAL
- (z1 * (- z2)) is complex ext-real real set
(((c3 * (- x2)) - (y1 * (- y2))) - (w1 * (- w2))) + (- (z1 * (- z2))) is complex ext-real real set
c3 * (- y2) is complex ext-real real Element of REAL
y1 * (- x2) is complex ext-real real Element of REAL
(c3 * (- y2)) + (y1 * (- x2)) is complex ext-real real Element of REAL
w1 * (- z2) is complex ext-real real Element of REAL
((c3 * (- y2)) + (y1 * (- x2))) + (w1 * (- z2)) is complex ext-real real Element of REAL
z1 * (- w2) is complex ext-real real Element of REAL
(((c3 * (- y2)) + (y1 * (- x2))) + (w1 * (- z2))) - (z1 * (- w2)) is complex ext-real real Element of REAL
- (z1 * (- w2)) is complex ext-real real set
(((c3 * (- y2)) + (y1 * (- x2))) + (w1 * (- z2))) + (- (z1 * (- w2))) is complex ext-real real set
c3 * (- w2) is complex ext-real real Element of REAL
(- x2) * w1 is complex ext-real real Element of REAL
(c3 * (- w2)) + ((- x2) * w1) is complex ext-real real Element of REAL
(- y2) * z1 is complex ext-real real Element of REAL
((c3 * (- w2)) + ((- x2) * w1)) + ((- y2) * z1) is complex ext-real real Element of REAL
(- z2) * y1 is complex ext-real real Element of REAL
(((c3 * (- w2)) + ((- x2) * w1)) + ((- y2) * z1)) - ((- z2) * y1) is complex ext-real real Element of REAL
- ((- z2) * y1) is complex ext-real real set
(((c3 * (- w2)) + ((- x2) * w1)) + ((- y2) * z1)) + (- ((- z2) * y1)) is complex ext-real real set
c3 * (- z2) is complex ext-real real Element of REAL
z1 * (- x2) is complex ext-real real Element of REAL
(c3 * (- z2)) + (z1 * (- x2)) is complex ext-real real Element of REAL
y1 * (- w2) is complex ext-real real Element of REAL
((c3 * (- z2)) + (z1 * (- x2))) + (y1 * (- w2)) is complex ext-real real Element of REAL
w1 * (- y2) is complex ext-real real Element of REAL
(((c3 * (- z2)) + (z1 * (- x2))) + (y1 * (- w2))) - (w1 * (- y2)) is complex ext-real real Element of REAL
- (w1 * (- y2)) is complex ext-real real set
(((c3 * (- z2)) + (z1 * (- x2))) + (y1 * (- w2))) + (- (w1 * (- y2))) is complex ext-real real set
[*((((c3 * (- x2)) - (y1 * (- y2))) - (w1 * (- w2))) - (z1 * (- z2))),((((c3 * (- y2)) + (y1 * (- x2))) + (w1 * (- z2))) - (z1 * (- w2))),((((c3 * (- w2)) + ((- x2) * w1)) + ((- y2) * z1)) - ((- z2) * y1)),((((c3 * (- z2)) + (z1 * (- x2))) + (y1 * (- w2))) - (w1 * (- y2)))*] is quaternion Element of QUATERNION
c3 * x2 is complex ext-real real Element of REAL
- (c3 * x2) is complex ext-real real Element of REAL
y1 * y2 is complex ext-real real Element of REAL
(- (c3 * x2)) + (y1 * y2) is complex ext-real real Element of REAL
w1 * w2 is complex ext-real real Element of REAL
((- (c3 * x2)) + (y1 * y2)) + (w1 * w2) is complex ext-real real Element of REAL
z1 * z2 is complex ext-real real Element of REAL
(((- (c3 * x2)) + (y1 * y2)) + (w1 * w2)) + (z1 * z2) is complex ext-real real Element of REAL
c3 * y2 is complex ext-real real Element of REAL
- (c3 * y2) is complex ext-real real Element of REAL
y1 * x2 is complex ext-real real Element of REAL
(- (c3 * y2)) - (y1 * x2) is complex ext-real real Element of REAL
- (y1 * x2) is complex ext-real real set
(- (c3 * y2)) + (- (y1 * x2)) is complex ext-real real set
w1 * z2 is complex ext-real real Element of REAL
((- (c3 * y2)) - (y1 * x2)) - (w1 * z2) is complex ext-real real Element of REAL
- (w1 * z2) is complex ext-real real set
((- (c3 * y2)) - (y1 * x2)) + (- (w1 * z2)) is complex ext-real real set
z1 * w2 is complex ext-real real Element of REAL
(((- (c3 * y2)) - (y1 * x2)) - (w1 * z2)) + (z1 * w2) is complex ext-real real Element of REAL
c3 * w2 is complex ext-real real Element of REAL
- (c3 * w2) is complex ext-real real Element of REAL
x2 * w1 is complex ext-real real Element of REAL
(- (c3 * w2)) - (x2 * w1) is complex ext-real real Element of REAL
- (x2 * w1) is complex ext-real real set
(- (c3 * w2)) + (- (x2 * w1)) is complex ext-real real set
y2 * z1 is complex ext-real real Element of REAL
((- (c3 * w2)) - (x2 * w1)) - (y2 * z1) is complex ext-real real Element of REAL
- (y2 * z1) is complex ext-real real set
((- (c3 * w2)) - (x2 * w1)) + (- (y2 * z1)) is complex ext-real real set
z2 * y1 is complex ext-real real Element of REAL
(((- (c3 * w2)) - (x2 * w1)) - (y2 * z1)) + (z2 * y1) is complex ext-real real Element of REAL
c3 * z2 is complex ext-real real Element of REAL
- (c3 * z2) is complex ext-real real Element of REAL
z1 * x2 is complex ext-real real Element of REAL
(- (c3 * z2)) - (z1 * x2) is complex ext-real real Element of REAL
- (z1 * x2) is complex ext-real real set
(- (c3 * z2)) + (- (z1 * x2)) is complex ext-real real set
y1 * w2 is complex ext-real real Element of REAL
((- (c3 * z2)) - (z1 * x2)) - (y1 * w2) is complex ext-real real Element of REAL
- (y1 * w2) is complex ext-real real set
((- (c3 * z2)) - (z1 * x2)) + (- (y1 * w2)) is complex ext-real real set
w1 * y2 is complex ext-real real Element of REAL
(((- (c3 * z2)) - (z1 * x2)) - (y1 * w2)) + (w1 * y2) is complex ext-real real Element of REAL
[*((((- (c3 * x2)) + (y1 * y2)) + (w1 * w2)) + (z1 * z2)),((((- (c3 * y2)) - (y1 * x2)) - (w1 * z2)) + (z1 * w2)),((((- (c3 * w2)) - (x2 * w1)) - (y2 * z1)) + (z2 * y1)),((((- (c3 * z2)) - (z1 * x2)) - (y1 * w2)) + (w1 * y2))*] is quaternion Element of QUATERNION
(c3 * x2) - (y1 * y2) is complex ext-real real Element of REAL
- (y1 * y2) is complex ext-real real set
(c3 * x2) + (- (y1 * y2)) is complex ext-real real set
((c3 * x2) - (y1 * y2)) - (w1 * w2) is complex ext-real real Element of REAL
- (w1 * w2) is complex ext-real real set
((c3 * x2) - (y1 * y2)) + (- (w1 * w2)) is complex ext-real real set
(((c3 * x2) - (y1 * y2)) - (w1 * w2)) - (z1 * z2) is complex ext-real real Element of REAL
- (z1 * z2) is complex ext-real real set
(((c3 * x2) - (y1 * y2)) - (w1 * w2)) + (- (z1 * z2)) is complex ext-real real set
(c3 * y2) + (y1 * x2) is complex ext-real real Element of REAL
((c3 * y2) + (y1 * x2)) + (w1 * z2) is complex ext-real real Element of REAL
(((c3 * y2) + (y1 * x2)) + (w1 * z2)) - (z1 * w2) is complex ext-real real Element of REAL
- (z1 * w2) is complex ext-real real set
(((c3 * y2) + (y1 * x2)) + (w1 * z2)) + (- (z1 * w2)) is complex ext-real real set
(c3 * w2) + (x2 * w1) is complex ext-real real Element of REAL
((c3 * w2) + (x2 * w1)) + (y2 * z1) is complex ext-real real Element of REAL
(((c3 * w2) + (x2 * w1)) + (y2 * z1)) - (z2 * y1) is complex ext-real real Element of REAL
- (z2 * y1) is complex ext-real real set
(((c3 * w2) + (x2 * w1)) + (y2 * z1)) + (- (z2 * y1)) is complex ext-real real set
(c3 * z2) + (z1 * x2) is complex ext-real real Element of REAL
((c3 * z2) + (z1 * x2)) + (y1 * w2) is complex ext-real real Element of REAL
(((c3 * z2) + (z1 * x2)) + (y1 * w2)) - (w1 * y2) is complex ext-real real Element of REAL
- (w1 * y2) is complex ext-real real set
(((c3 * z2) + (z1 * x2)) + (y1 * w2)) + (- (w1 * y2)) is complex ext-real real set
[*((((c3 * x2) - (y1 * y2)) - (w1 * w2)) - (z1 * z2)),((((c3 * y2) + (y1 * x2)) + (w1 * z2)) - (z1 * w2)),((((c3 * w2) + (x2 * w1)) + (y2 * z1)) - (z2 * y1)),((((c3 * z2) + (z1 * x2)) + (y1 * w2)) - (w1 * y2))*] is quaternion Element of QUATERNION
(c1 * (- c2)) + (c1 * c2) is quaternion Element of QUATERNION
((((- (c3 * x2)) + (y1 * y2)) + (w1 * w2)) + (z1 * z2)) + ((((c3 * x2) - (y1 * y2)) - (w1 * w2)) - (z1 * z2)) is complex ext-real real Element of REAL
((((- (c3 * y2)) - (y1 * x2)) - (w1 * z2)) + (z1 * w2)) + ((((c3 * y2) + (y1 * x2)) + (w1 * z2)) - (z1 * w2)) is complex ext-real real Element of REAL
((((- (c3 * w2)) - (x2 * w1)) - (y2 * z1)) + (z2 * y1)) + ((((c3 * w2) + (x2 * w1)) + (y2 * z1)) - (z2 * y1)) is complex ext-real real Element of REAL
((((- (c3 * z2)) - (z1 * x2)) - (y1 * w2)) + (w1 * y2)) + ((((c3 * z2) + (z1 * x2)) + (y1 * w2)) - (w1 * y2)) is complex ext-real real Element of REAL
[*(((((- (c3 * x2)) + (y1 * y2)) + (w1 * w2)) + (z1 * z2)) + ((((c3 * x2) - (y1 * y2)) - (w1 * w2)) - (z1 * z2))),(((((- (c3 * y2)) - (y1 * x2)) - (w1 * z2)) + (z1 * w2)) + ((((c3 * y2) + (y1 * x2)) + (w1 * z2)) - (z1 * w2))),(((((- (c3 * w2)) - (x2 * w1)) - (y2 * z1)) + (z2 * y1)) + ((((c3 * w2) + (x2 * w1)) + (y2 * z1)) - (z2 * y1))),(((((- (c3 * z2)) - (z1 * x2)) - (y1 * w2)) + (w1 * y2)) + ((((c3 * z2) + (z1 * x2)) + (y1 * w2)) - (w1 * y2)))*] is quaternion Element of QUATERNION
[*0,0*] is Element of COMPLEX
c1 is quaternion set
- c1 is quaternion Element of QUATERNION
c2 is quaternion set
- c2 is quaternion Element of QUATERNION
(- c1) * (- c2) is quaternion Element of QUATERNION
c1 * c2 is quaternion Element of QUATERNION
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
z1 is complex ext-real real Element of REAL
[*c3,y1,w1,z1*] is quaternion Element of QUATERNION
x2 is complex ext-real real Element of REAL
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
z2 is complex ext-real real Element of REAL
[*x2,y2,w2,z2*] is quaternion Element of QUATERNION
- c3 is complex ext-real real Element of REAL
- y1 is complex ext-real real Element of REAL
- w1 is complex ext-real real Element of REAL
- z1 is complex ext-real real Element of REAL
[*(- c3),(- y1),(- w1),(- z1)*] is quaternion Element of QUATERNION
- x2 is complex ext-real real Element of REAL
- y2 is complex ext-real real Element of REAL
- w2 is complex ext-real real Element of REAL
- z2 is complex ext-real real Element of REAL
[*(- x2),(- y2),(- w2),(- z2)*] is quaternion Element of QUATERNION
[*(- c3),(- y1),(- w1),(- z1)*] * [*(- x2),(- y2),(- w2),(- z2)*] is quaternion Element of QUATERNION
(- c3) * (- x2) is complex ext-real real Element of REAL
(- y1) * (- y2) is complex ext-real real Element of REAL
((- c3) * (- x2)) - ((- y1) * (- y2)) is complex ext-real real Element of REAL
- ((- y1) * (- y2)) is complex ext-real real set
((- c3) * (- x2)) + (- ((- y1) * (- y2))) is complex ext-real real set
(- w1) * (- w2) is complex ext-real real Element of REAL
(((- c3) * (- x2)) - ((- y1) * (- y2))) - ((- w1) * (- w2)) is complex ext-real real Element of REAL
- ((- w1) * (- w2)) is complex ext-real real set
(((- c3) * (- x2)) - ((- y1) * (- y2))) + (- ((- w1) * (- w2))) is complex ext-real real set
(- z1) * (- z2) is complex ext-real real Element of REAL
((((- c3) * (- x2)) - ((- y1) * (- y2))) - ((- w1) * (- w2))) - ((- z1) * (- z2)) is complex ext-real real Element of REAL
- ((- z1) * (- z2)) is complex ext-real real set
((((- c3) * (- x2)) - ((- y1) * (- y2))) - ((- w1) * (- w2))) + (- ((- z1) * (- z2))) is complex ext-real real set
(- c3) * (- y2) is complex ext-real real Element of REAL
(- y1) * (- x2) is complex ext-real real Element of REAL
((- c3) * (- y2)) + ((- y1) * (- x2)) is complex ext-real real Element of REAL
(- w1) * (- z2) is complex ext-real real Element of REAL
(((- c3) * (- y2)) + ((- y1) * (- x2))) + ((- w1) * (- z2)) is complex ext-real real Element of REAL
(- z1) * (- w2) is complex ext-real real Element of REAL
((((- c3) * (- y2)) + ((- y1) * (- x2))) + ((- w1) * (- z2))) - ((- z1) * (- w2)) is complex ext-real real Element of REAL
- ((- z1) * (- w2)) is complex ext-real real set
((((- c3) * (- y2)) + ((- y1) * (- x2))) + ((- w1) * (- z2))) + (- ((- z1) * (- w2))) is complex ext-real real set
(- c3) * (- w2) is complex ext-real real Element of REAL
(- x2) * (- w1) is complex ext-real real Element of REAL
((- c3) * (- w2)) + ((- x2) * (- w1)) is complex ext-real real Element of REAL
(- y2) * (- z1) is complex ext-real real Element of REAL
(((- c3) * (- w2)) + ((- x2) * (- w1))) + ((- y2) * (- z1)) is complex ext-real real Element of REAL
(- z2) * (- y1) is complex ext-real real Element of REAL
((((- c3) * (- w2)) + ((- x2) * (- w1))) + ((- y2) * (- z1))) - ((- z2) * (- y1)) is complex ext-real real Element of REAL
- ((- z2) * (- y1)) is complex ext-real real set
((((- c3) * (- w2)) + ((- x2) * (- w1))) + ((- y2) * (- z1))) + (- ((- z2) * (- y1))) is complex ext-real real set
(- c3) * (- z2) is complex ext-real real Element of REAL
(- z1) * (- x2) is complex ext-real real Element of REAL
((- c3) * (- z2)) + ((- z1) * (- x2)) is complex ext-real real Element of REAL
(- y1) * (- w2) is complex ext-real real Element of REAL
(((- c3) * (- z2)) + ((- z1) * (- x2))) + ((- y1) * (- w2)) is complex ext-real real Element of REAL
(- w1) * (- y2) is complex ext-real real Element of REAL
((((- c3) * (- z2)) + ((- z1) * (- x2))) + ((- y1) * (- w2))) - ((- w1) * (- y2)) is complex ext-real real Element of REAL
- ((- w1) * (- y2)) is complex ext-real real set
((((- c3) * (- z2)) + ((- z1) * (- x2))) + ((- y1) * (- w2))) + (- ((- w1) * (- y2))) is complex ext-real real set
[*(((((- c3) * (- x2)) - ((- y1) * (- y2))) - ((- w1) * (- w2))) - ((- z1) * (- z2))),(((((- c3) * (- y2)) + ((- y1) * (- x2))) + ((- w1) * (- z2))) - ((- z1) * (- w2))),(((((- c3) * (- w2)) + ((- x2) * (- w1))) + ((- y2) * (- z1))) - ((- z2) * (- y1))),(((((- c3) * (- z2)) + ((- z1) * (- x2))) + ((- y1) * (- w2))) - ((- w1) * (- y2)))*] is quaternion Element of QUATERNION
c3 * x2 is complex ext-real real Element of REAL
y1 * y2 is complex ext-real real Element of REAL
(c3 * x2) - (y1 * y2) is complex ext-real real Element of REAL
- (y1 * y2) is complex ext-real real set
(c3 * x2) + (- (y1 * y2)) is complex ext-real real set
w1 * w2 is complex ext-real real Element of REAL
((c3 * x2) - (y1 * y2)) - (w1 * w2) is complex ext-real real Element of REAL
- (w1 * w2) is complex ext-real real set
((c3 * x2) - (y1 * y2)) + (- (w1 * w2)) is complex ext-real real set
z1 * z2 is complex ext-real real Element of REAL
(((c3 * x2) - (y1 * y2)) - (w1 * w2)) - (z1 * z2) is complex ext-real real Element of REAL
- (z1 * z2) is complex ext-real real set
(((c3 * x2) - (y1 * y2)) - (w1 * w2)) + (- (z1 * z2)) is complex ext-real real set
c3 * y2 is complex ext-real real Element of REAL
y1 * x2 is complex ext-real real Element of REAL
(c3 * y2) + (y1 * x2) is complex ext-real real Element of REAL
w1 * z2 is complex ext-real real Element of REAL
((c3 * y2) + (y1 * x2)) + (w1 * z2) is complex ext-real real Element of REAL
z1 * w2 is complex ext-real real Element of REAL
(((c3 * y2) + (y1 * x2)) + (w1 * z2)) - (z1 * w2) is complex ext-real real Element of REAL
- (z1 * w2) is complex ext-real real set
(((c3 * y2) + (y1 * x2)) + (w1 * z2)) + (- (z1 * w2)) is complex ext-real real set
c3 * w2 is complex ext-real real Element of REAL
x2 * w1 is complex ext-real real Element of REAL
(c3 * w2) + (x2 * w1) is complex ext-real real Element of REAL
y2 * z1 is complex ext-real real Element of REAL
((c3 * w2) + (x2 * w1)) + (y2 * z1) is complex ext-real real Element of REAL
z2 * y1 is complex ext-real real Element of REAL
(((c3 * w2) + (x2 * w1)) + (y2 * z1)) - (z2 * y1) is complex ext-real real Element of REAL
- (z2 * y1) is complex ext-real real set
(((c3 * w2) + (x2 * w1)) + (y2 * z1)) + (- (z2 * y1)) is complex ext-real real set
c3 * z2 is complex ext-real real Element of REAL
z1 * x2 is complex ext-real real Element of REAL
(c3 * z2) + (z1 * x2) is complex ext-real real Element of REAL
y1 * w2 is complex ext-real real Element of REAL
((c3 * z2) + (z1 * x2)) + (y1 * w2) is complex ext-real real Element of REAL
w1 * y2 is complex ext-real real Element of REAL
(((c3 * z2) + (z1 * x2)) + (y1 * w2)) - (w1 * y2) is complex ext-real real Element of REAL
- (w1 * y2) is complex ext-real real set
(((c3 * z2) + (z1 * x2)) + (y1 * w2)) + (- (w1 * y2)) is complex ext-real real set
[*((((c3 * x2) - (y1 * y2)) - (w1 * w2)) - (z1 * z2)),((((c3 * y2) + (y1 * x2)) + (w1 * z2)) - (z1 * w2)),((((c3 * w2) + (x2 * w1)) + (y2 * z1)) - (z2 * y1)),((((c3 * z2) + (z1 * x2)) + (y1 * w2)) - (w1 * y2))*] is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
c1 - c2 is quaternion Element of QUATERNION
- c2 is quaternion set
c1 + (- c2) is quaternion set
c3 is quaternion set
(c1 - c2) * c3 is quaternion Element of QUATERNION
c1 * c3 is quaternion Element of QUATERNION
c2 * c3 is quaternion Element of QUATERNION
(c1 * c3) - (c2 * c3) is quaternion Element of QUATERNION
- (c2 * c3) is quaternion set
(c1 * c3) + (- (c2 * c3)) is quaternion set
- c2 is quaternion Element of QUATERNION
(- c2) * c3 is quaternion Element of QUATERNION
(c1 * c3) + ((- c2) * c3) is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
c1 * c2 is quaternion Element of QUATERNION
c3 is quaternion set
c2 - c3 is quaternion Element of QUATERNION
- c3 is quaternion set
c2 + (- c3) is quaternion set
c1 * (c2 - c3) is quaternion Element of QUATERNION
c1 * c3 is quaternion Element of QUATERNION
(c1 * c2) - (c1 * c3) is quaternion Element of QUATERNION
- (c1 * c3) is quaternion set
(c1 * c2) + (- (c1 * c3)) is quaternion set
- c3 is quaternion Element of QUATERNION
c1 * (- c3) is quaternion Element of QUATERNION
(c1 * c2) + (c1 * (- c3)) is quaternion Element of QUATERNION
c1 is complex ext-real real Element of REAL
c2 is complex ext-real real Element of REAL
- c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
- c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
[*c1,c2,c3,y1*] is quaternion Element of QUATERNION
[*c1,c2,c3,y1*] *' is quaternion Element of QUATERNION
Rea [*c1,c2,c3,y1*] is complex ext-real real Element of REAL
Im1 [*c1,c2,c3,y1*] is complex ext-real real Element of REAL
- (Im1 [*c1,c2,c3,y1*]) is complex ext-real real Element of REAL
(- (Im1 [*c1,c2,c3,y1*])) * <i> is quaternion set
(Rea [*c1,c2,c3,y1*]) + ((- (Im1 [*c1,c2,c3,y1*])) * <i>) is quaternion set
Im2 [*c1,c2,c3,y1*] is complex ext-real real Element of REAL
- (Im2 [*c1,c2,c3,y1*]) is complex ext-real real Element of REAL
(- (Im2 [*c1,c2,c3,y1*])) * <j> is quaternion set
((Rea [*c1,c2,c3,y1*]) + ((- (Im1 [*c1,c2,c3,y1*])) * <i>)) + ((- (Im2 [*c1,c2,c3,y1*])) * <j>) is quaternion Element of QUATERNION
Im3 [*c1,c2,c3,y1*] is complex ext-real real Element of REAL
- (Im3 [*c1,c2,c3,y1*]) is complex ext-real real Element of REAL
(- (Im3 [*c1,c2,c3,y1*])) * <k> is quaternion set
(((Rea [*c1,c2,c3,y1*]) + ((- (Im1 [*c1,c2,c3,y1*])) * <i>)) + ((- (Im2 [*c1,c2,c3,y1*])) * <j>)) + ((- (Im3 [*c1,c2,c3,y1*])) * <k>) is quaternion Element of QUATERNION
- y1 is complex ext-real real Element of REAL
[*c1,(- c2),(- c3),(- y1)*] is quaternion Element of QUATERNION
c1 is quaternion set
c1 *' is quaternion Element of QUATERNION
Rea c1 is complex ext-real real Element of REAL
Im1 c1 is complex ext-real real Element of REAL
- (Im1 c1) is complex ext-real real Element of REAL
(- (Im1 c1)) * <i> is quaternion set
(Rea c1) + ((- (Im1 c1)) * <i>) is quaternion set
Im2 c1 is complex ext-real real Element of REAL
- (Im2 c1) is complex ext-real real Element of REAL
(- (Im2 c1)) * <j> is quaternion set
((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>) is quaternion Element of QUATERNION
Im3 c1 is complex ext-real real Element of REAL
- (Im3 c1) is complex ext-real real Element of REAL
(- (Im3 c1)) * <k> is quaternion set
(((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>)) + ((- (Im3 c1)) * <k>) is quaternion Element of QUATERNION
(c1 *') *' is quaternion Element of QUATERNION
Rea (c1 *') is complex ext-real real Element of REAL
Im1 (c1 *') is complex ext-real real Element of REAL
- (Im1 (c1 *')) is complex ext-real real Element of REAL
(- (Im1 (c1 *'))) * <i> is quaternion set
(Rea (c1 *')) + ((- (Im1 (c1 *'))) * <i>) is quaternion set
Im2 (c1 *') is complex ext-real real Element of REAL
- (Im2 (c1 *')) is complex ext-real real Element of REAL
(- (Im2 (c1 *'))) * <j> is quaternion set
((Rea (c1 *')) + ((- (Im1 (c1 *'))) * <i>)) + ((- (Im2 (c1 *'))) * <j>) is quaternion Element of QUATERNION
Im3 (c1 *') is complex ext-real real Element of REAL
- (Im3 (c1 *')) is complex ext-real real Element of REAL
(- (Im3 (c1 *'))) * <k> is quaternion set
(((Rea (c1 *')) + ((- (Im1 (c1 *'))) * <i>)) + ((- (Im2 (c1 *'))) * <j>)) + ((- (Im3 (c1 *'))) * <k>) is quaternion Element of QUATERNION
- (- (Im1 c1)) is complex ext-real real Element of REAL
- (- (Im2 c1)) is complex ext-real real Element of REAL
- (- (Im3 c1)) is complex ext-real real Element of REAL
[*(Rea c1),(- (- (Im1 c1))),(- (- (Im2 c1))),(- (- (Im3 c1)))*] is quaternion Element of QUATERNION
c1 is quaternion set
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
z1 is complex ext-real real Element of REAL
[*c3,y1,w1,z1*] is quaternion Element of QUATERNION
c2 is quaternion set
x2 is complex ext-real real Element of REAL
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
z2 is complex ext-real real Element of REAL
[*x2,y2,w2,z2*] is quaternion Element of QUATERNION
(c2) is complex ext-real real Element of REAL
Rea c2 is complex ext-real real Element of REAL
(Rea c2) ^2 is complex ext-real real Element of REAL
(Rea c2) * (Rea c2) is complex ext-real real set
Im1 c2 is complex ext-real real Element of REAL
(Im1 c2) ^2 is complex ext-real real Element of REAL
(Im1 c2) * (Im1 c2) is complex ext-real real set
((Rea c2) ^2) + ((Im1 c2) ^2) is complex ext-real real Element of REAL
Im2 c2 is complex ext-real real Element of REAL
(Im2 c2) ^2 is complex ext-real real Element of REAL
(Im2 c2) * (Im2 c2) is complex ext-real real set
(((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2) is complex ext-real real Element of REAL
Im3 c2 is complex ext-real real Element of REAL
(Im3 c2) ^2 is complex ext-real real Element of REAL
(Im3 c2) * (Im3 c2) is complex ext-real real set
((((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2)) + ((Im3 c2) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2)) + ((Im3 c2) ^2)) is complex ext-real real Element of REAL
(c2) ^2 is complex ext-real real Element of REAL
(c2) * (c2) is complex ext-real real set
x2 * c3 is complex ext-real real Element of REAL
y2 * y1 is complex ext-real real Element of REAL
(x2 * c3) + (y2 * y1) is complex ext-real real Element of REAL
w2 * w1 is complex ext-real real Element of REAL
((x2 * c3) + (y2 * y1)) + (w2 * w1) is complex ext-real real Element of REAL
z2 * z1 is complex ext-real real Element of REAL
(((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1) is complex ext-real real Element of REAL
((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) / ((c2) ^2) is complex ext-real real Element of REAL
((c2) ^2) " is complex ext-real real set
((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) * (((c2) ^2) ") is complex ext-real real set
x2 * y1 is complex ext-real real Element of REAL
y2 * c3 is complex ext-real real Element of REAL
(x2 * y1) - (y2 * c3) is complex ext-real real Element of REAL
- (y2 * c3) is complex ext-real real set
(x2 * y1) + (- (y2 * c3)) is complex ext-real real set
w2 * z1 is complex ext-real real Element of REAL
((x2 * y1) - (y2 * c3)) - (w2 * z1) is complex ext-real real Element of REAL
- (w2 * z1) is complex ext-real real set
((x2 * y1) - (y2 * c3)) + (- (w2 * z1)) is complex ext-real real set
z2 * w1 is complex ext-real real Element of REAL
(((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1) is complex ext-real real Element of REAL
((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) * (((c2) ^2) ") is complex ext-real real set
x2 * w1 is complex ext-real real Element of REAL
y2 * z1 is complex ext-real real Element of REAL
(x2 * w1) + (y2 * z1) is complex ext-real real Element of REAL
w2 * c3 is complex ext-real real Element of REAL
((x2 * w1) + (y2 * z1)) - (w2 * c3) is complex ext-real real Element of REAL
- (w2 * c3) is complex ext-real real set
((x2 * w1) + (y2 * z1)) + (- (w2 * c3)) is complex ext-real real set
z2 * y1 is complex ext-real real Element of REAL
(((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1) is complex ext-real real Element of REAL
- (z2 * y1) is complex ext-real real set
(((x2 * w1) + (y2 * z1)) - (w2 * c3)) + (- (z2 * y1)) is complex ext-real real set
((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) * (((c2) ^2) ") is complex ext-real real set
x2 * z1 is complex ext-real real Element of REAL
y2 * w1 is complex ext-real real Element of REAL
(x2 * z1) - (y2 * w1) is complex ext-real real Element of REAL
- (y2 * w1) is complex ext-real real set
(x2 * z1) + (- (y2 * w1)) is complex ext-real real set
w2 * y1 is complex ext-real real Element of REAL
((x2 * z1) - (y2 * w1)) + (w2 * y1) is complex ext-real real Element of REAL
z2 * c3 is complex ext-real real Element of REAL
(((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3) is complex ext-real real Element of REAL
- (z2 * c3) is complex ext-real real set
(((x2 * z1) - (y2 * w1)) + (w2 * y1)) + (- (z2 * c3)) is complex ext-real real set
((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) * (((c2) ^2) ") is complex ext-real real set
[*(((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) / ((c2) ^2)),(((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) / ((c2) ^2)),(((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) / ((c2) ^2)),(((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) / ((c2) ^2))*] is quaternion Element of QUATERNION
c1 is set
c2 is set
q0 is complex ext-real real Element of REAL
q1 is complex ext-real real Element of REAL
q2 is complex ext-real real Element of REAL
q3 is complex ext-real real Element of REAL
[*q0,q1,q2,q3*] is quaternion Element of QUATERNION
r0 is complex ext-real real Element of REAL
r1 is complex ext-real real Element of REAL
r2 is complex ext-real real Element of REAL
r3 is complex ext-real real Element of REAL
[*r0,r1,r2,r3*] is quaternion Element of QUATERNION
r0 * q0 is complex ext-real real Element of REAL
r1 * q1 is complex ext-real real Element of REAL
(r0 * q0) + (r1 * q1) is complex ext-real real Element of REAL
r2 * q2 is complex ext-real real Element of REAL
((r0 * q0) + (r1 * q1)) + (r2 * q2) is complex ext-real real Element of REAL
r3 * q3 is complex ext-real real Element of REAL
(((r0 * q0) + (r1 * q1)) + (r2 * q2)) + (r3 * q3) is complex ext-real real Element of REAL
((((r0 * q0) + (r1 * q1)) + (r2 * q2)) + (r3 * q3)) / ((c2) ^2) is complex ext-real real Element of REAL
((c2) ^2) " is complex ext-real real set
((((r0 * q0) + (r1 * q1)) + (r2 * q2)) + (r3 * q3)) * (((c2) ^2) ") is complex ext-real real set
r0 * q1 is complex ext-real real Element of REAL
r1 * q0 is complex ext-real real Element of REAL
(r0 * q1) - (r1 * q0) is complex ext-real real Element of REAL
- (r1 * q0) is complex ext-real real set
(r0 * q1) + (- (r1 * q0)) is complex ext-real real set
r2 * q3 is complex ext-real real Element of REAL
((r0 * q1) - (r1 * q0)) - (r2 * q3) is complex ext-real real Element of REAL
- (r2 * q3) is complex ext-real real set
((r0 * q1) - (r1 * q0)) + (- (r2 * q3)) is complex ext-real real set
r3 * q2 is complex ext-real real Element of REAL
(((r0 * q1) - (r1 * q0)) - (r2 * q3)) + (r3 * q2) is complex ext-real real Element of REAL
((((r0 * q1) - (r1 * q0)) - (r2 * q3)) + (r3 * q2)) / ((c2) ^2) is complex ext-real real Element of REAL
((((r0 * q1) - (r1 * q0)) - (r2 * q3)) + (r3 * q2)) * (((c2) ^2) ") is complex ext-real real set
r0 * q2 is complex ext-real real Element of REAL
r1 * q3 is complex ext-real real Element of REAL
(r0 * q2) + (r1 * q3) is complex ext-real real Element of REAL
r2 * q0 is complex ext-real real Element of REAL
((r0 * q2) + (r1 * q3)) - (r2 * q0) is complex ext-real real Element of REAL
- (r2 * q0) is complex ext-real real set
((r0 * q2) + (r1 * q3)) + (- (r2 * q0)) is complex ext-real real set
r3 * q1 is complex ext-real real Element of REAL
(((r0 * q2) + (r1 * q3)) - (r2 * q0)) - (r3 * q1) is complex ext-real real Element of REAL
- (r3 * q1) is complex ext-real real set
(((r0 * q2) + (r1 * q3)) - (r2 * q0)) + (- (r3 * q1)) is complex ext-real real set
((((r0 * q2) + (r1 * q3)) - (r2 * q0)) - (r3 * q1)) / ((c2) ^2) is complex ext-real real Element of REAL
((((r0 * q2) + (r1 * q3)) - (r2 * q0)) - (r3 * q1)) * (((c2) ^2) ") is complex ext-real real set
r0 * q3 is complex ext-real real Element of REAL
r1 * q2 is complex ext-real real Element of REAL
(r0 * q3) - (r1 * q2) is complex ext-real real Element of REAL
- (r1 * q2) is complex ext-real real set
(r0 * q3) + (- (r1 * q2)) is complex ext-real real set
r2 * q1 is complex ext-real real Element of REAL
((r0 * q3) - (r1 * q2)) + (r2 * q1) is complex ext-real real Element of REAL
r3 * q0 is complex ext-real real Element of REAL
(((r0 * q3) - (r1 * q2)) + (r2 * q1)) - (r3 * q0) is complex ext-real real Element of REAL
- (r3 * q0) is complex ext-real real set
(((r0 * q3) - (r1 * q2)) + (r2 * q1)) + (- (r3 * q0)) is complex ext-real real set
((((r0 * q3) - (r1 * q2)) + (r2 * q1)) - (r3 * q0)) / ((c2) ^2) is complex ext-real real Element of REAL
((((r0 * q3) - (r1 * q2)) + (r2 * q1)) - (r3 * q0)) * (((c2) ^2) ") is complex ext-real real set
[*(((((r0 * q0) + (r1 * q1)) + (r2 * q2)) + (r3 * q3)) / ((c2) ^2)),(((((r0 * q1) - (r1 * q0)) - (r2 * q3)) + (r3 * q2)) / ((c2) ^2)),(((((r0 * q2) + (r1 * q3)) - (r2 * q0)) - (r3 * q1)) / ((c2) ^2)),(((((r0 * q3) - (r1 * q2)) + (r2 * q1)) - (r3 * q0)) / ((c2) ^2))*] is quaternion Element of QUATERNION
q09 is complex ext-real real Element of REAL
q19 is complex ext-real real Element of REAL
q29 is complex ext-real real Element of REAL
q39 is complex ext-real real Element of REAL
[*q09,q19,q29,q39*] is quaternion Element of QUATERNION
r09 is complex ext-real real Element of REAL
r19 is complex ext-real real Element of REAL
r29 is complex ext-real real Element of REAL
r39 is complex ext-real real Element of REAL
[*r09,r19,r29,r39*] is quaternion Element of QUATERNION
r09 * q09 is complex ext-real real Element of REAL
r19 * q19 is complex ext-real real Element of REAL
(r09 * q09) + (r19 * q19) is complex ext-real real Element of REAL
r29 * q29 is complex ext-real real Element of REAL
((r09 * q09) + (r19 * q19)) + (r29 * q29) is complex ext-real real Element of REAL
r39 * q39 is complex ext-real real Element of REAL
(((r09 * q09) + (r19 * q19)) + (r29 * q29)) + (r39 * q39) is complex ext-real real Element of REAL
((((r09 * q09) + (r19 * q19)) + (r29 * q29)) + (r39 * q39)) / ((c2) ^2) is complex ext-real real Element of REAL
((((r09 * q09) + (r19 * q19)) + (r29 * q29)) + (r39 * q39)) * (((c2) ^2) ") is complex ext-real real set
r09 * q19 is complex ext-real real Element of REAL
r19 * q09 is complex ext-real real Element of REAL
(r09 * q19) - (r19 * q09) is complex ext-real real Element of REAL
- (r19 * q09) is complex ext-real real set
(r09 * q19) + (- (r19 * q09)) is complex ext-real real set
r29 * q39 is complex ext-real real Element of REAL
((r09 * q19) - (r19 * q09)) - (r29 * q39) is complex ext-real real Element of REAL
- (r29 * q39) is complex ext-real real set
((r09 * q19) - (r19 * q09)) + (- (r29 * q39)) is complex ext-real real set
r39 * q29 is complex ext-real real Element of REAL
(((r09 * q19) - (r19 * q09)) - (r29 * q39)) + (r39 * q29) is complex ext-real real Element of REAL
((((r09 * q19) - (r19 * q09)) - (r29 * q39)) + (r39 * q29)) / ((c2) ^2) is complex ext-real real Element of REAL
((((r09 * q19) - (r19 * q09)) - (r29 * q39)) + (r39 * q29)) * (((c2) ^2) ") is complex ext-real real set
r09 * q29 is complex ext-real real Element of REAL
r19 * q39 is complex ext-real real Element of REAL
(r09 * q29) + (r19 * q39) is complex ext-real real Element of REAL
r29 * q09 is complex ext-real real Element of REAL
((r09 * q29) + (r19 * q39)) - (r29 * q09) is complex ext-real real Element of REAL
- (r29 * q09) is complex ext-real real set
((r09 * q29) + (r19 * q39)) + (- (r29 * q09)) is complex ext-real real set
r39 * q19 is complex ext-real real Element of REAL
(((r09 * q29) + (r19 * q39)) - (r29 * q09)) - (r39 * q19) is complex ext-real real Element of REAL
- (r39 * q19) is complex ext-real real set
(((r09 * q29) + (r19 * q39)) - (r29 * q09)) + (- (r39 * q19)) is complex ext-real real set
((((r09 * q29) + (r19 * q39)) - (r29 * q09)) - (r39 * q19)) / ((c2) ^2) is complex ext-real real Element of REAL
((((r09 * q29) + (r19 * q39)) - (r29 * q09)) - (r39 * q19)) * (((c2) ^2) ") is complex ext-real real set
r09 * q39 is complex ext-real real Element of REAL
r19 * q29 is complex ext-real real Element of REAL
(r09 * q39) - (r19 * q29) is complex ext-real real Element of REAL
- (r19 * q29) is complex ext-real real set
(r09 * q39) + (- (r19 * q29)) is complex ext-real real set
r29 * q19 is complex ext-real real Element of REAL
((r09 * q39) - (r19 * q29)) + (r29 * q19) is complex ext-real real Element of REAL
r39 * q09 is complex ext-real real Element of REAL
(((r09 * q39) - (r19 * q29)) + (r29 * q19)) - (r39 * q09) is complex ext-real real Element of REAL
- (r39 * q09) is complex ext-real real set
(((r09 * q39) - (r19 * q29)) + (r29 * q19)) + (- (r39 * q09)) is complex ext-real real set
((((r09 * q39) - (r19 * q29)) + (r29 * q19)) - (r39 * q09)) / ((c2) ^2) is complex ext-real real Element of REAL
((((r09 * q39) - (r19 * q29)) + (r29 * q19)) - (r39 * q09)) * (((c2) ^2) ") is complex ext-real real set
[*(((((r09 * q09) + (r19 * q19)) + (r29 * q29)) + (r39 * q39)) / ((c2) ^2)),(((((r09 * q19) - (r19 * q09)) - (r29 * q39)) + (r39 * q29)) / ((c2) ^2)),(((((r09 * q29) + (r19 * q39)) - (r29 * q09)) - (r39 * q19)) / ((c2) ^2)),(((((r09 * q39) - (r19 * q29)) + (r29 * q19)) - (r39 * q09)) / ((c2) ^2))*] is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
(c1,c2) is set
(c2) is complex ext-real real Element of REAL
Rea c2 is complex ext-real real Element of REAL
(Rea c2) ^2 is complex ext-real real Element of REAL
(Rea c2) * (Rea c2) is complex ext-real real set
Im1 c2 is complex ext-real real Element of REAL
(Im1 c2) ^2 is complex ext-real real Element of REAL
(Im1 c2) * (Im1 c2) is complex ext-real real set
((Rea c2) ^2) + ((Im1 c2) ^2) is complex ext-real real Element of REAL
Im2 c2 is complex ext-real real Element of REAL
(Im2 c2) ^2 is complex ext-real real Element of REAL
(Im2 c2) * (Im2 c2) is complex ext-real real set
(((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2) is complex ext-real real Element of REAL
Im3 c2 is complex ext-real real Element of REAL
(Im3 c2) ^2 is complex ext-real real Element of REAL
(Im3 c2) * (Im3 c2) is complex ext-real real set
((((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2)) + ((Im3 c2) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2)) + ((Im3 c2) ^2)) is complex ext-real real Element of REAL
(c2) ^2 is complex ext-real real Element of REAL
(c2) * (c2) is complex ext-real real set
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
z1 is complex ext-real real Element of REAL
[*c3,y1,w1,z1*] is quaternion Element of QUATERNION
x2 is complex ext-real real Element of REAL
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
z2 is complex ext-real real Element of REAL
[*x2,y2,w2,z2*] is quaternion Element of QUATERNION
x2 * c3 is complex ext-real real Element of REAL
y2 * y1 is complex ext-real real Element of REAL
(x2 * c3) + (y2 * y1) is complex ext-real real Element of REAL
w2 * w1 is complex ext-real real Element of REAL
((x2 * c3) + (y2 * y1)) + (w2 * w1) is complex ext-real real Element of REAL
z2 * z1 is complex ext-real real Element of REAL
(((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1) is complex ext-real real Element of REAL
((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) / ((c2) ^2) is complex ext-real real Element of REAL
((c2) ^2) " is complex ext-real real set
((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) * (((c2) ^2) ") is complex ext-real real set
x2 * y1 is complex ext-real real Element of REAL
y2 * c3 is complex ext-real real Element of REAL
(x2 * y1) - (y2 * c3) is complex ext-real real Element of REAL
- (y2 * c3) is complex ext-real real set
(x2 * y1) + (- (y2 * c3)) is complex ext-real real set
w2 * z1 is complex ext-real real Element of REAL
((x2 * y1) - (y2 * c3)) - (w2 * z1) is complex ext-real real Element of REAL
- (w2 * z1) is complex ext-real real set
((x2 * y1) - (y2 * c3)) + (- (w2 * z1)) is complex ext-real real set
z2 * w1 is complex ext-real real Element of REAL
(((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1) is complex ext-real real Element of REAL
((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) * (((c2) ^2) ") is complex ext-real real set
x2 * w1 is complex ext-real real Element of REAL
y2 * z1 is complex ext-real real Element of REAL
(x2 * w1) + (y2 * z1) is complex ext-real real Element of REAL
w2 * c3 is complex ext-real real Element of REAL
((x2 * w1) + (y2 * z1)) - (w2 * c3) is complex ext-real real Element of REAL
- (w2 * c3) is complex ext-real real set
((x2 * w1) + (y2 * z1)) + (- (w2 * c3)) is complex ext-real real set
z2 * y1 is complex ext-real real Element of REAL
(((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1) is complex ext-real real Element of REAL
- (z2 * y1) is complex ext-real real set
(((x2 * w1) + (y2 * z1)) - (w2 * c3)) + (- (z2 * y1)) is complex ext-real real set
((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) * (((c2) ^2) ") is complex ext-real real set
x2 * z1 is complex ext-real real Element of REAL
y2 * w1 is complex ext-real real Element of REAL
(x2 * z1) - (y2 * w1) is complex ext-real real Element of REAL
- (y2 * w1) is complex ext-real real set
(x2 * z1) + (- (y2 * w1)) is complex ext-real real set
w2 * y1 is complex ext-real real Element of REAL
((x2 * z1) - (y2 * w1)) + (w2 * y1) is complex ext-real real Element of REAL
z2 * c3 is complex ext-real real Element of REAL
(((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3) is complex ext-real real Element of REAL
- (z2 * c3) is complex ext-real real set
(((x2 * z1) - (y2 * w1)) + (w2 * y1)) + (- (z2 * c3)) is complex ext-real real set
((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) * (((c2) ^2) ") is complex ext-real real set
[*(((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) / ((c2) ^2)),(((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) / ((c2) ^2)),(((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) / ((c2) ^2)),(((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) / ((c2) ^2))*] is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
(c1,c2) is quaternion set
() is quaternion Element of QUATERNION
c1 is quaternion set
Rea c1 is complex ext-real real Element of REAL
Im1 c1 is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
c2 is quaternion set
(c1,c2) is quaternion Element of QUATERNION
Rea c2 is complex ext-real real Element of REAL
(Rea c2) * (Rea c1) is complex ext-real real Element of REAL
Im1 c2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c2) is complex ext-real real Element of REAL
((Rea c2) * (Rea c1)) + ((Im1 c1) * (Im1 c2)) is complex ext-real real Element of REAL
Im2 c2 is complex ext-real real Element of REAL
(Im2 c2) * (Im2 c1) is complex ext-real real Element of REAL
(((Rea c2) * (Rea c1)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c2) * (Im2 c1)) is complex ext-real real Element of REAL
Im3 c2 is complex ext-real real Element of REAL
(Im3 c2) * (Im3 c1) is complex ext-real real Element of REAL
((((Rea c2) * (Rea c1)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c2) * (Im2 c1))) + ((Im3 c2) * (Im3 c1)) is complex ext-real real Element of REAL
(c2) is complex ext-real real Element of REAL
(Rea c2) ^2 is complex ext-real real Element of REAL
(Rea c2) * (Rea c2) is complex ext-real real set
(Im1 c2) ^2 is complex ext-real real Element of REAL
(Im1 c2) * (Im1 c2) is complex ext-real real set
((Rea c2) ^2) + ((Im1 c2) ^2) is complex ext-real real Element of REAL
(Im2 c2) ^2 is complex ext-real real Element of REAL
(Im2 c2) * (Im2 c2) is complex ext-real real set
(((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2) is complex ext-real real Element of REAL
(Im3 c2) ^2 is complex ext-real real Element of REAL
(Im3 c2) * (Im3 c2) is complex ext-real real set
((((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2)) + ((Im3 c2) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2)) + ((Im3 c2) ^2)) is complex ext-real real Element of REAL
(c2) ^2 is complex ext-real real Element of REAL
(c2) * (c2) is complex ext-real real set
(((((Rea c2) * (Rea c1)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c2) * (Im2 c1))) + ((Im3 c2) * (Im3 c1))) / ((c2) ^2) is complex ext-real real Element of REAL
((c2) ^2) " is complex ext-real real set
(((((Rea c2) * (Rea c1)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c2) * (Im2 c1))) + ((Im3 c2) * (Im3 c1))) * (((c2) ^2) ") is complex ext-real real set
(Rea c2) * (Im1 c1) is complex ext-real real Element of REAL
(Im1 c2) * (Rea c1) is complex ext-real real Element of REAL
((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1)) is complex ext-real real Element of REAL
- ((Im1 c2) * (Rea c1)) is complex ext-real real set
((Rea c2) * (Im1 c1)) + (- ((Im1 c2) * (Rea c1))) is complex ext-real real set
(Im2 c2) * (Im3 c1) is complex ext-real real Element of REAL
(((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) - ((Im2 c2) * (Im3 c1)) is complex ext-real real Element of REAL
- ((Im2 c2) * (Im3 c1)) is complex ext-real real set
(((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) + (- ((Im2 c2) * (Im3 c1))) is complex ext-real real set
(Im3 c2) * (Im2 c1) is complex ext-real real Element of REAL
((((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) - ((Im2 c2) * (Im3 c1))) + ((Im3 c2) * (Im2 c1)) is complex ext-real real Element of REAL
(((((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) - ((Im2 c2) * (Im3 c1))) + ((Im3 c2) * (Im2 c1))) / ((c2) ^2) is complex ext-real real Element of REAL
(((((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) - ((Im2 c2) * (Im3 c1))) + ((Im3 c2) * (Im2 c1))) * (((c2) ^2) ") is complex ext-real real set
((((((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) - ((Im2 c2) * (Im3 c1))) + ((Im3 c2) * (Im2 c1))) / ((c2) ^2)) * () is quaternion set
((((((Rea c2) * (Rea c1)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c2) * (Im2 c1))) + ((Im3 c2) * (Im3 c1))) / ((c2) ^2)) + (((((((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) - ((Im2 c2) * (Im3 c1))) + ((Im3 c2) * (Im2 c1))) / ((c2) ^2)) * ()) is quaternion set
(Rea c2) * (Im2 c1) is complex ext-real real Element of REAL
(Im1 c2) * (Im3 c1) is complex ext-real real Element of REAL
((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1)) is complex ext-real real Element of REAL
(Im2 c2) * (Rea c1) is complex ext-real real Element of REAL
(((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) - ((Im2 c2) * (Rea c1)) is complex ext-real real Element of REAL
- ((Im2 c2) * (Rea c1)) is complex ext-real real set
(((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) + (- ((Im2 c2) * (Rea c1))) is complex ext-real real set
(Im3 c2) * (Im1 c1) is complex ext-real real Element of REAL
((((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) - ((Im2 c2) * (Rea c1))) - ((Im3 c2) * (Im1 c1)) is complex ext-real real Element of REAL
- ((Im3 c2) * (Im1 c1)) is complex ext-real real set
((((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) - ((Im2 c2) * (Rea c1))) + (- ((Im3 c2) * (Im1 c1))) is complex ext-real real set
(((((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) - ((Im2 c2) * (Rea c1))) - ((Im3 c2) * (Im1 c1))) / ((c2) ^2) is complex ext-real real Element of REAL
(((((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) - ((Im2 c2) * (Rea c1))) - ((Im3 c2) * (Im1 c1))) * (((c2) ^2) ") is complex ext-real real set
((((((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) - ((Im2 c2) * (Rea c1))) - ((Im3 c2) * (Im1 c1))) / ((c2) ^2)) * <j> is quaternion set
(((((((Rea c2) * (Rea c1)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c2) * (Im2 c1))) + ((Im3 c2) * (Im3 c1))) / ((c2) ^2)) + (((((((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) - ((Im2 c2) * (Im3 c1))) + ((Im3 c2) * (Im2 c1))) / ((c2) ^2)) * ())) + (((((((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) - ((Im2 c2) * (Rea c1))) - ((Im3 c2) * (Im1 c1))) / ((c2) ^2)) * <j>) is quaternion Element of QUATERNION
(Rea c2) * (Im3 c1) is complex ext-real real Element of REAL
(Im1 c2) * (Im2 c1) is complex ext-real real Element of REAL
((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1)) is complex ext-real real Element of REAL
- ((Im1 c2) * (Im2 c1)) is complex ext-real real set
((Rea c2) * (Im3 c1)) + (- ((Im1 c2) * (Im2 c1))) is complex ext-real real set
(Im2 c2) * (Im1 c1) is complex ext-real real Element of REAL
(((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1))) + ((Im2 c2) * (Im1 c1)) is complex ext-real real Element of REAL
(Im3 c2) * (Rea c1) is complex ext-real real Element of REAL
((((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1))) + ((Im2 c2) * (Im1 c1))) - ((Im3 c2) * (Rea c1)) is complex ext-real real Element of REAL
- ((Im3 c2) * (Rea c1)) is complex ext-real real set
((((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1))) + ((Im2 c2) * (Im1 c1))) + (- ((Im3 c2) * (Rea c1))) is complex ext-real real set
(((((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1))) + ((Im2 c2) * (Im1 c1))) - ((Im3 c2) * (Rea c1))) / ((c2) ^2) is complex ext-real real Element of REAL
(((((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1))) + ((Im2 c2) * (Im1 c1))) - ((Im3 c2) * (Rea c1))) * (((c2) ^2) ") is complex ext-real real set
((((((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1))) + ((Im2 c2) * (Im1 c1))) - ((Im3 c2) * (Rea c1))) / ((c2) ^2)) * <k> is quaternion set
((((((((Rea c2) * (Rea c1)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c2) * (Im2 c1))) + ((Im3 c2) * (Im3 c1))) / ((c2) ^2)) + (((((((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) - ((Im2 c2) * (Im3 c1))) + ((Im3 c2) * (Im2 c1))) / ((c2) ^2)) * ())) + (((((((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) - ((Im2 c2) * (Rea c1))) - ((Im3 c2) * (Im1 c1))) / ((c2) ^2)) * <j>)) + (((((((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1))) + ((Im2 c2) * (Im1 c1))) - ((Im3 c2) * (Rea c1))) / ((c2) ^2)) * <k>) is quaternion Element of QUATERNION
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
z1 is complex ext-real real Element of REAL
[*c3,y1,w1,z1*] is quaternion Element of QUATERNION
x2 is complex ext-real real Element of REAL
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
z2 is complex ext-real real Element of REAL
[*x2,y2,w2,z2*] is quaternion Element of QUATERNION
x2 * c3 is complex ext-real real Element of REAL
y2 * y1 is complex ext-real real Element of REAL
(x2 * c3) + (y2 * y1) is complex ext-real real Element of REAL
w2 * w1 is complex ext-real real Element of REAL
((x2 * c3) + (y2 * y1)) + (w2 * w1) is complex ext-real real Element of REAL
z2 * z1 is complex ext-real real Element of REAL
(((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1) is complex ext-real real Element of REAL
((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) * (((c2) ^2) ") is complex ext-real real set
x2 * y1 is complex ext-real real Element of REAL
y2 * c3 is complex ext-real real Element of REAL
(x2 * y1) - (y2 * c3) is complex ext-real real Element of REAL
- (y2 * c3) is complex ext-real real set
(x2 * y1) + (- (y2 * c3)) is complex ext-real real set
w2 * z1 is complex ext-real real Element of REAL
((x2 * y1) - (y2 * c3)) - (w2 * z1) is complex ext-real real Element of REAL
- (w2 * z1) is complex ext-real real set
((x2 * y1) - (y2 * c3)) + (- (w2 * z1)) is complex ext-real real set
z2 * w1 is complex ext-real real Element of REAL
(((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1) is complex ext-real real Element of REAL
((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) * (((c2) ^2) ") is complex ext-real real set
x2 * w1 is complex ext-real real Element of REAL
y2 * z1 is complex ext-real real Element of REAL
(x2 * w1) + (y2 * z1) is complex ext-real real Element of REAL
w2 * c3 is complex ext-real real Element of REAL
((x2 * w1) + (y2 * z1)) - (w2 * c3) is complex ext-real real Element of REAL
- (w2 * c3) is complex ext-real real set
((x2 * w1) + (y2 * z1)) + (- (w2 * c3)) is complex ext-real real set
z2 * y1 is complex ext-real real Element of REAL
(((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1) is complex ext-real real Element of REAL
- (z2 * y1) is complex ext-real real set
(((x2 * w1) + (y2 * z1)) - (w2 * c3)) + (- (z2 * y1)) is complex ext-real real set
((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) * (((c2) ^2) ") is complex ext-real real set
x2 * z1 is complex ext-real real Element of REAL
y2 * w1 is complex ext-real real Element of REAL
(x2 * z1) - (y2 * w1) is complex ext-real real Element of REAL
- (y2 * w1) is complex ext-real real set
(x2 * z1) + (- (y2 * w1)) is complex ext-real real set
w2 * y1 is complex ext-real real Element of REAL
((x2 * z1) - (y2 * w1)) + (w2 * y1) is complex ext-real real Element of REAL
z2 * c3 is complex ext-real real Element of REAL
(((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3) is complex ext-real real Element of REAL
- (z2 * c3) is complex ext-real real set
(((x2 * z1) - (y2 * w1)) + (w2 * y1)) + (- (z2 * c3)) is complex ext-real real set
((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) * (((c2) ^2) ") is complex ext-real real set
[*(((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) / ((c2) ^2)),(((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) / ((c2) ^2)),(((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) / ((c2) ^2)),(((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) / ((c2) ^2))*] is quaternion Element of QUATERNION
(((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) / ((c2) ^2)) * () is quaternion set
(((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) / ((c2) ^2)) + ((((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) / ((c2) ^2)) * ()) is quaternion set
(((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) / ((c2) ^2)) * <j> is quaternion set
((((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) / ((c2) ^2)) + ((((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) / ((c2) ^2)) * ())) + ((((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) / ((c2) ^2)) * <j>) is quaternion Element of QUATERNION
(((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) / ((c2) ^2)) * <k> is quaternion set
(((((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) / ((c2) ^2)) + ((((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) / ((c2) ^2)) * ())) + ((((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) / ((c2) ^2)) * <j>)) + ((((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) / ((c2) ^2)) * <k>) is quaternion Element of QUATERNION
c1 is quaternion set
((),c1) is quaternion Element of QUATERNION
c1 is quaternion set
(c1) is quaternion set
((),c1) is quaternion Element of QUATERNION
c1 is quaternion set
(c1) is quaternion Element of QUATERNION
((),c1) is quaternion Element of QUATERNION
Rea c1 is complex ext-real real Element of REAL
(c1) is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
Im1 c1 is complex ext-real real Element of REAL
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
(c1) ^2 is complex ext-real real Element of REAL
(c1) * (c1) is complex ext-real real set
(Rea c1) / ((c1) ^2) is complex ext-real real Element of REAL
((c1) ^2) " is complex ext-real real set
(Rea c1) * (((c1) ^2) ") is complex ext-real real set
(Im1 c1) / ((c1) ^2) is complex ext-real real Element of REAL
(Im1 c1) * (((c1) ^2) ") is complex ext-real real set
((Im1 c1) / ((c1) ^2)) * () is quaternion set
((Rea c1) / ((c1) ^2)) - (((Im1 c1) / ((c1) ^2)) * ()) is quaternion set
- (((Im1 c1) / ((c1) ^2)) * ()) is quaternion set
((Rea c1) / ((c1) ^2)) + (- (((Im1 c1) / ((c1) ^2)) * ())) is quaternion set
(Im2 c1) / ((c1) ^2) is complex ext-real real Element of REAL
(Im2 c1) * (((c1) ^2) ") is complex ext-real real set
((Im2 c1) / ((c1) ^2)) * <j> is quaternion set
(((Rea c1) / ((c1) ^2)) - (((Im1 c1) / ((c1) ^2)) * ())) - (((Im2 c1) / ((c1) ^2)) * <j>) is quaternion Element of QUATERNION
- (((Im2 c1) / ((c1) ^2)) * <j>) is quaternion set
(((Rea c1) / ((c1) ^2)) - (((Im1 c1) / ((c1) ^2)) * ())) + (- (((Im2 c1) / ((c1) ^2)) * <j>)) is quaternion set
(Im3 c1) / ((c1) ^2) is complex ext-real real Element of REAL
(Im3 c1) * (((c1) ^2) ") is complex ext-real real set
((Im3 c1) / ((c1) ^2)) * <k> is quaternion set
((((Rea c1) / ((c1) ^2)) - (((Im1 c1) / ((c1) ^2)) * ())) - (((Im2 c1) / ((c1) ^2)) * <j>)) - (((Im3 c1) / ((c1) ^2)) * <k>) is quaternion Element of QUATERNION
- (((Im3 c1) / ((c1) ^2)) * <k>) is quaternion set
((((Rea c1) / ((c1) ^2)) - (((Im1 c1) / ((c1) ^2)) * ())) - (((Im2 c1) / ((c1) ^2)) * <j>)) + (- (((Im3 c1) / ((c1) ^2)) * <k>)) is quaternion set
[*1,0*] is Element of COMPLEX
[*1,0,0,0*] is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
[*c2,c3,y1,w1*] is quaternion Element of QUATERNION
z1 is complex ext-real real Element of REAL
x2 is complex ext-real real Element of REAL
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
[*z1,x2,y2,w2*] is quaternion Element of QUATERNION
z1 * c2 is complex ext-real real Element of REAL
x2 * c3 is complex ext-real real Element of REAL
(z1 * c2) + (x2 * c3) is complex ext-real real Element of REAL
y2 * y1 is complex ext-real real Element of REAL
((z1 * c2) + (x2 * c3)) + (y2 * y1) is complex ext-real real Element of REAL
w2 * w1 is complex ext-real real Element of REAL
(((z1 * c2) + (x2 * c3)) + (y2 * y1)) + (w2 * w1) is complex ext-real real Element of REAL
((((z1 * c2) + (x2 * c3)) + (y2 * y1)) + (w2 * w1)) / ((c1) ^2) is complex ext-real real Element of REAL
((((z1 * c2) + (x2 * c3)) + (y2 * y1)) + (w2 * w1)) * (((c1) ^2) ") is complex ext-real real set
z1 * c3 is complex ext-real real Element of REAL
x2 * c2 is complex ext-real real Element of REAL
(z1 * c3) - (x2 * c2) is complex ext-real real Element of REAL
- (x2 * c2) is complex ext-real real set
(z1 * c3) + (- (x2 * c2)) is complex ext-real real set
y2 * w1 is complex ext-real real Element of REAL
((z1 * c3) - (x2 * c2)) - (y2 * w1) is complex ext-real real Element of REAL
- (y2 * w1) is complex ext-real real set
((z1 * c3) - (x2 * c2)) + (- (y2 * w1)) is complex ext-real real set
w2 * y1 is complex ext-real real Element of REAL
(((z1 * c3) - (x2 * c2)) - (y2 * w1)) + (w2 * y1) is complex ext-real real Element of REAL
((((z1 * c3) - (x2 * c2)) - (y2 * w1)) + (w2 * y1)) / ((c1) ^2) is complex ext-real real Element of REAL
((((z1 * c3) - (x2 * c2)) - (y2 * w1)) + (w2 * y1)) * (((c1) ^2) ") is complex ext-real real set
z1 * y1 is complex ext-real real Element of REAL
x2 * w1 is complex ext-real real Element of REAL
(z1 * y1) + (x2 * w1) is complex ext-real real Element of REAL
y2 * c2 is complex ext-real real Element of REAL
((z1 * y1) + (x2 * w1)) - (y2 * c2) is complex ext-real real Element of REAL
- (y2 * c2) is complex ext-real real set
((z1 * y1) + (x2 * w1)) + (- (y2 * c2)) is complex ext-real real set
w2 * c3 is complex ext-real real Element of REAL
(((z1 * y1) + (x2 * w1)) - (y2 * c2)) - (w2 * c3) is complex ext-real real Element of REAL
- (w2 * c3) is complex ext-real real set
(((z1 * y1) + (x2 * w1)) - (y2 * c2)) + (- (w2 * c3)) is complex ext-real real set
((((z1 * y1) + (x2 * w1)) - (y2 * c2)) - (w2 * c3)) / ((c1) ^2) is complex ext-real real Element of REAL
((((z1 * y1) + (x2 * w1)) - (y2 * c2)) - (w2 * c3)) * (((c1) ^2) ") is complex ext-real real set
z1 * w1 is complex ext-real real Element of REAL
x2 * y1 is complex ext-real real Element of REAL
(z1 * w1) - (x2 * y1) is complex ext-real real Element of REAL
- (x2 * y1) is complex ext-real real set
(z1 * w1) + (- (x2 * y1)) is complex ext-real real set
y2 * c3 is complex ext-real real Element of REAL
((z1 * w1) - (x2 * y1)) + (y2 * c3) is complex ext-real real Element of REAL
w2 * c2 is complex ext-real real Element of REAL
(((z1 * w1) - (x2 * y1)) + (y2 * c3)) - (w2 * c2) is complex ext-real real Element of REAL
- (w2 * c2) is complex ext-real real set
(((z1 * w1) - (x2 * y1)) + (y2 * c3)) + (- (w2 * c2)) is complex ext-real real set
((((z1 * w1) - (x2 * y1)) + (y2 * c3)) - (w2 * c2)) / ((c1) ^2) is complex ext-real real Element of REAL
((((z1 * w1) - (x2 * y1)) + (y2 * c3)) - (w2 * c2)) * (((c1) ^2) ") is complex ext-real real set
[*(((((z1 * c2) + (x2 * c3)) + (y2 * y1)) + (w2 * w1)) / ((c1) ^2)),(((((z1 * c3) - (x2 * c2)) - (y2 * w1)) + (w2 * y1)) / ((c1) ^2)),(((((z1 * y1) + (x2 * w1)) - (y2 * c2)) - (w2 * c3)) / ((c1) ^2)),(((((z1 * w1) - (x2 * y1)) + (y2 * c3)) - (w2 * c2)) / ((c1) ^2))*] is quaternion Element of QUATERNION
z1 / ((c1) ^2) is complex ext-real real Element of REAL
z1 * (((c1) ^2) ") is complex ext-real real set
x2 / ((c1) ^2) is complex ext-real real Element of REAL
x2 * (((c1) ^2) ") is complex ext-real real set
- (x2 / ((c1) ^2)) is complex ext-real real Element of REAL
(- (x2 / ((c1) ^2))) * () is quaternion set
(z1 / ((c1) ^2)) + ((- (x2 / ((c1) ^2))) * ()) is quaternion set
y2 / ((c1) ^2) is complex ext-real real Element of REAL
y2 * (((c1) ^2) ") is complex ext-real real set
- (y2 / ((c1) ^2)) is complex ext-real real Element of REAL
(- (y2 / ((c1) ^2))) * <j> is quaternion set
((z1 / ((c1) ^2)) + ((- (x2 / ((c1) ^2))) * ())) + ((- (y2 / ((c1) ^2))) * <j>) is quaternion Element of QUATERNION
w2 / ((c1) ^2) is complex ext-real real Element of REAL
w2 * (((c1) ^2) ") is complex ext-real real set
- (w2 / ((c1) ^2)) is complex ext-real real Element of REAL
(- (w2 / ((c1) ^2))) * <k> is quaternion set
(((z1 / ((c1) ^2)) + ((- (x2 / ((c1) ^2))) * ())) + ((- (y2 / ((c1) ^2))) * <j>)) + ((- (w2 / ((c1) ^2))) * <k>) is quaternion Element of QUATERNION
(x2 / ((c1) ^2)) * () is quaternion set
- ((x2 / ((c1) ^2)) * ()) is quaternion Element of QUATERNION
(z1 / ((c1) ^2)) + (- ((x2 / ((c1) ^2)) * ())) is quaternion set
((z1 / ((c1) ^2)) + (- ((x2 / ((c1) ^2)) * ()))) + ((- (y2 / ((c1) ^2))) * <j>) is quaternion Element of QUATERNION
(((z1 / ((c1) ^2)) + (- ((x2 / ((c1) ^2)) * ()))) + ((- (y2 / ((c1) ^2))) * <j>)) + ((- (w2 / ((c1) ^2))) * <k>) is quaternion Element of QUATERNION
(z1 / ((c1) ^2)) - ((x2 / ((c1) ^2)) * ()) is quaternion set
- ((x2 / ((c1) ^2)) * ()) is quaternion set
(z1 / ((c1) ^2)) + (- ((x2 / ((c1) ^2)) * ())) is quaternion set
(y2 / ((c1) ^2)) * <j> is quaternion set
- ((y2 / ((c1) ^2)) * <j>) is quaternion Element of QUATERNION
((z1 / ((c1) ^2)) - ((x2 / ((c1) ^2)) * ())) + (- ((y2 / ((c1) ^2)) * <j>)) is quaternion Element of QUATERNION
(((z1 / ((c1) ^2)) - ((x2 / ((c1) ^2)) * ())) + (- ((y2 / ((c1) ^2)) * <j>))) + ((- (w2 / ((c1) ^2))) * <k>) is quaternion Element of QUATERNION
((z1 / ((c1) ^2)) - ((x2 / ((c1) ^2)) * ())) - ((y2 / ((c1) ^2)) * <j>) is quaternion Element of QUATERNION
- ((y2 / ((c1) ^2)) * <j>) is quaternion set
((z1 / ((c1) ^2)) - ((x2 / ((c1) ^2)) * ())) + (- ((y2 / ((c1) ^2)) * <j>)) is quaternion set
(w2 / ((c1) ^2)) * <k> is quaternion set
- ((w2 / ((c1) ^2)) * <k>) is quaternion Element of QUATERNION
(((z1 / ((c1) ^2)) - ((x2 / ((c1) ^2)) * ())) - ((y2 / ((c1) ^2)) * <j>)) + (- ((w2 / ((c1) ^2)) * <k>)) is quaternion Element of QUATERNION
c1 is quaternion set
(c1) is quaternion Element of QUATERNION
((),c1) is quaternion Element of QUATERNION
Rea (c1) is complex ext-real real Element of REAL
Rea c1 is complex ext-real real Element of REAL
(c1) is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
Im1 c1 is complex ext-real real Element of REAL
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
(c1) ^2 is complex ext-real real Element of REAL
(c1) * (c1) is complex ext-real real set
(Rea c1) / ((c1) ^2) is complex ext-real real Element of REAL
((c1) ^2) " is complex ext-real real set
(Rea c1) * (((c1) ^2) ") is complex ext-real real set
Im1 (c1) is complex ext-real real Element of REAL
(Im1 c1) / ((c1) ^2) is complex ext-real real Element of REAL
(Im1 c1) * (((c1) ^2) ") is complex ext-real real set
- ((Im1 c1) / ((c1) ^2)) is complex ext-real real Element of REAL
Im2 (c1) is complex ext-real real Element of REAL
(Im2 c1) / ((c1) ^2) is complex ext-real real Element of REAL
(Im2 c1) * (((c1) ^2) ") is complex ext-real real set
- ((Im2 c1) / ((c1) ^2)) is complex ext-real real Element of REAL
Im3 (c1) is complex ext-real real Element of REAL
(Im3 c1) / ((c1) ^2) is complex ext-real real Element of REAL
(Im3 c1) * (((c1) ^2) ") is complex ext-real real set
- ((Im3 c1) / ((c1) ^2)) is complex ext-real real Element of REAL
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
[*c2,c3,y1,w1*] is quaternion Element of QUATERNION
z1 is complex ext-real real Element of REAL
x2 is complex ext-real real Element of REAL
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
[*z1,x2,y2,w2*] is quaternion Element of QUATERNION
z1 * c2 is complex ext-real real Element of REAL
x2 * c3 is complex ext-real real Element of REAL
(z1 * c2) + (x2 * c3) is complex ext-real real Element of REAL
y2 * y1 is complex ext-real real Element of REAL
((z1 * c2) + (x2 * c3)) + (y2 * y1) is complex ext-real real Element of REAL
w2 * w1 is complex ext-real real Element of REAL
(((z1 * c2) + (x2 * c3)) + (y2 * y1)) + (w2 * w1) is complex ext-real real Element of REAL
((((z1 * c2) + (x2 * c3)) + (y2 * y1)) + (w2 * w1)) / ((c1) ^2) is complex ext-real real Element of REAL
((((z1 * c2) + (x2 * c3)) + (y2 * y1)) + (w2 * w1)) * (((c1) ^2) ") is complex ext-real real set
z1 * c3 is complex ext-real real Element of REAL
x2 * c2 is complex ext-real real Element of REAL
(z1 * c3) - (x2 * c2) is complex ext-real real Element of REAL
- (x2 * c2) is complex ext-real real set
(z1 * c3) + (- (x2 * c2)) is complex ext-real real set
y2 * w1 is complex ext-real real Element of REAL
((z1 * c3) - (x2 * c2)) - (y2 * w1) is complex ext-real real Element of REAL
- (y2 * w1) is complex ext-real real set
((z1 * c3) - (x2 * c2)) + (- (y2 * w1)) is complex ext-real real set
w2 * y1 is complex ext-real real Element of REAL
(((z1 * c3) - (x2 * c2)) - (y2 * w1)) + (w2 * y1) is complex ext-real real Element of REAL
((((z1 * c3) - (x2 * c2)) - (y2 * w1)) + (w2 * y1)) / ((c1) ^2) is complex ext-real real Element of REAL
((((z1 * c3) - (x2 * c2)) - (y2 * w1)) + (w2 * y1)) * (((c1) ^2) ") is complex ext-real real set
z1 * y1 is complex ext-real real Element of REAL
x2 * w1 is complex ext-real real Element of REAL
(z1 * y1) + (x2 * w1) is complex ext-real real Element of REAL
y2 * c2 is complex ext-real real Element of REAL
((z1 * y1) + (x2 * w1)) - (y2 * c2) is complex ext-real real Element of REAL
- (y2 * c2) is complex ext-real real set
((z1 * y1) + (x2 * w1)) + (- (y2 * c2)) is complex ext-real real set
w2 * c3 is complex ext-real real Element of REAL
(((z1 * y1) + (x2 * w1)) - (y2 * c2)) - (w2 * c3) is complex ext-real real Element of REAL
- (w2 * c3) is complex ext-real real set
(((z1 * y1) + (x2 * w1)) - (y2 * c2)) + (- (w2 * c3)) is complex ext-real real set
((((z1 * y1) + (x2 * w1)) - (y2 * c2)) - (w2 * c3)) / ((c1) ^2) is complex ext-real real Element of REAL
((((z1 * y1) + (x2 * w1)) - (y2 * c2)) - (w2 * c3)) * (((c1) ^2) ") is complex ext-real real set
z1 * w1 is complex ext-real real Element of REAL
x2 * y1 is complex ext-real real Element of REAL
(z1 * w1) - (x2 * y1) is complex ext-real real Element of REAL
- (x2 * y1) is complex ext-real real set
(z1 * w1) + (- (x2 * y1)) is complex ext-real real set
y2 * c3 is complex ext-real real Element of REAL
((z1 * w1) - (x2 * y1)) + (y2 * c3) is complex ext-real real Element of REAL
w2 * c2 is complex ext-real real Element of REAL
(((z1 * w1) - (x2 * y1)) + (y2 * c3)) - (w2 * c2) is complex ext-real real Element of REAL
- (w2 * c2) is complex ext-real real set
(((z1 * w1) - (x2 * y1)) + (y2 * c3)) + (- (w2 * c2)) is complex ext-real real set
((((z1 * w1) - (x2 * y1)) + (y2 * c3)) - (w2 * c2)) / ((c1) ^2) is complex ext-real real Element of REAL
((((z1 * w1) - (x2 * y1)) + (y2 * c3)) - (w2 * c2)) * (((c1) ^2) ") is complex ext-real real set
[*(((((z1 * c2) + (x2 * c3)) + (y2 * y1)) + (w2 * w1)) / ((c1) ^2)),(((((z1 * c3) - (x2 * c2)) - (y2 * w1)) + (w2 * y1)) / ((c1) ^2)),(((((z1 * y1) + (x2 * w1)) - (y2 * c2)) - (w2 * c3)) / ((c1) ^2)),(((((z1 * w1) - (x2 * y1)) + (y2 * c3)) - (w2 * c2)) / ((c1) ^2))*] is quaternion Element of QUATERNION
[*1,0*] is Element of COMPLEX
[*1,0,0,0*] is quaternion Element of QUATERNION
z1 / ((c1) ^2) is complex ext-real real Element of REAL
z1 * (((c1) ^2) ") is complex ext-real real set
x2 / ((c1) ^2) is complex ext-real real Element of REAL
x2 * (((c1) ^2) ") is complex ext-real real set
- (x2 / ((c1) ^2)) is complex ext-real real Element of REAL
y2 / ((c1) ^2) is complex ext-real real Element of REAL
y2 * (((c1) ^2) ") is complex ext-real real set
- (y2 / ((c1) ^2)) is complex ext-real real Element of REAL
w2 / ((c1) ^2) is complex ext-real real Element of REAL
w2 * (((c1) ^2) ") is complex ext-real real set
- (w2 / ((c1) ^2)) is complex ext-real real Element of REAL
[*(z1 / ((c1) ^2)),(- (x2 / ((c1) ^2))),(- (y2 / ((c1) ^2))),(- (w2 / ((c1) ^2)))*] is quaternion Element of QUATERNION
c1 is quaternion set
Rea c1 is complex ext-real real Element of REAL
Im1 c1 is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
c2 is quaternion set
(c1,c2) is quaternion Element of QUATERNION
Rea (c1,c2) is complex ext-real real Element of REAL
Rea c2 is complex ext-real real Element of REAL
(Rea c2) * (Rea c1) is complex ext-real real Element of REAL
Im1 c2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c2) is complex ext-real real Element of REAL
((Rea c2) * (Rea c1)) + ((Im1 c1) * (Im1 c2)) is complex ext-real real Element of REAL
Im2 c2 is complex ext-real real Element of REAL
(Im2 c2) * (Im2 c1) is complex ext-real real Element of REAL
(((Rea c2) * (Rea c1)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c2) * (Im2 c1)) is complex ext-real real Element of REAL
Im3 c2 is complex ext-real real Element of REAL
(Im3 c2) * (Im3 c1) is complex ext-real real Element of REAL
((((Rea c2) * (Rea c1)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c2) * (Im2 c1))) + ((Im3 c2) * (Im3 c1)) is complex ext-real real Element of REAL
(c2) is complex ext-real real Element of REAL
(Rea c2) ^2 is complex ext-real real Element of REAL
(Rea c2) * (Rea c2) is complex ext-real real set
(Im1 c2) ^2 is complex ext-real real Element of REAL
(Im1 c2) * (Im1 c2) is complex ext-real real set
((Rea c2) ^2) + ((Im1 c2) ^2) is complex ext-real real Element of REAL
(Im2 c2) ^2 is complex ext-real real Element of REAL
(Im2 c2) * (Im2 c2) is complex ext-real real set
(((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2) is complex ext-real real Element of REAL
(Im3 c2) ^2 is complex ext-real real Element of REAL
(Im3 c2) * (Im3 c2) is complex ext-real real set
((((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2)) + ((Im3 c2) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2)) + ((Im3 c2) ^2)) is complex ext-real real Element of REAL
(c2) ^2 is complex ext-real real Element of REAL
(c2) * (c2) is complex ext-real real set
(((((Rea c2) * (Rea c1)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c2) * (Im2 c1))) + ((Im3 c2) * (Im3 c1))) / ((c2) ^2) is complex ext-real real Element of REAL
((c2) ^2) " is complex ext-real real set
(((((Rea c2) * (Rea c1)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c2) * (Im2 c1))) + ((Im3 c2) * (Im3 c1))) * (((c2) ^2) ") is complex ext-real real set
Im1 (c1,c2) is complex ext-real real Element of REAL
(Rea c2) * (Im1 c1) is complex ext-real real Element of REAL
(Im1 c2) * (Rea c1) is complex ext-real real Element of REAL
((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1)) is complex ext-real real Element of REAL
- ((Im1 c2) * (Rea c1)) is complex ext-real real set
((Rea c2) * (Im1 c1)) + (- ((Im1 c2) * (Rea c1))) is complex ext-real real set
(Im2 c2) * (Im3 c1) is complex ext-real real Element of REAL
(((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) - ((Im2 c2) * (Im3 c1)) is complex ext-real real Element of REAL
- ((Im2 c2) * (Im3 c1)) is complex ext-real real set
(((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) + (- ((Im2 c2) * (Im3 c1))) is complex ext-real real set
(Im3 c2) * (Im2 c1) is complex ext-real real Element of REAL
((((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) - ((Im2 c2) * (Im3 c1))) + ((Im3 c2) * (Im2 c1)) is complex ext-real real Element of REAL
(((((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) - ((Im2 c2) * (Im3 c1))) + ((Im3 c2) * (Im2 c1))) / ((c2) ^2) is complex ext-real real Element of REAL
(((((Rea c2) * (Im1 c1)) - ((Im1 c2) * (Rea c1))) - ((Im2 c2) * (Im3 c1))) + ((Im3 c2) * (Im2 c1))) * (((c2) ^2) ") is complex ext-real real set
Im2 (c1,c2) is complex ext-real real Element of REAL
(Rea c2) * (Im2 c1) is complex ext-real real Element of REAL
(Im1 c2) * (Im3 c1) is complex ext-real real Element of REAL
((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1)) is complex ext-real real Element of REAL
(Im2 c2) * (Rea c1) is complex ext-real real Element of REAL
(((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) - ((Im2 c2) * (Rea c1)) is complex ext-real real Element of REAL
- ((Im2 c2) * (Rea c1)) is complex ext-real real set
(((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) + (- ((Im2 c2) * (Rea c1))) is complex ext-real real set
(Im3 c2) * (Im1 c1) is complex ext-real real Element of REAL
((((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) - ((Im2 c2) * (Rea c1))) - ((Im3 c2) * (Im1 c1)) is complex ext-real real Element of REAL
- ((Im3 c2) * (Im1 c1)) is complex ext-real real set
((((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) - ((Im2 c2) * (Rea c1))) + (- ((Im3 c2) * (Im1 c1))) is complex ext-real real set
(((((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) - ((Im2 c2) * (Rea c1))) - ((Im3 c2) * (Im1 c1))) / ((c2) ^2) is complex ext-real real Element of REAL
(((((Rea c2) * (Im2 c1)) + ((Im1 c2) * (Im3 c1))) - ((Im2 c2) * (Rea c1))) - ((Im3 c2) * (Im1 c1))) * (((c2) ^2) ") is complex ext-real real set
Im3 (c1,c2) is complex ext-real real Element of REAL
(Rea c2) * (Im3 c1) is complex ext-real real Element of REAL
(Im1 c2) * (Im2 c1) is complex ext-real real Element of REAL
((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1)) is complex ext-real real Element of REAL
- ((Im1 c2) * (Im2 c1)) is complex ext-real real set
((Rea c2) * (Im3 c1)) + (- ((Im1 c2) * (Im2 c1))) is complex ext-real real set
(Im2 c2) * (Im1 c1) is complex ext-real real Element of REAL
(((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1))) + ((Im2 c2) * (Im1 c1)) is complex ext-real real Element of REAL
(Im3 c2) * (Rea c1) is complex ext-real real Element of REAL
((((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1))) + ((Im2 c2) * (Im1 c1))) - ((Im3 c2) * (Rea c1)) is complex ext-real real Element of REAL
- ((Im3 c2) * (Rea c1)) is complex ext-real real set
((((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1))) + ((Im2 c2) * (Im1 c1))) + (- ((Im3 c2) * (Rea c1))) is complex ext-real real set
(((((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1))) + ((Im2 c2) * (Im1 c1))) - ((Im3 c2) * (Rea c1))) / ((c2) ^2) is complex ext-real real Element of REAL
(((((Rea c2) * (Im3 c1)) - ((Im1 c2) * (Im2 c1))) + ((Im2 c2) * (Im1 c1))) - ((Im3 c2) * (Rea c1))) * (((c2) ^2) ") is complex ext-real real set
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
z1 is complex ext-real real Element of REAL
[*c3,y1,w1,z1*] is quaternion Element of QUATERNION
x2 is complex ext-real real Element of REAL
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
z2 is complex ext-real real Element of REAL
[*x2,y2,w2,z2*] is quaternion Element of QUATERNION
x2 * c3 is complex ext-real real Element of REAL
y2 * y1 is complex ext-real real Element of REAL
(x2 * c3) + (y2 * y1) is complex ext-real real Element of REAL
w2 * w1 is complex ext-real real Element of REAL
((x2 * c3) + (y2 * y1)) + (w2 * w1) is complex ext-real real Element of REAL
z2 * z1 is complex ext-real real Element of REAL
(((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1) is complex ext-real real Element of REAL
((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) * (((c2) ^2) ") is complex ext-real real set
x2 * y1 is complex ext-real real Element of REAL
y2 * c3 is complex ext-real real Element of REAL
(x2 * y1) - (y2 * c3) is complex ext-real real Element of REAL
- (y2 * c3) is complex ext-real real set
(x2 * y1) + (- (y2 * c3)) is complex ext-real real set
w2 * z1 is complex ext-real real Element of REAL
((x2 * y1) - (y2 * c3)) - (w2 * z1) is complex ext-real real Element of REAL
- (w2 * z1) is complex ext-real real set
((x2 * y1) - (y2 * c3)) + (- (w2 * z1)) is complex ext-real real set
z2 * w1 is complex ext-real real Element of REAL
(((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1) is complex ext-real real Element of REAL
((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) * (((c2) ^2) ") is complex ext-real real set
x2 * w1 is complex ext-real real Element of REAL
y2 * z1 is complex ext-real real Element of REAL
(x2 * w1) + (y2 * z1) is complex ext-real real Element of REAL
w2 * c3 is complex ext-real real Element of REAL
((x2 * w1) + (y2 * z1)) - (w2 * c3) is complex ext-real real Element of REAL
- (w2 * c3) is complex ext-real real set
((x2 * w1) + (y2 * z1)) + (- (w2 * c3)) is complex ext-real real set
z2 * y1 is complex ext-real real Element of REAL
(((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1) is complex ext-real real Element of REAL
- (z2 * y1) is complex ext-real real set
(((x2 * w1) + (y2 * z1)) - (w2 * c3)) + (- (z2 * y1)) is complex ext-real real set
((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) * (((c2) ^2) ") is complex ext-real real set
x2 * z1 is complex ext-real real Element of REAL
y2 * w1 is complex ext-real real Element of REAL
(x2 * z1) - (y2 * w1) is complex ext-real real Element of REAL
- (y2 * w1) is complex ext-real real set
(x2 * z1) + (- (y2 * w1)) is complex ext-real real set
w2 * y1 is complex ext-real real Element of REAL
((x2 * z1) - (y2 * w1)) + (w2 * y1) is complex ext-real real Element of REAL
z2 * c3 is complex ext-real real Element of REAL
(((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3) is complex ext-real real Element of REAL
- (z2 * c3) is complex ext-real real set
(((x2 * z1) - (y2 * w1)) + (w2 * y1)) + (- (z2 * c3)) is complex ext-real real set
((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) / ((c2) ^2) is complex ext-real real Element of REAL
((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) * (((c2) ^2) ") is complex ext-real real set
[*(((((x2 * c3) + (y2 * y1)) + (w2 * w1)) + (z2 * z1)) / ((c2) ^2)),(((((x2 * y1) - (y2 * c3)) - (w2 * z1)) + (z2 * w1)) / ((c2) ^2)),(((((x2 * w1) + (y2 * z1)) - (w2 * c3)) - (z2 * y1)) / ((c2) ^2)),(((((x2 * z1) - (y2 * w1)) + (w2 * y1)) - (z2 * c3)) / ((c2) ^2))*] is quaternion Element of QUATERNION
c1 is quaternion set
(c1) is quaternion Element of QUATERNION
((),c1) is quaternion Element of QUATERNION
c1 * (c1) is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
[*c2,c3,y1,w1*] is quaternion Element of QUATERNION
[*1,0*] is Element of COMPLEX
[*1,0,0,0*] is quaternion Element of QUATERNION
Rea c1 is complex ext-real real Element of REAL
Im1 c1 is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
(c1) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
(c1) ^2 is complex ext-real real Element of REAL
(c1) * (c1) is complex ext-real real set
c2 ^2 is complex ext-real real Element of REAL
c2 * c2 is complex ext-real real set
c3 ^2 is complex ext-real real Element of REAL
c3 * c3 is complex ext-real real set
(c2 ^2) + (c3 ^2) is complex ext-real real Element of REAL
y1 ^2 is complex ext-real real Element of REAL
y1 * y1 is complex ext-real real set
((c2 ^2) + (c3 ^2)) + (y1 ^2) is complex ext-real real Element of REAL
w1 ^2 is complex ext-real real Element of REAL
w1 * w1 is complex ext-real real set
(((c2 ^2) + (c3 ^2)) + (y1 ^2)) + (w1 ^2) is complex ext-real real Element of REAL
c2 * 1 is complex ext-real real Element of REAL
c3 * 0 is complex ext-real real Element of REAL
(c2 * 1) + (c3 * 0) is complex ext-real real Element of REAL
y1 * 0 is complex ext-real real Element of REAL
((c2 * 1) + (c3 * 0)) + (y1 * 0) is complex ext-real real Element of REAL
w1 * 0 is complex ext-real real Element of REAL
(((c2 * 1) + (c3 * 0)) + (y1 * 0)) + (w1 * 0) is complex ext-real real Element of REAL
((((c2 * 1) + (c3 * 0)) + (y1 * 0)) + (w1 * 0)) / ((c1) ^2) is complex ext-real real Element of REAL
((c1) ^2) " is complex ext-real real set
((((c2 * 1) + (c3 * 0)) + (y1 * 0)) + (w1 * 0)) * (((c1) ^2) ") is complex ext-real real set
c2 * 0 is complex ext-real real Element of REAL
c3 * 1 is complex ext-real real Element of REAL
(c2 * 0) - (c3 * 1) is complex ext-real real Element of REAL
- (c3 * 1) is complex ext-real real set
(c2 * 0) + (- (c3 * 1)) is complex ext-real real set
((c2 * 0) - (c3 * 1)) - (y1 * 0) is complex ext-real real Element of REAL
- (y1 * 0) is complex ext-real real set
((c2 * 0) - (c3 * 1)) + (- (y1 * 0)) is complex ext-real real set
(((c2 * 0) - (c3 * 1)) - (y1 * 0)) + (w1 * 0) is complex ext-real real Element of REAL
((((c2 * 0) - (c3 * 1)) - (y1 * 0)) + (w1 * 0)) / ((c1) ^2) is complex ext-real real Element of REAL
((((c2 * 0) - (c3 * 1)) - (y1 * 0)) + (w1 * 0)) * (((c1) ^2) ") is complex ext-real real set
(c2 * 0) + (c3 * 0) is complex ext-real real Element of REAL
y1 * 1 is complex ext-real real Element of REAL
((c2 * 0) + (c3 * 0)) - (y1 * 1) is complex ext-real real Element of REAL
- (y1 * 1) is complex ext-real real set
((c2 * 0) + (c3 * 0)) + (- (y1 * 1)) is complex ext-real real set
(((c2 * 0) + (c3 * 0)) - (y1 * 1)) - (w1 * 0) is complex ext-real real Element of REAL
- (w1 * 0) is complex ext-real real set
(((c2 * 0) + (c3 * 0)) - (y1 * 1)) + (- (w1 * 0)) is complex ext-real real set
((((c2 * 0) + (c3 * 0)) - (y1 * 1)) - (w1 * 0)) / ((c1) ^2) is complex ext-real real Element of REAL
((((c2 * 0) + (c3 * 0)) - (y1 * 1)) - (w1 * 0)) * (((c1) ^2) ") is complex ext-real real set
(c2 * 0) - (c3 * 0) is complex ext-real real Element of REAL
- (c3 * 0) is complex ext-real real set
(c2 * 0) + (- (c3 * 0)) is complex ext-real real set
((c2 * 0) - (c3 * 0)) + (y1 * 0) is complex ext-real real Element of REAL
w1 * 1 is complex ext-real real Element of REAL
(((c2 * 0) - (c3 * 0)) + (y1 * 0)) - (w1 * 1) is complex ext-real real Element of REAL
- (w1 * 1) is complex ext-real real set
(((c2 * 0) - (c3 * 0)) + (y1 * 0)) + (- (w1 * 1)) is complex ext-real real set
((((c2 * 0) - (c3 * 0)) + (y1 * 0)) - (w1 * 1)) / ((c1) ^2) is complex ext-real real Element of REAL
((((c2 * 0) - (c3 * 0)) + (y1 * 0)) - (w1 * 1)) * (((c1) ^2) ") is complex ext-real real set
[*(((((c2 * 1) + (c3 * 0)) + (y1 * 0)) + (w1 * 0)) / ((c1) ^2)),(((((c2 * 0) - (c3 * 1)) - (y1 * 0)) + (w1 * 0)) / ((c1) ^2)),(((((c2 * 0) + (c3 * 0)) - (y1 * 1)) - (w1 * 0)) / ((c1) ^2)),(((((c2 * 0) - (c3 * 0)) + (y1 * 0)) - (w1 * 1)) / ((c1) ^2))*] is quaternion Element of QUATERNION
c2 / ((c1) ^2) is complex ext-real real Element of REAL
c2 * (((c1) ^2) ") is complex ext-real real set
- c3 is complex ext-real real Element of REAL
(- c3) / ((c1) ^2) is complex ext-real real Element of REAL
(- c3) * (((c1) ^2) ") is complex ext-real real set
- y1 is complex ext-real real Element of REAL
(- y1) / ((c1) ^2) is complex ext-real real Element of REAL
(- y1) * (((c1) ^2) ") is complex ext-real real set
- w1 is complex ext-real real Element of REAL
(- w1) / ((c1) ^2) is complex ext-real real Element of REAL
(- w1) * (((c1) ^2) ") is complex ext-real real set
[*(c2 / ((c1) ^2)),((- c3) / ((c1) ^2)),((- y1) / ((c1) ^2)),((- w1) / ((c1) ^2))*] is quaternion Element of QUATERNION
c2 * (c2 / ((c1) ^2)) is complex ext-real real Element of REAL
c3 * ((- c3) / ((c1) ^2)) is complex ext-real real Element of REAL
(c2 * (c2 / ((c1) ^2))) - (c3 * ((- c3) / ((c1) ^2))) is complex ext-real real Element of REAL
- (c3 * ((- c3) / ((c1) ^2))) is complex ext-real real set
(c2 * (c2 / ((c1) ^2))) + (- (c3 * ((- c3) / ((c1) ^2)))) is complex ext-real real set
y1 * ((- y1) / ((c1) ^2)) is complex ext-real real Element of REAL
((c2 * (c2 / ((c1) ^2))) - (c3 * ((- c3) / ((c1) ^2)))) - (y1 * ((- y1) / ((c1) ^2))) is complex ext-real real Element of REAL
- (y1 * ((- y1) / ((c1) ^2))) is complex ext-real real set
((c2 * (c2 / ((c1) ^2))) - (c3 * ((- c3) / ((c1) ^2)))) + (- (y1 * ((- y1) / ((c1) ^2)))) is complex ext-real real set
w1 * ((- w1) / ((c1) ^2)) is complex ext-real real Element of REAL
(((c2 * (c2 / ((c1) ^2))) - (c3 * ((- c3) / ((c1) ^2)))) - (y1 * ((- y1) / ((c1) ^2)))) - (w1 * ((- w1) / ((c1) ^2))) is complex ext-real real Element of REAL
- (w1 * ((- w1) / ((c1) ^2))) is complex ext-real real set
(((c2 * (c2 / ((c1) ^2))) - (c3 * ((- c3) / ((c1) ^2)))) - (y1 * ((- y1) / ((c1) ^2)))) + (- (w1 * ((- w1) / ((c1) ^2)))) is complex ext-real real set
c2 * ((- c3) / ((c1) ^2)) is complex ext-real real Element of REAL
c3 * (c2 / ((c1) ^2)) is complex ext-real real Element of REAL
(c2 * ((- c3) / ((c1) ^2))) + (c3 * (c2 / ((c1) ^2))) is complex ext-real real Element of REAL
y1 * ((- w1) / ((c1) ^2)) is complex ext-real real Element of REAL
((c2 * ((- c3) / ((c1) ^2))) + (c3 * (c2 / ((c1) ^2)))) + (y1 * ((- w1) / ((c1) ^2))) is complex ext-real real Element of REAL
w1 * ((- y1) / ((c1) ^2)) is complex ext-real real Element of REAL
(((c2 * ((- c3) / ((c1) ^2))) + (c3 * (c2 / ((c1) ^2)))) + (y1 * ((- w1) / ((c1) ^2)))) - (w1 * ((- y1) / ((c1) ^2))) is complex ext-real real Element of REAL
- (w1 * ((- y1) / ((c1) ^2))) is complex ext-real real set
(((c2 * ((- c3) / ((c1) ^2))) + (c3 * (c2 / ((c1) ^2)))) + (y1 * ((- w1) / ((c1) ^2)))) + (- (w1 * ((- y1) / ((c1) ^2)))) is complex ext-real real set
c2 * ((- y1) / ((c1) ^2)) is complex ext-real real Element of REAL
(c2 / ((c1) ^2)) * y1 is complex ext-real real Element of REAL
(c2 * ((- y1) / ((c1) ^2))) + ((c2 / ((c1) ^2)) * y1) is complex ext-real real Element of REAL
((- c3) / ((c1) ^2)) * w1 is complex ext-real real Element of REAL
((c2 * ((- y1) / ((c1) ^2))) + ((c2 / ((c1) ^2)) * y1)) + (((- c3) / ((c1) ^2)) * w1) is complex ext-real real Element of REAL
((- w1) / ((c1) ^2)) * c3 is complex ext-real real Element of REAL
(((c2 * ((- y1) / ((c1) ^2))) + ((c2 / ((c1) ^2)) * y1)) + (((- c3) / ((c1) ^2)) * w1)) - (((- w1) / ((c1) ^2)) * c3) is complex ext-real real Element of REAL
- (((- w1) / ((c1) ^2)) * c3) is complex ext-real real set
(((c2 * ((- y1) / ((c1) ^2))) + ((c2 / ((c1) ^2)) * y1)) + (((- c3) / ((c1) ^2)) * w1)) + (- (((- w1) / ((c1) ^2)) * c3)) is complex ext-real real set
c2 * ((- w1) / ((c1) ^2)) is complex ext-real real Element of REAL
w1 * (c2 / ((c1) ^2)) is complex ext-real real Element of REAL
(c2 * ((- w1) / ((c1) ^2))) + (w1 * (c2 / ((c1) ^2))) is complex ext-real real Element of REAL
c3 * ((- y1) / ((c1) ^2)) is complex ext-real real Element of REAL
((c2 * ((- w1) / ((c1) ^2))) + (w1 * (c2 / ((c1) ^2)))) + (c3 * ((- y1) / ((c1) ^2))) is complex ext-real real Element of REAL
y1 * ((- c3) / ((c1) ^2)) is complex ext-real real Element of REAL
(((c2 * ((- w1) / ((c1) ^2))) + (w1 * (c2 / ((c1) ^2)))) + (c3 * ((- y1) / ((c1) ^2)))) - (y1 * ((- c3) / ((c1) ^2))) is complex ext-real real Element of REAL
- (y1 * ((- c3) / ((c1) ^2))) is complex ext-real real set
(((c2 * ((- w1) / ((c1) ^2))) + (w1 * (c2 / ((c1) ^2)))) + (c3 * ((- y1) / ((c1) ^2)))) + (- (y1 * ((- c3) / ((c1) ^2)))) is complex ext-real real set
[*((((c2 * (c2 / ((c1) ^2))) - (c3 * ((- c3) / ((c1) ^2)))) - (y1 * ((- y1) / ((c1) ^2)))) - (w1 * ((- w1) / ((c1) ^2)))),((((c2 * ((- c3) / ((c1) ^2))) + (c3 * (c2 / ((c1) ^2)))) + (y1 * ((- w1) / ((c1) ^2)))) - (w1 * ((- y1) / ((c1) ^2)))),((((c2 * ((- y1) / ((c1) ^2))) + ((c2 / ((c1) ^2)) * y1)) + (((- c3) / ((c1) ^2)) * w1)) - (((- w1) / ((c1) ^2)) * c3)),((((c2 * ((- w1) / ((c1) ^2))) + (w1 * (c2 / ((c1) ^2)))) + (c3 * ((- y1) / ((c1) ^2)))) - (y1 * ((- c3) / ((c1) ^2))))*] is quaternion Element of QUATERNION
((c1) ^2) / ((c1) ^2) is complex ext-real real Element of REAL
((c1) ^2) * (((c1) ^2) ") is complex ext-real real set
[*(((c1) ^2) / ((c1) ^2)),0,0,0*] is quaternion Element of QUATERNION
c1 is quaternion set
(c1) is quaternion Element of QUATERNION
((),c1) is quaternion Element of QUATERNION
(c1) * c1 is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
[*c2,c3,y1,w1*] is quaternion Element of QUATERNION
[*1,0*] is Element of COMPLEX
[*1,0,0,0*] is quaternion Element of QUATERNION
Rea c1 is complex ext-real real Element of REAL
Im1 c1 is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
(c1) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
(c1) ^2 is complex ext-real real Element of REAL
(c1) * (c1) is complex ext-real real set
c2 ^2 is complex ext-real real Element of REAL
c2 * c2 is complex ext-real real set
c3 ^2 is complex ext-real real Element of REAL
c3 * c3 is complex ext-real real set
(c2 ^2) + (c3 ^2) is complex ext-real real Element of REAL
y1 ^2 is complex ext-real real Element of REAL
y1 * y1 is complex ext-real real set
((c2 ^2) + (c3 ^2)) + (y1 ^2) is complex ext-real real Element of REAL
w1 ^2 is complex ext-real real Element of REAL
w1 * w1 is complex ext-real real set
(((c2 ^2) + (c3 ^2)) + (y1 ^2)) + (w1 ^2) is complex ext-real real Element of REAL
c2 * 1 is complex ext-real real Element of REAL
c3 * 0 is complex ext-real real Element of REAL
(c2 * 1) + (c3 * 0) is complex ext-real real Element of REAL
y1 * 0 is complex ext-real real Element of REAL
((c2 * 1) + (c3 * 0)) + (y1 * 0) is complex ext-real real Element of REAL
w1 * 0 is complex ext-real real Element of REAL
(((c2 * 1) + (c3 * 0)) + (y1 * 0)) + (w1 * 0) is complex ext-real real Element of REAL
((((c2 * 1) + (c3 * 0)) + (y1 * 0)) + (w1 * 0)) / ((c1) ^2) is complex ext-real real Element of REAL
((c1) ^2) " is complex ext-real real set
((((c2 * 1) + (c3 * 0)) + (y1 * 0)) + (w1 * 0)) * (((c1) ^2) ") is complex ext-real real set
c2 * 0 is complex ext-real real Element of REAL
c3 * 1 is complex ext-real real Element of REAL
(c2 * 0) - (c3 * 1) is complex ext-real real Element of REAL
- (c3 * 1) is complex ext-real real set
(c2 * 0) + (- (c3 * 1)) is complex ext-real real set
((c2 * 0) - (c3 * 1)) - (y1 * 0) is complex ext-real real Element of REAL
- (y1 * 0) is complex ext-real real set
((c2 * 0) - (c3 * 1)) + (- (y1 * 0)) is complex ext-real real set
(((c2 * 0) - (c3 * 1)) - (y1 * 0)) + (w1 * 0) is complex ext-real real Element of REAL
((((c2 * 0) - (c3 * 1)) - (y1 * 0)) + (w1 * 0)) / ((c1) ^2) is complex ext-real real Element of REAL
((((c2 * 0) - (c3 * 1)) - (y1 * 0)) + (w1 * 0)) * (((c1) ^2) ") is complex ext-real real set
(c2 * 0) + (c3 * 0) is complex ext-real real Element of REAL
y1 * 1 is complex ext-real real Element of REAL
((c2 * 0) + (c3 * 0)) - (y1 * 1) is complex ext-real real Element of REAL
- (y1 * 1) is complex ext-real real set
((c2 * 0) + (c3 * 0)) + (- (y1 * 1)) is complex ext-real real set
(((c2 * 0) + (c3 * 0)) - (y1 * 1)) - (w1 * 0) is complex ext-real real Element of REAL
- (w1 * 0) is complex ext-real real set
(((c2 * 0) + (c3 * 0)) - (y1 * 1)) + (- (w1 * 0)) is complex ext-real real set
((((c2 * 0) + (c3 * 0)) - (y1 * 1)) - (w1 * 0)) / ((c1) ^2) is complex ext-real real Element of REAL
((((c2 * 0) + (c3 * 0)) - (y1 * 1)) - (w1 * 0)) * (((c1) ^2) ") is complex ext-real real set
(c2 * 0) - (c3 * 0) is complex ext-real real Element of REAL
- (c3 * 0) is complex ext-real real set
(c2 * 0) + (- (c3 * 0)) is complex ext-real real set
((c2 * 0) - (c3 * 0)) + (y1 * 0) is complex ext-real real Element of REAL
w1 * 1 is complex ext-real real Element of REAL
(((c2 * 0) - (c3 * 0)) + (y1 * 0)) - (w1 * 1) is complex ext-real real Element of REAL
- (w1 * 1) is complex ext-real real set
(((c2 * 0) - (c3 * 0)) + (y1 * 0)) + (- (w1 * 1)) is complex ext-real real set
((((c2 * 0) - (c3 * 0)) + (y1 * 0)) - (w1 * 1)) / ((c1) ^2) is complex ext-real real Element of REAL
((((c2 * 0) - (c3 * 0)) + (y1 * 0)) - (w1 * 1)) * (((c1) ^2) ") is complex ext-real real set
[*(((((c2 * 1) + (c3 * 0)) + (y1 * 0)) + (w1 * 0)) / ((c1) ^2)),(((((c2 * 0) - (c3 * 1)) - (y1 * 0)) + (w1 * 0)) / ((c1) ^2)),(((((c2 * 0) + (c3 * 0)) - (y1 * 1)) - (w1 * 0)) / ((c1) ^2)),(((((c2 * 0) - (c3 * 0)) + (y1 * 0)) - (w1 * 1)) / ((c1) ^2))*] is quaternion Element of QUATERNION
c2 / ((c1) ^2) is complex ext-real real Element of REAL
c2 * (((c1) ^2) ") is complex ext-real real set
- c3 is complex ext-real real Element of REAL
(- c3) / ((c1) ^2) is complex ext-real real Element of REAL
(- c3) * (((c1) ^2) ") is complex ext-real real set
- y1 is complex ext-real real Element of REAL
(- y1) / ((c1) ^2) is complex ext-real real Element of REAL
(- y1) * (((c1) ^2) ") is complex ext-real real set
- w1 is complex ext-real real Element of REAL
(- w1) / ((c1) ^2) is complex ext-real real Element of REAL
(- w1) * (((c1) ^2) ") is complex ext-real real set
[*(c2 / ((c1) ^2)),((- c3) / ((c1) ^2)),((- y1) / ((c1) ^2)),((- w1) / ((c1) ^2))*] is quaternion Element of QUATERNION
c2 * (c2 / ((c1) ^2)) is complex ext-real real Element of REAL
c3 * ((- c3) / ((c1) ^2)) is complex ext-real real Element of REAL
(c2 * (c2 / ((c1) ^2))) - (c3 * ((- c3) / ((c1) ^2))) is complex ext-real real Element of REAL
- (c3 * ((- c3) / ((c1) ^2))) is complex ext-real real set
(c2 * (c2 / ((c1) ^2))) + (- (c3 * ((- c3) / ((c1) ^2)))) is complex ext-real real set
y1 * ((- y1) / ((c1) ^2)) is complex ext-real real Element of REAL
((c2 * (c2 / ((c1) ^2))) - (c3 * ((- c3) / ((c1) ^2)))) - (y1 * ((- y1) / ((c1) ^2))) is complex ext-real real Element of REAL
- (y1 * ((- y1) / ((c1) ^2))) is complex ext-real real set
((c2 * (c2 / ((c1) ^2))) - (c3 * ((- c3) / ((c1) ^2)))) + (- (y1 * ((- y1) / ((c1) ^2)))) is complex ext-real real set
w1 * ((- w1) / ((c1) ^2)) is complex ext-real real Element of REAL
(((c2 * (c2 / ((c1) ^2))) - (c3 * ((- c3) / ((c1) ^2)))) - (y1 * ((- y1) / ((c1) ^2)))) - (w1 * ((- w1) / ((c1) ^2))) is complex ext-real real Element of REAL
- (w1 * ((- w1) / ((c1) ^2))) is complex ext-real real set
(((c2 * (c2 / ((c1) ^2))) - (c3 * ((- c3) / ((c1) ^2)))) - (y1 * ((- y1) / ((c1) ^2)))) + (- (w1 * ((- w1) / ((c1) ^2)))) is complex ext-real real set
c2 * ((- c3) / ((c1) ^2)) is complex ext-real real Element of REAL
c3 * (c2 / ((c1) ^2)) is complex ext-real real Element of REAL
(c2 * ((- c3) / ((c1) ^2))) + (c3 * (c2 / ((c1) ^2))) is complex ext-real real Element of REAL
y1 * ((- w1) / ((c1) ^2)) is complex ext-real real Element of REAL
((c2 * ((- c3) / ((c1) ^2))) + (c3 * (c2 / ((c1) ^2)))) + (y1 * ((- w1) / ((c1) ^2))) is complex ext-real real Element of REAL
w1 * ((- y1) / ((c1) ^2)) is complex ext-real real Element of REAL
(((c2 * ((- c3) / ((c1) ^2))) + (c3 * (c2 / ((c1) ^2)))) + (y1 * ((- w1) / ((c1) ^2)))) - (w1 * ((- y1) / ((c1) ^2))) is complex ext-real real Element of REAL
- (w1 * ((- y1) / ((c1) ^2))) is complex ext-real real set
(((c2 * ((- c3) / ((c1) ^2))) + (c3 * (c2 / ((c1) ^2)))) + (y1 * ((- w1) / ((c1) ^2)))) + (- (w1 * ((- y1) / ((c1) ^2)))) is complex ext-real real set
c2 * ((- y1) / ((c1) ^2)) is complex ext-real real Element of REAL
(c2 / ((c1) ^2)) * y1 is complex ext-real real Element of REAL
(c2 * ((- y1) / ((c1) ^2))) + ((c2 / ((c1) ^2)) * y1) is complex ext-real real Element of REAL
((- c3) / ((c1) ^2)) * w1 is complex ext-real real Element of REAL
((c2 * ((- y1) / ((c1) ^2))) + ((c2 / ((c1) ^2)) * y1)) + (((- c3) / ((c1) ^2)) * w1) is complex ext-real real Element of REAL
((- w1) / ((c1) ^2)) * c3 is complex ext-real real Element of REAL
(((c2 * ((- y1) / ((c1) ^2))) + ((c2 / ((c1) ^2)) * y1)) + (((- c3) / ((c1) ^2)) * w1)) - (((- w1) / ((c1) ^2)) * c3) is complex ext-real real Element of REAL
- (((- w1) / ((c1) ^2)) * c3) is complex ext-real real set
(((c2 * ((- y1) / ((c1) ^2))) + ((c2 / ((c1) ^2)) * y1)) + (((- c3) / ((c1) ^2)) * w1)) + (- (((- w1) / ((c1) ^2)) * c3)) is complex ext-real real set
c2 * ((- w1) / ((c1) ^2)) is complex ext-real real Element of REAL
w1 * (c2 / ((c1) ^2)) is complex ext-real real Element of REAL
(c2 * ((- w1) / ((c1) ^2))) + (w1 * (c2 / ((c1) ^2))) is complex ext-real real Element of REAL
c3 * ((- y1) / ((c1) ^2)) is complex ext-real real Element of REAL
((c2 * ((- w1) / ((c1) ^2))) + (w1 * (c2 / ((c1) ^2)))) + (c3 * ((- y1) / ((c1) ^2))) is complex ext-real real Element of REAL
y1 * ((- c3) / ((c1) ^2)) is complex ext-real real Element of REAL
(((c2 * ((- w1) / ((c1) ^2))) + (w1 * (c2 / ((c1) ^2)))) + (c3 * ((- y1) / ((c1) ^2)))) - (y1 * ((- c3) / ((c1) ^2))) is complex ext-real real Element of REAL
- (y1 * ((- c3) / ((c1) ^2))) is complex ext-real real set
(((c2 * ((- w1) / ((c1) ^2))) + (w1 * (c2 / ((c1) ^2)))) + (c3 * ((- y1) / ((c1) ^2)))) + (- (y1 * ((- c3) / ((c1) ^2)))) is complex ext-real real set
[*((((c2 * (c2 / ((c1) ^2))) - (c3 * ((- c3) / ((c1) ^2)))) - (y1 * ((- y1) / ((c1) ^2)))) - (w1 * ((- w1) / ((c1) ^2)))),((((c2 * ((- c3) / ((c1) ^2))) + (c3 * (c2 / ((c1) ^2)))) + (y1 * ((- w1) / ((c1) ^2)))) - (w1 * ((- y1) / ((c1) ^2)))),((((c2 * ((- y1) / ((c1) ^2))) + ((c2 / ((c1) ^2)) * y1)) + (((- c3) / ((c1) ^2)) * w1)) - (((- w1) / ((c1) ^2)) * c3)),((((c2 * ((- w1) / ((c1) ^2))) + (w1 * (c2 / ((c1) ^2)))) + (c3 * ((- y1) / ((c1) ^2)))) - (y1 * ((- c3) / ((c1) ^2))))*] is quaternion Element of QUATERNION
((c1) ^2) / ((c1) ^2) is complex ext-real real Element of REAL
((c1) ^2) * (((c1) ^2) ") is complex ext-real real set
[*(((c1) ^2) / ((c1) ^2)),0,0,0*] is quaternion Element of QUATERNION
c1 is quaternion set
(c1,c1) is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
[*c2,c3,y1,w1*] is quaternion Element of QUATERNION
(c1) is complex ext-real real Element of REAL
Rea c1 is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
Im1 c1 is complex ext-real real Element of REAL
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
(c1) ^2 is complex ext-real real Element of REAL
(c1) * (c1) is complex ext-real real set
c2 ^2 is complex ext-real real Element of REAL
c2 * c2 is complex ext-real real set
c3 ^2 is complex ext-real real Element of REAL
c3 * c3 is complex ext-real real set
(c2 ^2) + (c3 ^2) is complex ext-real real Element of REAL
y1 ^2 is complex ext-real real Element of REAL
y1 * y1 is complex ext-real real set
((c2 ^2) + (c3 ^2)) + (y1 ^2) is complex ext-real real Element of REAL
w1 ^2 is complex ext-real real Element of REAL
w1 * w1 is complex ext-real real set
(((c2 ^2) + (c3 ^2)) + (y1 ^2)) + (w1 ^2) is complex ext-real real Element of REAL
c2 * c2 is complex ext-real real Element of REAL
c3 * c3 is complex ext-real real Element of REAL
(c2 * c2) + (c3 * c3) is complex ext-real real Element of REAL
y1 * y1 is complex ext-real real Element of REAL
((c2 * c2) + (c3 * c3)) + (y1 * y1) is complex ext-real real Element of REAL
w1 * w1 is complex ext-real real Element of REAL
(((c2 * c2) + (c3 * c3)) + (y1 * y1)) + (w1 * w1) is complex ext-real real Element of REAL
((((c2 * c2) + (c3 * c3)) + (y1 * y1)) + (w1 * w1)) / ((c1) ^2) is complex ext-real real Element of REAL
((c1) ^2) " is complex ext-real real set
((((c2 * c2) + (c3 * c3)) + (y1 * y1)) + (w1 * w1)) * (((c1) ^2) ") is complex ext-real real set
c2 * c3 is complex ext-real real Element of REAL
c3 * c2 is complex ext-real real Element of REAL
(c2 * c3) - (c3 * c2) is complex ext-real real Element of REAL
- (c3 * c2) is complex ext-real real set
(c2 * c3) + (- (c3 * c2)) is complex ext-real real set
y1 * w1 is complex ext-real real Element of REAL
((c2 * c3) - (c3 * c2)) - (y1 * w1) is complex ext-real real Element of REAL
- (y1 * w1) is complex ext-real real set
((c2 * c3) - (c3 * c2)) + (- (y1 * w1)) is complex ext-real real set
w1 * y1 is complex ext-real real Element of REAL
(((c2 * c3) - (c3 * c2)) - (y1 * w1)) + (w1 * y1) is complex ext-real real Element of REAL
((((c2 * c3) - (c3 * c2)) - (y1 * w1)) + (w1 * y1)) / ((c1) ^2) is complex ext-real real Element of REAL
((((c2 * c3) - (c3 * c2)) - (y1 * w1)) + (w1 * y1)) * (((c1) ^2) ") is complex ext-real real set
c2 * y1 is complex ext-real real Element of REAL
c3 * w1 is complex ext-real real Element of REAL
(c2 * y1) + (c3 * w1) is complex ext-real real Element of REAL
y1 * c2 is complex ext-real real Element of REAL
((c2 * y1) + (c3 * w1)) - (y1 * c2) is complex ext-real real Element of REAL
- (y1 * c2) is complex ext-real real set
((c2 * y1) + (c3 * w1)) + (- (y1 * c2)) is complex ext-real real set
w1 * c3 is complex ext-real real Element of REAL
(((c2 * y1) + (c3 * w1)) - (y1 * c2)) - (w1 * c3) is complex ext-real real Element of REAL
- (w1 * c3) is complex ext-real real set
(((c2 * y1) + (c3 * w1)) - (y1 * c2)) + (- (w1 * c3)) is complex ext-real real set
((((c2 * y1) + (c3 * w1)) - (y1 * c2)) - (w1 * c3)) / ((c1) ^2) is complex ext-real real Element of REAL
((((c2 * y1) + (c3 * w1)) - (y1 * c2)) - (w1 * c3)) * (((c1) ^2) ") is complex ext-real real set
c2 * w1 is complex ext-real real Element of REAL
c3 * y1 is complex ext-real real Element of REAL
(c2 * w1) - (c3 * y1) is complex ext-real real Element of REAL
- (c3 * y1) is complex ext-real real set
(c2 * w1) + (- (c3 * y1)) is complex ext-real real set
y1 * c3 is complex ext-real real Element of REAL
((c2 * w1) - (c3 * y1)) + (y1 * c3) is complex ext-real real Element of REAL
w1 * c2 is complex ext-real real Element of REAL
(((c2 * w1) - (c3 * y1)) + (y1 * c3)) - (w1 * c2) is complex ext-real real Element of REAL
- (w1 * c2) is complex ext-real real set
(((c2 * w1) - (c3 * y1)) + (y1 * c3)) + (- (w1 * c2)) is complex ext-real real set
((((c2 * w1) - (c3 * y1)) + (y1 * c3)) - (w1 * c2)) / ((c1) ^2) is complex ext-real real Element of REAL
((((c2 * w1) - (c3 * y1)) + (y1 * c3)) - (w1 * c2)) * (((c1) ^2) ") is complex ext-real real set
[*(((((c2 * c2) + (c3 * c3)) + (y1 * y1)) + (w1 * w1)) / ((c1) ^2)),(((((c2 * c3) - (c3 * c2)) - (y1 * w1)) + (w1 * y1)) / ((c1) ^2)),(((((c2 * y1) + (c3 * w1)) - (y1 * c2)) - (w1 * c3)) / ((c1) ^2)),(((((c2 * w1) - (c3 * y1)) + (y1 * c3)) - (w1 * c2)) / ((c1) ^2))*] is quaternion Element of QUATERNION
((c1) ^2) / ((c1) ^2) is complex ext-real real Element of REAL
((c1) ^2) * (((c1) ^2) ") is complex ext-real real set
[*(((c1) ^2) / ((c1) ^2)),0,0,0*] is quaternion Element of QUATERNION
[*1,0,0,0*] is quaternion Element of QUATERNION
[*1,0*] is Element of COMPLEX
c1 is quaternion set
- c1 is quaternion Element of QUATERNION
((- c1)) is quaternion Element of QUATERNION
((),(- c1)) is quaternion Element of QUATERNION
(c1) is quaternion Element of QUATERNION
((),c1) is quaternion Element of QUATERNION
- (c1) is quaternion Element of QUATERNION
[*1,0*] is Element of COMPLEX
[*1,0,0,0*] is quaternion Element of QUATERNION
c2 is complex ext-real real Element of REAL
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
[*c2,c3,y1,w1*] is quaternion Element of QUATERNION
- c2 is complex ext-real real Element of REAL
- c3 is complex ext-real real Element of REAL
- y1 is complex ext-real real Element of REAL
- w1 is complex ext-real real Element of REAL
[*(- c2),(- c3),(- y1),(- w1)*] is quaternion Element of QUATERNION
((- c1)) is complex ext-real real Element of REAL
Rea (- c1) is complex ext-real real Element of REAL
(Rea (- c1)) ^2 is complex ext-real real Element of REAL
(Rea (- c1)) * (Rea (- c1)) is complex ext-real real set
Im1 (- c1) is complex ext-real real Element of REAL
(Im1 (- c1)) ^2 is complex ext-real real Element of REAL
(Im1 (- c1)) * (Im1 (- c1)) is complex ext-real real set
((Rea (- c1)) ^2) + ((Im1 (- c1)) ^2) is complex ext-real real Element of REAL
Im2 (- c1) is complex ext-real real Element of REAL
(Im2 (- c1)) ^2 is complex ext-real real Element of REAL
(Im2 (- c1)) * (Im2 (- c1)) is complex ext-real real set
(((Rea (- c1)) ^2) + ((Im1 (- c1)) ^2)) + ((Im2 (- c1)) ^2) is complex ext-real real Element of REAL
Im3 (- c1) is complex ext-real real Element of REAL
(Im3 (- c1)) ^2 is complex ext-real real Element of REAL
(Im3 (- c1)) * (Im3 (- c1)) is complex ext-real real set
((((Rea (- c1)) ^2) + ((Im1 (- c1)) ^2)) + ((Im2 (- c1)) ^2)) + ((Im3 (- c1)) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea (- c1)) ^2) + ((Im1 (- c1)) ^2)) + ((Im2 (- c1)) ^2)) + ((Im3 (- c1)) ^2)) is complex ext-real real Element of REAL
(c1) is complex ext-real real Element of REAL
Rea c1 is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
Im1 c1 is complex ext-real real Element of REAL
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
c2 * 1 is complex ext-real real Element of REAL
c3 * 0 is complex ext-real real Element of REAL
(c2 * 1) + (c3 * 0) is complex ext-real real Element of REAL
y1 * 0 is complex ext-real real Element of REAL
((c2 * 1) + (c3 * 0)) + (y1 * 0) is complex ext-real real Element of REAL
w1 * 0 is complex ext-real real Element of REAL
(((c2 * 1) + (c3 * 0)) + (y1 * 0)) + (w1 * 0) is complex ext-real real Element of REAL
(c1) ^2 is complex ext-real real Element of REAL
(c1) * (c1) is complex ext-real real set
((((c2 * 1) + (c3 * 0)) + (y1 * 0)) + (w1 * 0)) / ((c1) ^2) is complex ext-real real Element of REAL
((c1) ^2) " is complex ext-real real set
((((c2 * 1) + (c3 * 0)) + (y1 * 0)) + (w1 * 0)) * (((c1) ^2) ") is complex ext-real real set
c2 * 0 is complex ext-real real Element of REAL
c3 * 1 is complex ext-real real Element of REAL
(c2 * 0) - (c3 * 1) is complex ext-real real Element of REAL
- (c3 * 1) is complex ext-real real set
(c2 * 0) + (- (c3 * 1)) is complex ext-real real set
((c2 * 0) - (c3 * 1)) - (y1 * 0) is complex ext-real real Element of REAL
- (y1 * 0) is complex ext-real real set
((c2 * 0) - (c3 * 1)) + (- (y1 * 0)) is complex ext-real real set
(((c2 * 0) - (c3 * 1)) - (y1 * 0)) + (w1 * 0) is complex ext-real real Element of REAL
((((c2 * 0) - (c3 * 1)) - (y1 * 0)) + (w1 * 0)) / ((c1) ^2) is complex ext-real real Element of REAL
((((c2 * 0) - (c3 * 1)) - (y1 * 0)) + (w1 * 0)) * (((c1) ^2) ") is complex ext-real real set
(c2 * 0) + (c3 * 0) is complex ext-real real Element of REAL
y1 * 1 is complex ext-real real Element of REAL
((c2 * 0) + (c3 * 0)) - (y1 * 1) is complex ext-real real Element of REAL
- (y1 * 1) is complex ext-real real set
((c2 * 0) + (c3 * 0)) + (- (y1 * 1)) is complex ext-real real set
(((c2 * 0) + (c3 * 0)) - (y1 * 1)) - (w1 * 0) is complex ext-real real Element of REAL
- (w1 * 0) is complex ext-real real set
(((c2 * 0) + (c3 * 0)) - (y1 * 1)) + (- (w1 * 0)) is complex ext-real real set
((((c2 * 0) + (c3 * 0)) - (y1 * 1)) - (w1 * 0)) / ((c1) ^2) is complex ext-real real Element of REAL
((((c2 * 0) + (c3 * 0)) - (y1 * 1)) - (w1 * 0)) * (((c1) ^2) ") is complex ext-real real set
(c2 * 0) - (c3 * 0) is complex ext-real real Element of REAL
- (c3 * 0) is complex ext-real real set
(c2 * 0) + (- (c3 * 0)) is complex ext-real real set
((c2 * 0) - (c3 * 0)) + (y1 * 0) is complex ext-real real Element of REAL
w1 * 1 is complex ext-real real Element of REAL
(((c2 * 0) - (c3 * 0)) + (y1 * 0)) - (w1 * 1) is complex ext-real real Element of REAL
- (w1 * 1) is complex ext-real real set
(((c2 * 0) - (c3 * 0)) + (y1 * 0)) + (- (w1 * 1)) is complex ext-real real set
((((c2 * 0) - (c3 * 0)) + (y1 * 0)) - (w1 * 1)) / ((c1) ^2) is complex ext-real real Element of REAL
((((c2 * 0) - (c3 * 0)) + (y1 * 0)) - (w1 * 1)) * (((c1) ^2) ") is complex ext-real real set
[*(((((c2 * 1) + (c3 * 0)) + (y1 * 0)) + (w1 * 0)) / ((c1) ^2)),(((((c2 * 0) - (c3 * 1)) - (y1 * 0)) + (w1 * 0)) / ((c1) ^2)),(((((c2 * 0) + (c3 * 0)) - (y1 * 1)) - (w1 * 0)) / ((c1) ^2)),(((((c2 * 0) - (c3 * 0)) + (y1 * 0)) - (w1 * 1)) / ((c1) ^2))*] is quaternion Element of QUATERNION
c2 / ((c1) ^2) is complex ext-real real Element of REAL
c2 * (((c1) ^2) ") is complex ext-real real set
c3 / ((c1) ^2) is complex ext-real real Element of REAL
c3 * (((c1) ^2) ") is complex ext-real real set
- (c3 / ((c1) ^2)) is complex ext-real real Element of REAL
y1 / ((c1) ^2) is complex ext-real real Element of REAL
y1 * (((c1) ^2) ") is complex ext-real real set
- (y1 / ((c1) ^2)) is complex ext-real real Element of REAL
w1 / ((c1) ^2) is complex ext-real real Element of REAL
w1 * (((c1) ^2) ") is complex ext-real real set
- (w1 / ((c1) ^2)) is complex ext-real real Element of REAL
[*(c2 / ((c1) ^2)),(- (c3 / ((c1) ^2))),(- (y1 / ((c1) ^2))),(- (w1 / ((c1) ^2)))*] is quaternion Element of QUATERNION
(- c2) * 1 is complex ext-real real Element of REAL
(- c3) * 0 is complex ext-real real Element of REAL
((- c2) * 1) + ((- c3) * 0) is complex ext-real real Element of REAL
(- y1) * 0 is complex ext-real real Element of REAL
(((- c2) * 1) + ((- c3) * 0)) + ((- y1) * 0) is complex ext-real real Element of REAL
(- w1) * 0 is complex ext-real real Element of REAL
((((- c2) * 1) + ((- c3) * 0)) + ((- y1) * 0)) + ((- w1) * 0) is complex ext-real real Element of REAL
((- c1)) ^2 is complex ext-real real Element of REAL
((- c1)) * ((- c1)) is complex ext-real real set
(((((- c2) * 1) + ((- c3) * 0)) + ((- y1) * 0)) + ((- w1) * 0)) / (((- c1)) ^2) is complex ext-real real Element of REAL
(((- c1)) ^2) " is complex ext-real real set
(((((- c2) * 1) + ((- c3) * 0)) + ((- y1) * 0)) + ((- w1) * 0)) * ((((- c1)) ^2) ") is complex ext-real real set
(- c2) * 0 is complex ext-real real Element of REAL
(- c3) * 1 is complex ext-real real Element of REAL
((- c2) * 0) - ((- c3) * 1) is complex ext-real real Element of REAL
- ((- c3) * 1) is complex ext-real real set
((- c2) * 0) + (- ((- c3) * 1)) is complex ext-real real set
(((- c2) * 0) - ((- c3) * 1)) - ((- y1) * 0) is complex ext-real real Element of REAL
- ((- y1) * 0) is complex ext-real real set
(((- c2) * 0) - ((- c3) * 1)) + (- ((- y1) * 0)) is complex ext-real real set
((((- c2) * 0) - ((- c3) * 1)) - ((- y1) * 0)) + ((- w1) * 0) is complex ext-real real Element of REAL
(((((- c2) * 0) - ((- c3) * 1)) - ((- y1) * 0)) + ((- w1) * 0)) / (((- c1)) ^2) is complex ext-real real Element of REAL
(((((- c2) * 0) - ((- c3) * 1)) - ((- y1) * 0)) + ((- w1) * 0)) * ((((- c1)) ^2) ") is complex ext-real real set
((- c2) * 0) + ((- c3) * 0) is complex ext-real real Element of REAL
(- y1) * 1 is complex ext-real real Element of REAL
(((- c2) * 0) + ((- c3) * 0)) - ((- y1) * 1) is complex ext-real real Element of REAL
- ((- y1) * 1) is complex ext-real real set
(((- c2) * 0) + ((- c3) * 0)) + (- ((- y1) * 1)) is complex ext-real real set
((((- c2) * 0) + ((- c3) * 0)) - ((- y1) * 1)) - ((- w1) * 0) is complex ext-real real Element of REAL
- ((- w1) * 0) is complex ext-real real set
((((- c2) * 0) + ((- c3) * 0)) - ((- y1) * 1)) + (- ((- w1) * 0)) is complex ext-real real set
(((((- c2) * 0) + ((- c3) * 0)) - ((- y1) * 1)) - ((- w1) * 0)) / (((- c1)) ^2) is complex ext-real real Element of REAL
(((((- c2) * 0) + ((- c3) * 0)) - ((- y1) * 1)) - ((- w1) * 0)) * ((((- c1)) ^2) ") is complex ext-real real set
((- c2) * 0) - ((- c3) * 0) is complex ext-real real Element of REAL
- ((- c3) * 0) is complex ext-real real set
((- c2) * 0) + (- ((- c3) * 0)) is complex ext-real real set
(((- c2) * 0) - ((- c3) * 0)) + ((- y1) * 0) is complex ext-real real Element of REAL
(- w1) * 1 is complex ext-real real Element of REAL
((((- c2) * 0) - ((- c3) * 0)) + ((- y1) * 0)) - ((- w1) * 1) is complex ext-real real Element of REAL
- ((- w1) * 1) is complex ext-real real set
((((- c2) * 0) - ((- c3) * 0)) + ((- y1) * 0)) + (- ((- w1) * 1)) is complex ext-real real set
(((((- c2) * 0) - ((- c3) * 0)) + ((- y1) * 0)) - ((- w1) * 1)) / (((- c1)) ^2) is complex ext-real real Element of REAL
(((((- c2) * 0) - ((- c3) * 0)) + ((- y1) * 0)) - ((- w1) * 1)) * ((((- c1)) ^2) ") is complex ext-real real set
[*((((((- c2) * 1) + ((- c3) * 0)) + ((- y1) * 0)) + ((- w1) * 0)) / (((- c1)) ^2)),((((((- c2) * 0) - ((- c3) * 1)) - ((- y1) * 0)) + ((- w1) * 0)) / (((- c1)) ^2)),((((((- c2) * 0) + ((- c3) * 0)) - ((- y1) * 1)) - ((- w1) * 0)) / (((- c1)) ^2)),((((((- c2) * 0) - ((- c3) * 0)) + ((- y1) * 0)) - ((- w1) * 1)) / (((- c1)) ^2))*] is quaternion Element of QUATERNION
- (c2 / ((c1) ^2)) is complex ext-real real Element of REAL
[*(- (c2 / ((c1) ^2))),(c3 / ((c1) ^2)),(y1 / ((c1) ^2)),(w1 / ((c1) ^2))*] is quaternion Element of QUATERNION
(c1) + ((- c1)) is quaternion Element of QUATERNION
(c2 / ((c1) ^2)) + (- (c2 / ((c1) ^2))) is complex ext-real real Element of REAL
(- (c3 / ((c1) ^2))) + (c3 / ((c1) ^2)) is complex ext-real real Element of REAL
(- (y1 / ((c1) ^2))) + (y1 / ((c1) ^2)) is complex ext-real real Element of REAL
(- (w1 / ((c1) ^2))) + (w1 / ((c1) ^2)) is complex ext-real real Element of REAL
[*((c2 / ((c1) ^2)) + (- (c2 / ((c1) ^2)))),((- (c3 / ((c1) ^2))) + (c3 / ((c1) ^2))),((- (y1 / ((c1) ^2))) + (y1 / ((c1) ^2))),((- (w1 / ((c1) ^2))) + (w1 / ((c1) ^2)))*] is quaternion Element of QUATERNION
[*0,0*] is Element of COMPLEX
K7(QUATERNION,QUATERNION) is V16() set
K6(K7(QUATERNION,QUATERNION)) is set
K7(K7(QUATERNION,QUATERNION),QUATERNION) is V16() set
K6(K7(K7(QUATERNION,QUATERNION),QUATERNION)) is set
() is V16() Function-like V30( QUATERNION , QUATERNION ) Element of K6(K7(QUATERNION,QUATERNION))
() is V16() Function-like V30(K7(QUATERNION,QUATERNION), QUATERNION ) Element of K6(K7(K7(QUATERNION,QUATERNION),QUATERNION))
() is V16() Function-like V30(K7(QUATERNION,QUATERNION), QUATERNION ) Element of K6(K7(K7(QUATERNION,QUATERNION),QUATERNION))
() is V16() Function-like V30(K7(QUATERNION,QUATERNION), QUATERNION ) Element of K6(K7(K7(QUATERNION,QUATERNION),QUATERNION))
() is V16() Function-like V30(K7(QUATERNION,QUATERNION), QUATERNION ) Element of K6(K7(K7(QUATERNION,QUATERNION),QUATERNION))
() is V16() Function-like V30( QUATERNION , QUATERNION ) Element of K6(K7(QUATERNION,QUATERNION))
addLoopStr(# QUATERNION,(),() #) is strict addLoopStr
the carrier of addLoopStr(# QUATERNION,(),() #) is set
the addF of addLoopStr(# QUATERNION,(),() #) is V16() Function-like V30(K7( the carrier of addLoopStr(# QUATERNION,(),() #), the carrier of addLoopStr(# QUATERNION,(),() #)), the carrier of addLoopStr(# QUATERNION,(),() #)) Element of K6(K7(K7( the carrier of addLoopStr(# QUATERNION,(),() #), the carrier of addLoopStr(# QUATERNION,(),() #)), the carrier of addLoopStr(# QUATERNION,(),() #)))
K7( the carrier of addLoopStr(# QUATERNION,(),() #), the carrier of addLoopStr(# QUATERNION,(),() #)) is V16() set
K7(K7( the carrier of addLoopStr(# QUATERNION,(),() #), the carrier of addLoopStr(# QUATERNION,(),() #)), the carrier of addLoopStr(# QUATERNION,(),() #)) is V16() set
K6(K7(K7( the carrier of addLoopStr(# QUATERNION,(),() #), the carrier of addLoopStr(# QUATERNION,(),() #)), the carrier of addLoopStr(# QUATERNION,(),() #))) is set
0. addLoopStr(# QUATERNION,(),() #) is zero Element of the carrier of addLoopStr(# QUATERNION,(),() #)
the ZeroF of addLoopStr(# QUATERNION,(),() #) is Element of the carrier of addLoopStr(# QUATERNION,(),() #)
c1 is strict addLoopStr
the carrier of c1 is set
the addF of c1 is V16() Function-like V30(K7( the carrier of c1, the carrier of c1), the carrier of c1) Element of K6(K7(K7( the carrier of c1, the carrier of c1), the carrier of c1))
K7( the carrier of c1, the carrier of c1) is V16() set
K7(K7( the carrier of c1, the carrier of c1), the carrier of c1) is V16() set
K6(K7(K7( the carrier of c1, the carrier of c1), the carrier of c1)) is set
0. c1 is zero Element of the carrier of c1
the ZeroF of c1 is Element of the carrier of c1
c2 is strict addLoopStr
the carrier of c2 is set
the addF of c2 is V16() Function-like V30(K7( the carrier of c2, the carrier of c2), the carrier of c2) Element of K6(K7(K7( the carrier of c2, the carrier of c2), the carrier of c2))
K7( the carrier of c2, the carrier of c2) is V16() set
K7(K7( the carrier of c2, the carrier of c2), the carrier of c2) is V16() set
K6(K7(K7( the carrier of c2, the carrier of c2), the carrier of c2)) is set
0. c2 is zero Element of the carrier of c2
the ZeroF of c2 is Element of the carrier of c2
() is strict addLoopStr
the carrier of () is non zero set
c1 is Element of the carrier of ()
c1 is quaternion Element of the carrier of ()
c3 is quaternion set
c2 is quaternion Element of the carrier of ()
y1 is quaternion set
c1 + c2 is quaternion Element of the carrier of ()
the addF of () is V16() Function-like V30(K7( the carrier of (), the carrier of ()), the carrier of ()) Element of K6(K7(K7( the carrier of (), the carrier of ()), the carrier of ()))
K7( the carrier of (), the carrier of ()) is V16() set
K7(K7( the carrier of (), the carrier of ()), the carrier of ()) is V16() set
K6(K7(K7( the carrier of (), the carrier of ()), the carrier of ())) is set
the addF of () . (c1,c2) is quaternion Element of the carrier of ()
[c1,c2] is set
the addF of () . [c1,c2] is set
c3 + y1 is quaternion Element of QUATERNION
w1 is quaternion Element of QUATERNION
z1 is quaternion Element of QUATERNION
() . (w1,z1) is quaternion Element of QUATERNION
[w1,z1] is set
() . [w1,z1] is set
c1 + c2 is quaternion Element of QUATERNION
0. () is quaternion zero Element of the carrier of ()
the ZeroF of () is quaternion Element of the carrier of ()
c1 is quaternion Element of the carrier of ()
c2 is quaternion Element of the carrier of ()
c1 + c2 is quaternion Element of the carrier of ()
the addF of () . (c1,c2) is quaternion Element of the carrier of ()
[c1,c2] is set
the addF of () . [c1,c2] is set
c1 + c2 is quaternion Element of QUATERNION
c2 + c1 is quaternion Element of the carrier of ()
the addF of () . (c2,c1) is quaternion Element of the carrier of ()
[c2,c1] is set
the addF of () . [c2,c1] is set
c2 + c1 is quaternion Element of QUATERNION
c1 is quaternion Element of the carrier of ()
c2 is quaternion Element of the carrier of ()
c1 + c2 is quaternion Element of the carrier of ()
the addF of () . (c1,c2) is quaternion Element of the carrier of ()
[c1,c2] is set
the addF of () . [c1,c2] is set
c1 + c2 is quaternion Element of QUATERNION
c3 is quaternion Element of the carrier of ()
(c1 + c2) + c3 is quaternion Element of the carrier of ()
the addF of () . ((c1 + c2),c3) is quaternion Element of the carrier of ()
[(c1 + c2),c3] is set
the addF of () . [(c1 + c2),c3] is set
(c1 + c2) + c3 is quaternion Element of QUATERNION
c2 + c3 is quaternion Element of the carrier of ()
the addF of () . (c2,c3) is quaternion Element of the carrier of ()
[c2,c3] is set
the addF of () . [c2,c3] is set
c2 + c3 is quaternion Element of QUATERNION
c1 + (c2 + c3) is quaternion Element of the carrier of ()
the addF of () . (c1,(c2 + c3)) is quaternion Element of the carrier of ()
[c1,(c2 + c3)] is set
the addF of () . [c1,(c2 + c3)] is set
c1 + (c2 + c3) is quaternion Element of QUATERNION
c1 is quaternion Element of the carrier of ()
c1 + (0. ()) is quaternion Element of the carrier of ()
the addF of () . (c1,(0. ())) is quaternion Element of the carrier of ()
[c1,(0. ())] is set
the addF of () . [c1,(0. ())] is set
c1 + (0. ()) is quaternion Element of QUATERNION
c2 is quaternion Element of QUATERNION
the addF of () . (c2,()) is set
[c2,()] is set
the addF of () . [c2,()] is set
() . (c2,()) is quaternion Element of QUATERNION
() . [c2,()] is set
c2 + () is quaternion Element of QUATERNION
c1 is quaternion Element of the carrier of ()
c2 is quaternion Element of QUATERNION
- c2 is quaternion Element of QUATERNION
c3 is quaternion Element of the carrier of ()
c1 + c3 is quaternion Element of the carrier of ()
the addF of () . (c1,c3) is quaternion Element of the carrier of ()
[c1,c3] is set
the addF of () . [c1,c3] is set
c1 + c3 is quaternion Element of QUATERNION
c1 is quaternion Element of the carrier of ()
c2 is quaternion set
- c1 is quaternion Element of the carrier of ()
- c2 is quaternion Element of QUATERNION
c3 is quaternion Element of QUATERNION
- c3 is quaternion Element of QUATERNION
y1 is quaternion Element of the carrier of ()
y1 + c1 is quaternion Element of the carrier of ()
the addF of () . (y1,c1) is quaternion Element of the carrier of ()
[y1,c1] is set
the addF of () . [y1,c1] is set
y1 + c1 is quaternion Element of QUATERNION
- c1 is quaternion Element of QUATERNION
c1 is quaternion Element of the carrier of ()
c3 is quaternion set
c2 is quaternion Element of the carrier of ()
y1 is quaternion set
c1 - c2 is quaternion Element of the carrier of ()
- c2 is quaternion Element of the carrier of ()
- c2 is quaternion Element of QUATERNION
c1 + (- c2) is quaternion Element of the carrier of ()
the addF of () . (c1,(- c2)) is quaternion Element of the carrier of ()
[c1,(- c2)] is set
the addF of () . [c1,(- c2)] is set
c1 + (- c2) is quaternion Element of QUATERNION
c3 - y1 is quaternion Element of QUATERNION
- y1 is quaternion set
c3 + (- y1) is quaternion set
c1 - c2 is quaternion Element of QUATERNION
- c2 is quaternion set
c1 + (- c2) is quaternion set
c1 is quaternion Element of the carrier of ()
c2 is quaternion Element of the carrier of ()
c1 + c2 is quaternion Element of the carrier of ()
the addF of () . (c1,c2) is quaternion Element of the carrier of ()
[c1,c2] is set
the addF of () . [c1,c2] is set
c1 + c2 is quaternion Element of QUATERNION
c2 + c1 is quaternion Element of the carrier of ()
the addF of () . (c2,c1) is quaternion Element of the carrier of ()
[c2,c1] is set
the addF of () . [c2,c1] is set
c2 + c1 is quaternion Element of QUATERNION
c3 is quaternion Element of the carrier of ()
y1 is quaternion Element of the carrier of ()
c3 + y1 is quaternion Element of the carrier of ()
the addF of () . (c3,y1) is quaternion Element of the carrier of ()
[c3,y1] is set
the addF of () . [c3,y1] is set
c3 + y1 is quaternion Element of QUATERNION
w1 is quaternion Element of the carrier of ()
(c3 + y1) + w1 is quaternion Element of the carrier of ()
the addF of () . ((c3 + y1),w1) is quaternion Element of the carrier of ()
[(c3 + y1),w1] is set
the addF of () . [(c3 + y1),w1] is set
(c3 + y1) + w1 is quaternion Element of QUATERNION
y1 + w1 is quaternion Element of the carrier of ()
the addF of () . (y1,w1) is quaternion Element of the carrier of ()
[y1,w1] is set
the addF of () . [y1,w1] is set
y1 + w1 is quaternion Element of QUATERNION
c3 + (y1 + w1) is quaternion Element of the carrier of ()
the addF of () . (c3,(y1 + w1)) is quaternion Element of the carrier of ()
[c3,(y1 + w1)] is set
the addF of () . [c3,(y1 + w1)] is set
c3 + (y1 + w1) is quaternion Element of QUATERNION
z1 is quaternion Element of the carrier of ()
z1 + (0. ()) is quaternion Element of the carrier of ()
the addF of () . (z1,(0. ())) is quaternion Element of the carrier of ()
[z1,(0. ())] is set
the addF of () . [z1,(0. ())] is set
z1 + (0. ()) is quaternion Element of QUATERNION
doubleLoopStr(# QUATERNION,(),(),(),() #) is strict doubleLoopStr
the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #) is set
the addF of doubleLoopStr(# QUATERNION,(),(),(),() #) is V16() Function-like V30(K7( the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #), the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)), the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)) Element of K6(K7(K7( the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #), the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)), the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)))
K7( the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #), the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)) is V16() set
K7(K7( the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #), the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)), the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)) is V16() set
K6(K7(K7( the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #), the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)), the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #))) is set
the multF of doubleLoopStr(# QUATERNION,(),(),(),() #) is V16() Function-like V30(K7( the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #), the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)), the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)) Element of K6(K7(K7( the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #), the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)), the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)))
1. doubleLoopStr(# QUATERNION,(),(),(),() #) is Element of the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)
the OneF of doubleLoopStr(# QUATERNION,(),(),(),() #) is Element of the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)
0. doubleLoopStr(# QUATERNION,(),(),(),() #) is zero Element of the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)
the ZeroF of doubleLoopStr(# QUATERNION,(),(),(),() #) is Element of the carrier of doubleLoopStr(# QUATERNION,(),(),(),() #)
c1 is strict doubleLoopStr
the carrier of c1 is set
the addF of c1 is V16() Function-like V30(K7( the carrier of c1, the carrier of c1), the carrier of c1) Element of K6(K7(K7( the carrier of c1, the carrier of c1), the carrier of c1))
K7( the carrier of c1, the carrier of c1) is V16() set
K7(K7( the carrier of c1, the carrier of c1), the carrier of c1) is V16() set
K6(K7(K7( the carrier of c1, the carrier of c1), the carrier of c1)) is set
the multF of c1 is V16() Function-like V30(K7( the carrier of c1, the carrier of c1), the carrier of c1) Element of K6(K7(K7( the carrier of c1, the carrier of c1), the carrier of c1))
1. c1 is Element of the carrier of c1
the OneF of c1 is Element of the carrier of c1
0. c1 is zero Element of the carrier of c1
the ZeroF of c1 is Element of the carrier of c1
c2 is strict doubleLoopStr
the carrier of c2 is set
the addF of c2 is V16() Function-like V30(K7( the carrier of c2, the carrier of c2), the carrier of c2) Element of K6(K7(K7( the carrier of c2, the carrier of c2), the carrier of c2))
K7( the carrier of c2, the carrier of c2) is V16() set
K7(K7( the carrier of c2, the carrier of c2), the carrier of c2) is V16() set
K6(K7(K7( the carrier of c2, the carrier of c2), the carrier of c2)) is set
the multF of c2 is V16() Function-like V30(K7( the carrier of c2, the carrier of c2), the carrier of c2) Element of K6(K7(K7( the carrier of c2, the carrier of c2), the carrier of c2))
1. c2 is Element of the carrier of c2
the OneF of c2 is Element of the carrier of c2
0. c2 is zero Element of the carrier of c2
the ZeroF of c2 is Element of the carrier of c2
() is strict doubleLoopStr
the carrier of () is non zero set
c1 is Element of the carrier of ()
c3 is quaternion Element of the carrier of ()
c1 is quaternion set
y1 is quaternion Element of the carrier of ()
c2 is quaternion set
c3 + y1 is quaternion Element of the carrier of ()
the addF of () is V16() Function-like V30(K7( the carrier of (), the carrier of ()), the carrier of ()) Element of K6(K7(K7( the carrier of (), the carrier of ()), the carrier of ()))
K7( the carrier of (), the carrier of ()) is V16() set
K7(K7( the carrier of (), the carrier of ()), the carrier of ()) is V16() set
K6(K7(K7( the carrier of (), the carrier of ()), the carrier of ())) is set
the addF of () . (c3,y1) is quaternion Element of the carrier of ()
[c3,y1] is set
the addF of () . [c3,y1] is set
c1 + c2 is quaternion Element of QUATERNION
w1 is quaternion Element of QUATERNION
z1 is quaternion Element of QUATERNION
() . (w1,z1) is quaternion Element of QUATERNION
[w1,z1] is set
() . [w1,z1] is set
c3 + y1 is quaternion Element of QUATERNION
c3 * y1 is quaternion Element of the carrier of ()
the multF of () is V16() Function-like V30(K7( the carrier of (), the carrier of ()), the carrier of ()) Element of K6(K7(K7( the carrier of (), the carrier of ()), the carrier of ()))
the multF of () . (c3,y1) is quaternion Element of the carrier of ()
the multF of () . [c3,y1] is set
c1 * c2 is quaternion Element of QUATERNION
w1 is quaternion Element of QUATERNION
z1 is quaternion Element of QUATERNION
() . (w1,z1) is quaternion Element of QUATERNION
[w1,z1] is set
() . [w1,z1] is set
c3 * y1 is quaternion Element of QUATERNION
c1 is quaternion Element of the carrier of ()
1. () is quaternion Element of the carrier of ()
the OneF of () is quaternion Element of the carrier of ()
c1 * (1. ()) is quaternion Element of the carrier of ()
the multF of () . (c1,(1. ())) is quaternion Element of the carrier of ()
[c1,(1. ())] is set
the multF of () . [c1,(1. ())] is set
c1 * (1. ()) is quaternion Element of QUATERNION
(1. ()) * c1 is quaternion Element of the carrier of ()
the multF of () . ((1. ()),c1) is quaternion Element of the carrier of ()
[(1. ()),c1] is set
the multF of () . [(1. ()),c1] is set
(1. ()) * c1 is quaternion Element of QUATERNION
1. () is quaternion Element of the carrier of ()
the OneF of () is quaternion Element of the carrier of ()
1_ () is quaternion Element of the carrier of ()
0. () is quaternion zero Element of the carrier of ()
the ZeroF of () is quaternion Element of the carrier of ()
c1 is quaternion Element of the carrier of ()
c2 is quaternion Element of the carrier of ()
c1 + c2 is quaternion Element of the carrier of ()
the addF of () . (c1,c2) is quaternion Element of the carrier of ()
[c1,c2] is set
the addF of () . [c1,c2] is set
c1 + c2 is quaternion Element of QUATERNION
c3 is quaternion Element of the carrier of ()
(c1 + c2) + c3 is quaternion Element of the carrier of ()
the addF of () . ((c1 + c2),c3) is quaternion Element of the carrier of ()
[(c1 + c2),c3] is set
the addF of () . [(c1 + c2),c3] is set
(c1 + c2) + c3 is quaternion Element of QUATERNION
c2 + c3 is quaternion Element of the carrier of ()
the addF of () . (c2,c3) is quaternion Element of the carrier of ()
[c2,c3] is set
the addF of () . [c2,c3] is set
c2 + c3 is quaternion Element of QUATERNION
c1 + (c2 + c3) is quaternion Element of the carrier of ()
the addF of () . (c1,(c2 + c3)) is quaternion Element of the carrier of ()
[c1,(c2 + c3)] is set
the addF of () . [c1,(c2 + c3)] is set
c1 + (c2 + c3) is quaternion Element of QUATERNION
y1 is quaternion Element of QUATERNION
w1 is quaternion Element of QUATERNION
[y1,w1] is set
the addF of () . [y1,w1] is set
z1 is quaternion Element of QUATERNION
[( the addF of () . [y1,w1]),z1] is set
() . [( the addF of () . [y1,w1]),z1] is set
() . (y1,w1) is quaternion Element of QUATERNION
() . [y1,w1] is set
() . ((() . (y1,w1)),z1) is quaternion Element of QUATERNION
[(() . (y1,w1)),z1] is set
() . [(() . (y1,w1)),z1] is set
y1 + w1 is quaternion Element of QUATERNION
() . ((y1 + w1),z1) is quaternion Element of QUATERNION
[(y1 + w1),z1] is set
() . [(y1 + w1),z1] is set
(y1 + w1) + z1 is quaternion Element of QUATERNION
w1 + z1 is quaternion Element of QUATERNION
y1 + (w1 + z1) is quaternion Element of QUATERNION
() . (y1,(w1 + z1)) is quaternion Element of QUATERNION
[y1,(w1 + z1)] is set
() . [y1,(w1 + z1)] is set
() . (w1,z1) is quaternion Element of QUATERNION
[w1,z1] is set
() . [w1,z1] is set
[y1,(() . (w1,z1))] is set
() . [y1,(() . (w1,z1))] is set
the addF of () . [w1,z1] is set
[y1,( the addF of () . [w1,z1])] is set
() . [y1,( the addF of () . [w1,z1])] is set
c1 is quaternion Element of the carrier of ()
c1 + (0. ()) is quaternion Element of the carrier of ()
the addF of () . (c1,(0. ())) is quaternion Element of the carrier of ()
[c1,(0. ())] is set
the addF of () . [c1,(0. ())] is set
c1 + (0. ()) is quaternion Element of QUATERNION
c2 is quaternion Element of QUATERNION
the addF of () . (c2,()) is set
[c2,()] is set
the addF of () . [c2,()] is set
() . (c2,()) is quaternion Element of QUATERNION
() . [c2,()] is set
c2 + () is quaternion Element of QUATERNION
c1 is quaternion Element of the carrier of ()
c2 is quaternion Element of QUATERNION
- c2 is quaternion Element of QUATERNION
c3 is quaternion Element of the carrier of ()
c1 + c3 is quaternion Element of the carrier of ()
the addF of () . (c1,c3) is quaternion Element of the carrier of ()
[c1,c3] is set
the addF of () . [c1,c3] is set
c1 + c3 is quaternion Element of QUATERNION
c1 is quaternion Element of the carrier of ()
c2 is quaternion Element of the carrier of ()
c1 + c2 is quaternion Element of the carrier of ()
the addF of () . (c1,c2) is quaternion Element of the carrier of ()
[c1,c2] is set
the addF of () . [c1,c2] is set
c1 + c2 is quaternion Element of QUATERNION
c2 + c1 is quaternion Element of the carrier of ()
the addF of () . (c2,c1) is quaternion Element of the carrier of ()
[c2,c1] is set
the addF of () . [c2,c1] is set
c2 + c1 is quaternion Element of QUATERNION
c1 is quaternion Element of the carrier of ()
c2 is quaternion Element of the carrier of ()
c1 * c2 is quaternion Element of the carrier of ()
the multF of () . (c1,c2) is quaternion Element of the carrier of ()
[c1,c2] is set
the multF of () . [c1,c2] is set
c1 * c2 is quaternion Element of QUATERNION
c3 is quaternion Element of the carrier of ()
(c1 * c2) * c3 is quaternion Element of the carrier of ()
the multF of () . ((c1 * c2),c3) is quaternion Element of the carrier of ()
[(c1 * c2),c3] is set
the multF of () . [(c1 * c2),c3] is set
(c1 * c2) * c3 is quaternion Element of QUATERNION
c2 * c3 is quaternion Element of the carrier of ()
the multF of () . (c2,c3) is quaternion Element of the carrier of ()
[c2,c3] is set
the multF of () . [c2,c3] is set
c2 * c3 is quaternion Element of QUATERNION
c1 * (c2 * c3) is quaternion Element of the carrier of ()
the multF of () . (c1,(c2 * c3)) is quaternion Element of the carrier of ()
[c1,(c2 * c3)] is set
the multF of () . [c1,(c2 * c3)] is set
c1 * (c2 * c3) is quaternion Element of QUATERNION
y1 is quaternion Element of QUATERNION
w1 is quaternion Element of QUATERNION
the multF of () . (y1,w1) is set
[y1,w1] is set
the multF of () . [y1,w1] is set
z1 is quaternion Element of QUATERNION
() . (( the multF of () . (y1,w1)),z1) is set
[( the multF of () . (y1,w1)),z1] is set
() . [( the multF of () . (y1,w1)),z1] is set
() . (y1,w1) is quaternion Element of QUATERNION
() . [y1,w1] is set
() . ((() . (y1,w1)),z1) is quaternion Element of QUATERNION
[(() . (y1,w1)),z1] is set
() . [(() . (y1,w1)),z1] is set
y1 * w1 is quaternion Element of QUATERNION
() . ((y1 * w1),z1) is quaternion Element of QUATERNION
[(y1 * w1),z1] is set
() . [(y1 * w1),z1] is set
(y1 * w1) * z1 is quaternion Element of QUATERNION
w1 * z1 is quaternion Element of QUATERNION
y1 * (w1 * z1) is quaternion Element of QUATERNION
() . (y1,(w1 * z1)) is quaternion Element of QUATERNION
[y1,(w1 * z1)] is set
() . [y1,(w1 * z1)] is set
() . (w1,z1) is quaternion Element of QUATERNION
[w1,z1] is set
() . [w1,z1] is set
() . (y1,(() . (w1,z1))) is quaternion Element of QUATERNION
[y1,(() . (w1,z1))] is set
() . [y1,(() . (w1,z1))] is set
the multF of () . (w1,z1) is set
the multF of () . [w1,z1] is set
() . (y1,( the multF of () . (w1,z1))) is set
[y1,( the multF of () . (w1,z1))] is set
() . [y1,( the multF of () . (w1,z1))] is set
c1 is quaternion Element of the carrier of ()
c2 is quaternion Element of the carrier of ()
c3 is quaternion Element of the carrier of ()
c2 + c3 is quaternion Element of the carrier of ()
the addF of () . (c2,c3) is quaternion Element of the carrier of ()
[c2,c3] is set
the addF of () . [c2,c3] is set
c2 + c3 is quaternion Element of QUATERNION
c1 * (c2 + c3) is quaternion Element of the carrier of ()
the multF of () . (c1,(c2 + c3)) is quaternion Element of the carrier of ()
[c1,(c2 + c3)] is set
the multF of () . [c1,(c2 + c3)] is set
c1 * (c2 + c3) is quaternion Element of QUATERNION
c1 * c2 is quaternion Element of the carrier of ()
the multF of () . (c1,c2) is quaternion Element of the carrier of ()
[c1,c2] is set
the multF of () . [c1,c2] is set
c1 * c2 is quaternion Element of QUATERNION
c1 * c3 is quaternion Element of the carrier of ()
the multF of () . (c1,c3) is quaternion Element of the carrier of ()
[c1,c3] is set
the multF of () . [c1,c3] is set
c1 * c3 is quaternion Element of QUATERNION
(c1 * c2) + (c1 * c3) is quaternion Element of the carrier of ()
the addF of () . ((c1 * c2),(c1 * c3)) is quaternion Element of the carrier of ()
[(c1 * c2),(c1 * c3)] is set
the addF of () . [(c1 * c2),(c1 * c3)] is set
(c1 * c2) + (c1 * c3) is quaternion Element of QUATERNION
(c2 + c3) * c1 is quaternion Element of the carrier of ()
the multF of () . ((c2 + c3),c1) is quaternion Element of the carrier of ()
[(c2 + c3),c1] is set
the multF of () . [(c2 + c3),c1] is set
(c2 + c3) * c1 is quaternion Element of QUATERNION
c2 * c1 is quaternion Element of the carrier of ()
the multF of () . (c2,c1) is quaternion Element of the carrier of ()
[c2,c1] is set
the multF of () . [c2,c1] is set
c2 * c1 is quaternion Element of QUATERNION
c3 * c1 is quaternion Element of the carrier of ()
the multF of () . (c3,c1) is quaternion Element of the carrier of ()
[c3,c1] is set
the multF of () . [c3,c1] is set
c3 * c1 is quaternion Element of QUATERNION
(c2 * c1) + (c3 * c1) is quaternion Element of the carrier of ()
the addF of () . ((c2 * c1),(c3 * c1)) is quaternion Element of the carrier of ()
[(c2 * c1),(c3 * c1)] is set
the addF of () . [(c2 * c1),(c3 * c1)] is set
(c2 * c1) + (c3 * c1) is quaternion Element of QUATERNION
y1 is quaternion Element of QUATERNION
w1 is quaternion Element of QUATERNION
z1 is quaternion Element of QUATERNION
the addF of () . (w1,z1) is set
[w1,z1] is set
the addF of () . [w1,z1] is set
() . (y1,( the addF of () . (w1,z1))) is set
[y1,( the addF of () . (w1,z1))] is set
() . [y1,( the addF of () . (w1,z1))] is set
() . (w1,z1) is quaternion Element of QUATERNION
() . [w1,z1] is set
() . (y1,(() . (w1,z1))) is quaternion Element of QUATERNION
[y1,(() . (w1,z1))] is set
() . [y1,(() . (w1,z1))] is set
w1 + z1 is quaternion Element of QUATERNION
() . (y1,(w1 + z1)) is quaternion Element of QUATERNION
[y1,(w1 + z1)] is set
() . [y1,(w1 + z1)] is set
y1 * (w1 + z1) is quaternion Element of QUATERNION
y1 * w1 is quaternion Element of QUATERNION
y1 * z1 is quaternion Element of QUATERNION
(y1 * w1) + (y1 * z1) is quaternion Element of QUATERNION
() . ((y1 * w1),(y1 * z1)) is quaternion Element of QUATERNION
[(y1 * w1),(y1 * z1)] is set
() . [(y1 * w1),(y1 * z1)] is set
() . (y1,w1) is quaternion Element of QUATERNION
[y1,w1] is set
() . [y1,w1] is set
() . ((() . (y1,w1)),(y1 * z1)) is quaternion Element of QUATERNION
[(() . (y1,w1)),(y1 * z1)] is set
() . [(() . (y1,w1)),(y1 * z1)] is set
() . (y1,z1) is quaternion Element of QUATERNION
[y1,z1] is set
() . [y1,z1] is set
() . ((() . (y1,w1)),(() . (y1,z1))) is quaternion Element of QUATERNION
[(() . (y1,w1)),(() . (y1,z1))] is set
() . [(() . (y1,w1)),(() . (y1,z1))] is set
the addF of () . ((() . (y1,w1)),(() . (y1,z1))) is set
the addF of () . [(() . (y1,w1)),(() . (y1,z1))] is set
the multF of () . (y1,w1) is set
the multF of () . [y1,w1] is set
the addF of () . (( the multF of () . (y1,w1)),(() . (y1,z1))) is set
[( the multF of () . (y1,w1)),(() . (y1,z1))] is set
the addF of () . [( the multF of () . (y1,w1)),(() . (y1,z1))] is set
() . (( the addF of () . (w1,z1)),y1) is set
[( the addF of () . (w1,z1)),y1] is set
() . [( the addF of () . (w1,z1)),y1] is set
() . ((() . (w1,z1)),y1) is quaternion Element of QUATERNION
[(() . (w1,z1)),y1] is set
() . [(() . (w1,z1)),y1] is set
() . ((w1 + z1),y1) is quaternion Element of QUATERNION
[(w1 + z1),y1] is set
() . [(w1 + z1),y1] is set
(w1 + z1) * y1 is quaternion Element of QUATERNION
w1 * y1 is quaternion Element of QUATERNION
z1 * y1 is quaternion Element of QUATERNION
(w1 * y1) + (z1 * y1) is quaternion Element of QUATERNION
() . ((w1 * y1),(z1 * y1)) is quaternion Element of QUATERNION
[(w1 * y1),(z1 * y1)] is set
() . [(w1 * y1),(z1 * y1)] is set
() . (w1,y1) is quaternion Element of QUATERNION
[w1,y1] is set
() . [w1,y1] is set
() . ((() . (w1,y1)),(z1 * y1)) is quaternion Element of QUATERNION
[(() . (w1,y1)),(z1 * y1)] is set
() . [(() . (w1,y1)),(z1 * y1)] is set
() . (z1,y1) is quaternion Element of QUATERNION
[z1,y1] is set
() . [z1,y1] is set
() . ((() . (w1,y1)),(() . (z1,y1))) is quaternion Element of QUATERNION
[(() . (w1,y1)),(() . (z1,y1))] is set
() . [(() . (w1,y1)),(() . (z1,y1))] is set
the addF of () . ((() . (w1,y1)),(() . (z1,y1))) is set
the addF of () . [(() . (w1,y1)),(() . (z1,y1))] is set
the multF of () . (w1,y1) is set
the multF of () . [w1,y1] is set
the addF of () . (( the multF of () . (w1,y1)),(() . (z1,y1))) is set
[( the multF of () . (w1,y1)),(() . (z1,y1))] is set
the addF of () . [( the multF of () . (w1,y1)),(() . (z1,y1))] is set
c1 is quaternion Element of the carrier of ()
c2 is quaternion Element of QUATERNION
(c2) is quaternion Element of QUATERNION
((),c2) is quaternion Element of QUATERNION
c3 is quaternion Element of the carrier of ()
c1 * c3 is quaternion Element of the carrier of ()
the multF of () . (c1,c3) is quaternion Element of the carrier of ()
[c1,c3] is set
the multF of () . [c1,c3] is set
c1 * c3 is quaternion Element of QUATERNION
c1 is quaternion Element of the carrier of ()
c2 is quaternion set
- c1 is quaternion Element of the carrier of ()
- c2 is quaternion Element of QUATERNION
c3 is quaternion Element of QUATERNION
- c3 is quaternion Element of QUATERNION
y1 is quaternion Element of the carrier of ()
y1 + c1 is quaternion Element of the carrier of ()
the addF of () . (y1,c1) is quaternion Element of the carrier of ()
[y1,c1] is set
the addF of () . [y1,c1] is set
y1 + c1 is quaternion Element of QUATERNION
- c1 is quaternion Element of QUATERNION
c1 is quaternion Element of the carrier of ()
c3 is quaternion set
c2 is quaternion Element of the carrier of ()
y1 is quaternion set
c1 - c2 is quaternion Element of the carrier of ()
- c2 is quaternion Element of the carrier of ()
- c2 is quaternion Element of QUATERNION
c1 + (- c2) is quaternion Element of the carrier of ()
the addF of () . (c1,(- c2)) is quaternion Element of the carrier of ()
[c1,(- c2)] is set
the addF of () . [c1,(- c2)] is set
c1 + (- c2) is quaternion Element of QUATERNION
c3 - y1 is quaternion Element of QUATERNION
- y1 is quaternion set
c3 + (- y1) is quaternion set
c1 - c2 is quaternion Element of QUATERNION
- c2 is quaternion set
c1 + (- c2) is quaternion set
c1 is quaternion Element of the carrier of ()
c1 *' is quaternion set
Rea c1 is complex ext-real real Element of REAL
Im1 c1 is complex ext-real real Element of REAL
- (Im1 c1) is complex ext-real real Element of REAL
(- (Im1 c1)) * <i> is quaternion set
(Rea c1) + ((- (Im1 c1)) * <i>) is quaternion set
Im2 c1 is complex ext-real real Element of REAL
- (Im2 c1) is complex ext-real real Element of REAL
(- (Im2 c1)) * <j> is quaternion set
((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>) is quaternion Element of QUATERNION
Im3 c1 is complex ext-real real Element of REAL
- (Im3 c1) is complex ext-real real Element of REAL
(- (Im3 c1)) * <k> is quaternion set
(((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>)) + ((- (Im3 c1)) * <k>) is quaternion Element of QUATERNION
- (1_ ()) is quaternion Element of the carrier of ()
- (1_ ()) is quaternion Element of QUATERNION
c1 is quaternion Element of the carrier of ()
- c1 is quaternion Element of the carrier of ()
- c1 is quaternion Element of QUATERNION
(- (1_ ())) * c1 is quaternion Element of the carrier of ()
the multF of () . ((- (1_ ())),c1) is quaternion Element of the carrier of ()
[(- (1_ ())),c1] is set
the multF of () . [(- (1_ ())),c1] is set
(- (1_ ())) * c1 is quaternion Element of QUATERNION
c2 is quaternion Element of QUATERNION
(- ()) * c2 is quaternion Element of QUATERNION
((0. ())) is quaternion Element of the carrier of ()
Rea (0. ()) is complex ext-real real Element of REAL
Im1 (0. ()) is complex ext-real real Element of REAL
- (Im1 (0. ())) is complex ext-real real Element of REAL
(- (Im1 (0. ()))) * <i> is quaternion set
(Rea (0. ())) + ((- (Im1 (0. ()))) * <i>) is quaternion set
Im2 (0. ()) is complex ext-real real Element of REAL
- (Im2 (0. ())) is complex ext-real real Element of REAL
(- (Im2 (0. ()))) * <j> is quaternion set
((Rea (0. ())) + ((- (Im1 (0. ()))) * <i>)) + ((- (Im2 (0. ()))) * <j>) is quaternion Element of QUATERNION
Im3 (0. ()) is complex ext-real real Element of REAL
- (Im3 (0. ())) is complex ext-real real Element of REAL
(- (Im3 (0. ()))) * <k> is quaternion set
(((Rea (0. ())) + ((- (Im1 (0. ()))) * <i>)) + ((- (Im2 (0. ()))) * <j>)) + ((- (Im3 (0. ()))) * <k>) is quaternion Element of QUATERNION
c1 is quaternion Element of the carrier of ()
(c1) is quaternion Element of the carrier of ()
Rea c1 is complex ext-real real Element of REAL
Im1 c1 is complex ext-real real Element of REAL
- (Im1 c1) is complex ext-real real Element of REAL
(- (Im1 c1)) * <i> is quaternion set
(Rea c1) + ((- (Im1 c1)) * <i>) is quaternion set
Im2 c1 is complex ext-real real Element of REAL
- (Im2 c1) is complex ext-real real Element of REAL
(- (Im2 c1)) * <j> is quaternion set
((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>) is quaternion Element of QUATERNION
Im3 c1 is complex ext-real real Element of REAL
- (Im3 c1) is complex ext-real real Element of REAL
(- (Im3 c1)) * <k> is quaternion set
(((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>)) + ((- (Im3 c1)) * <k>) is quaternion Element of QUATERNION
((1. ())) is quaternion Element of the carrier of ()
Rea (1. ()) is complex ext-real real Element of REAL
Im1 (1. ()) is complex ext-real real Element of REAL
- (Im1 (1. ())) is complex ext-real real Element of REAL
(- (Im1 (1. ()))) * <i> is quaternion set
(Rea (1. ())) + ((- (Im1 (1. ()))) * <i>) is quaternion set
Im2 (1. ()) is complex ext-real real Element of REAL
- (Im2 (1. ())) is complex ext-real real Element of REAL
(- (Im2 (1. ()))) * <j> is quaternion set
((Rea (1. ())) + ((- (Im1 (1. ()))) * <i>)) + ((- (Im2 (1. ()))) * <j>) is quaternion Element of QUATERNION
Im3 (1. ()) is complex ext-real real Element of REAL
- (Im3 (1. ())) is complex ext-real real Element of REAL
(- (Im3 (1. ()))) * <k> is quaternion set
(((Rea (1. ())) + ((- (Im1 (1. ()))) * <i>)) + ((- (Im2 (1. ()))) * <j>)) + ((- (Im3 (1. ()))) * <k>) is quaternion Element of QUATERNION
1r is Element of COMPLEX
((0. ())) is complex ext-real real Element of REAL
(Rea (0. ())) ^2 is complex ext-real real Element of REAL
(Rea (0. ())) * (Rea (0. ())) is complex ext-real real set
(Im1 (0. ())) ^2 is complex ext-real real Element of REAL
(Im1 (0. ())) * (Im1 (0. ())) is complex ext-real real set
((Rea (0. ())) ^2) + ((Im1 (0. ())) ^2) is complex ext-real real Element of REAL
(Im2 (0. ())) ^2 is complex ext-real real Element of REAL
(Im2 (0. ())) * (Im2 (0. ())) is complex ext-real real set
(((Rea (0. ())) ^2) + ((Im1 (0. ())) ^2)) + ((Im2 (0. ())) ^2) is complex ext-real real Element of REAL
(Im3 (0. ())) ^2 is complex ext-real real Element of REAL
(Im3 (0. ())) * (Im3 (0. ())) is complex ext-real real set
((((Rea (0. ())) ^2) + ((Im1 (0. ())) ^2)) + ((Im2 (0. ())) ^2)) + ((Im3 (0. ())) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea (0. ())) ^2) + ((Im1 (0. ())) ^2)) + ((Im2 (0. ())) ^2)) + ((Im3 (0. ())) ^2)) is complex ext-real real Element of REAL
c1 is quaternion Element of the carrier of ()
(c1) is complex ext-real real Element of REAL
Rea c1 is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
Im1 c1 is complex ext-real real Element of REAL
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
((1. ())) is complex ext-real real Element of REAL
(Rea (1. ())) ^2 is complex ext-real real Element of REAL
(Rea (1. ())) * (Rea (1. ())) is complex ext-real real set
(Im1 (1. ())) ^2 is complex ext-real real Element of REAL
(Im1 (1. ())) * (Im1 (1. ())) is complex ext-real real set
((Rea (1. ())) ^2) + ((Im1 (1. ())) ^2) is complex ext-real real Element of REAL
(Im2 (1. ())) ^2 is complex ext-real real Element of REAL
(Im2 (1. ())) * (Im2 (1. ())) is complex ext-real real set
(((Rea (1. ())) ^2) + ((Im1 (1. ())) ^2)) + ((Im2 (1. ())) ^2) is complex ext-real real Element of REAL
(Im3 (1. ())) ^2 is complex ext-real real Element of REAL
(Im3 (1. ())) * (Im3 (1. ())) is complex ext-real real set
((((Rea (1. ())) ^2) + ((Im1 (1. ())) ^2)) + ((Im2 (1. ())) ^2)) + ((Im3 (1. ())) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea (1. ())) ^2) + ((Im1 (1. ())) ^2)) + ((Im2 (1. ())) ^2)) + ((Im3 (1. ())) ^2)) is complex ext-real real Element of REAL
((1. ())) is quaternion Element of QUATERNION
((),(1. ())) is quaternion Element of QUATERNION
(()) is quaternion Element of QUATERNION
((),()) is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
c2 *' is quaternion Element of QUATERNION
Rea c2 is complex ext-real real Element of REAL
Im1 c2 is complex ext-real real Element of REAL
- (Im1 c2) is complex ext-real real Element of REAL
(- (Im1 c2)) * <i> is quaternion set
(Rea c2) + ((- (Im1 c2)) * <i>) is quaternion set
Im2 c2 is complex ext-real real Element of REAL
- (Im2 c2) is complex ext-real real Element of REAL
(- (Im2 c2)) * <j> is quaternion set
((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>) is quaternion Element of QUATERNION
Im3 c2 is complex ext-real real Element of REAL
- (Im3 c2) is complex ext-real real Element of REAL
(- (Im3 c2)) * <k> is quaternion set
(((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>)) + ((- (Im3 c2)) * <k>) is quaternion Element of QUATERNION
c1 * (c2 *') is quaternion Element of QUATERNION
c1 is quaternion set
Rea c1 is complex ext-real real Element of REAL
Im1 c1 is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
c2 is quaternion set
(c1,c2) is quaternion Element of QUATERNION
c2 *' is quaternion Element of QUATERNION
Rea c2 is complex ext-real real Element of REAL
Im1 c2 is complex ext-real real Element of REAL
- (Im1 c2) is complex ext-real real Element of REAL
(- (Im1 c2)) * <i> is quaternion set
(Rea c2) + ((- (Im1 c2)) * <i>) is quaternion set
Im2 c2 is complex ext-real real Element of REAL
- (Im2 c2) is complex ext-real real Element of REAL
(- (Im2 c2)) * <j> is quaternion set
((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>) is quaternion Element of QUATERNION
Im3 c2 is complex ext-real real Element of REAL
- (Im3 c2) is complex ext-real real Element of REAL
(- (Im3 c2)) * <k> is quaternion set
(((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>)) + ((- (Im3 c2)) * <k>) is quaternion Element of QUATERNION
c1 * (c2 *') is quaternion Element of QUATERNION
(Rea c1) * (Rea c2) is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c2) is complex ext-real real Element of REAL
((Rea c1) * (Rea c2)) + ((Im1 c1) * (Im1 c2)) is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c2) is complex ext-real real Element of REAL
(((Rea c1) * (Rea c2)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c1) * (Im2 c2)) is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c2) is complex ext-real real Element of REAL
((((Rea c1) * (Rea c2)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c1) * (Im2 c2))) + ((Im3 c1) * (Im3 c2)) is complex ext-real real Element of REAL
(Rea c1) * (- (Im1 c2)) is complex ext-real real Element of REAL
(Im1 c1) * (Rea c2) is complex ext-real real Element of REAL
((Rea c1) * (- (Im1 c2))) + ((Im1 c1) * (Rea c2)) is complex ext-real real Element of REAL
(Im2 c1) * (Im3 c2) is complex ext-real real Element of REAL
(((Rea c1) * (- (Im1 c2))) + ((Im1 c1) * (Rea c2))) - ((Im2 c1) * (Im3 c2)) is complex ext-real real Element of REAL
- ((Im2 c1) * (Im3 c2)) is complex ext-real real set
(((Rea c1) * (- (Im1 c2))) + ((Im1 c1) * (Rea c2))) + (- ((Im2 c1) * (Im3 c2))) is complex ext-real real set
(Im3 c1) * (Im2 c2) is complex ext-real real Element of REAL
((((Rea c1) * (- (Im1 c2))) + ((Im1 c1) * (Rea c2))) - ((Im2 c1) * (Im3 c2))) + ((Im3 c1) * (Im2 c2)) is complex ext-real real Element of REAL
(Rea c1) * (- (Im2 c2)) is complex ext-real real Element of REAL
(Rea c2) * (Im2 c1) is complex ext-real real Element of REAL
((Rea c1) * (- (Im2 c2))) + ((Rea c2) * (Im2 c1)) is complex ext-real real Element of REAL
(Im1 c2) * (Im3 c1) is complex ext-real real Element of REAL
(((Rea c1) * (- (Im2 c2))) + ((Rea c2) * (Im2 c1))) - ((Im1 c2) * (Im3 c1)) is complex ext-real real Element of REAL
- ((Im1 c2) * (Im3 c1)) is complex ext-real real set
(((Rea c1) * (- (Im2 c2))) + ((Rea c2) * (Im2 c1))) + (- ((Im1 c2) * (Im3 c1))) is complex ext-real real set
(Im3 c2) * (Im1 c1) is complex ext-real real Element of REAL
((((Rea c1) * (- (Im2 c2))) + ((Rea c2) * (Im2 c1))) - ((Im1 c2) * (Im3 c1))) + ((Im3 c2) * (Im1 c1)) is complex ext-real real Element of REAL
(Rea c1) * (- (Im3 c2)) is complex ext-real real Element of REAL
(Im3 c1) * (Rea c2) is complex ext-real real Element of REAL
((Rea c1) * (- (Im3 c2))) + ((Im3 c1) * (Rea c2)) is complex ext-real real Element of REAL
(Im1 c1) * (Im2 c2) is complex ext-real real Element of REAL
(((Rea c1) * (- (Im3 c2))) + ((Im3 c1) * (Rea c2))) - ((Im1 c1) * (Im2 c2)) is complex ext-real real Element of REAL
- ((Im1 c1) * (Im2 c2)) is complex ext-real real set
(((Rea c1) * (- (Im3 c2))) + ((Im3 c1) * (Rea c2))) + (- ((Im1 c1) * (Im2 c2))) is complex ext-real real set
(Im2 c1) * (Im1 c2) is complex ext-real real Element of REAL
((((Rea c1) * (- (Im3 c2))) + ((Im3 c1) * (Rea c2))) - ((Im1 c1) * (Im2 c2))) + ((Im2 c1) * (Im1 c2)) is complex ext-real real Element of REAL
[*(((((Rea c1) * (Rea c2)) + ((Im1 c1) * (Im1 c2))) + ((Im2 c1) * (Im2 c2))) + ((Im3 c1) * (Im3 c2))),(((((Rea c1) * (- (Im1 c2))) + ((Im1 c1) * (Rea c2))) - ((Im2 c1) * (Im3 c2))) + ((Im3 c1) * (Im2 c2))),(((((Rea c1) * (- (Im2 c2))) + ((Rea c2) * (Im2 c1))) - ((Im1 c2) * (Im3 c1))) + ((Im3 c2) * (Im1 c1))),(((((Rea c1) * (- (Im3 c2))) + ((Im3 c1) * (Rea c2))) - ((Im1 c1) * (Im2 c2))) + ((Im2 c1) * (Im1 c2)))*] is quaternion Element of QUATERNION
c3 is complex ext-real real Element of REAL
y1 is complex ext-real real Element of REAL
w1 is complex ext-real real Element of REAL
z1 is complex ext-real real Element of REAL
[*c3,y1,w1,z1*] is quaternion Element of QUATERNION
x2 is complex ext-real real Element of REAL
y2 is complex ext-real real Element of REAL
w2 is complex ext-real real Element of REAL
z2 is complex ext-real real Element of REAL
[*x2,y2,w2,z2*] is quaternion Element of QUATERNION
- y2 is complex ext-real real Element of REAL
- w2 is complex ext-real real Element of REAL
- z2 is complex ext-real real Element of REAL
[*x2,(- y2),(- w2),(- z2)*] is quaternion Element of QUATERNION
[*c3,y1,w1,z1*] * [*x2,(- y2),(- w2),(- z2)*] is quaternion Element of QUATERNION
c3 * x2 is complex ext-real real Element of REAL
y1 * (- y2) is complex ext-real real Element of REAL
(c3 * x2) - (y1 * (- y2)) is complex ext-real real Element of REAL
- (y1 * (- y2)) is complex ext-real real set
(c3 * x2) + (- (y1 * (- y2))) is complex ext-real real set
w1 * (- w2) is complex ext-real real Element of REAL
((c3 * x2) - (y1 * (- y2))) - (w1 * (- w2)) is complex ext-real real Element of REAL
- (w1 * (- w2)) is complex ext-real real set
((c3 * x2) - (y1 * (- y2))) + (- (w1 * (- w2))) is complex ext-real real set
z1 * (- z2) is complex ext-real real Element of REAL
(((c3 * x2) - (y1 * (- y2))) - (w1 * (- w2))) - (z1 * (- z2)) is complex ext-real real Element of REAL
- (z1 * (- z2)) is complex ext-real real set
(((c3 * x2) - (y1 * (- y2))) - (w1 * (- w2))) + (- (z1 * (- z2))) is complex ext-real real set
c3 * (- y2) is complex ext-real real Element of REAL
y1 * x2 is complex ext-real real Element of REAL
(c3 * (- y2)) + (y1 * x2) is complex ext-real real Element of REAL
w1 * (- z2) is complex ext-real real Element of REAL
((c3 * (- y2)) + (y1 * x2)) + (w1 * (- z2)) is complex ext-real real Element of REAL
z1 * (- w2) is complex ext-real real Element of REAL
(((c3 * (- y2)) + (y1 * x2)) + (w1 * (- z2))) - (z1 * (- w2)) is complex ext-real real Element of REAL
- (z1 * (- w2)) is complex ext-real real set
(((c3 * (- y2)) + (y1 * x2)) + (w1 * (- z2))) + (- (z1 * (- w2))) is complex ext-real real set
c3 * (- w2) is complex ext-real real Element of REAL
x2 * w1 is complex ext-real real Element of REAL
(c3 * (- w2)) + (x2 * w1) is complex ext-real real Element of REAL
(- y2) * z1 is complex ext-real real Element of REAL
((c3 * (- w2)) + (x2 * w1)) + ((- y2) * z1) is complex ext-real real Element of REAL
(- z2) * y1 is complex ext-real real Element of REAL
(((c3 * (- w2)) + (x2 * w1)) + ((- y2) * z1)) - ((- z2) * y1) is complex ext-real real Element of REAL
- ((- z2) * y1) is complex ext-real real set
(((c3 * (- w2)) + (x2 * w1)) + ((- y2) * z1)) + (- ((- z2) * y1)) is complex ext-real real set
c3 * (- z2) is complex ext-real real Element of REAL
z1 * x2 is complex ext-real real Element of REAL
(c3 * (- z2)) + (z1 * x2) is complex ext-real real Element of REAL
y1 * (- w2) is complex ext-real real Element of REAL
((c3 * (- z2)) + (z1 * x2)) + (y1 * (- w2)) is complex ext-real real Element of REAL
w1 * (- y2) is complex ext-real real Element of REAL
(((c3 * (- z2)) + (z1 * x2)) + (y1 * (- w2))) - (w1 * (- y2)) is complex ext-real real Element of REAL
- (w1 * (- y2)) is complex ext-real real set
(((c3 * (- z2)) + (z1 * x2)) + (y1 * (- w2))) + (- (w1 * (- y2))) is complex ext-real real set
[*((((c3 * x2) - (y1 * (- y2))) - (w1 * (- w2))) - (z1 * (- z2))),((((c3 * (- y2)) + (y1 * x2)) + (w1 * (- z2))) - (z1 * (- w2))),((((c3 * (- w2)) + (x2 * w1)) + ((- y2) * z1)) - ((- z2) * y1)),((((c3 * (- z2)) + (z1 * x2)) + (y1 * (- w2))) - (w1 * (- y2)))*] is quaternion Element of QUATERNION
c1 is quaternion set
(c1,c1) is quaternion Element of QUATERNION
c1 *' is quaternion Element of QUATERNION
Rea c1 is complex ext-real real Element of REAL
Im1 c1 is complex ext-real real Element of REAL
- (Im1 c1) is complex ext-real real Element of REAL
(- (Im1 c1)) * <i> is quaternion set
(Rea c1) + ((- (Im1 c1)) * <i>) is quaternion set
Im2 c1 is complex ext-real real Element of REAL
- (Im2 c1) is complex ext-real real Element of REAL
(- (Im2 c1)) * <j> is quaternion set
((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>) is quaternion Element of QUATERNION
Im3 c1 is complex ext-real real Element of REAL
- (Im3 c1) is complex ext-real real Element of REAL
(- (Im3 c1)) * <k> is quaternion set
(((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>)) + ((- (Im3 c1)) * <k>) is quaternion Element of QUATERNION
c1 * (c1 *') is quaternion Element of QUATERNION
(c1) is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
(c1) ^2 is complex ext-real real Element of REAL
(c1) * (c1) is complex ext-real real set
(Rea c1) * (Rea c1) is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real Element of REAL
((Rea c1) * (Rea c1)) + ((Im1 c1) * (Im1 c1)) is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real Element of REAL
(((Rea c1) * (Rea c1)) + ((Im1 c1) * (Im1 c1))) + ((Im2 c1) * (Im2 c1)) is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real Element of REAL
((((Rea c1) * (Rea c1)) + ((Im1 c1) * (Im1 c1))) + ((Im2 c1) * (Im2 c1))) + ((Im3 c1) * (Im3 c1)) is complex ext-real real Element of REAL
(Rea c1) * (- (Im1 c1)) is complex ext-real real Element of REAL
(Im1 c1) * (Rea c1) is complex ext-real real Element of REAL
((Rea c1) * (- (Im1 c1))) + ((Im1 c1) * (Rea c1)) is complex ext-real real Element of REAL
(Im2 c1) * (Im3 c1) is complex ext-real real Element of REAL
(((Rea c1) * (- (Im1 c1))) + ((Im1 c1) * (Rea c1))) - ((Im2 c1) * (Im3 c1)) is complex ext-real real Element of REAL
- ((Im2 c1) * (Im3 c1)) is complex ext-real real set
(((Rea c1) * (- (Im1 c1))) + ((Im1 c1) * (Rea c1))) + (- ((Im2 c1) * (Im3 c1))) is complex ext-real real set
(Im3 c1) * (Im2 c1) is complex ext-real real Element of REAL
((((Rea c1) * (- (Im1 c1))) + ((Im1 c1) * (Rea c1))) - ((Im2 c1) * (Im3 c1))) + ((Im3 c1) * (Im2 c1)) is complex ext-real real Element of REAL
(Rea c1) * (- (Im2 c1)) is complex ext-real real Element of REAL
(Rea c1) * (Im2 c1) is complex ext-real real Element of REAL
((Rea c1) * (- (Im2 c1))) + ((Rea c1) * (Im2 c1)) is complex ext-real real Element of REAL
(Im1 c1) * (Im3 c1) is complex ext-real real Element of REAL
(((Rea c1) * (- (Im2 c1))) + ((Rea c1) * (Im2 c1))) - ((Im1 c1) * (Im3 c1)) is complex ext-real real Element of REAL
- ((Im1 c1) * (Im3 c1)) is complex ext-real real set
(((Rea c1) * (- (Im2 c1))) + ((Rea c1) * (Im2 c1))) + (- ((Im1 c1) * (Im3 c1))) is complex ext-real real set
(Im3 c1) * (Im1 c1) is complex ext-real real Element of REAL
((((Rea c1) * (- (Im2 c1))) + ((Rea c1) * (Im2 c1))) - ((Im1 c1) * (Im3 c1))) + ((Im3 c1) * (Im1 c1)) is complex ext-real real Element of REAL
(Rea c1) * (- (Im3 c1)) is complex ext-real real Element of REAL
(Im3 c1) * (Rea c1) is complex ext-real real Element of REAL
((Rea c1) * (- (Im3 c1))) + ((Im3 c1) * (Rea c1)) is complex ext-real real Element of REAL
(Im1 c1) * (Im2 c1) is complex ext-real real Element of REAL
(((Rea c1) * (- (Im3 c1))) + ((Im3 c1) * (Rea c1))) - ((Im1 c1) * (Im2 c1)) is complex ext-real real Element of REAL
- ((Im1 c1) * (Im2 c1)) is complex ext-real real set
(((Rea c1) * (- (Im3 c1))) + ((Im3 c1) * (Rea c1))) + (- ((Im1 c1) * (Im2 c1))) is complex ext-real real set
(Im2 c1) * (Im1 c1) is complex ext-real real Element of REAL
((((Rea c1) * (- (Im3 c1))) + ((Im3 c1) * (Rea c1))) - ((Im1 c1) * (Im2 c1))) + ((Im2 c1) * (Im1 c1)) is complex ext-real real Element of REAL
[*(((((Rea c1) * (Rea c1)) + ((Im1 c1) * (Im1 c1))) + ((Im2 c1) * (Im2 c1))) + ((Im3 c1) * (Im3 c1))),(((((Rea c1) * (- (Im1 c1))) + ((Im1 c1) * (Rea c1))) - ((Im2 c1) * (Im3 c1))) + ((Im3 c1) * (Im2 c1))),(((((Rea c1) * (- (Im2 c1))) + ((Rea c1) * (Im2 c1))) - ((Im1 c1) * (Im3 c1))) + ((Im3 c1) * (Im1 c1))),(((((Rea c1) * (- (Im3 c1))) + ((Im3 c1) * (Rea c1))) - ((Im1 c1) * (Im2 c1))) + ((Im2 c1) * (Im1 c1)))*] is quaternion Element of QUATERNION
[*(((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)),0*] is Element of COMPLEX
c1 is quaternion set
(c1,c1) is quaternion Element of QUATERNION
c1 *' is quaternion Element of QUATERNION
Rea c1 is complex ext-real real Element of REAL
Im1 c1 is complex ext-real real Element of REAL
- (Im1 c1) is complex ext-real real Element of REAL
(- (Im1 c1)) * <i> is quaternion set
(Rea c1) + ((- (Im1 c1)) * <i>) is quaternion set
Im2 c1 is complex ext-real real Element of REAL
- (Im2 c1) is complex ext-real real Element of REAL
(- (Im2 c1)) * <j> is quaternion set
((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>) is quaternion Element of QUATERNION
Im3 c1 is complex ext-real real Element of REAL
- (Im3 c1) is complex ext-real real Element of REAL
(- (Im3 c1)) * <k> is quaternion set
(((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>)) + ((- (Im3 c1)) * <k>) is quaternion Element of QUATERNION
c1 * (c1 *') is quaternion Element of QUATERNION
Rea (c1,c1) is complex ext-real real Element of REAL
(c1) is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
(c1) ^2 is complex ext-real real Element of REAL
(c1) * (c1) is complex ext-real real set
Im1 (c1,c1) is complex ext-real real Element of REAL
Im2 (c1,c1) is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real Element of REAL
((Rea c1) * (Rea c1)) + ((Im1 c1) * (Im1 c1)) is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real Element of REAL
(((Rea c1) * (Rea c1)) + ((Im1 c1) * (Im1 c1))) + ((Im2 c1) * (Im2 c1)) is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real Element of REAL
((((Rea c1) * (Rea c1)) + ((Im1 c1) * (Im1 c1))) + ((Im2 c1) * (Im2 c1))) + ((Im3 c1) * (Im3 c1)) is complex ext-real real Element of REAL
(Rea c1) * (- (Im1 c1)) is complex ext-real real Element of REAL
(Im1 c1) * (Rea c1) is complex ext-real real Element of REAL
((Rea c1) * (- (Im1 c1))) + ((Im1 c1) * (Rea c1)) is complex ext-real real Element of REAL
(Im2 c1) * (Im3 c1) is complex ext-real real Element of REAL
(((Rea c1) * (- (Im1 c1))) + ((Im1 c1) * (Rea c1))) - ((Im2 c1) * (Im3 c1)) is complex ext-real real Element of REAL
- ((Im2 c1) * (Im3 c1)) is complex ext-real real set
(((Rea c1) * (- (Im1 c1))) + ((Im1 c1) * (Rea c1))) + (- ((Im2 c1) * (Im3 c1))) is complex ext-real real set
(Im3 c1) * (Im2 c1) is complex ext-real real Element of REAL
((((Rea c1) * (- (Im1 c1))) + ((Im1 c1) * (Rea c1))) - ((Im2 c1) * (Im3 c1))) + ((Im3 c1) * (Im2 c1)) is complex ext-real real Element of REAL
(Rea c1) * (- (Im2 c1)) is complex ext-real real Element of REAL
(Rea c1) * (Im2 c1) is complex ext-real real Element of REAL
((Rea c1) * (- (Im2 c1))) + ((Rea c1) * (Im2 c1)) is complex ext-real real Element of REAL
(Im1 c1) * (Im3 c1) is complex ext-real real Element of REAL
(((Rea c1) * (- (Im2 c1))) + ((Rea c1) * (Im2 c1))) - ((Im1 c1) * (Im3 c1)) is complex ext-real real Element of REAL
- ((Im1 c1) * (Im3 c1)) is complex ext-real real set
(((Rea c1) * (- (Im2 c1))) + ((Rea c1) * (Im2 c1))) + (- ((Im1 c1) * (Im3 c1))) is complex ext-real real set
(Im3 c1) * (Im1 c1) is complex ext-real real Element of REAL
((((Rea c1) * (- (Im2 c1))) + ((Rea c1) * (Im2 c1))) - ((Im1 c1) * (Im3 c1))) + ((Im3 c1) * (Im1 c1)) is complex ext-real real Element of REAL
(Rea c1) * (- (Im3 c1)) is complex ext-real real Element of REAL
(Im3 c1) * (Rea c1) is complex ext-real real Element of REAL
((Rea c1) * (- (Im3 c1))) + ((Im3 c1) * (Rea c1)) is complex ext-real real Element of REAL
(Im1 c1) * (Im2 c1) is complex ext-real real Element of REAL
(((Rea c1) * (- (Im3 c1))) + ((Im3 c1) * (Rea c1))) - ((Im1 c1) * (Im2 c1)) is complex ext-real real Element of REAL
- ((Im1 c1) * (Im2 c1)) is complex ext-real real set
(((Rea c1) * (- (Im3 c1))) + ((Im3 c1) * (Rea c1))) + (- ((Im1 c1) * (Im2 c1))) is complex ext-real real set
(Im2 c1) * (Im1 c1) is complex ext-real real Element of REAL
((((Rea c1) * (- (Im3 c1))) + ((Im3 c1) * (Rea c1))) - ((Im1 c1) * (Im2 c1))) + ((Im2 c1) * (Im1 c1)) is complex ext-real real Element of REAL
[*(((((Rea c1) * (Rea c1)) + ((Im1 c1) * (Im1 c1))) + ((Im2 c1) * (Im2 c1))) + ((Im3 c1) * (Im3 c1))),(((((Rea c1) * (- (Im1 c1))) + ((Im1 c1) * (Rea c1))) - ((Im2 c1) * (Im3 c1))) + ((Im3 c1) * (Im2 c1))),(((((Rea c1) * (- (Im2 c1))) + ((Rea c1) * (Im2 c1))) - ((Im1 c1) * (Im3 c1))) + ((Im3 c1) * (Im1 c1))),(((((Rea c1) * (- (Im3 c1))) + ((Im3 c1) * (Rea c1))) - ((Im1 c1) * (Im2 c1))) + ((Im2 c1) * (Im1 c1)))*] is quaternion Element of QUATERNION
[*((c1) ^2),0,0,0*] is quaternion Element of QUATERNION
c1 is quaternion set
(c1) is complex ext-real real Element of REAL
Rea c1 is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
Im1 c1 is complex ext-real real Element of REAL
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
Im2 c1 is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
Im3 c1 is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
c2 is quaternion set
(c1,c2) is quaternion Element of QUATERNION
c2 *' is quaternion Element of QUATERNION
Rea c2 is complex ext-real real Element of REAL
Im1 c2 is complex ext-real real Element of REAL
- (Im1 c2) is complex ext-real real Element of REAL
(- (Im1 c2)) * <i> is quaternion set
(Rea c2) + ((- (Im1 c2)) * <i>) is quaternion set
Im2 c2 is complex ext-real real Element of REAL
- (Im2 c2) is complex ext-real real Element of REAL
(- (Im2 c2)) * <j> is quaternion set
((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>) is quaternion Element of QUATERNION
Im3 c2 is complex ext-real real Element of REAL
- (Im3 c2) is complex ext-real real Element of REAL
(- (Im3 c2)) * <k> is quaternion set
(((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>)) + ((- (Im3 c2)) * <k>) is quaternion Element of QUATERNION
c1 * (c2 *') is quaternion Element of QUATERNION
((c1,c2)) is complex ext-real real Element of REAL
Rea (c1,c2) is complex ext-real real Element of REAL
(Rea (c1,c2)) ^2 is complex ext-real real Element of REAL
(Rea (c1,c2)) * (Rea (c1,c2)) is complex ext-real real set
Im1 (c1,c2) is complex ext-real real Element of REAL
(Im1 (c1,c2)) ^2 is complex ext-real real Element of REAL
(Im1 (c1,c2)) * (Im1 (c1,c2)) is complex ext-real real set
((Rea (c1,c2)) ^2) + ((Im1 (c1,c2)) ^2) is complex ext-real real Element of REAL
Im2 (c1,c2) is complex ext-real real Element of REAL
(Im2 (c1,c2)) ^2 is complex ext-real real Element of REAL
(Im2 (c1,c2)) * (Im2 (c1,c2)) is complex ext-real real set
(((Rea (c1,c2)) ^2) + ((Im1 (c1,c2)) ^2)) + ((Im2 (c1,c2)) ^2) is complex ext-real real Element of REAL
Im3 (c1,c2) is complex ext-real real Element of REAL
(Im3 (c1,c2)) ^2 is complex ext-real real Element of REAL
(Im3 (c1,c2)) * (Im3 (c1,c2)) is complex ext-real real set
((((Rea (c1,c2)) ^2) + ((Im1 (c1,c2)) ^2)) + ((Im2 (c1,c2)) ^2)) + ((Im3 (c1,c2)) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea (c1,c2)) ^2) + ((Im1 (c1,c2)) ^2)) + ((Im2 (c1,c2)) ^2)) + ((Im3 (c1,c2)) ^2)) is complex ext-real real Element of REAL
(c2) is complex ext-real real Element of REAL
(Rea c2) ^2 is complex ext-real real Element of REAL
(Rea c2) * (Rea c2) is complex ext-real real set
(Im1 c2) ^2 is complex ext-real real Element of REAL
(Im1 c2) * (Im1 c2) is complex ext-real real set
((Rea c2) ^2) + ((Im1 c2) ^2) is complex ext-real real Element of REAL
(Im2 c2) ^2 is complex ext-real real Element of REAL
(Im2 c2) * (Im2 c2) is complex ext-real real set
(((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2) is complex ext-real real Element of REAL
(Im3 c2) ^2 is complex ext-real real Element of REAL
(Im3 c2) * (Im3 c2) is complex ext-real real set
((((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2)) + ((Im3 c2) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c2) ^2) + ((Im1 c2) ^2)) + ((Im2 c2) ^2)) + ((Im3 c2) ^2)) is complex ext-real real Element of REAL
(c1) * (c2) is complex ext-real real Element of REAL
((c2 *')) is complex ext-real real Element of REAL
Rea (c2 *') is complex ext-real real Element of REAL
(Rea (c2 *')) ^2 is complex ext-real real Element of REAL
(Rea (c2 *')) * (Rea (c2 *')) is complex ext-real real set
Im1 (c2 *') is complex ext-real real Element of REAL
(Im1 (c2 *')) ^2 is complex ext-real real Element of REAL
(Im1 (c2 *')) * (Im1 (c2 *')) is complex ext-real real set
((Rea (c2 *')) ^2) + ((Im1 (c2 *')) ^2) is complex ext-real real Element of REAL
Im2 (c2 *') is complex ext-real real Element of REAL
(Im2 (c2 *')) ^2 is complex ext-real real Element of REAL
(Im2 (c2 *')) * (Im2 (c2 *')) is complex ext-real real set
(((Rea (c2 *')) ^2) + ((Im1 (c2 *')) ^2)) + ((Im2 (c2 *')) ^2) is complex ext-real real Element of REAL
Im3 (c2 *') is complex ext-real real Element of REAL
(Im3 (c2 *')) ^2 is complex ext-real real Element of REAL
(Im3 (c2 *')) * (Im3 (c2 *')) is complex ext-real real set
((((Rea (c2 *')) ^2) + ((Im1 (c2 *')) ^2)) + ((Im2 (c2 *')) ^2)) + ((Im3 (c2 *')) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea (c2 *')) ^2) + ((Im1 (c2 *')) ^2)) + ((Im2 (c2 *')) ^2)) + ((Im3 (c2 *')) ^2)) is complex ext-real real Element of REAL
(c1) * ((c2 *')) is complex ext-real real Element of REAL
c1 is quaternion set
(c1,c1) is quaternion Element of QUATERNION
c1 *' is quaternion Element of QUATERNION
Rea c1 is complex ext-real real Element of REAL
Im1 c1 is complex ext-real real Element of REAL
- (Im1 c1) is complex ext-real real Element of REAL
(- (Im1 c1)) * <i> is quaternion set
(Rea c1) + ((- (Im1 c1)) * <i>) is quaternion set
Im2 c1 is complex ext-real real Element of REAL
- (Im2 c1) is complex ext-real real Element of REAL
(- (Im2 c1)) * <j> is quaternion set
((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>) is quaternion Element of QUATERNION
Im3 c1 is complex ext-real real Element of REAL
- (Im3 c1) is complex ext-real real Element of REAL
(- (Im3 c1)) * <k> is quaternion set
(((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>)) + ((- (Im3 c1)) * <k>) is quaternion Element of QUATERNION
c1 * (c1 *') is quaternion Element of QUATERNION
(c1) is complex ext-real real Element of REAL
(Rea c1) ^2 is complex ext-real real Element of REAL
(Rea c1) * (Rea c1) is complex ext-real real set
(Im1 c1) ^2 is complex ext-real real Element of REAL
(Im1 c1) * (Im1 c1) is complex ext-real real set
((Rea c1) ^2) + ((Im1 c1) ^2) is complex ext-real real Element of REAL
(Im2 c1) ^2 is complex ext-real real Element of REAL
(Im2 c1) * (Im2 c1) is complex ext-real real set
(((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2) is complex ext-real real Element of REAL
(Im3 c1) ^2 is complex ext-real real Element of REAL
(Im3 c1) * (Im3 c1) is complex ext-real real set
((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2) is complex ext-real real Element of REAL
sqrt (((((Rea c1) ^2) + ((Im1 c1) ^2)) + ((Im2 c1) ^2)) + ((Im3 c1) ^2)) is complex ext-real real Element of REAL
(c1) ^2 is complex ext-real real Element of REAL
(c1) * (c1) is complex ext-real real set
[*0,0*] is Element of COMPLEX
c1 is quaternion set
c2 is quaternion set
c1 + c2 is quaternion Element of QUATERNION
c3 is quaternion set
((c1 + c2),c3) is quaternion Element of QUATERNION
c3 *' is quaternion Element of QUATERNION
Rea c3 is complex ext-real real Element of REAL
Im1 c3 is complex ext-real real Element of REAL
- (Im1 c3) is complex ext-real real Element of REAL
(- (Im1 c3)) * <i> is quaternion set
(Rea c3) + ((- (Im1 c3)) * <i>) is quaternion set
Im2 c3 is complex ext-real real Element of REAL
- (Im2 c3) is complex ext-real real Element of REAL
(- (Im2 c3)) * <j> is quaternion set
((Rea c3) + ((- (Im1 c3)) * <i>)) + ((- (Im2 c3)) * <j>) is quaternion Element of QUATERNION
Im3 c3 is complex ext-real real Element of REAL
- (Im3 c3) is complex ext-real real Element of REAL
(- (Im3 c3)) * <k> is quaternion set
(((Rea c3) + ((- (Im1 c3)) * <i>)) + ((- (Im2 c3)) * <j>)) + ((- (Im3 c3)) * <k>) is quaternion Element of QUATERNION
(c1 + c2) * (c3 *') is quaternion Element of QUATERNION
(c1,c3) is quaternion Element of QUATERNION
c1 * (c3 *') is quaternion Element of QUATERNION
(c2,c3) is quaternion Element of QUATERNION
c2 * (c3 *') is quaternion Element of QUATERNION
(c1,c3) + (c2,c3) is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
(c1,c2) is quaternion Element of QUATERNION
c2 *' is quaternion Element of QUATERNION
Rea c2 is complex ext-real real Element of REAL
Im1 c2 is complex ext-real real Element of REAL
- (Im1 c2) is complex ext-real real Element of REAL
(- (Im1 c2)) * <i> is quaternion set
(Rea c2) + ((- (Im1 c2)) * <i>) is quaternion set
Im2 c2 is complex ext-real real Element of REAL
- (Im2 c2) is complex ext-real real Element of REAL
(- (Im2 c2)) * <j> is quaternion set
((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>) is quaternion Element of QUATERNION
Im3 c2 is complex ext-real real Element of REAL
- (Im3 c2) is complex ext-real real Element of REAL
(- (Im3 c2)) * <k> is quaternion set
(((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>)) + ((- (Im3 c2)) * <k>) is quaternion Element of QUATERNION
c1 * (c2 *') is quaternion Element of QUATERNION
c3 is quaternion set
c2 + c3 is quaternion Element of QUATERNION
(c1,(c2 + c3)) is quaternion Element of QUATERNION
(c2 + c3) *' is quaternion Element of QUATERNION
Rea (c2 + c3) is complex ext-real real Element of REAL
Im1 (c2 + c3) is complex ext-real real Element of REAL
- (Im1 (c2 + c3)) is complex ext-real real Element of REAL
(- (Im1 (c2 + c3))) * <i> is quaternion set
(Rea (c2 + c3)) + ((- (Im1 (c2 + c3))) * <i>) is quaternion set
Im2 (c2 + c3) is complex ext-real real Element of REAL
- (Im2 (c2 + c3)) is complex ext-real real Element of REAL
(- (Im2 (c2 + c3))) * <j> is quaternion set
((Rea (c2 + c3)) + ((- (Im1 (c2 + c3))) * <i>)) + ((- (Im2 (c2 + c3))) * <j>) is quaternion Element of QUATERNION
Im3 (c2 + c3) is complex ext-real real Element of REAL
- (Im3 (c2 + c3)) is complex ext-real real Element of REAL
(- (Im3 (c2 + c3))) * <k> is quaternion set
(((Rea (c2 + c3)) + ((- (Im1 (c2 + c3))) * <i>)) + ((- (Im2 (c2 + c3))) * <j>)) + ((- (Im3 (c2 + c3))) * <k>) is quaternion Element of QUATERNION
c1 * ((c2 + c3) *') is quaternion Element of QUATERNION
(c1,c3) is quaternion Element of QUATERNION
c3 *' is quaternion Element of QUATERNION
Rea c3 is complex ext-real real Element of REAL
Im1 c3 is complex ext-real real Element of REAL
- (Im1 c3) is complex ext-real real Element of REAL
(- (Im1 c3)) * <i> is quaternion set
(Rea c3) + ((- (Im1 c3)) * <i>) is quaternion set
Im2 c3 is complex ext-real real Element of REAL
- (Im2 c3) is complex ext-real real Element of REAL
(- (Im2 c3)) * <j> is quaternion set
((Rea c3) + ((- (Im1 c3)) * <i>)) + ((- (Im2 c3)) * <j>) is quaternion Element of QUATERNION
Im3 c3 is complex ext-real real Element of REAL
- (Im3 c3) is complex ext-real real Element of REAL
(- (Im3 c3)) * <k> is quaternion set
(((Rea c3) + ((- (Im1 c3)) * <i>)) + ((- (Im2 c3)) * <j>)) + ((- (Im3 c3)) * <k>) is quaternion Element of QUATERNION
c1 * (c3 *') is quaternion Element of QUATERNION
(c1,c2) + (c1,c3) is quaternion Element of QUATERNION
(c2 *') + (c3 *') is quaternion Element of QUATERNION
c1 * ((c2 *') + (c3 *')) is quaternion Element of QUATERNION
c1 is quaternion set
- c1 is quaternion Element of QUATERNION
c2 is quaternion set
((- c1),c2) is quaternion Element of QUATERNION
c2 *' is quaternion Element of QUATERNION
Rea c2 is complex ext-real real Element of REAL
Im1 c2 is complex ext-real real Element of REAL
- (Im1 c2) is complex ext-real real Element of REAL
(- (Im1 c2)) * <i> is quaternion set
(Rea c2) + ((- (Im1 c2)) * <i>) is quaternion set
Im2 c2 is complex ext-real real Element of REAL
- (Im2 c2) is complex ext-real real Element of REAL
(- (Im2 c2)) * <j> is quaternion set
((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>) is quaternion Element of QUATERNION
Im3 c2 is complex ext-real real Element of REAL
- (Im3 c2) is complex ext-real real Element of REAL
(- (Im3 c2)) * <k> is quaternion set
(((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>)) + ((- (Im3 c2)) * <k>) is quaternion Element of QUATERNION
(- c1) * (c2 *') is quaternion Element of QUATERNION
(c1,c2) is quaternion Element of QUATERNION
c1 * (c2 *') is quaternion Element of QUATERNION
- (c1,c2) is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
(c1,c2) is quaternion Element of QUATERNION
c2 *' is quaternion Element of QUATERNION
Rea c2 is complex ext-real real Element of REAL
Im1 c2 is complex ext-real real Element of REAL
- (Im1 c2) is complex ext-real real Element of REAL
(- (Im1 c2)) * <i> is quaternion set
(Rea c2) + ((- (Im1 c2)) * <i>) is quaternion set
Im2 c2 is complex ext-real real Element of REAL
- (Im2 c2) is complex ext-real real Element of REAL
(- (Im2 c2)) * <j> is quaternion set
((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>) is quaternion Element of QUATERNION
Im3 c2 is complex ext-real real Element of REAL
- (Im3 c2) is complex ext-real real Element of REAL
(- (Im3 c2)) * <k> is quaternion set
(((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>)) + ((- (Im3 c2)) * <k>) is quaternion Element of QUATERNION
c1 * (c2 *') is quaternion Element of QUATERNION
- (c1,c2) is quaternion Element of QUATERNION
- c2 is quaternion Element of QUATERNION
(c1,(- c2)) is quaternion Element of QUATERNION
(- c2) *' is quaternion Element of QUATERNION
Rea (- c2) is complex ext-real real Element of REAL
Im1 (- c2) is complex ext-real real Element of REAL
- (Im1 (- c2)) is complex ext-real real Element of REAL
(- (Im1 (- c2))) * <i> is quaternion set
(Rea (- c2)) + ((- (Im1 (- c2))) * <i>) is quaternion set
Im2 (- c2) is complex ext-real real Element of REAL
- (Im2 (- c2)) is complex ext-real real Element of REAL
(- (Im2 (- c2))) * <j> is quaternion set
((Rea (- c2)) + ((- (Im1 (- c2))) * <i>)) + ((- (Im2 (- c2))) * <j>) is quaternion Element of QUATERNION
Im3 (- c2) is complex ext-real real Element of REAL
- (Im3 (- c2)) is complex ext-real real Element of REAL
(- (Im3 (- c2))) * <k> is quaternion set
(((Rea (- c2)) + ((- (Im1 (- c2))) * <i>)) + ((- (Im2 (- c2))) * <j>)) + ((- (Im3 (- c2))) * <k>) is quaternion Element of QUATERNION
c1 * ((- c2) *') is quaternion Element of QUATERNION
- (c2 *') is quaternion Element of QUATERNION
c1 * (- (c2 *')) is quaternion Element of QUATERNION
- (c1 * (c2 *')) is quaternion Element of QUATERNION
c1 is quaternion set
- c1 is quaternion Element of QUATERNION
c2 is quaternion set
- c2 is quaternion Element of QUATERNION
((- c1),(- c2)) is quaternion Element of QUATERNION
(- c2) *' is quaternion Element of QUATERNION
Rea (- c2) is complex ext-real real Element of REAL
Im1 (- c2) is complex ext-real real Element of REAL
- (Im1 (- c2)) is complex ext-real real Element of REAL
(- (Im1 (- c2))) * <i> is quaternion set
(Rea (- c2)) + ((- (Im1 (- c2))) * <i>) is quaternion set
Im2 (- c2) is complex ext-real real Element of REAL
- (Im2 (- c2)) is complex ext-real real Element of REAL
(- (Im2 (- c2))) * <j> is quaternion set
((Rea (- c2)) + ((- (Im1 (- c2))) * <i>)) + ((- (Im2 (- c2))) * <j>) is quaternion Element of QUATERNION
Im3 (- c2) is complex ext-real real Element of REAL
- (Im3 (- c2)) is complex ext-real real Element of REAL
(- (Im3 (- c2))) * <k> is quaternion set
(((Rea (- c2)) + ((- (Im1 (- c2))) * <i>)) + ((- (Im2 (- c2))) * <j>)) + ((- (Im3 (- c2))) * <k>) is quaternion Element of QUATERNION
(- c1) * ((- c2) *') is quaternion Element of QUATERNION
(c1,c2) is quaternion Element of QUATERNION
c2 *' is quaternion Element of QUATERNION
Rea c2 is complex ext-real real Element of REAL
Im1 c2 is complex ext-real real Element of REAL
- (Im1 c2) is complex ext-real real Element of REAL
(- (Im1 c2)) * <i> is quaternion set
(Rea c2) + ((- (Im1 c2)) * <i>) is quaternion set
Im2 c2 is complex ext-real real Element of REAL
- (Im2 c2) is complex ext-real real Element of REAL
(- (Im2 c2)) * <j> is quaternion set
((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>) is quaternion Element of QUATERNION
Im3 c2 is complex ext-real real Element of REAL
- (Im3 c2) is complex ext-real real Element of REAL
(- (Im3 c2)) * <k> is quaternion set
(((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>)) + ((- (Im3 c2)) * <k>) is quaternion Element of QUATERNION
c1 * (c2 *') is quaternion Element of QUATERNION
- (c2 *') is quaternion Element of QUATERNION
(- c1) * (- (c2 *')) is quaternion Element of QUATERNION
c1 is quaternion set
c2 is quaternion set
c1 - c2 is quaternion Element of QUATERNION
- c2 is quaternion set
c1 + (- c2) is quaternion set
c3 is quaternion set
((c1 - c2),c3) is quaternion Element of QUATERNION
c3 *' is quaternion Element of QUATERNION
Rea c3 is complex ext-real real Element of REAL
Im1 c3 is complex ext-real real Element of REAL
- (Im1 c3) is complex ext-real real Element of REAL
(- (Im1 c3)) * <i> is quaternion set
(Rea c3) + ((- (Im1 c3)) * <i>) is quaternion set
Im2 c3 is complex ext-real real Element of REAL
- (Im2 c3) is complex ext-real real Element of REAL
(- (Im2 c3)) * <j> is quaternion set
((Rea c3) + ((- (Im1 c3)) * <i>)) + ((- (Im2 c3)) * <j>) is quaternion Element of QUATERNION
Im3 c3 is complex ext-real real Element of REAL
- (Im3 c3) is complex ext-real real Element of REAL
(- (Im3 c3)) * <k> is quaternion set
(((Rea c3) + ((- (Im1 c3)) * <i>)) + ((- (Im2 c3)) * <j>)) + ((- (Im3 c3)) * <k>) is quaternion Element of QUATERNION
(c1 - c2) * (c3 *') is quaternion Element of QUATERNION
(c1,c3) is quaternion Element of QUATERNION
c1 * (c3 *') is quaternion Element of QUATERNION
(c2,c3) is quaternion Element of QUATERNION
c2 * (c3 *') is quaternion Element of QUATERNION
(c1,c3) - (c2,c3) is quaternion Element of QUATERNION
- (c2,c3) is quaternion set
(c1,c3) + (- (c2,c3)) is quaternion set
c1 is quaternion set
c2 is quaternion set
(c1,c2) is quaternion Element of QUATERNION
c2 *' is quaternion Element of QUATERNION
Rea c2 is complex ext-real real Element of REAL
Im1 c2 is complex ext-real real Element of REAL
- (Im1 c2) is complex ext-real real Element of REAL
(- (Im1 c2)) * <i> is quaternion set
(Rea c2) + ((- (Im1 c2)) * <i>) is quaternion set
Im2 c2 is complex ext-real real Element of REAL
- (Im2 c2) is complex ext-real real Element of REAL
(- (Im2 c2)) * <j> is quaternion set
((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>) is quaternion Element of QUATERNION
Im3 c2 is complex ext-real real Element of REAL
- (Im3 c2) is complex ext-real real Element of REAL
(- (Im3 c2)) * <k> is quaternion set
(((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>)) + ((- (Im3 c2)) * <k>) is quaternion Element of QUATERNION
c1 * (c2 *') is quaternion Element of QUATERNION
c3 is quaternion set
c2 - c3 is quaternion Element of QUATERNION
- c3 is quaternion set
c2 + (- c3) is quaternion set
(c1,(c2 - c3)) is quaternion Element of QUATERNION
(c2 - c3) *' is quaternion Element of QUATERNION
Rea (c2 - c3) is complex ext-real real Element of REAL
Im1 (c2 - c3) is complex ext-real real Element of REAL
- (Im1 (c2 - c3)) is complex ext-real real Element of REAL
(- (Im1 (c2 - c3))) * <i> is quaternion set
(Rea (c2 - c3)) + ((- (Im1 (c2 - c3))) * <i>) is quaternion set
Im2 (c2 - c3) is complex ext-real real Element of REAL
- (Im2 (c2 - c3)) is complex ext-real real Element of REAL
(- (Im2 (c2 - c3))) * <j> is quaternion set
((Rea (c2 - c3)) + ((- (Im1 (c2 - c3))) * <i>)) + ((- (Im2 (c2 - c3))) * <j>) is quaternion Element of QUATERNION
Im3 (c2 - c3) is complex ext-real real Element of REAL
- (Im3 (c2 - c3)) is complex ext-real real Element of REAL
(- (Im3 (c2 - c3))) * <k> is quaternion set
(((Rea (c2 - c3)) + ((- (Im1 (c2 - c3))) * <i>)) + ((- (Im2 (c2 - c3))) * <j>)) + ((- (Im3 (c2 - c3))) * <k>) is quaternion Element of QUATERNION
c1 * ((c2 - c3) *') is quaternion Element of QUATERNION
(c1,c3) is quaternion Element of QUATERNION
c3 *' is quaternion Element of QUATERNION
Rea c3 is complex ext-real real Element of REAL
Im1 c3 is complex ext-real real Element of REAL
- (Im1 c3) is complex ext-real real Element of REAL
(- (Im1 c3)) * <i> is quaternion set
(Rea c3) + ((- (Im1 c3)) * <i>) is quaternion set
Im2 c3 is complex ext-real real Element of REAL
- (Im2 c3) is complex ext-real real Element of REAL
(- (Im2 c3)) * <j> is quaternion set
((Rea c3) + ((- (Im1 c3)) * <i>)) + ((- (Im2 c3)) * <j>) is quaternion Element of QUATERNION
Im3 c3 is complex ext-real real Element of REAL
- (Im3 c3) is complex ext-real real Element of REAL
(- (Im3 c3)) * <k> is quaternion set
(((Rea c3) + ((- (Im1 c3)) * <i>)) + ((- (Im2 c3)) * <j>)) + ((- (Im3 c3)) * <k>) is quaternion Element of QUATERNION
c1 * (c3 *') is quaternion Element of QUATERNION
(c1,c2) - (c1,c3) is quaternion Element of QUATERNION
- (c1,c3) is quaternion set
(c1,c2) + (- (c1,c3)) is quaternion set
(c2 *') - (c3 *') is quaternion Element of QUATERNION
- (c3 *') is quaternion set
(c2 *') + (- (c3 *')) is quaternion set
c1 * ((c2 *') - (c3 *')) is quaternion Element of QUATERNION
(c1 * (c2 *')) - (c1 * (c3 *')) is quaternion Element of QUATERNION
- (c1 * (c3 *')) is quaternion set
(c1 * (c2 *')) + (- (c1 * (c3 *'))) is quaternion set
c1 is quaternion set
(c1,c1) is quaternion Element of QUATERNION
c1 *' is quaternion Element of QUATERNION
Rea c1 is complex ext-real real Element of REAL
Im1 c1 is complex ext-real real Element of REAL
- (Im1 c1) is complex ext-real real Element of REAL
(- (Im1 c1)) * <i> is quaternion set
(Rea c1) + ((- (Im1 c1)) * <i>) is quaternion set
Im2 c1 is complex ext-real real Element of REAL
- (Im2 c1) is complex ext-real real Element of REAL
(- (Im2 c1)) * <j> is quaternion set
((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>) is quaternion Element of QUATERNION
Im3 c1 is complex ext-real real Element of REAL
- (Im3 c1) is complex ext-real real Element of REAL
(- (Im3 c1)) * <k> is quaternion set
(((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>)) + ((- (Im3 c1)) * <k>) is quaternion Element of QUATERNION
c1 * (c1 *') is quaternion Element of QUATERNION
c2 is quaternion set
c1 + c2 is quaternion Element of QUATERNION
((c1 + c2),(c1 + c2)) is quaternion Element of QUATERNION
(c1 + c2) *' is quaternion Element of QUATERNION
Rea (c1 + c2) is complex ext-real real Element of REAL
Im1 (c1 + c2) is complex ext-real real Element of REAL
- (Im1 (c1 + c2)) is complex ext-real real Element of REAL
(- (Im1 (c1 + c2))) * <i> is quaternion set
(Rea (c1 + c2)) + ((- (Im1 (c1 + c2))) * <i>) is quaternion set
Im2 (c1 + c2) is complex ext-real real Element of REAL
- (Im2 (c1 + c2)) is complex ext-real real Element of REAL
(- (Im2 (c1 + c2))) * <j> is quaternion set
((Rea (c1 + c2)) + ((- (Im1 (c1 + c2))) * <i>)) + ((- (Im2 (c1 + c2))) * <j>) is quaternion Element of QUATERNION
Im3 (c1 + c2) is complex ext-real real Element of REAL
- (Im3 (c1 + c2)) is complex ext-real real Element of REAL
(- (Im3 (c1 + c2))) * <k> is quaternion set
(((Rea (c1 + c2)) + ((- (Im1 (c1 + c2))) * <i>)) + ((- (Im2 (c1 + c2))) * <j>)) + ((- (Im3 (c1 + c2))) * <k>) is quaternion Element of QUATERNION
(c1 + c2) * ((c1 + c2) *') is quaternion Element of QUATERNION
(c1,c2) is quaternion Element of QUATERNION
c2 *' is quaternion Element of QUATERNION
Rea c2 is complex ext-real real Element of REAL
Im1 c2 is complex ext-real real Element of REAL
- (Im1 c2) is complex ext-real real Element of REAL
(- (Im1 c2)) * <i> is quaternion set
(Rea c2) + ((- (Im1 c2)) * <i>) is quaternion set
Im2 c2 is complex ext-real real Element of REAL
- (Im2 c2) is complex ext-real real Element of REAL
(- (Im2 c2)) * <j> is quaternion set
((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>) is quaternion Element of QUATERNION
Im3 c2 is complex ext-real real Element of REAL
- (Im3 c2) is complex ext-real real Element of REAL
(- (Im3 c2)) * <k> is quaternion set
(((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>)) + ((- (Im3 c2)) * <k>) is quaternion Element of QUATERNION
c1 * (c2 *') is quaternion Element of QUATERNION
(c1,c1) + (c1,c2) is quaternion Element of QUATERNION
(c2,c1) is quaternion Element of QUATERNION
c2 * (c1 *') is quaternion Element of QUATERNION
((c1,c1) + (c1,c2)) + (c2,c1) is quaternion Element of QUATERNION
(c2,c2) is quaternion Element of QUATERNION
c2 * (c2 *') is quaternion Element of QUATERNION
(((c1,c1) + (c1,c2)) + (c2,c1)) + (c2,c2) is quaternion Element of QUATERNION
(c1 *') + (c2 *') is quaternion Element of QUATERNION
(c1 + c2) * ((c1 *') + (c2 *')) is quaternion Element of QUATERNION
(c1 + c2) * (c1 *') is quaternion Element of QUATERNION
(c1 + c2) * (c2 *') is quaternion Element of QUATERNION
((c1 + c2) * (c1 *')) + ((c1 + c2) * (c2 *')) is quaternion Element of QUATERNION
(c1 * (c1 *')) + (c2 * (c1 *')) is quaternion Element of QUATERNION
((c1 * (c1 *')) + (c2 * (c1 *'))) + ((c1 + c2) * (c2 *')) is quaternion Element of QUATERNION
(c1,c1) + (c2,c1) is quaternion Element of QUATERNION
(c1,c2) + (c2,c2) is quaternion Element of QUATERNION
((c1,c1) + (c2,c1)) + ((c1,c2) + (c2,c2)) is quaternion Element of QUATERNION
((c1,c1) + (c2,c1)) + (c1,c2) is quaternion Element of QUATERNION
(((c1,c1) + (c2,c1)) + (c1,c2)) + (c2,c2) is quaternion Element of QUATERNION
c1 is quaternion set
(c1,c1) is quaternion Element of QUATERNION
c1 *' is quaternion Element of QUATERNION
Rea c1 is complex ext-real real Element of REAL
Im1 c1 is complex ext-real real Element of REAL
- (Im1 c1) is complex ext-real real Element of REAL
(- (Im1 c1)) * <i> is quaternion set
(Rea c1) + ((- (Im1 c1)) * <i>) is quaternion set
Im2 c1 is complex ext-real real Element of REAL
- (Im2 c1) is complex ext-real real Element of REAL
(- (Im2 c1)) * <j> is quaternion set
((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>) is quaternion Element of QUATERNION
Im3 c1 is complex ext-real real Element of REAL
- (Im3 c1) is complex ext-real real Element of REAL
(- (Im3 c1)) * <k> is quaternion set
(((Rea c1) + ((- (Im1 c1)) * <i>)) + ((- (Im2 c1)) * <j>)) + ((- (Im3 c1)) * <k>) is quaternion Element of QUATERNION
c1 * (c1 *') is quaternion Element of QUATERNION
c2 is quaternion set
c1 - c2 is quaternion Element of QUATERNION
- c2 is quaternion set
c1 + (- c2) is quaternion set
((c1 - c2),(c1 - c2)) is quaternion Element of QUATERNION
(c1 - c2) *' is quaternion Element of QUATERNION
Rea (c1 - c2) is complex ext-real real Element of REAL
Im1 (c1 - c2) is complex ext-real real Element of REAL
- (Im1 (c1 - c2)) is complex ext-real real Element of REAL
(- (Im1 (c1 - c2))) * <i> is quaternion set
(Rea (c1 - c2)) + ((- (Im1 (c1 - c2))) * <i>) is quaternion set
Im2 (c1 - c2) is complex ext-real real Element of REAL
- (Im2 (c1 - c2)) is complex ext-real real Element of REAL
(- (Im2 (c1 - c2))) * <j> is quaternion set
((Rea (c1 - c2)) + ((- (Im1 (c1 - c2))) * <i>)) + ((- (Im2 (c1 - c2))) * <j>) is quaternion Element of QUATERNION
Im3 (c1 - c2) is complex ext-real real Element of REAL
- (Im3 (c1 - c2)) is complex ext-real real Element of REAL
(- (Im3 (c1 - c2))) * <k> is quaternion set
(((Rea (c1 - c2)) + ((- (Im1 (c1 - c2))) * <i>)) + ((- (Im2 (c1 - c2))) * <j>)) + ((- (Im3 (c1 - c2))) * <k>) is quaternion Element of QUATERNION
(c1 - c2) * ((c1 - c2) *') is quaternion Element of QUATERNION
(c1,c2) is quaternion Element of QUATERNION
c2 *' is quaternion Element of QUATERNION
Rea c2 is complex ext-real real Element of REAL
Im1 c2 is complex ext-real real Element of REAL
- (Im1 c2) is complex ext-real real Element of REAL
(- (Im1 c2)) * <i> is quaternion set
(Rea c2) + ((- (Im1 c2)) * <i>) is quaternion set
Im2 c2 is complex ext-real real Element of REAL
- (Im2 c2) is complex ext-real real Element of REAL
(- (Im2 c2)) * <j> is quaternion set
((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>) is quaternion Element of QUATERNION
Im3 c2 is complex ext-real real Element of REAL
- (Im3 c2) is complex ext-real real Element of REAL
(- (Im3 c2)) * <k> is quaternion set
(((Rea c2) + ((- (Im1 c2)) * <i>)) + ((- (Im2 c2)) * <j>)) + ((- (Im3 c2)) * <k>) is quaternion Element of QUATERNION
c1 * (c2 *') is quaternion Element of QUATERNION
(c1,c1) - (c1,c2) is quaternion Element of QUATERNION
- (c1,c2) is quaternion set
(c1,c1) + (- (c1,c2)) is quaternion set
(c2,c1) is quaternion Element of QUATERNION
c2 * (c1 *') is quaternion Element of QUATERNION
((c1,c1) - (c1,c2)) - (c2,c1) is quaternion Element of QUATERNION
- (c2,c1) is quaternion set
((c1,c1) - (c1,c2)) + (- (c2,c1)) is quaternion set
(c2,c2) is quaternion Element of QUATERNION
c2 * (c2 *') is quaternion Element of QUATERNION
(((c1,c1) - (c1,c2)) - (c2,c1)) + (c2,c2) is quaternion Element of QUATERNION
(c1 *') - (c2 *') is quaternion Element of QUATERNION
- (c2 *') is quaternion set
(c1 *') + (- (c2 *')) is quaternion set
(c1 - c2) * ((c1 *') - (c2 *')) is quaternion Element of QUATERNION
- c2 is quaternion Element of QUATERNION
c1 + (- c2) is quaternion Element of QUATERNION
(c1 + (- c2)) * (c1 *') is quaternion Element of QUATERNION
- (c2 *') is quaternion Element of QUATERNION
(c1 + (- c2)) * (- (c2 *')) is quaternion Element of QUATERNION
((c1 + (- c2)) * (c1 *')) + ((c1 + (- c2)) * (- (c2 *'))) is quaternion Element of QUATERNION
(- c2) * (c1 *') is quaternion Element of QUATERNION
(c1 * (c1 *')) + ((- c2) * (c1 *')) is quaternion Element of QUATERNION
((c1 * (c1 *')) + ((- c2) * (c1 *'))) + ((c1 + (- c2)) * (- (c2 *'))) is quaternion Element of QUATERNION
(c1,c1) + ((- c2) * (c1 *')) is quaternion Element of QUATERNION
c1 * (- (c2 *')) is quaternion Element of QUATERNION
(- c2) * (- (c2 *')) is quaternion Element of QUATERNION
(c1 * (- (c2 *'))) + ((- c2) * (- (c2 *'))) is quaternion Element of QUATERNION
((c1,c1) + ((- c2) * (c1 *'))) + ((c1 * (- (c2 *'))) + ((- c2) * (- (c2 *')))) is quaternion Element of QUATERNION
- (c2 * (c1 *')) is quaternion Element of QUATERNION
(c1,c1) + (- (c2 * (c1 *'))) is quaternion Element of QUATERNION
((c1,c1) + (- (c2 * (c1 *')))) + ((c1 * (- (c2 *'))) + ((- c2) * (- (c2 *')))) is quaternion Element of QUATERNION
- (c1 * (c2 *')) is quaternion Element of QUATERNION
(- (c1 * (c2 *'))) + ((- c2) * (- (c2 *'))) is quaternion Element of QUATERNION
((c1,c1) + (- (c2 * (c1 *')))) + ((- (c1 * (c2 *'))) + ((- c2) * (- (c2 *')))) is quaternion Element of QUATERNION
- (c2,c1) is quaternion Element of QUATERNION
(c1,c1) + (- (c2,c1)) is quaternion Element of QUATERNION
- (c1,c2) is quaternion Element of QUATERNION
(- (c1,c2)) + (c2,c2) is quaternion Element of QUATERNION
((c1,c1) + (- (c2,c1))) + ((- (c1,c2)) + (c2,c2)) is quaternion Element of QUATERNION
((c1,c1) + (- (c2,c1))) + (- (c1,c2)) is quaternion Element of QUATERNION
(((c1,c1) + (- (c2,c1))) + (- (c1,c2))) + (c2,c2) is quaternion Element of QUATERNION
(c1,c1) + (- (c1,c2)) is quaternion Element of QUATERNION
((c1,c1) + (- (c1,c2))) + (- (c2,c1)) is quaternion Element of QUATERNION
(((c1,c1) + (- (c1,c2))) + (- (c2,c1))) + (c2,c2) is quaternion Element of QUATERNION