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glSyMM-calcs.OUT
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Maxima 5.9.0 http://maxima.sourceforge.net
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
This is a development version of Maxima. The function bug_report()
provides bug reporting information.
(C1) BATCH(glSyMM-calcs.max)
batching /home/paulo/WORK/glSyMM/glSyMM-calcs.max
(C2) e_x : MATRIX([1], [0], [0], [0])
[ 1 ]
[ ]
[ 0 ]
(D2) [ ]
[ 0 ]
[ ]
[ 0 ]
(C3) e_y : MATRIX([0], [1], [0], [0])
[ 0 ]
[ ]
[ 1 ]
(D3) [ ]
[ 0 ]
[ ]
[ 0 ]
(C4) e_z : MATRIX([0], [0], [1], [0])
[ 0 ]
[ ]
[ 0 ]
(D4) [ ]
[ 1 ]
[ ]
[ 0 ]
2
(C5) glRotate(THETA, x, y, z) := MATRIX([COS(THETA) + x (1 - COS(THETA)),
x y (1 - COS(THETA)) - z SIN(THETA), y SIN(THETA) + x z (1 - COS(THETA)), 0],
2
[z SIN(THETA) + y x (1 - COS(THETA)), COS(THETA) + y (1 - COS(THETA)),
y z (1 - COS(THETA)) - x SIN(THETA), 0],
[x z (1 - COS(THETA)) - y SIN(THETA), x SIN(THETA) + y z (1 - COS(THETA)),
2
COS(THETA) + z (1 - COS(THETA)), 0], [0, 0, 0, 1])
2
(D5) glRotate(THETA, x, y, z) := MATRIX([COS(THETA) + x (1 - COS(THETA)),
x y (1 - COS(THETA)) - z SIN(THETA), y SIN(THETA) + x z (1 - COS(THETA)), 0],
2
[z SIN(THETA) + y x (1 - COS(THETA)), COS(THETA) + y (1 - COS(THETA)),
y z (1 - COS(THETA)) - x SIN(THETA), 0],
[x z (1 - COS(THETA)) - y SIN(THETA), x SIN(THETA) + y z (1 - COS(THETA)),
2
COS(THETA) + z (1 - COS(THETA)), 0], [0, 0, 0, 1])
(C6) ERRE_1 : glRotate(a, 0, 0, 1)
[ COS(a) - SIN(a) 0 0 ]
[ ]
[ SIN(a) COS(a) 0 0 ]
(D6) [ ]
[ 0 0 1 0 ]
[ ]
[ 0 0 0 1 ]
(C7) ERRE_2 : glRotate(b, COS(a), SIN(a), 0)
[ 2 ]
[ COS(b) + COS (a) (1 - COS(b)) ]
[ ]
(D7) Col 1 = [ COS(a) SIN(a) (1 - COS(b)) ]
[ ]
[ - SIN(a) SIN(b) ]
[ ]
[ 0 ]
[ COS(a) SIN(a) (1 - COS(b)) ] [ SIN(a) SIN(b) ]
[ ] [ ]
[ 2 ] [ - COS(a) SIN(b) ]
Col 2 = [ COS(b) + SIN (a) (1 - COS(b)) ] Col 3 = [ ]
[ ] [ COS(b) ]
[ COS(a) SIN(b) ] [ ]
[ ] [ 0 ]
[ 0 ]
[ 0 ]
[ ]
[ 0 ]
Col 4 = [ ]
[ 0 ]
[ ]
[ 1 ]
(C8) ERRE_21 : TRIGSIMP(EXPAND(ERRE_2 . ERRE_1))
[ COS(a) - SIN(a) COS(b) SIN(a) SIN(b) 0 ]
[ ]
[ SIN(a) COS(a) COS(b) - COS(a) SIN(b) 0 ]
(D8) [ ]
[ 0 SIN(b) COS(b) 0 ]
[ ]
[ 0 0 0 1 ]
(C9) ERRE_21i : TRIGSIMP(EXPAND(INVERT(ERRE_21)))
[ COS(a) SIN(a) 0 0 ]
[ ]
[ - SIN(a) COS(b) COS(a) COS(b) SIN(b) 0 ]
(D9) [ ]
[ SIN(a) SIN(b) - COS(a) SIN(b) COS(b) 0 ]
[ ]
[ 0 0 0 1 ]
(C10) ERRE_12 : TRIGSIMP(EXPAND(ERRE_1 . ERRE_2))
[ 2 2 ]
[ 2 COS(a) SIN (a) COS(b) - 2 COS(a) SIN (a) + COS(a) ]
[ ]
[ 3 3 ]
(D10) Col 1 = [ (2 SIN (a) - SIN(a)) COS(b) - 2 SIN (a) + 2 SIN(a) ]
[ ]
[ - SIN(a) SIN(b) ]
[ ]
[ 0 ]
[ 3 3 ]
[ (2 SIN (a) - 2 SIN(a)) COS(b) - 2 SIN (a) + SIN(a) ]
[ ]
[ 2 2 ]
Col 2 = [ (COS(a) - 2 COS(a) SIN (a)) COS(b) + 2 COS(a) SIN (a) ]
[ ]
[ COS(a) SIN(b) ]
[ ]
[ 0 ]
[ 2 COS(a) SIN(a) SIN(b) ] [ 0 ]
[ ] [ ]
[ 2 ] [ 0 ]
Col 3 = [ (2 SIN (a) - 1) SIN(b) ] Col 4 = [ ]
[ ] [ 0 ]
[ COS(b) ] [ ]
[ ] [ 1 ]
[ 0 ]
(C11) ERRE_12i : TRIGSIMP(EXPAND(INVERT(ERRE_12)))
[ 2 2 ]
[ 2 COS(a) SIN (a) COS(b) - 2 COS(a) SIN (a) + COS(a) ]
[ ]
[ 3 3 ]
(D11) Col 1 = [ (2 SIN (a) - 2 SIN(a)) COS(b) - 2 SIN (a) + SIN(a) ]
[ ]
[ 2 COS(a) SIN(a) SIN(b) ]
[ ]
[ 0 ]
[ 3 3 ]
[ (2 SIN (a) - SIN(a)) COS(b) - 2 SIN (a) + 2 SIN(a) ]
[ ]
[ 2 2 ]
Col 2 = [ (COS(a) - 2 COS(a) SIN (a)) COS(b) + 2 COS(a) SIN (a) ]
[ ]
[ 2 ]
[ (2 SIN (a) - 1) SIN(b) ]
[ ]
[ 0 ]
[ - SIN(a) SIN(b) ] [ 0 ]
[ ] [ ]
[ COS(a) SIN(b) ] [ 0 ]
Col 3 = [ ] Col 4 = [ ]
[ COS(b) ] [ 0 ]
[ ] [ ]
[ 0 ] [ 1 ]
(C12) e_xx : ERRE_21 . e_x
[ COS(a) ]
[ ]
[ SIN(a) ]
(D12) [ ]
[ 0 ]
[ ]
[ 0 ]
(C13) e_yy : ERRE_21 . e_y
[ - SIN(a) COS(b) ]
[ ]
[ COS(a) COS(b) ]
(D13) [ ]
[ SIN(b) ]
[ ]
[ 0 ]
(C14) e_zz : ERRE_21 . e_z
[ SIN(a) SIN(b) ]
[ ]
[ - COS(a) SIN(b) ]
(D14) [ ]
[ COS(b) ]
[ ]
[ 0 ]
(C15) e_XX : ERRE_12 . e_x
[ 2 2 ]
[ 2 COS(a) SIN (a) COS(b) - 2 COS(a) SIN (a) + COS(a) ]
[ ]
[ 3 3 ]
(D15) [ (2 SIN (a) - SIN(a)) COS(b) - 2 SIN (a) + 2 SIN(a) ]
[ ]
[ - SIN(a) SIN(b) ]
[ ]
[ 0 ]
(C16) e_YY : ERRE_12 . e_y
[ 3 3 ]
[ (2 SIN (a) - 2 SIN(a)) COS(b) - 2 SIN (a) + SIN(a) ]
[ ]
[ 2 2 ]
(D16) [ (COS(a) - 2 COS(a) SIN (a)) COS(b) + 2 COS(a) SIN (a) ]
[ ]
[ COS(a) SIN(b) ]
[ ]
[ 0 ]
(C17) e_ZZ : ERRE_12 . e_z
[ 2 COS(a) SIN(a) SIN(b) ]
[ ]
[ 2 ]
(D17) [ (2 SIN (a) - 1) SIN(b) ]
[ ]
[ COS(b) ]
[ ]
[ 0 ]
(C18) ei_xx : ERRE_21i . e_x
[ COS(a) ]
[ ]
[ - SIN(a) COS(b) ]
(D18) [ ]
[ SIN(a) SIN(b) ]
[ ]
[ 0 ]
(C19) ei_yy : ERRE_21i . e_y
[ SIN(a) ]
[ ]
[ COS(a) COS(b) ]
(D19) [ ]
[ - COS(a) SIN(b) ]
[ ]
[ 0 ]
(C20) ei_zz : ERRE_21i . e_z
[ 0 ]
[ ]
[ SIN(b) ]
(D20) [ ]
[ COS(b) ]
[ ]
[ 0 ]
(C21) ei_XX : ERRE_12i . e_x
[ 2 2 ]
[ 2 COS(a) SIN (a) COS(b) - 2 COS(a) SIN (a) + COS(a) ]
[ ]
[ 3 3 ]
(D21) [ (2 SIN (a) - 2 SIN(a)) COS(b) - 2 SIN (a) + SIN(a) ]
[ ]
[ 2 COS(a) SIN(a) SIN(b) ]
[ ]
[ 0 ]
(C22) ei_YY : ERRE_12i . e_y
[ 3 3 ]
[ (2 SIN (a) - SIN(a)) COS(b) - 2 SIN (a) + 2 SIN(a) ]
[ ]
[ 2 2 ]
(D22) [ (COS(a) - 2 COS(a) SIN (a)) COS(b) + 2 COS(a) SIN (a) ]
[ ]
[ 2 ]
[ (2 SIN (a) - 1) SIN(b) ]
[ ]
[ 0 ]
(C23) ei_ZZ : ERRE_12i . e_z
[ - SIN(a) SIN(b) ]
[ ]
[ COS(a) SIN(b) ]
(D23) [ ]
[ COS(b) ]
[ ]
[ 0 ]