|\^/| Maple 10 (SUN SPARC SOLARIS) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2005 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. "jk: START of 0.mapleinit" [cos(x) -sin(x)] Rot := [ ] [sin(x) cos(x) ] Rot := x -> rtable(1 .. 2, 1 .. 2, {(1, 1) = cos(x), (1, 2) = -sin(x), (2, 1) = sin(x), (2, 2) = cos(x)}, ================================================================ > C := <<2,1>|<3,1>>; CInv := MI(C); [2 3] C = [ ] [1 1] [-1 3] CInv = [ ] [ 1 -2] > Rot(theta); [cos(theta) -sin(theta)] [ ] [sin(theta) cos(theta) ] :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: > R := Rot(Pi/2); [0 -1] R = [ ] [1 0] > WeirdR := CInv . R . C; [ 7 10] WeirdR = [ ] [-5 -7] > WeirdRSqrd := WeirdR . WeirdR ; [-1 0] WeirdRSqrd = [ ] [ 0 -1] :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: > Q := Rot(Pi/3); [ 1/2] [ 3 ] [1/2 - ----] [ 2 ] Q = [ ] [ 1/2 ] [3 ] [---- 1/2 ] [ 2 ] > WeirdQ := CInv . Q . C ; [ 1/2 ] [ 7 3 1/2 ] [1/2 + ------ 5 3 ] [ 2 ] WeirdQ = [ ] [ 1/2 1/2] [ 5 3 7 3 ] [ - ------ 1/2 - ------] [ 2 2 ] > WeirdQSqrd := simplify(WeirdQ . WeirdQ) ; [ 1/2 ] [ 7 3 1/2 ] [- 1/2 + ------ 5 3 ] [ 2 ] WeirdQSqrd = [ ] [ 1/2 1/2] [ 5 3 7 3 ] [ - ------ - 1/2 - ------] [ 2 2 ] > QSqrd := Q . Q ; [ 1/2] [ 3 ] [-1/2 - ----] [ 2 ] QSqrd = [ ] [ 1/2 ] [3 ] [---- -1/2 ] [ 2 ] > WeirdifyQSqrd := CInv . QSqrd . C ; [ 1/2 ] [ 7 3 1/2 ] [- 1/2 + ------ 5 3 ] [ 2 ] WeirdifyQSqrd = [ ] [ 1/2 1/2] [ 5 3 7 3 ] [ - ------ - 1/2 - ------] [ 2 2 ] > simplify(WeirdifyQSqrd - WeirdQSqrd) ; [0 0] [ ] [0 0] > WeirdQCubed := simplify(WeirdQ . WeirdQ . WeirdQ) ; [-1 0] WeirdQCubed = [ ] [ 0 -1] :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: > P := CInv . Rot(t) . C ; [cos(t) + 7 sin(t) 10 sin(t) ] P = [ ] [ -5 sin(t) cos(t) - 7 sin(t)] > PtoFourth := P^4 ; PtoFourth = [ 2 2 2 [(%2 - 50 sin(t) ) + %4 %3 , 2 2 2 2 ] (%2 - 50 sin(t) ) %4 + %4 (-50 sin(t) + %1 )] [ 2 2 2 2 [%3 (%2 - 50 sin(t) ) + (-50 sin(t) + %1 ) %3 , 2 2 2] %4 %3 + (-50 sin(t) + %1 ) ] %1 := cos(t) - 7 sin(t) %2 := cos(t) + 7 sin(t) %3 := -5 %2 sin(t) - 5 sin(t) %1 %4 := 10 %2 sin(t) + 10 sin(t) %1 > PtoFourth := simplify(PtoFourth) ; PtoFourth = [ 3 4 2 2 ] [56 cos(t) sin(t) - 28 sin(t) cos(t) + 8 cos(t) - 8 cos(t) + 1 , 40 sin(t) cos(t) (2 cos(t) - 1) ] [ ] [ 2 3 4 2 ] [-20 sin(t) cos(t) (2 cos(t) - 1) , -56 cos(t) sin(t) + 28 sin(t) cos(t) + 8 cos(t) - 8 cos(t) + 1] > NewPtoFourth := subs(t = Pi/4, PtoFourth); [-1 0] NewPtoFourth = [ ] [ 0 -1] %%%% End of "change-of-basis.txt"