(%i2) x: -sqrt(2)/2$
(%i3) y: sqrt(2)/-2$
(%i4) ratsimp([x,y]);
(%o4) [-1/sqrt(2),-sqrt(2)/2]
(%i5) :lisp $x
((MTIMES SIMP) -1 ((MEXPT) 2 ((RAT SIMP) -1 2)))
(%i5) :lisp $y
((MTIMES SIMP) ((RAT SIMP) -1 2) ((MEXPT SIMP) 2 ((RAT SIMP) 1 2)))
I think there shouldn't be a difference. The second mexpt has a simp flag. If I understand
right this prevents y from being simplified.
This might be the reason for my following observation (rotation matrices):
(%i5) M: matrix([cos(%pi/4),-sin(%pi/4)],[sin(%pi/4),cos(%pi/4)])$
(%i6) N: matrix([cos(%pi/2),-sin(%pi/2)],[sin(%pi/2),cos(%pi/2)])$
(%i7) (M.N).[1,0];
(%o7) matrix([-1/sqrt(2)],[1/sqrt(2)]) <<----------
(%i8) D: matrix([cos(3*%pi/4),-sin(3*%pi/4)],[sin(3*%pi/4),cos(3*%pi/4)])$
(%i9) D.[1,0];
(%o9) matrix([-sqrt(2)/2],[1/sqrt(2)]) <<----------
Volker