/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ /* [ Created with wxMaxima version 12.04.0 ] */ /* [wxMaxima: input start ] */ p:matrix(1/sqrt(2)*[0,1,-1],1/sqrt(6)*[2,-1,-1],1/sqrt(3)*[1,1,1]); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ r:matrix([cos(t),-sin(t),0],[sin(t),cos(t),0],[0,0,1]).p; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ m1:matrix([a,0,0],[0,b,0],[0,0,c]).transpose(r); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ m2:r.matrix([a,0,0],[0,b,0],[0,0,c]); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ trigsimp(m1.m2); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ trigsimp(m2.m1); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ trigsimp(charpoly(%, x)); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ solve([%], [x]); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ w:m2.[1,1,1]; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ wt:[1,1,1].m1; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ z:[1,1,1].m2; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ trigsimp(w.w); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ trigsimp(wt.wt); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ trigsimp(z.z); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ w[1]^2+w[2]^2; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ trigsimp(%); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ w[3]^2; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ w[1]^2+w[2]^2-w[3]^2; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ trigsimp(%); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ expand(%); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ w[1]^2+w[2]^2=w[3]^2; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ trigsimp(%); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ expand(%); /* [wxMaxima: input end ] */ /* Maxima can't load/batch files which end with a comment! */ "Created with wxMaxima"$