Hello, can anyone tell me how I can use sage to check that the following two (fairly simple) expressions coincide. Some unneeded background: both come from identities in character theory for complex reflection groups, Sage was able to solve similar expressions, see below, and this is the smallest example I have were it doesn't work ?
sage: f -(e^(2/3*I*pi) + 1)*e^(2/15*I*pi - 32*XX) + 3*(e^(2/3*I*pi) + 1)*e^(2/15*I*pi - 12*XX) - 5*(e^(2/3*I*pi) + 1)*e^(2/15*I*pi + 4*XX) + 3*(e^(2/3*I*pi) + 1)*e^(2/15*I*pi + 8*XX) - 5*(e^(2/3*I*pi) + 1)*e^(4*XX) + 6*(e^(2/3*I*pi) + 1)*e^(8*XX) - (e^(2/3*I*pi) + 1)*e^(28*XX) + 3*(((e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(-12*XX) - 5*(((e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(-8*XX) + 3*(((e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(8*XX) - (((e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(28*XX) - 5*(((((e^(2/15*I*pi) - 1)*e^(4/15*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(2/15*I*pi) + 1)*e^(4/15*I*pi) - 1)*e^(4*XX) + 5*(((((e^(4/15*I*pi) - 1)*e^(2/15*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(4/15*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(4*XX) + 3*(((((e^(2/15*I*pi) - 1)*e^(4/15*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(2/15*I*pi) + 1)*e^(4/15*I*pi) - 1)*e^(8*XX) - 3*(((((e^(4/15*I*pi) - 1)*e^(2/15*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(4/15*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(8*XX) + 3*(((((e^(2/15*I*pi) - 1)*e^(4/15*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(2/15*I*pi) + 1)*e^(4/15*I*pi) - 1)*e^(-12*XX) - 3*(((((e^(4/15*I*pi) - 1)*e^(2/15*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(4/15*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(-12*XX) - (((((e^(2/15*I*pi) - 1)*e^(4/15*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(2/15*I*pi) + 1)*e^(4/15*I*pi) - 1)*e^(-32*XX) + (((((e^(4/15*I*pi) - 1)*e^(2/15*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(4/15*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(-32*XX) - ((((e^(4/15*I*pi) - 1)*e^(2/15*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(-32*XX) + 3*((((e^(4/15*I*pi) - 1)*e^(2/15*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(-12*XX) - 5*((((e^(4/15*I*pi) - 1)*e^(2/15*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(4*XX) + 3*((((e^(4/15*I*pi) - 1)*e^(2/15*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(2/15*I*pi) - 1)*e^(8*XX) + 5*e^(4/15*I*pi + 4*XX) + 5*e^(14/15*I*pi + 4*XX) + 5*e^(8/15*I*pi + 4*XX) + 5*e^(2/15*I*pi + 4*XX) + 5*e^(2/3*I*pi + 4*XX) + 5*e^(6/5*I*pi - 8*XX) + 5*e^(4/5*I*pi - 8*XX) + 5*e^(2/5*I*pi - 8*XX) - 3*e^(4/15*I*pi + 8*XX) - 3*e^(14/15*I*pi + 8*XX) - 3*e^(8/15*I*pi + 8*XX) - 3*e^(2/15*I*pi + 8*XX) - 3*e^(4/15*I*pi - 12*XX) - 3*e^(14/15*I*pi - 12*XX) - 3*e^(8/15*I*pi - 12*XX) - 3*e^(2/15*I*pi - 12*XX) - 6*e^(2/3*I*pi + 8*XX) - 3*e^(6/5*I*pi + 8*XX) - 3*e^(4/5*I*pi + 8*XX) - 3*e^(2/5*I*pi + 8*XX) - 3*e^(6/5*I*pi - 12*XX) - 3*e^(4/5*I*pi - 12*XX) - 3*e^(2/5*I*pi - 12*XX) + e^(4/15*I*pi - 32*XX) + e^(14/15*I*pi - 32*XX) + e^(8/15*I*pi - 32*XX) + e^(2/15*I*pi - 32*XX) + e^(6/5*I*pi + 28*XX) + e^(4/5*I*pi + 28*XX) + e^(2/5*I*pi + 28*XX) + e^(2/3*I*pi + 28*XX) + 5*e^(-8*XX) - 6*e^(8*XX) + e^(88*XX) sage: g e^(-32*XX) - 2*e^(28*XX) + e^(88*XX) Other similar examples were property simplified: sage: h (((e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(-42*XX) - 5*(((e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(-6*XX) + 5*(((e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(6*XX) - (((e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(2/5*I*pi) + 1)*e^(18*XX) + 5*e^(6/5*I*pi - 6*XX) + 5*e^(4/5*I*pi - 6*XX) + 5*e^(2/5*I*pi - 6*XX) - 5*e^(6/5*I*pi + 6*XX) - 5*e^(4/5*I*pi + 6*XX) - 5*e^(2/5*I*pi + 6*XX) - 4*e^(1/10*I*pi + 3*XX) + 4*e^(7/10*I*pi + 3*XX) + 4*e^(3/10*I*pi + 3*XX) + 4*e^(1/10*I*pi + 3*XX) - 4*e^(7/10*I*pi + 3*XX) - 4*e^(3/10*I*pi + 3*XX) - 4*e^(6/5*I*pi + 3*XX) - 4*e^(4/5*I*pi + 3*XX) - 4*e^(2/5*I*pi + 3*XX) + 4*e^(6/5*I*pi + 3*XX) + 4*e^(4/5*I*pi + 3*XX) + 4*e^(2/5*I*pi + 3*XX) + 2*e^(1/10*I*pi + 18*XX) - 2*e^(7/10*I*pi + 18*XX) - 2*e^(3/10*I*pi + 18*XX) - 2*e^(1/10*I*pi + 18*XX) + 2*e^(7/10*I*pi + 18*XX) + 2*e^(3/10*I*pi + 18*XX) + 2*e^(1/10*I*pi - 12*XX) - 2*e^(7/10*I*pi - 12*XX) - 2*e^(3/10*I*pi - 12*XX) - 2*e^(1/10*I*pi - 12*XX) + 2*e^(7/10*I*pi - 12*XX) + 2*e^(3/10*I*pi - 12*XX) + e^(6/5*I*pi + 18*XX) + e^(4/5*I*pi + 18*XX) + e^(2/5*I*pi + 18*XX) - e^(6/5*I*pi - 42*XX) - e^(4/5*I*pi - 42*XX) - e^(2/5*I*pi - 42*XX) + 5*e^(-6*XX) - 5*e^(6*XX) - e^(18*XX) + e^(78*XX) sage: h.factor().expand() e^(-42*XX) - 2*e^(18*XX) + e^(78*XX) I now tested the first equality by taking the first terms of the Taylor expansion of f and numerically evaluated the coefficients which turn out to coincide with the coefficients of the Taylor expansion of g. Thanks for pointer or further ideas! Christian -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
