This a sample program that I wrote which is supposed to test a function that I wrote "proj" to project a function onto a basis.  In particular, in this example I use a Fourier mode.  When I project a function which is a sum of two terms I get an incorrect answer.  When I project each term I get the correct answer.

Any ideas why this yielding an inconsistent result?  Also, if maple has it's own version of proj that is more stable I'm happy to use that.

I have the following expression which is a sum of three terms.  The first term has a -(H1+H2)^2 and the second one has a (H1+H2)^2 term and I would like to simplify this by dividing the equation by (H1+H2)^2 but I can't figure out how to force maple to do that.  Any help would be greatly appreciated.

(-2*H1*H2-H2^2-H1^2)*`ϕt`+(H1^2+2*H1*H2+H2^2)*`ηt`*Ut+4*H2*H1*Uc*`ηc` = 0

Also, f someone can direct me to where I can learn to present equations better in this file that would be icing on the cake.