Actually, yesterday was the first time I really tried to use Sage for
symbolic computations and it was quite frustrating for me.
1) It would be really nice if it was faster.
2) It seems to me that
((x+y)*y).coeff(y^2)
and
((x+y)*y).expand().coeff(y^2)
should return the same coefficient 1 (while the first one returns
zero).
3) I think that
((x+x*y)/x).simplify()
should return 1+y, instead of the original expression, otherwise, what
is simplify simplifying?
4) It would be nice to be able to get the part of given degree in the
given list of variables, and write
f3 = fp.homogeneous_part([up, vp], 3)
instead of something like
f3 = (fp.coeff(up,3).coeff(vp,0)*up^3*vp^0
+ fp.coeff(up,2).coeff(vp,1)*up^2*vp^1
+ fp.coeff(up,1).coeff(vp,2)*up^1*vp^2
+ fp.coeff(up,0).coeff(vp,3)*up^0*vp^3)
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