On Fri, Apr 20, 2012 at 1:02 PM, Tom Bachmann <e_mc...@web.de> wrote: > On 20.04.2012 19:50, Aaron Meurer wrote: >> >> On Fri, Apr 20, 2012 at 2:07 AM, Tom Bachmann<e_mc...@web.de> wrote: >>> >>> That could be true. The groebner algorithms actually use a minimal sparse >>> representation internally. But running trigsimp_groebner on smallExpr for >>> me >>> hangs on "a * d_hat - b * c_hat" - (not even the conversion to sparse or >>> reduction, yet) just a multiplication of (huge) polys. >>> >>> As I said, I'll run some timing tests to figure out the bottleneck. But >>> I'm >>> not sure this algorithm can work with such huge expressions. Even the >>> "staircase" function (which just enumerates all monomials below a certain >>> degree) takes ages (I am not sure why, yet. The dense representation does >>> not seem to be a problem.) >> >> >> Is staircase() different from monomials()? According to the docstring >> of monomials(), this suffers from combinatorial explosion. Where >> exactly is staircase used? >> > > It avoids some (hopefully many...) of the monomials by taking only those not > divisible by leading monomials of the groebner basis. (These monomials form > a basis of the quotient space, which is the most basic property of groebner > bases.)
>From what I can see, the final result may be smaller, but it still has to run the loop for each monomial, so it doesn't seem to me to be any more time efficient (just space efficient). Aaron Meurer > > As I said earlier, the algorithm essentially tries general fractions of > increasing degrees and sees of they are equivalent to the fraction we are > simplifying. > > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to sympy@googlegroups.com. > To unsubscribe from this group, send email to > sympy+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
