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.)
On 20.04.2012 08:53, Aaron Meurer wrote:
I just remembered something important (I'm not sure why I forgot about
it before). It's going to be slow with multiple generators simply
because the polys are slow with multiple generators. This is because
the recursive dense representation used in the polys is highly
inefficient for polynomials over many variables. This is because as a
"dense" representation, it tends to waste a lot of space, and as a
"recursive" representation, many of the functions are literally
written recursively, which is expensive in Python (take dmp_mul for
example).
So we really need to work toward a sparse representation in the polys
to start to get a real speedup here.
Aaron Meurer
On Fri, Apr 20, 2012 at 1:29 AM, Tom Bachmann<e_mc...@web.de> wrote:
I tried the expressions from
https://groups.google.com/d/topic/sympy/3y6orHV2_4k/discussion (see
the tarball linked to in the first post). I just tried the small
expression with n=1, but it just hung on the reduction step. Any
thoughts on how to make this faster? Those expressions would make good
stress tests for this.
Well these expressions are *huge*. I will run some timing tests, but I think
all parts of the algorithm will break down (i.e. become infeasible
computationally) long before that length.
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