Re: factoring lists in Singular

On May 14, 8:44 pm, Waldek Hebisch <hebi...@xxxxxxxxxxxxxxxx> wrote:
Singular is pretty good at computing Groeber bases, and more
general operating on multivariate polynomials.

Overall Singular is probably the best free open source math software
system for computing Groebner basis over fields. It is slow in
some cases, of course. Cocoalib is also rumored to be pretty
good, but I haven't benchmarked it. Singular has unusually good
support for a wide range of term orders. If you have a *lot* of RAM,
Magma is much much faster than Singular currently at many Groebner
basis computations (Allan Steel spent about five years
implementing and heavily tuning a variant of Faugere's F4 in Magma).

It probably has
more functions to compute some specific properties of ideals.

It has *tons* of such functions, motivated by a wide range of
research applications of algebraic geometry.

However, a it is hard to give a simple and accurate statement.
For example, I found on the net a few examples of polynomials
that take quite a lot of time to factor using Singular --

You might be referring to all the threads about this on sage-devel?

I have tried them in FriCAS and pretty quickly obtained the
anwer. This is _not_ to claim that FriCAS is faster, rather,
to disprove claim "Singular has very fast polynomial
multiplication, so it must be faster at factoring polynomials"

Multivariate polynomial factorization in Singular is very
sketchy. In fact, as far as I can tell, general multivariate
factorization is comparably bad still in all open source math
software. I say "bad", because Magma blows everything
else away speedwise at polynomial factorization. See these
trac tickets for some discussion of major efficiency issues
with Singular as compared to Magma:

"singular factorize is randomly slow"
http://trac.sagemath.org/sage_trac/ticket/1343

"multivariate polynomial factorization over GF(p) (sucks)"
http://trac.sagemath.org/sage_trac/ticket/2152

I've been told some of the Singular group is actively
working on improving their polynomial factorization; I hope
they succeed. There is also at least one Sage developer
(Joel Mohler) working on polynomial factorization for Sage.
I don't know what the latest status of this is.

-- William
.

Relevant Pages

  • Re: factoring lists in Singular
    ... why is it easier to generate Groebner bases of the ideals ... After factoring we have polynomials of low degree, ... I am not aware of a text explicitely comparing FriCAS and Singular. ...
    (sci.math.symbolic)
  • Re: factoring lists in Singular
    ... polynomials that Maple 11 has had problems with. ... (My solution sets ... Singular to perform these simplifications? ... What's the problem with Maple? ...
    (sci.math.symbolic)
  • Re: factoring lists in Singular
    ... The corresponding command in Singular seems to be ... in Singular corresponds to the FriCAS/etc. ... v22l and v21l have a common root as polynomials in s. ...
    (sci.math.symbolic)
  • Re: Question abot the SVD of 1-dimensional data
    ... >problems computing the rank in a naive way but if I find the SVD of the ... >Finally suppose I add noise in the form of small random values to my ... >between the first n+1 singular values and the rest is not as large as I ... and use there the chebyhev basis (chebyshev polynomials of the first kind) ...
    (sci.math.num-analysis)
  • Re: JSH: Resolution now possible
    ... >polynomial factorization which adds to even more years of arguing ... >roots of monic polynomials with integer coefficients. ... >against the math community, well within most of your lifetimes. ... and your academic colleagues probably won't be ...
    (sci.math)