On Wed, Dec 12, 2007 at 10:12:07AM -0600, Daniel R. Grayson wrote:
> The Macaulay2 code for factorization just calls the Singular-Factory library
> that we link against.  So I don't know why it should be faster than Singular!

I did wonder about that.  However, my testing indicates that M2 consistently 
takes about 1.5 seconds for this factorization, but singular takes much longer 
(and the time isn't consistent at all).  I'd love to know if I'm just being 
tremendously stupid and missing something -- so it might be good if somebody 
else wants to confirm or deny my timings for the example at
http://sage.math.washington.edu/home/jbmohler/singular/factorize01.singular

How do you link against singular?  I thought the singular library mode was new 
in the last 6 months and that M2 was around longer than that?

In any case, mpolynomial factorization, gcd, and division algorithms in 
singular 
pretty much entirely stop me cold computing in a fraction field of 
mpolynomials.  
My solution for the moment is to hack in calls to mathematica or magma from the 
libsingular code in sage.  I had a version of that hackage with M2, but the 
pexpect sage wrapper for M2 choked up on my polynomials (about 1/4 mb in string 
form.)  This "choked up" might merit more precise diagnosis investigation 
itself.

--
Joel

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