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exact division of multivariate polynomial
http://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2473
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Author:  mickael [ Mon Nov 24, 2014 3:42 pm ]
Post subject:  exact division of multivariate polynomial

Hi all,

I have two multivariate polynomials A and B over the integer ring.
I know that B divides exactly A. I need to perform this division using the monomial ordering that I choose.
I can't find in the documentation any exact division function.

The following code does not work :
int degre=4;
ring r=integer,(x,y,z,t),lp;
poly s1=(1+x+y+z+t)^5;
poly s2=s1+1;
poly p=s2*s1;
poly q=p/s2;

I obtain the following message.
? division over a coefficient domain only implemented for terms
? error occurred in or before STDIN line 6: `poly q=p/s2;`
….

If I replace r by the following definition, it works :
ring r=0,(x,y,z,t),lp;

Does it exist a function for exact division?



Mickaël

Author:  levandov [ Thu Oct 01, 2015 4:23 pm ]
Post subject:  Re: exact division of multivariate polynomial

Hi,

there's a function
division()
which does division with rest. Googling through Manual
or checking the index of the Manual is a good idea to try.

If you want to know that q divides p exactly,
this could be checked via
NF(p,q);
it gives 0 iff p = a*q for some a.
Cheers

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