#12198: is_squarefree() over multivariate rings does not work
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Reporter: MvanBeek | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-4.8
Component: algebraic geometry | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Changes (by vbraun):
* owner: tbd => AlexGhitza
* component: PLEASE CHANGE => algebraic geometry
Comment:
Singular seems to have issues with square-free factorization over ZZ:
{{{
SINGULAR /
Development
A Computer Algebra System for Polynomial Computations / version
3-1-3
0<
by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann \ March
2011
FB Mathematik der Universitaet, D-67653 Kaiserslautern \
> ring R = integer,(x,y), dp;
> poly p = x^2+y^2;
> sqrfree(p);
? not implemented
? error occurred in or before STDIN line 3: `sqrfree(p);`
}}}
This might be implemented in a more recent version, don't know about that.
Looking at the Singular source there is a `isSqrFreeZ` function in the
factory that should do the right thing. Its not clear to me why the code
path doesn't end up there.
Over QQ it works fine:
{{{
> ring Q = 0,(x,y),dp;
> poly p = x^2+y^2;
> sqrfree(p);
_[1]=x2+y2
}}}
I haven't found a way to test square-freeness (as opposed to compute the
squarefree factorization) from the Singular command line, is this function
not exposed to the Singular interpreter?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12198#comment:1>
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