#16381: primary decomposition doesn't work when ideal is in a quotient
polynomial
ring
-------------------------------------+-------------------------------------
Reporter: was | Owner: malb
Type: defect | Status: needs_review
Priority: minor | Milestone: sage-6.3
Component: commutative | Resolution:
algebra | Merged in:
Keywords: sd59 | Reviewers:
Authors: Martin Albrecht | Work issues:
Report Upstream: N/A | Commit:
Branch: u/malb/trac_16381 | c237b07be5568f9f19b2333f12dc46efe8a82ea5
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Comment (by mmarco):
Am i missing something or singular can give incorrect anwers in this case?
:
{{{
SINGULAR /
Development
A Computer Algebra System for Polynomial Computations / version
3-1-6
0<
by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann \ Dec 2012
FB Mathematik der Universitaet, D-67653 Kaiserslautern \
> ring r=0,(x,y,z),dp;
> ideal i=z2-x2-y2;
> qring q = i;
> setring q;
> ideal j0=y2;
> ideal j1=x-z;
> ideal j2=x+z;
> LIB "primdec.lib";
// ** loaded /home/mmarco/sage/local/share/singular/primdec.lib
(14732,2012-03-30)
// ** loaded /home/mmarco/sage/local/share/singular/ring.lib
(15322,2012-10-12)
// ** loaded /home/mmarco/sage/local/share/singular/absfact.lib
(14191,2011-05-04)
// ** loaded /home/mmarco/sage/local/share/singular/triang.lib
(13499,2010-10-15)
// ** loaded /home/mmarco/sage/local/share/singular/matrix.lib
(13658,2010-11-16)
// ** loaded /home/mmarco/sage/local/share/singular/nctools.lib
(14246,2011-05-26)
// ** loaded /home/mmarco/sage/local/share/singular/inout.lib
(13499,2010-10-15)
// ** loaded /home/mmarco/sage/local/share/singular/random.lib
(14661,2012-03-05)
// ** loaded /home/mmarco/sage/local/share/singular/poly.lib
(14852,2012-04-30)
// ** loaded /home/mmarco/sage/local/share/singular/elim.lib
(14661,2012-03-05)
// ** loaded /home/mmarco/sage/local/share/singular/general.lib
(14191,2011-05-04)
> primdecGTZ(j0);
[1]:
[1]:
_[1]=y2
[2]:
_[1]=y
}}}
but j0 is the inttersection of j1 and j2, which are prime ideals:
{{{
> intersect(j1,j2);
_[1]=x2-z2
_[2]=xy2+y2z
> factorize(xy2+y2z);
[1]:
_[1]=1
_[2]=x+z
_[3]=y
[2]:
1,1,2
> primdecGTZ(j1);
[1]:
[1]:
_[1]=x-z
[2]:
_[1]=x-z
> primdecGTZ(j2);
[1]:
[1]:
_[1]=x+z
[2]:
_[1]=x+z
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/16381#comment:5>
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