#12803: quotient of ideals throws up Singular bug
-------------------------------------------------+-------------------------
       Reporter:  mariah                         |        Owner:  malb
           Type:  defect                         |       Status:  new
       Priority:  major                          |    Milestone:  sage-6.4
      Component:  commutative algebra            |   Resolution:
       Keywords:                                 |    Merged in:
        Authors:                                 |    Reviewers:
Report Upstream:  Fixed upstream, in a later     |  Work issues:
  stable release.                                |       Commit:
         Branch:                                 |     Stopgaps:  #17679
   Dependencies:                                 |
-------------------------------------------------+-------------------------
Description changed by jdemeyer:

Old description:

> {{{
> sage: var('x,y,z')
> (x, y, z)
> sage: R = ZZ[x,y,z]
> sage: A = R.ideal([x^2, x*y, x*z])
> sage: B = R.ideal([x])
> sage: A.quotient(B)
> ---------------------------------------------------------------------------
> RuntimeError                              Traceback (most recent call
> last)
>
> /home/mariah/sage/sage-4.8-x86_64-Linux-core2-fc/<ipython console> in
> <module>()
>
> /home/mariah/sage/sage-4.8-x86_64-Linux-core2-fc/local/lib/python2.6
> /site-packages/sage/rings/polynomial/multi_polynomial_ideal.pyc in
> wrapper(*args, **kwds)
>     500         """
>     501         with LibSingularDefaultContext():
> --> 502             return func(*args, **kwds)
>     503     return wrapper
>     504
>
> /home/mariah/sage/sage-4.8-x86_64-Linux-core2-fc/local/lib/python2.6
> /site-packages/sage/rings/polynomial/multi_polynomial_ideal.pyc in
> quotient(self, J)
>    2224         import sage.libs.singular
>    2225         quotient = sage.libs.singular.ff.quotient
> -> 2226         return R.ideal(quotient(self, J))
>    2227
>    2228     @require_field
>
> /home/mariah/sage/sage-4.8-x86_64-Linux-core2-fc/local/lib/python2.6
> /site-packages/sage/libs/singular/function.so in
> sage.libs.singular.function.SingularFunction.__call__
> (sage/libs/singular/function.cpp:10130)()
>
> /home/mariah/sage/sage-4.8-x86_64-Linux-core2-fc/local/lib/python2.6
> /site-packages/sage/libs/singular/function.so in
> sage.libs.singular.function.call_function
> (sage/libs/singular/function.cpp:11392)()
>
> /home/mariah/sage/sage-4.8-x86_64-Linux-core2-fc/local/lib/python2.6
> /site-packages/sage/libs/singular/function.so in
> sage.libs.singular.function.call_function
> (sage/libs/singular/function.cpp:11306)()
>
> RuntimeError: Segmentation fault
> sage:
> }}}
>
> There is at least another one (fixed in 4.0.1, see ticket #17254):
>
> {{{
> R.<xe,xv> = ZZ[]
>
> J = Ideal(4*xv^3+3*xv^2, 3*xe*xv^2+xe-2*xv);
>
> I  = Ideal(-3, -3*xv-1, -3);
> I2 = Ideal(-3, -3*xv-1);
> assert( I  == I2 )
>
> Q1 = J.quotient(I) # wrong
> Q2 = J.quotient(I2)
>
> assert( Q1 == Q2 ) # fails
> }}}

New description:

 This is a bug in Singular 3.1.7 (fixed in 4.0.1, see ticket #17254):

 {{{
 R.<xe,xv> = ZZ[]

 J = Ideal(4*xv^3+3*xv^2, 3*xe*xv^2+xe-2*xv);

 I  = Ideal(-3, -3*xv-1, -3);
 I2 = Ideal(-3, -3*xv-1);
 assert( I  == I2 )

 Q1 = J.quotient(I) # wrong
 Q2 = J.quotient(I2)

 assert( Q1 == Q2 ) # fails
 }}}

--

--
Ticket URL: <http://trac.sagemath.org/ticket/12803#comment:11>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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