already fixed it seems: http://trac.sagemath.org/ticket/16485
On Friday 27 Jun 2014 17:43:13 Nicolas M. Thiery wrote:
> Hi!
>
> I have a zero-dimensional ideal of polynomials over the rational, and
> getting an error when requesting the solutions over QQbar:
>
> sage: R.<p00,p01,p02,p10,p11,p12> = QQ[]
> sage: eq = [5/9*p00^2 + 2/3*p00*p01 + 1/3*p01^2 + 2/9*p00*p02 +
> 2/3*p01*p02 + 5/9*p02^2 - 5/9, ....: 5/9*p00*p10 + 1/3*p01*p10 +
> 1/9*p02*p10 + 1/3*p00*p11 + 1/3*p01*p11 + 1/3*p02*p11 + 1/9*p00*p12 +
> 1/3*p01*p12 + 5/9*p02*p12 - 4/9, ....: 5/9*p00*p10 + 1/3*p01*p10 +
> 1/9*p02*p10 + 1/3*p00*p11 + 1/3*p01*p11 + 1/3*p02*p11 + 1/9*p00*p12 +
> 1/3*p01*p12 + 5/9*p02*p12 - 4/9, ....: 5/9*p10^2 + 2/3*p10*p11 +
> 1/3*p11^2 + 2/9*p10*p12 + 2/3*p11*p12 + 5/9*p12^2 - 5/9, ....: p00^2
> + p01^2 + p02^2 - 1,
> ....: p00*p10 + p01*p11 + p02*p12,
> ....: p00*p10 + p01*p11 + p02*p12,
> ....: p10^2 + p11^2 + p12^2 - 1]
> sage: I.dimension()
> 0
> sage: I.vector_space_dimension()
> 16
> sage: I.variety()
> []
>
> So far, so good. However:
>
> sage: I.variety(QQbar)
> ...
>
> /opt/sage-git/local/lib/python2.7/site-packages/sage/rings/polynomial/multi
> _polynomial_ideal.pyc in _variety(T, V, v) 2619 vbar =
> v.copy()
> 2620 vbar[variable] = root
> -> 2621 Tbar = [ f.subs({variable:root}) for f in T ]
> 2622 _variety(Tbar,V,vbar)
> 2623
>
>
> /opt/sage-git/local/lib/python2.7/site-packages/sage/rings/polynomial/multi
> _polynomial_libsingular.so in
> sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular.
> subs
> (build/cythonized/sage/rings/polynomial/multi_polynomial_libsingular.cpp:22
> 725)() TypeError: keys do not match self's parent
>
> I manage to get some of the solutions via a triangular decomposition,
> but not all of them::
>
> sage: J1, J2 = I.triangular_decomposition()
> sage: J2.variety(QQbar)
> [{p12: -0.9082482904638630?, p00: -0.4082482904638630?, p11:
> 0.09175170953613699?, p01: -0.9082482904638630?, p10: -0.4082482904638630?,
> p02: 0.09175170953613699?}, {p12: -0.09175170953613699?, p00:
> 0.4082482904638630?, p11: 0.9082482904638630?, p01: -0.09175170953613699?,
> p10: 0.4082482904638630?, p02: 0.9082482904638630?}, {p12:
> 0.09175170953613699?, p00: -0.4082482904638630?, p11: -0.9082482904638630?,
> p01: 0.09175170953613699?, p10: -0.4082482904638630?, p02:
> -0.9082482904638630?}, {p12: 0.9082482904638630?, p00: 0.4082482904638630?,
> p11: -0.09175170953613699?, p01: 0.9082482904638630?, p10:
> 0.4082482904638630?, p02: -0.09175170953613699?}] sage: J1.variety(QQbar)
> *BANG AS ABOVE*
>
> Any insight? Should I file a ticket?
>
> Cheers,
> Nicolas
> --
> Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
> http://Nicolas.Thiery.name/
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