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:22725)()
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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