#18669: Use PARI to compute rational_diagonal_form()
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Reporter: jdemeyer | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.8
Component: quadratic forms | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jdemeyer/use_pari_to_compute_rational_diagonal_form__|
3ee588dd37871a4a28e7db768e66ab4a44dacd3e
Dependencies: #18656 | Stopgaps:
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Comment (by mmarco):
Are you sure it always works as expected?
BEfore your changes, we have:
{{{
sage: Q = matrix(QQ,[[0,1],[1,0]])
sage: F = QuadraticForm(Q)
sage: F.rational_diagonal_form()
Quadratic form in 2 variables over Rational Field with coefficients:
[ 1 0 ]
[ * -1/4 ]
}}}
But if we try to do what you propose:
{{{
sage: Q = matrix(QQ,[[0,1],[1,0]])
sage: F = QuadraticForm(Q)
sage: F.rational_diagonal_form()
Quadratic form in 2 variables over Rational Field with coefficients:
[ 1 0 ]
[ * -1/4 ]
sage: F._pari_()
[0, 1; 1, 0]
sage: F._pari_().qfgaussred()
[1/2, 1; -1, -1/2]
sage: MS = MatrixSpace(QQ,2,2)
sage: D = MS()
sage: D[0,0] = R[0,0]
sage: D[1,1] = R[1,1]
sage: Q.parent()(D)
[ 1/2 0]
[ 0 -1/2]
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/18669#comment:5>
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