#11543: Hashing algebraic numbers takes far too long
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Reporter: rbeezer | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.2
Component: algebra | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Hashing algebraic numbers can take a very long time. I've traced this to
line 2421 of sage/rings/qqbar.py which can be re-created by the
following code.
{{{
sage: A=matrix(QQ, 4, 4, [1, 2, -2, 2, 1, 0, -1, -1, 0, -1, 1, 1, -1, 2,
1/2, 0])
sage: e = A.eigenvalues()[3]
sage: K = (A-e).kernel()
sage: P = K.basis_matrix()
sage: x = P.list()[3]
sage: from sage.rings.qqbar import ANExtensionElement, AlgebraicGenerator,
ANRoot, AAPoly
sage: QQbar_I_nf = QuadraticField(-1, 'I', embedding=CC.gen())
sage: QQbar_I_generator = AlgebraicGenerator(QQbar_I_nf,
ANRoot(AAPoly.gen()**2 + 1, CIF(0, 1)))
sage: QQbar_hash_offset =
AlgebraicNumber(ANExtensionElement(QQbar_I_generator, ~ZZ(123456789) +
QQbar_I_nf.gen()/ZZ(987654321)))
sage: time h = hash((x + QQbar_hash_offset).interval_exact(CIF))
Time: CPU 58.31 s, Wall: 58.48 s
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11543>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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