#6059: speed regresion in hilbert_symbol after #5834
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Reporter: tornaria | Owner: tornaria
Type: defect | Status: new
Priority: major | Milestone: sage-4.0
Component: number theory | Keywords: regression
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The following hilbert symbol computation
{{{
sage: a=(next_prime(10**22)*next_prime(10**23))
sage: time hilbert_symbol(a,-1,2)
CPU times: user 0.62 s, sys: 0.06 s, total: 0.68 s
Wall time: 0.68 s
1
}}}
used to be almost instant before the patch in #5834 (in 4.0.alpha0).
The patch extends hilbert_symbol to work with rationals, by using the
{{{squarefree_part()}}} function. However, that function needs to factor.
Fortunately, we don't need the actual squarefree part to compute the
hilbert symbol, rather we could use {{{numerator()*denominator()}}} to
achieve the same result; the hilbert symbol can thus be computed without
factoring.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6059>
Sage <http://sagemath.org/>
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