#13596: Improvements to IntegerMod is_square
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Reporter: roed | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.12
Component: basic arithmetic | Resolution:
Keywords: | Merged in:
Authors: David Roe, Peter | Reviewers: Francis Clarke, Peter
Bruin | Bruin
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #15193 | Stopgaps:
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Changes (by {'newvalue': u'David Roe, Peter Bruin', 'oldvalue': u'David Roe'}):
* status: needs_work => needs_review
* dependencies: #12415 => #15193
* author: David Roe => David Roe, Peter Bruin
Old description:
> Currently we fall back on PARI if 4 divides the modulus, and we don't
> check first to see if the jacobi symbol is -1 (in which case we can
> declare a quadratic non-residue without factoring the modulus). This
> patch fixes both problems.
New description:
Currently we don't check first to see if the Jacobi symbol is -1 (in which
case we can declare non-squareness without factoring the modulus). This
patch fixes this. If this test does not prove that the element is not a
square, we now call PARI's `Zn_issquare` function with the factored
modulus.
Apply: [attachment:13596_new.patch]
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Ticket URL: <http://trac.sagemath.org/ticket/13596#comment:16>
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