#11930: disallow non-smooth hyperelliptic curves, and let hyperelliptic curves
know
they are not singular
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Reporter: dkrenn | Owner: cremona
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.8
Component: elliptic curves | Keywords: hyperelliptic
curve, singular, sd35
Work_issues: | Upstream: N/A
Reviewer: Marco Streng, Damiano Testa | Author: Daniel Krenn,
Marco Streng, Damiano Testa
Merged: | Dependencies:
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Comment(by mstreng):
To check whether a polynomial has repeated roots, this patch uses both
GCDs and resultants. It tries the GCD first, because that is fastest. If
that fails, it tries the resultant.
The reason for needing both gcds and resultants is actually quite funny:
Qp has no gcd currently implemented in Sage, while extensions of Qp have
no resultants in Sage!
With 4.8.alpha4, I get
{{{
sage: P.<x> = Qp(5,7)[]
sage: x.gcd(x)
# AttributeError: 'Polynomial_padic_capped_relative_dense' object has no
attribute 'gcd'
sage: x.resultant(x)
# 0
sage: K.<a> = Qp(5,7).extension(x^2-5)
sage: P.<x> = K[]
sage: x.gcd(x)
# (1 + O(a^14))*x
sage: x.resultant(x)
# TypeError: no conversion of this ring to a Singular ring defined
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11930#comment:17>
Sage <http://www.sagemath.org>
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