#11960: bug in matrix of frobenius when p = 3
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Reporter: jen | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-7.2
Component: number theory | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Changes (by kedlaya):
* milestone: => sage-7.2
Comment:
I think matrix_of_frobenius is only failing because the short Weierstrass
equation has bad reduction at 3. If you manually write down a Weierstrass
equation of the form {{{y^2 = P(x)}}} with good reduction at 3, everything
works:
{{{
sage: E = EllipticCurve('83a1')
sage: E
Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 + x over Rational
Field
sage: pr.<x> = PolynomialRing(QQ)
sage: a = x^3 + x^2 + x
sage: b = x + 1
sage: C = HyperellipticCurve(a + b^2/4)
sage: C.matrix_of_frobenius(3)
[ 2*3 + 3^5 + 2*3^6 + 3^8 + 3^11 + 2*3^12 +
2*3^13 + 2*3^14 + 2*3^15 + 3^16 + 3^18 + 3^19 + O(3^20) 2*3
+ 2*3^2 + 2*3^3 + 2*3^7 + 3^8 + 2*3^9 + 2*3^10 + 2*3^11 + 2*3^13 + 3^14 +
3^15 + 2*3^16 + 3^17 + 3^19 + O(3^20)]
[2*3 + 3^2 + 2*3^5 + 3^6 + 2*3^7 + 2*3^9 + 3^10 + 3^11 + 3^12 + 3^13 +
2*3^14 + 2*3^15 + 2*3^16 + 2*3^17 + 2*3^18 + 3^19 + O(3^20)
2 + 2*3^2 + 2*3^3 + 2*3^4 + 3^5 + 2*3^7 + 3^8 + 2*3^9 + 2*3^10 + 3^11 +
3^16 + 2*3^17 + 3^18 + 3^19 + O(3^20)]
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/11960#comment:2>
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