#7711: integral() does not reduce coefficients in finite field
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Reporter: zimmerma | Owner: malb
Type: defect | Status: new
Priority: major | Milestone: sage-4.3
Component: commutative algebra | Keywords:
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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Consider the following example:
{{{
sage: P.<x,z> = PolynomialRing(GF(2147483647))
sage: Q.<y> = PolynomialRing(P)
sage: p=x+y+z
sage: p.integral()
1/2*y^2 + (x + z)*y
}}}
Note the leading coefficient 1/2 is not reduced mod 2147483647.
For smaller p this seems to work:
{{{
sage: P.<x,z> = PolynomialRing(GF(2147483629))
sage: Q.<y> = PolynomialRing(P)
sage: p=x+y+z
sage: p.integral()
-1073741814*y^2 + (x + z)*y
}}}
It works also when the smaller ring P has only one variable:
{{{
sage: P.<x> = PolynomialRing(GF(2147483647))
sage: Q.<y> = PolynomialRing(P)
sage: p=x+y
sage: p.integral()
1073741824*y^2 + x*y
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7711>
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