#11537: units in polynomial rings with prime power characteristic
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Reporter: tdupu | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.1
Component: algebra | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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{{{
sage: p = 101
sage: S.<t> = PolynomialRing(ZZ.quotient_ring(p^3))
sage: f = 1+p*t^2
sage: f.is_unit()
True
}}}
{{{
sage: S.<t> = PolynomialRing(ZZ.quotient_ring(p^3),1)
sage: t = S.0
sage: f = 1+p*t^2
sage: f.is_unit()
False
sage: f.inverse_of_unit()
...
ArithmeticError: Element is not a unit.
}}}
{{{
sage: S1.<t> = PolynomialRing(ZZ.quotient_ring(p^3),1)
sage: S2.<tt> = PolynomialRing(ZZ.quotient_ring(p^3))
sage: S1
Multivariate Polynomial Ring in t over Ring of integers modulo 1030301
sage: S2
Univariate Polynomial Ring in tt over Ring of integers modulo 1030301
sage: S1 == S2
False
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11537>
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