#17520: Division by monomials in LaurentPolynomialRings should not be in the
fraction field
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Reporter: mmarco | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.5
Component: commutative algebra | Keywords: Laurent polynomials
Merged in: | Authors: Miguel Marco
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Right now, if we divide a Laurent Polynomial by a monomial, the result
will live in the fraction field of the corresponding polynomial ring:
{{{
sage: R.<s,q,t>=LaurentPolynomialRing(QQ)
sage: f=s^2*q+q^(-1)*t
sage: f
s^2*q + q^-1*t
sage: f.parent()
Multivariate Laurent Polynomial Ring in s, q, t over Rational Field
sage: f/s
(s^2*q^2 + t)/(s*q)
sage: (f/s).parent()
Fraction Field of Multivariate Polynomial Ring in s, q, t over Rational
Field
}}}
But monomials here are units, so dividing by them should result in an
element of the same ring.
This patch solves this:
{{{
sage: R.<s,q,t>=LaurentPolynomialRing(QQ)
sage: f=s^2*q+q^(-1)*t
sage: f.parent()
Multivariate Laurent Polynomial Ring in s, q, t over Rational Field
sage: f/s
s*q + s^-1*q^-1*t
sage: (f/s).parent()
Multivariate Laurent Polynomial Ring in s, q, t over Rational Field
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/17520>
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