Opened 4 years ago

#21283 new defect

Inverse of a multivariate power series

Reported by: kedlaya Owned by:
Priority: major Milestone: sage-7.4
Component: algebra Keywords: multivariate series, fraction field
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description

Multivariate polynomials exhibit this behavior:

sage: T.<a,b> = PolynomialRing(QQ, 2)
sage: (~a).parent()
Fraction Field of Multivariate Polynomial Ring in a, b over Rational Field

But multivariate power series don't (and should):

sage: R.<x,y> = PowerSeriesRing(QQ, 2)
sage: (~x).parent()
...
NotImplementedError: Multiplicative inverse of multivariate power series currently implemented only if constant coefficient is a unit.

This is the primary issue holding up resolution of the mostly unrelated issue #8972.

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