#12404: is_squarefree() incorrect over imperfect fields
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Reporter: saraedum | Owner:
malb
Type: defect | Status:
needs_work
Priority: minor | Milestone:
Component: commutative algebra | Resolution:
Keywords: sd40.5 | Work issues:
coherence with squarefree_decomposition, fix error
Report Upstream: Not yet reported upstream; Will do shortly. | Reviewers:
Paul Zimmermann
Authors: Julian Rueth | Merged in:
Dependencies: #9054, #12988 | Stopgaps:
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Changes (by zimmerma):
* status: needs_review => needs_work
* reviewer: => Paul Zimmermann
* work_issues: => coherence with squarefree_decomposition, fix error
Comment:
the documentation of {{{is_squarefree}}} says that {{{f}}} is not square-
free if {{{g^2}}}
divides {{{f}}} where {{{g}}} is a non-unit. In particular {{{4*x}}} is
not considered
square free by {{{is_squarefree}}}, but it is by
{{{squarefree_decomposition}}}:
{{{
sage: R.<x> = ZZ[]
sage: f = 4*x
sage: f.is_squarefree()
False
sage: f.squarefree_decomposition()
(4) * x
}}}
Sage should be coherent in that matter. Personally I prefer not to
decompose the coefficient content.
Moreover the following produces an error:
{{{
sage: R.<x> = ZZ[]
sage: f = 2*x^2
sage: f.is_squarefree()
...
AttributeError: 'int' object has no attribute 'is_zero'
}}}
Paul
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12404#comment:9>
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