#13053: wrong sign in square-free decomposition of polynomials over ZZ
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Reporter: saraedum | Owner: tbd
Type: defect | Status: needs_info
Priority: major | Milestone: sage-6.2
Component: factorization | Resolution:
Keywords: sd40.5 FLINT NTL ZZ | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by rws):
FWIW in Mathematica, `FactorTermsList[-x^2, x]` results in `{-1, 1, x^2}`
(where the first is the content), despite the definition in
http://mathworld.wolfram.com/Content.html
"(1) The content of an integer polynomial P in Z[x], denoted cont(P), is
the largest integer k>=1 such that P/k also has integer coefficients. (2)
Gauss's lemma for contents states that if P and Q are two polynomials with
integer coefficients, then cont(PQ)=cont(P)cont(Q) (Séroul 2000, p. 287)."
Note that while the Mathematica output violates (1) it still satisfies
(2).
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Ticket URL: <http://trac.sagemath.org/ticket/13053#comment:8>
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