#16613: fix content of polynomials
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Reporter: vdelecroix | Owner:
Type: defect | Status: needs_info
Priority: major | Milestone: sage-6.4
Component: commutative algebra | Resolution:
Keywords: | Merged in:
Authors: Vincent Delecroix | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Changes (by bruno):
* status: new => needs_info
* cc: mkosters, davidloeffler (added)
Comment:
The content of a polynomial is sometimes defined as the gcd of its
coefficients, and sometimes as the ideal generated by the coefficients. In
!SageMath, we have inconsistencies between polynomial rings:
* For Flint, NTL, p-adics and multivariate polynomial rings, `content`
returns the gcd of the coefficients.
* The generic implementation (for the class
`rings.polynomial.polynomial_element.Polynomial`) returns an ideal. This
is means that for polynomials over ''weird'' rings, and for all sparsely
represented univariate polynomials, `content` returns an ideal.
'''I propose to make all the implementations return a element of the base
ring rather than an ideal.'''
Rationale:
* This means changing only one method.
* This is consistent with
[http://fr.mathworks.com/help/symbolic/mupad_ref/content.html MuPAD],
[http://www.maplesoft.com/support/help/Maple/view.aspx?path=content
Maple], [http://reference.wolfram.com/language/ref/FactorTermsList.html
Mathematica] (though the name of the function is different) and
[http://magma.maths.usyd.edu.au/magma/handbook/text/214#1841 Magma] (also
for the [http://magma.maths.usyd.edu.au/magma/handbook/text/227#2005
multivariate case])
* This is the definition taken for instance by von zur Gathen and Gerhard
in ''Modern Computer Algebra'' or Cohen in ''A course in Computational
Number Theory''.
P.S.: I cc the author and reviewer of #12218 in which the generic
`content` was implemented.
--
Ticket URL: <http://trac.sagemath.org/ticket/16613#comment:2>
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