#11747: is_monomial and is_term
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Reporter: was | Owner: AlexGhitza
Type: defect | Status: new
Priority: minor | Milestone: sage-4.7.2
Component: algebra | Keywords: sd32
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Ut oh, the word "monomial" turns out to be ambiguous! There are two
definitions!:
http://en.wikipedia.org/wiki/Monomial
And in Sage we evidently have *randomly* (?) and inconsistenly chosen
between the two definitions, which is very unfortunate.
{{{
sage: R.<x> =QQ[]
sage: (2*x).is_monomial() # definition 2 in univariate poly
True
sage: (x).is_monomial()
True
sage: R.<x,y> =QQ[]
sage: (2*x).is_monomial() # definition 1 in multivariate poly
False
sage: x.is_monomial()
True
}}}
Etc. Fortunately, {{{is_monomial()}}} is called in only about 5 or 6
places in the entire Sage source library, according to
{{{search_src('is_monomial')}}}.
Reading the argument in Wikipedia further, and discussing this with Tom
Boothby, we've decided the following would work for us.
1. Introduce a new method {{{is_term}}}, which returns True for
{{{a*x^i*y^j...}}}, i.e. it allows a coefficient. Fortunately,
{{{is_term}}} is currently used nowhere in Sage.
2. Unify {{{is_monomial}}} to require the coefficient to be 1. This means
changing univariate polynomials to be consistent with multivariate
polynomials.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11747>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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