#11747: is_monomial and is_term
---------------------------+------------------------------------------------
Reporter: was | Owner: AlexGhitza
Type: defect | Status: positive_review
Priority: minor | Milestone: sage-4.7.2
Component: algebra | Keywords: sd32
Work_issues: | Upstream: N/A
Reviewer: Mike Hansen | Author: William Stein
Merged: | Dependencies:
---------------------------+------------------------------------------------
Changes (by newvalueoldvalue):
* reviewer: => Mike Hansen
* author: => William Stein
Old description:
> 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.
New description:
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.
----
Apply [attachment:trac_11747.patch] to the Sage library.
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11747#comment:4>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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