#17550: sorted variables in multivariate polynomial ring wrong order
---------------------------+----------------------------------------------
Reporter: dkrenn | Owner:
Type: defect | Status: needs_info
Priority: major | Milestone: sage-duplicate/invalid/wontfix
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues: document this better
Branch: | Commit:
Dependencies: | Stopgaps:
---------------------------+----------------------------------------------
Comment (by bruno):
Replying to [comment:7 dkrenn]:
> Replying to [comment:4 bruno]:
> > [...] Yet, the order on the variables themselves doesn't change
between "degrevlex" and "deglex". This is due to the fact that there are
two distinct changes between these two orders.
>
> What do you mean by this? This should (IMHO) change...
This is described in the reference manual
http://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/term_order.html.
The "two changes" I mentioned are the fact that in "degrevlex" one
considers the ''**last** variable whose exponent is **larger**'' while in
"deglex" one considers the ''**first** variable whose exponent is
**smaller**''. Thus, if you have as first variable `a` and second variable
`b`, the comparison between the two monomials `a` and `b` is:
* degrevlex: `a > b` since both monomials have degree `1` and `b` is
the last variable whose exponent is smaller in the monomial `a` (0) than
in the monomial `b` (1);
* deglex: `a > b` since both monomials have degree `1` and `a` is the
first variable whose exponent is larger in the monomial `a` (1) than in
the monomial `b` (0).
Note that, unless I make a mistake, all orders defined in SageMath satisfy
`a > b`.
I do not understand what you mean by "This should change". The way the
orders are defined in SageMath seems consistent with the literature and
the other softwares.
--
Ticket URL: <http://trac.sagemath.org/ticket/17550#comment:8>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
