#10716: Adding a weighted_degree function to Singular multivariate polynomials
-------------------------------------+-------------------------------------
Reporter: jsrn | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-6.3
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: multivariate | Reviewers: Marshall Hampton
polynomials,degree,Singular | Work issues:
Authors: Johan S. R. | Commit:
Nielsen, Luis Felipe Tabera | 811b79657358bcc6c1201715cd35ffab9a42e346
Alonso | Stopgaps:
Report Upstream: N/A |
Branch: |
u/lftabera/weighted_degree |
Dependencies: |
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Comment (by lftabera):
This patch will have no effect on that. There are no rings with int
weighted order or Integer weighted order.
When you create a multivariate polynomial ring, you select a TermOrder,
with degrevlex as default.
However, in some cases, a user may want to compute the degree of a
polynomial with a weighted term order that is *different* from the term
order of the underlying ring. In this, and only in this case the
weighted_degree method will play a role. In `QQ['x,y']` and `GF(p)['x,y']`
singular will be used, so for usual operations of addition and
multiplication will use the singular implementation of term orders. This
patch will not change that.
{{{
sage: K=PolynomialRing(QQ, 'a,b,c', order=TermOrder('wdeglex',(7,8,9)))
sage: a,b,c=K.gens()
sage: f = a+b**3+c**4
sage: f.degree() # uses the weights of K, it is singular who compute this.
36
sage: f.weighted_degree([7,8,9]) #My patch, not computed using singular.
36
sage: f.weighted_degree([1,3,-3]) #My patch, not computed using singular.
9
sage: #The term order of the underlying ring does not change.
sage: f.parent().term_order()
Weighted degree lexicographic term order with weights (7, 8, 9)
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/10716#comment:37>
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