#1956: implement multivariate power series arithmetic
--------------------------------------------------+-------------------------
Reporter: was | Owner: pernici
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.6.1
Component: commutative algebra | Keywords: multivariate
power series
Author: Niles Johnson | Upstream: N/A
Reviewer: Martin Albrecht, Simon King | Merged:
Work_issues: multivariate series on 1 generator |
--------------------------------------------------+-------------------------
Comment(by SimonKing):
Replying to [comment:64 pernici]:
> Multivariate series in one variable differ from univariate series;
> is it the intended behaviour?
I don't know whether it is intended, but I'd like to mention that there
already is a difference between univariate polynomials and multivariate
polynomials in one variable:
{{{
sage: R_uni = PolynomialRing(QQ,'x')
sage: R_uni
Univariate Polynomial Ring in x over Rational Field
sage: R_multi = PolynomialRing(QQ,'x',1)
sage: R_multi
Multivariate Polynomial Ring in x over Rational Field
sage: timeit('a = R_uni.random_element()')
625 loops, best of 3: 48.4 µs per loop
sage: timeit('a = R_multi.random_element()')
625 loops, best of 3: 192 µs per loop
sage: a = R_uni.random_element()
sage: b = R_multi(a)
sage: a.leading_coefficient()
-27
sage: hasattr(b,'leading_coefficient')
False
sage: b.lc()
-27
sage: hasattr(a,'lc')
False
}}}
While it is clear that there is a difference in the timings for
`random_element`, I don't like that the names are different for methods
that do essentially the same.
Things are different in the case of `degrees` (which exists only for
multivariate polynomials). Since the word is plural (it denotes the tuple
of maximal exponents of each variable, not necessarily occuring in a
single monomial), it doesn't really make sense in the univariate case.
However, I do think that in that case (and similar cases) there should be
a method of univariate polynomials emulating the corresponding method for
multivariate polynomials with one variable.
So, I don't mind about the different timings; but I think methods should
be more or less equivalent.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1956#comment:66>
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 post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
