#1956: implement multivariate power series arithmetic
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Reporter: was | Owner: malb
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.6
Component: commutative algebra | Keywords: multivariate power
series
Author: Niles Johnson | Upstream: N/A
Reviewer: Martin Albrecht, Simon King | Merged:
Work_issues: |
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Comment(by malb):
You are right, I cannot reproduce my problem. As instructed above, I can
indeed apply the patch cleanly.
Some more comments (I'm really not the best person to review this code):
Here are some performance figures:
{{{
#!python
sage: R.<t,u,v> = PowerSeriesRing(QQ); R
Multivariate Power Series Ring in t, u, v over Rational Field
sage: f = R.random_element(prec=20,bound=20)
sage: fp = f.polynomial()
sage: %timeit f^2 # power series
125 loops, best of 3: 2.89 ms per loop
sage: %timeit fp^2 # polynomials
625 loops, best of 3: 82.4 µs per loop
sage: R.<t,u,v> = PowerSeriesRing(GF(127)); R
Multivariate Power Series Ring in t, u, v over Finite Field of size 127
sage: f = R.random_element(prec=20,bound=20)
sage: fp = f.polynomial()
sage: %timeit f^2 # power series
625 loops, best of 3: 1.06 ms per loop
sage: %timeit fp^2 # polynomials
625 loops, best of 3: 15.3 µs per loop
}}}
I also noticed that this is rather slow:
{{{
#!python
sage: sage: R.<t,u,v> = PowerSeriesRing(GF(127)); R
Multivariate Power Series Ring in t, u, v over Finite Field of size 127
sage: f = R.random_element(prec=20,bound=20)
sage: p = f.polynomial()
sage: fp = f.polynomial()
sage: %timeit R(fp)
25 loops, best of 3: 11.1 ms per loop
}}}
Conversion to Magma didn't seem to work at all, or am I doing it wrong?
{{{
#!python
sage: magma(f)
In file "/home/malb/.sage//temp/road/7093//interface//tmp7130", line 1,
column 16:
>> _sage_[4]:=-63*u^4 + 11*t*v^8 - 17*t^3*u^4*v^3 - 61*t^4*u^5*v^2 +
16*t^5*u^
^
User error: Identifier 'u' has not been declared or assigned
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1956#comment:46>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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