#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 niles):
Replying to [comment:46 malb]:
>
> Here are some performance figures:
> <SNIP>
Thanks; I think these are outside the scope of this ticket (although
important!) Here are the numbers I get:
{{{
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: 2.67 ms per loop
sage: %timeit fp^2 # polynomials
625 loops, best of 3: 52.3 µs per loop
}}}
The arithmetic is done in a univariate power series ring over a
multivariate power series ring (called the "background ring" in the code):
{{{
sage: R._bg_ps_ring()
Power Series Ring in T over Multivariate Polynomial Ring in t, u, v over
Rational Field
sage: fb = f._bg_value
sage: %timeit fb^2
125 loops, best of 3: 2.61 ms per loop
}}}
So the speed is a limitation of univariate power series rings over
multivariate polynomial rings . . .
{{{
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: 1.48 ms per loop
sage: %timeit fp^2 # polynomials
625 loops, best of 3: 20.8 µs per loop
sage: fb = f._bg_value # univariate power series over multivariate
polynomials
sage: %timeit fb^2
625 loops, best of 3: 1.42 ms per loop
}}}
>
> Conversion to Magma didn't seem to work at all, or am I doing it wrong?
>
I don't know anything about converting to magma, but the following are
also broken:
{{{
sage: magma(fp)
TypeError: Error evaluating Magma code.
IN:_sage_[5]:=SageCreateWithNames(PolynomialRing(_sage_ref2,3,negdeglex),["t","u","v"]);
OUT:
>>
_sage_[5]:=SageCreateWithNames(PolynomialRing(_sage_ref2,3,negdeglex),["t",
^
User error: Identifier 'negdeglex' has not been declared or assigned
sage:magma(fb)
>> _sage_[6]:=32*t^4*T^4 + 30*t^2*u*v^5*T^8 - 21*t^3*u^3*v^3*T^9 +
56*t*u^7*v^
^
User error: Identifier 't' has not been declared or assigned
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1956#comment:47>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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