#5453: [with patch, needs review] Create a ring for working with polynomials in
countably infinitely many variables
---------------------------------+------------------------------------------
Reporter: mhansen | Owner: mhansen
Type: enhancement | Status: assigned
Priority: major | Milestone: sage-3.4.2
Component: commutative algebra | Keywords:
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Comment(by SimonKing):
(Concerning the patches: Please first apply {{{trac_5453.patch}}} and then
{{{symmetric_polynomial.patch}}}. The third patch is now obsolete.)
I sorted the above mentioned import problem out (import of
{{{Permutation_class}}}). Instead of importing this class and doing
{{{is_instance}}}, I now test the presence of the attribute
{{{to_cycles()}.
And, to my surprise, the arithmetics is faster than the "dense"
implementation. I don't know the reason.
Here, I make some very basic timings for {{{InfinitePolynomialRing}}}
versus {{{SymmetricPolynomialRing}}}:
{{{
sage: X.<x,y> = SymmetricPolynomialRing(QQ)
sage: Y.<a,b> = InfinitePolynomialRing(QQ)
sage: p=x[10]*y[2]^3+2*x[1]*y[3]
sage: p2=x[100]*y[20]^3+2*x[10]*y[30]
sage: q=a[10]*b[2]^3+2*a[1]*b[3]
sage: q2=a[100]*b[20]^3+2*a[10]*b[30]
sage: timeit('r=p*p2')
625 loops, best of 3: 1.15 ms per loop
sage: timeit('r=q*q2')
125 loops, best of 3: 3.68 ms per loop
sage: timeit('r=p+p2')
625 loops, best of 3: 1.14 ms per loop
sage: timeit('r=q+q2')
125 loops, best of 3: 3.69 ms per loop
}}}
Cheers,
Simon
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5453#comment:17>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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