#5453: [with patch, needs review] Create a ring for working with polynomials in
countably infinitely many variables
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Reporter: mhansen | Owner: mhansen
Type: enhancement | Status: assigned
Priority: major | Milestone: sage-3.4.1
Component: commutative algebra | Keywords:
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Changes (by mhansen):
* owner: malb => mhansen
* status: new => assigned
Comment:
Replying to [comment:1 SimonKing]:
> Cool! Thank you that you started an implementation!
Actually, it's code that I've had on the combinat patch server for awhile
since I have code that makes use of these things.
> I don't quite understand how the method `stretch` works, but I'll try to
figure out.
Stretch is actually something that I needed.
> However, I think a more useful thing to implement would be the action by
permutation of variables. I.e.,
> {{{
> sage: X.<x,y> = InfinitePolynomialRing(QQ)
> sage: P = Permutation(((0,1),(2,3,4)))
> sage: a = x[3] + y[2] + x[0]*y[1]
> sage: a^P
> x1*y0 + x4 + y3
> }}}
> That's to say, {{{x[i]}}} is mapped by {{{P}}} to {{{x[P(i)]}}}.
Sure.
> However I am not sure whether it is a good idea to implement things on
top of usual finitely generated polynomial algebras. After all, they are
parent structures and are thus cached -- and my successively fill up
memory.
> What happens if you do the following?
> ...
> Does it soon fill up the whole memory with huge (but finite) polynomial
rings? And is much time being spent with creating these rings?
Yep (that's what you can with infinite loops :-) For my application,
doing the arithmetic will the primary bottleneck.
Like I said, this was a very basic implementation that I wrote because it
does what I need and I was able to write it relatively quickly. I used
the existing finite polynomial rings because they already do fast
arithmetic that I (personally) have no desire to duplicate.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5453#comment:3>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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