#5453: [with patch, needs review] Create a ring for working with polynomials in
countably infinitely many variables
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Reporter: mhansen | Owner: malb
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.4.1
Component: commutative algebra | Keywords:
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Comment(by SimonKing):
Dear Mike,
Cool! Thank you that you started an implementation!
Certainly from your patch I learn a lot about how to create a (unique)
parent structure.
I don't quite understand how the method `stretch` works, but I'll try to
figure out. 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)]}}}.
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?
{{{
sage: X.<x> = InfinitePolynomialRing(QQ)
sage: p = x[0]
sage: while(1):
....: p = p.stretch(2)
....: print p
}}}
Does it soon fill up the whole memory with huge (but finite) polynomial
rings? And is much time being spent with creating these rings?
Sorry that I can't test the example myself (will only be possible next
week). But perhaps you can tell me what happens.
Cheers,
Simon
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5453#comment:1>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
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