#5453: [with patch, needs work] 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):
Replying to [comment:21 malb]:
> I think at least the interface should be agreed upon first.
>
> {{{
> sage: X.<x,y> = SymmetricPolynomialRing(QQ)
> sage: Y.<a,b> = InfinitePolynomialRing(QQ)
> }}}
>
> should be one name only and a parameters {{{dense}}}/{{{sparse}}} just
like matrices.
Makes sense.
I vote for the name {{{SymmetricPolynomialRing}}}, since Aschenbrenner and
Hillar use the notion "Symmetric Ideals", e.g. in arXiv:math/0411514
("Finite generation of symmetric ideals"). Of course, when choosing this
name, a permutation action should be implemented. But this can be easily
done for Mike's approach as well.
But then, we should also agree on monomial orderings. Meanwhile, I am
implementing support for different orderings (lex, deglex, degrevlex). But
in either case, I have
X.gen(i)[m] < X.gen(j)[n] iff i<j or (i==j and m<n)
Is this acceptable for you, Mike and Martin?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5453#comment:22>
Sage <http://sagemath.org/>
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