#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-3.4.2
Component: commutative algebra | Keywords:
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Comment(by SimonKing):
Dear Florent,
thank you very much for the input!
Replying to [comment:26 hivert]:
> Let me add my two cents: It seems to me that the if something is called
"the ring of symmetric polynomials" this is *not* what you implement under
the name {{{SymetricPolynomialRing}}} so that I'm against such a name.
It is correct that the ''polynomials'' are not symmetric. But the ring has
an action of an infinite symmetric group, and the (or at least ''my'')
motivation was an implementation of Symmetric Ideals (they do deserve the
attribute 'symmetric') and their Gröbner bases (see ticket #5566). So, it
is not the 'ring of symmetric polynomials' but a 'symmetric ring of
polynomials'.
> Another argument is that it is extremely likely that some people working
in combinatorics will need "the ring of symmetric polynomials" (in a
finite number of variable).
That's half right. Aren't these called 'invariant rings' rather than
'symmetric rings'?
> We already have a the ring of "symmetric functions" that is the case of
an infinite number of variables. Note that, whether they are polynomials
or not is always subject to discussion: they have an infinite number of
monomials but they have a finite degree. We (combinatorician) choose the
name functions for those finite degree series in an infinite number of
variables.
Here we clearly talk about polynomials: The elements of the 'infinite' or
'symmetric' polynomial ring are ''finite'' sums of monomials. While the
number of variables in the ring is infinite, the number of variables
occuring in one polynomial is finite.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5453#comment:27>
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