Re: infinite polynomial ring as a free commutative algebra

[John Cremona]

Try asking on the sage-algebra list? I have CC'd that list.

John Cremona

On Jul 7, 5:30 pm, jeremy chabot <chabo...@gmail.com> wrote:
> Yes but I want to define a coalgebra and use a coproduct and tensor
> which rings dont have. If I could do these things with the ring
> structure then please tell me how. thanks
>
> On Jul 6, 8:53 pm, Mike Hansen <mhan...@gmail.com> wrote:
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> > On Wed, Jul 6, 2011 at 9:51 AM, jeremy chabot <chabo...@gmail.com> wrote:
> > > Hi, I am trying to implement  the infinite polynomial ring as a free
> > > commutative algebra.
>
> > > I am unsure of exactly how to do this. So far I have:
>
> > > --------------------------------------------------------------------------- ­--------
> > > X.<x>=InfinitePolynomialRIng(QQ)
> > > --------------------------------------------------------------------------- ­-------
> > > class Practice3(CombinatorialFreeModule):
> > >    def __init__(self, R, X, **keywords):
> > >        self._group= X
> > >        CombinatorialFreeModule.__init__(self, R, self._group,
> > > category=AlgebrasWithBasis(QQ))
> > >        return
> > > --------------------------------------------------------------------------- ­--------
>
> > I'm not sure exactly what you're trying to do.  It seems like you just
> > want to use InfinitePolynomialRing directly:
>
> > sage: X.<x> = InfinitePolynomialRing(QQ)
> > sage: x[1]*x[2] + x[3]
> > x_3 + x_2*x_1
> > sage: _*x[100]
> > x_100*x_3 + x_100*x_2*x_1
>
> > --Mike