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:
> 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

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