Sorry to reply to myself, here is what I really want to do.

continuing my last post I will put the entire code again).

sage: R=PolynomialRing(QQ,2,'z')
sage: z=R.gens()
sage: x=tuple([z[0]])
sage: p=SFAPower(QQ)
sage: f=p([2,1]).expand(1,alphabet=x)
sage: f
z0^3
sage: f in R
False
sage: f==z[0]^3
True
sage: z[0]^3 in R
True
sage: y=tuple([z[1]])
sage: g=p([2,1]).expand(1,alphabet=y)
sage: g
z1^3
sage: f*g
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call
last)

/home/arattan/Sage/<ipython console> in <module>()

/usr/local/sage-3.4/local/lib/python2.5/site-packages/sage/structure/
element.so in sage.structure.element.RingElement.__mul__ (sage/
structure/element.c:9813)()

/usr/local/sage-3.4/local/lib/python2.5/site-packages/sage/structure/
coerce.so in sage.structure.coerce.CoercionModel_cache_maps.bin_op
(sage/structure/coerce.c:6584)()

TypeError: unsupported operand parent(s) for '*': 'Multivariate
Polynomial Ring in z0 over Rational Field' and 'Multivariate
Polynomial Ring in z1 over Rational Field'
sage:
----------------------------------------

Basically, I want to be able to multiply f and g and I can't, probably
because they are not recognized as being in the same polynomial ring.


On 30 May, 11:30, amps <arat...@gmail.com> wrote:
> Hello,
>
> I am wondering how to coerce a symmetric function in a certain number
> of variables into a polynomial ring with larger variables.  I am
> getting some rather confusing output.
>
> ----------------------------------------------------------------------
> | Sage Version 3.4.2, Release Date: 2009-05-05                       |
> | Type notebook() for the GUI, and license() for information.        |
> ----------------------------------------------------------------------
> sage: R=PolynomialRing(QQ,2,'z')
> sage: z=R.gens()
> sage: x=tuple([z[0]])
> sage: x
> (z0,)
> sage: p=SFAPower(QQ)
> sage: f=p([2,1]).expand(1,alphabet=x)
> sage: f in R
> False
> sage: f
> z0^3
> sage: f==z[0]^3
> True
> sage: z[0]^3 in R
> True
> sage:
>
> --------------------------------------------------------
>
> as you can see, f seems to be both in and not in R.  I want the
> polynomial to be a symmetric polynomial in a subset of variables in
> the ring R.
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