### S.from_polynomial(f) -- convert a polynomial to symmetric functions BUT with a parameter

I thought I'd ask a variation of an earlier question that was unanswered.

I use:

```
P.<x,y>=PolynomialRing(QQ)
S=SymmetricFunctions(QQ)
S.inject_shorthands()
f=x+y
e(S.from_polynomial(f))
```

resulting in `e[1]`

(or x+y)

So that works, but when I try to do that for a polynomial with **parameters**, say

```
f=x+y+a+b
```

it complains that `a`

and `b`

are not defined. If I add them to the ring I get `e[1]`

, but I suspect this is equivalent now to `x+y+a+b`

(I didn't check because it should be `e[1]+a+b`

).

Do I need to keep the ring defined the same but define maybe S as;

`S = SymmetricFunctions(QQ[x,y])`

?

This causes the error claiming that the function is not a symmetric polynomial.

By the way, I know I could use something like,

```
a=maxima.eval('elem([2,e1,e2],(x+y+a+b)/2,[x,y])')
```

to get `e1/2 + (a+b)/2`

, but I then can't use `eval`

or `sage_eval`

on the result because there are parsing errors for larger equations, e.g. python complains about the use of '^' instead of '**' for exponentiation, etc. My other posted ~~question ~~question, http://ask.sagemath.org/question/26728/successive-calls-to-maxima/, is in direct relation to this phenomena.