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The answer is actually implicit in the linked page: elementary functions have the property that (with Sage's notation) e[i, j, ...] = e[i]*e[j]*.... So there you have your polynomial.

Apparently you are right. I use Sage 7.0 on Debian unstable. I installed Sage unpacking the file distributed on Sage's website (for amd64). However, probably I did (by mistake) checkout another version and then checkout again versio 7.0. This might have corrupted something. I tried on another computer (same environment, but without that error with checkout) and it works. So probably it is my fault and that is the culprit.

Suppose I do the following:

sage: SF=SymmetricFunctions(QQ)
sage: poly=SF.e()(SF.from_polynomial(x^2+y^2))
sage: poly
e[1, 1] - 2*e[2]

Now I would like to substitute e[1, 1] in that expression. However:

sage: poly.subs({SF.e()[1, 1]: 1})
e[1, 1] - 2*e[2]

Does not do what I want (in fact it does not do anything). Is there a way to substitute a specific elementary polynomial?

Is it possible to run multiple instances of Sage? If I try, the second one complains that Sage crashed and lets me send a bug report. But Sage did not crash, it is just that another instance is going. Is it intended? Is there any workaround?

(I might use the notebook to do multiple things a time, I guess, but I really work better the the IPython console)

Sure, that's a possibility, but I hoped not having to type the expression twice (my main aim was actually that of proof reading expressions in a more natural writing). Thanks anyway!

SymmetricFunctions, together with the various provided bases, is very good at writing a symmetric polynomial as the linear combination of what is called elementary functions here: mathworld.wolfram.com/SymmetricPolynomial.html. However, a different result says that a symmetric polynomial can be written as a polynomial on what is called elementary symmetric polynomials in the same paper. Can that be computed with Sage?

I notice that some operations have a hold property that does it. But sum apparently has not. Is there a general solution?

Hi.

I would like to ask Sage not to perform a certain symbolic computation until I tell it to. This is because I would like first to show with view the thing I am typing, and then execute it later. So, for instance, I would like something like

sage: view(noexec(sum(1/k^4, k, 1, oo)))

(which should show the summation formula without executing it) and

sage: view(sum(1/k^4, k, 1, oo))

(which should show the result, as it actually does).

Is this possible?