On 2015-01-24, john_perry_usm <[email protected]> wrote:
>
>
>> Try the following:
>>
>> sage: e = SymmetricFunctions(QQ).e() # construct the symmetric functions 
>> with the e basis 
>> sage: m = SymmetricFunctions(QQ).m() # ditto but with the monomial basis
>> sage: m421 = m[4, 2, 1] # create the monomial you care about
>> sage: e(m421) # coerce the monomial into the ring with the e basis
>> e[3, 2, 1, 1] - 2*e[3, 2, 2] ...
>>
>
> That's not obviously the same as the result I specified. I left out that I 
> know the number of variables I have available; in the example above, I have 
> three variables, so I'm looking specifically for e1=x1+x2+x3, etc. I don't 
> see how I get that from the expression e[3,2,1,1] - 2*e[3,2,2] ...
>
> I'm quite new to this topic, hence my lack of clarity. Sorry about this.

You can do e[3,2,1,1].expand(3) to get it expanded in x0, x1, and x2.
(more generally, x[i1,i2,...,im].expand(k) will give the expansion in 
x0,x1,...,x(k-1).

Dima

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