On Fri, Jan 23, 2015 at 8:13 PM, 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. > Well, it is the result in when working with (countably) infinitely many variables. There is a standard map from these to symmetric polynomials in 3 variables (obtained by setting x_i = 0 for i > 3), however from what I can tell, the only way sage implements this is with the expand method -- which is not what you want. In the case of the elementary symmetric polynomials basis (and only that basis), you can obtain the result that you are looking for by restricting the size of the parts to the number of variables you are working with. In sage this can be done with the following code (continuing from where I left off before): sage: em421 = e(m421) # coerce the monomial into the e basis sage: em421.restrict_parts(3) # restrict the size of the parts to at most 3 e[3, 2, 1, 1] - 2*e[3, 2, 2] - e[3, 3, 1] This agrees with the result that you got by hand since e[a, b, c, ...] = e_a*e_b*e_c*... > 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. > > john perry > >> -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. > -- Andrew -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
