Gentlemen! I only returned to this today, but I get it now. Thanks! I'm not sure whom to mark as "best answer", though; both seem equally good.
john perry On Saturday, January 24, 2015 at 2:54:22 PM UTC-6, Andrew Ohana wrote: > > > > On Fri, Jan 23, 2015 at 8:13 PM, john_perry_usm <[email protected] > <javascript:>> 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] <javascript:>. >> To post to this group, send email to [email protected] >> <javascript:>. >> 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.
