I posted this question http://ask.sagemath.org/question/200/multi-symmetric-functions-and-multi-partitions on AskSage and it was suggested I post the question here. This is what I originally asked:
"Does sage support manipulating multi-symmetric functions/polynomials and/or multi-partitions? Multi-symmetric functions are like the usual symmetric ones, except the symmetric group acts by permuting "vectors" of variables simultaneously, e.g. for an two vectors $x=(x1,x2…),y=(y1,y2,…)$, $\Sigma_2$, acts by permuting $x,y$. A multi- partition of a $n$-tuple $B=(b1,…,bn)$ of natural numbers is a unordered set of $n$-tuples $A1,…,Al$ with $A1+⋯+Al=B$. I'd like to have a combinatorial class of multi-partitions with similar functionality as partitions, e.g. .first(), .last() methods and iter(). I'd also like to have a class like SymmetricFunctionAlgebra, but with multi-symmetric functions instead. I've had a bit of a poke around and there's some functionality in Maxima (in the Sym) package that might help, but not quite like what I want (that I can find). So, before writing code, I'm asking here. If the code needs to be written, I'm quite keen to make it my first (hopefully of many) contribution to sage..." To give a little more info, I'm working on a problem trying to determine when a certain set of polynomials generates the function field of the multi-symmetric polynomials over a field. As a first step, I'm trying to write some code to investigate the relations between symmetrized monomials in the inverse limit ring, i.e. the ring of multi-symmetric functions. Using Groebner bases seems to be much too slow for this purpose. At the moment, I'm just exploring this ring rather than trying to come up with an method of solving the problem. Ultimately I'd like to contribute back with multi-partition class as described above and a MultiSymmetricFunctionAlgebra class or something along those lines. Cheers, Paul. -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to sage-combinat-de...@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
