ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 24 Nov 2013 17:30:13 +0100Expand a polynomial into Schubert basishttps://ask.sagemath.org/question/10772/expand-a-polynomial-into-schubert-basis/Hi,
I have a few polynomials, such as
(x1^3*x2 + x1^2*x2^2 + x1*x2^3 + x1^3*x3 + 2*x1^2*x2*x3 + 2*x1*x2^2*x3+ x2^3*x3)*x1^7*x2^5*x3^3*x4
and I would like to expand it into Schubert polynomials. The only way I've found is to use
A = AbstractPolynomialRing(ZZ)
Schub = A.schubert_basis_on_vectors()
And use `Schub(from_expr(expr))` where I can plug in the polynomial that I have for expr. The documentation for AbstractPolynomialRing is here:
[Multivariate Polynomials with Several Bases](http://combinat.sagemath.org/doc/reference/combinat/sage/combinat/multivariate_polynomials/multivariate_polynomials.html)
However, it seems that AbstractPolynomialRing is not available in SAGE. I would really appreciate it if you know another way to do it, or point me to how to make this method work. Thank you. anhSun, 24 Nov 2013 17:30:13 +0100https://ask.sagemath.org/question/10772/multi-symmetric functions and multi-partitionshttps://ask.sagemath.org/question/7761/multi-symmetric-functions-and-multi-partitions/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 $x=(x_1,x_2\dotsc), y=(y_1,y_2,\dotsc)$, $\Sigma_2$, acts by permuting $x,y$. A multi-partition of a $n$-tuple $B=(b_1,\dotsc,b_n)$ of natural numbers is a unordered set of $n$-tuples $A_1,\dotsc,A_l$ with $A_1 + \dotsm + A_l = B$.
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...
Paul BryanThu, 11 Nov 2010 19:45:56 +0100https://ask.sagemath.org/question/7761/