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### 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

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.

 2 retagged FrédéricC 2539 ●3 ●28 ●53

### 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

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.