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I want to expand a given polynomial in $n$ variables, homogeneous of degree $k$ as a linear combination of Non-Symmetric Macdonald polynomials $E_{\alpha}$ where $\alpha$ varies over $\mathbb{Z}^n_{\geq 0}$ with $\sum \alpha_i = k$.

Background: We know that these Macdonald polynomials do indeed form a basis of the vector space of homogeneous degree $k$ polynomials in $n$ variables. The Non-Symmetric Macdonald polynomials I am interested in is the type $GL_n$ kind. And their sage implementation can be found here: sage documentation

Bottom line is that we have a basis of a vector space already implemented in sage. Now how do we use it to compute coefficients of any vector when written in terms of this basis?

I want to expand a given polynomial in $n$ variables, homogeneous of degree $k$ as a linear combination of Non-Symmetric Macdonald polynomials $E_{\alpha}$ where $\alpha$ varies over $\mathbb{Z}^n_{\geq 0}$ with $\sum \alpha_i = k$.

Background: We know that these Macdonald polynomials do indeed form a basis of the vector space of homogeneous degree $k$ polynomials in $n$ variables. The Non-Symmetric Macdonald polynomials I am interested in is the type $GL_n$ kind. And their sage implementation can be found here: sage documentation

Bottom line is that we have a basis of a vector space already implemented in sage. Now how do we use it to compute coefficients of any vector when written in terms of this basis?