Question: convert a multivariate polynomial into a linear homogeneous polynomial

At the first note that in this question all polynomials have parametric coefficients. Let F be a list of polynomials and f be a polynomial. I want to convert F and f into a linear homogeneous FF and ff resp. At the first I want to sortvthe monomials appears in F and f  w.r.t. a monomial order T and then replace by the new variables A_i.

For example if


(a,b,c are parameters and x,y,z are variables) then I want to convert F and f into FF and ff resp:

please note that the variables appears in F and f are:

where sorted by T=plex(x,y,z). Please note that we consider all constants and alone parameters (4, b-4, c-1) as A9. I want to convert v into

and then F into FF and f into ff.


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