The command CoefficientsInParameters(p, d, R) returns a list, lp, of polynomials involving the last d variables only.

The integer d should be positive and less than the number of variables. The last d variables are regarded as parameters, , and the other variables, , are regarded as unknowns.

The common zeros of the polynomials in  form the variety of  where the polynomial  is identically zero when regarded as a polynomial in  with coefficients in  where  is the algebraic closure of the ground field of R.

More precisely, the function will extract from p the polynomials of , which are the coefficients of p when regarded as a polynomial in . Moreover, the extracted polynomials might be simplified while preserving the variety defined by them.

This command is part of the RegularChains[ParametricSystemTools] package, so it can be used in the form CoefficientsInParameters(..) only after executing the command with(RegularChains[ParametricSystemTools]). However, it can always be accessed through the long form of the command by using RegularChains[ParametricSystemTools][CoefficientsInParameters](..).