RegularChains[ParametricSystemTools]
CoefficientsInParameters
return the coefficients of a polynomial with respect to parameters
Calling Sequence
Parameters
Description
Examples
CoefficientsInParameters(p, d, R)
p
-
polynomial in the ring
d
number of parameters
R
polynomial ring
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](..).
See Also
DefiningSet
ParametricSystemTools
RegularChains
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