return the coefficients of a polynomial with respect to parameters - Maple Help

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RegularChains[ParametricSystemTools][CoefficientsInParameters] - return the coefficients of a polynomial with respect to parameters

Calling Sequence

CoefficientsInParameters(p, d, R)

Parameters

p

-

polynomial in the ring

d

-

number of parameters

R

-

polynomial ring

Description

• 

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, U1,...,Ud, and the other variables, X1,...,Xn, are regarded as unknowns.

• 

The common zeros of the polynomials in lp form the variety of Kd where the polynomial p is identically zero when regarded as a polynomial in X1,...,Xn with coefficients in K[U1,...,Ud] where K is the algebraic closure of the ground field of R.

• 

More precisely, the function will extract from p the polynomials of K[U1,...,Ud], which are the coefficients of p when regarded as a polynomial in K[U1,...,Ud][X1,...,Xn]. 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](..).

Examples

withRegularChains:

withParametricSystemTools:

R:=PolynomialRingx,a,b,c

R:=polynomial_ring

(1)

p:=ax2+a2x+bc

p:=a2x+ax2+bc

(2)

CoefficientsInParametersp,3,R

a,bc

(3)

See Also

DefiningSet, ParametricSystemTools, RegularChains


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