CoefficientsInParameters - Maple Help
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RegularChains[ParametricSystemTools]

  

CoefficientsInParameters

  

return the coefficients of a polynomial with respect to parameters

 

Calling Sequence

Parameters

Description

Examples

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, , 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](..).

Examples

(1)

(2)

(3)

See Also

DefiningSet

ParametricSystemTools

RegularChains

 


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