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RegularChains

  

Separant

  

separant of a nonconstant polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Separant(p, R)

Parameters

R

-

polynomial ring

p

-

polynomial of R

Description

• 

The function call Separant(p,R) returns the separant of p with respect to the variable ordering of R, that is, the derivative of p with respect to its main variable.

• 

It is assumed that p is nonconstant polynomial, and that the characteristic of R is zero.

• 

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

Examples

withRegularChains:

RPolynomialRingx,y,z

R:=polynomial_ring

(1)

py+1x3+z+4x+3

p:=y+1x3+z+4x+3

(2)

MainVariablep,R

x

(3)

Separantp,R

3x2y+3x2+z+4

(4)

Change the ordering of the variable.

RPolynomialRingz,y,x

R:=polynomial_ring

(5)

pexpandy+1x3+z+4x+3

p:=x3y+x3+xz+4x+3

(6)

MainVariablep,R

z

(7)

Separantp,R

x

(8)

See Also

Initial

MainDegree

MainVariable

PolynomialRing

Rank

RegularChains

Tail

 


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