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DifferentialAlgebra[Tools]

  

Separant

  

returns the separant of a differential polynomial

 

Calling Sequence

Parameters

Options

Description

Examples

Calling Sequence

Separant(ideal, v, opts)

Separant(p, v, R, opts)

Separant(L, v, R, opts)

Parameters

ideal

-

a differential ideal

p

-

a differential polynomial

v (optional)

-

a variable

L

-

a list or a set of differential polynomials

R

-

a differential polynomial ring

opts (optional)

-

a sequence of options

Options

• 

The opts arguments may contain one or more of the options below.

• 

fullset = boolean. In the case of the function call Separant(ideal,v), applies the function also over the differential polynomials which state that the derivatives of the parameters are zero. Default value is false.

• 

notation = jet, tjet, diff or Diff. Specifies the notation used for the result of the function call. If not specified, the notation of the first argument is used.

• 

memout = nonnegative. Specifies a memory limit, in MB, for the computation. Default is zero (no memory out).

Description

• 

The function call Separant(p,v,R) returns the separant of p regarded as a univariate polynomial in v, that is the partial derivative of p with respect to v. The differential polynomial p is assumed to be non-numeric.

• 

The function call Separant(L,v,R) returns the list or the set of the separants of the elements of L with respect to v.

• 

If ideal is a regular differential chain, the function call Separant(ideal,v) returns the list of the separants of the chain elements. If ideal is a list of regular differential chains, the function call Separant(ideal,v) returns a list of lists of separants.

• 

When the parameter v is omitted, it is understood to be the leading derivative of the processed differential polynomial with respect to the ranking of R, or the one of its embedding polynomial ring, if R is an ideal.

• 

This command is part of the DifferentialAlgebra:-Tools package. It can be called using the form Separant(...) after executing the command with(DifferentialAlgebra:-Tools). It can also be directly called using the form DifferentialAlgebra[Tools][Separant](...).

Examples

withDifferentialAlgebra:withTools:

RDifferentialRingderivations=x,y,blocks=v,u,p,parameters=p

R:=differential_ring

(1)

idealRosenfeldGroebnerux24u,ux,yvyu+p,vx,xux,R

ideal:=regular_differential_chain,regular_differential_chain

(2)

Equationsideal1

vx,xux,puxuyuuxuy+4uvy,ux24u,uy22u

(3)

The separants, in the usual sense.

Separantideal1

1,4u,2ux,2uy

(4)

The separant with respect to ux,y

Separantux,yvyu+p,ux,y,R

vy

(5)

See Also

DifferentialAlgebra

LeadingDerivative

 


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