returns the leading derivative of a differential polynomial - Maple Help

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DifferentialAlgebra[Tools][LeadingDerivative] - returns the leading derivative of a differential polynomial

Calling Sequence

LeadingDerivative(ideal, opts)

LeadingDerivative(p, R, opts)

LeadingDerivative(L, R, opts)

Parameters

ideal

-

a differential ideal

p

-

a differential polynomial

L

-

a list or a set of differential polynomials

R

-

a differential polynomial ring or ideal

opts (optional)

-

a sequence of options

Description

• 

The function call LeadingDerivative(p,R) returns the leading derivative of p with respect to the ranking of R or the one of its embedding polynomial ring if R is an ideal. The polynomial p is assumed to be non-numeric. It may, however, only depend on independent variables. In this case, the leading independent variable is returned.

• 

The function call LeadingDerivative(L,R) returns the list or the set of the leading derivatives of the elements of L with respect to the ranking of R.

• 

If ideal is a regular differential chain, the function call LeadingDerivative(ideal) returns the list of the leading derivatives of the chain elements. If ideal is a list of regular differential chains, the function call LeadingDerivative(ideal) returns a list of lists of leading derivatives.

• 

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

Examples

withDifferentialAlgebra:withTools:

R:=DifferentialRingderivations=x,y,blocks=v,u,p,parameters=p

R:=differential_ring

(1)

LeadingDerivativeux,yvyu+p,R

ux,y

(2)

ideal:=RosenfeldGroebnerux24u,ux,yvyu+p,vx,xux,R

ideal:=regular_differential_chain,regular_differential_chain

(3)

Equationsideal1

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

(4)

LeadingDerivativeideal1

vx,x,vy,ux,uy

(5)

See Also

DifferentialAlgebra, DifferentialRing


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