returns the leading rank of a differential polynomial - Maple Help

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DifferentialAlgebra[Tools][LeadingRank] - returns the leading rank of a differential polynomial

Calling Sequence

LeadingRank(ideal, opts)

LeadingRank(p, R, opts)

LeadingRank(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 LeadingRank(p,R) returns the leading rank of p with respect to the ranking of R, or of its embedding ring, if R is an ideal.

• 

The function is extended to numeric polynomials: the leading rank of 0 is 0. The leading rank of any nonzero numerical polynomial is 1. It is also extended to differential polynomials which involve independent variables only.

• 

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

• 

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

• 

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

Examples

withDifferentialAlgebra:withTools:

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

R:=differential_ring

(1)

LeadingRankux,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)

LeadingRankideal1

vx,x,vy,ux2,uy2

(5)

LeadingRank0,421,R

0,1

(6)

See Also

DifferentialAlgebra, LeadingDerivative


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