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DifferentialAlgebra[Tools]

  

Tail

  

returns the tail of a differential polynomial

 

Calling Sequence

Parameters

Options

Description

Examples

Calling Sequence

Tail(ideal, v, opts)

Tail(p, v, R, opts)

Tail(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 or ideal

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 Tail(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 Tail(p,v,R) returns the tail of p regarded as a univariate polynomial in v, that is the differential polynomial p, regarded as a univariate polynomial in v, minus its leading monomial with respect to this variable, If p does not depend on v then the function call returns 0.

• 

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

• 

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

• 

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. In that case, p must be non-numeric.

• 

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

Examples

withDifferentialAlgebra:withTools:

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

Rdifferential_ring

(1)

The tail, with respect to the leading derivative

Tailux,yvyu+p,R

u+p

(2)

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

idealregular_differential_chain,regular_differential_chain

(3)

Equationsideal1

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

(4)

The tails of the equations, with respect to ux

Tailideal1,ux

vx,x,4vyu,4u,0

(5)

See Also

DifferentialAlgebra

LeadingDerivative

LeadingCoefficient