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DifferentialAlgebra

  

BelongsTo

  

decides membership in differential ideals

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

BelongsTo(p, ideal, opts)

BelongsTo(L, ideal, opts)

Parameters

p

-

a differential polynomial

L

-

a list or a set of differential polynomials

ideal

-

a differential ideal

opts (optional)

-

a sequence of options

Description

• 

The function call BelongsTo(p,ideal) returns true if the differential polynomial p belongs to the differential ideal represented by ideal, else it returns false.

• 

If ideal is a list of regular differential chains, the function returns true if and only if p belongs to all the elements of the list. If the first argument, L, is a list or a set off differential polynomials, the call BelongsTo(L, ideal) returns a list or a set of true / false.

• 

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

Examples

withDifferentialAlgebra:

RDifferentialRingderivations=t,blocks=u

R:=differential_ring

(1)

Every differential polynomial belongs to the unit differential ideal

BelongsTout,

true

(2)

idealRosenfeldGroebnerut24u,R

ideal:=regular_differential_chain,regular_differential_chain

(3)

The two first differential polynomials do not belong to ideal but their product does.

BelongsTout,ut,t2,utut,t2,ideal

false,false,true

(4)

See Also

DifferentialAlgebra

NormalForm

ReducedForm

DifferentialPrem

 


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