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diffalg[delta_polynomial] - return the delta-polynomial generated by two differential polynomials

Calling Sequence

delta_polynomial (p, q, R)

Parameters

p, q

-

differential polynomials in R

R

-

differential polynomial ring

Description

• 

Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.

• 

The delta_polynomial command returns the delta-polynomial of p and q, that is

  

separantq,Rφpseparantp,Rψq

  

where phi and psi  are  the derivation operators of least order such that phi (up) = psi (uq) where up and uq are the leaders of p and q.

  

The delta-polynomial is sometimes called the cross-derivative.

• 

The differential polynomials p and q must not belong to the ground field of R. Their leaders must be derivatives of the same differential indeterminate but not be derivatives of each other. Otherwise, the delta-polynomial is not defined and delta_polynomial returns an error message.

• 

Delta-polynomials are constructed when dealing with partial differential polynomials to obtain regular differential systems.

• 

The command with(diffalg,delta_polynomial) allows the use of the abbreviated form of this command.

Examples

Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.

withdiffalg:

R:=differential_ringderivations=x,y,ranking=lexu,v

R:=PDE_ring

(1)

p:=uy+v[]:

q:=v[]ux2+vy,y:

leaderp,R,leaderq,R

uy,ux

(2)

delta_polynomialp,q,R

ux2vy2uxv[]vx+vy,y,y

(3)

See Also

diffalg(deprecated), diffalg(deprecated)/differential_algebra, diffalg(deprecated)/differential_ring, diffalg(deprecated)[leader], DifferentialAlgebra[Tools][DeltaPolynomial]


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