return the delta-polynomial generated by two differential polynomials
delta_polynomial (p, q, R)
differential polynomials in R
differential polynomial ring
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
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.
R ≔ differential_ring⁡derivations=x,y,ranking=lexu,v
p ≔ uy+v:
q ≔ v⁢ux2+vy,y:
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