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.