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

The function differential_sprem is an implementation of Ritt's reduction algorithm. It is an extension of the pseudo-remainder algorithm to differential polynomials.

L is assumed to form a differentially triangular set.

Let  denote L or equations(C).

The function differential_sprem returns a differential polynomial r such that

(a)  

(b) No proper derivative of the leaders of the elements of  appears in .

(c) The degree according to a leader of any element  of  is strictly less in  than in .

(d) The differential polynomial h is a power product of factors of the  initials and the separants of the elements of A.

The differential_sprem(q, L, R, 'h') calling sequence returns an error message if   contains 0. If  contains a non zero element of the ground field of R, it returns zero.

The differential_sprem(q, C, 'h') calling sequence requires that q belong to the differential ring in which C is defined.

The function rewrite_rules shows how the equations of C are interpreted by the pseudo-reduction algorithm.

Then r is zero if and only if q belongs to C.

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