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

The function reduced returns true if p is reduced with respect to F  or with respect to the equations of P.  It returns false otherwise.

A differential polynomial p is said to be partially reduced with respect to a polynomial q if no proper derivative of the leader of q appears in p.

A differential polynomial p is said to be fully reduced with respect to a polynomial q if it is partially reduced with respect to q and if its degree in the leader of q is less than the degree of q in this leader.

A differential polynomial p is said to be reduced with respect to a set of differential polynomials F if it is reduced with respect to each element of F.

If code is omitted, it is assumed to be 'fully'.

If the second form of the function is used and P is a radical differential ideal defined  by a list of characterizable differential ideals then the function is mapped over all the components of the ideal.

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