diffalg[reduced]  test if a differential polynomial is reduced with respect to a set of differential polynomials

Calling Sequence


reduced (p, F, R, code)
reduced (p, P, code)


Parameters


p



differential polynomial in R

F



differential polynomial or list/set of differential polynomials in R

R



differential polynomial ring

code



(optional) name; 'fully' or 'partially'

P



characterizable differential ideal





Description


•

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'.

•

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



Examples


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