test if a differential polynomial is reduced with respect to a set of differential polynomials
reduced (p, F, R, code)
reduced (p, P, code)
differential polynomial in R
differential polynomial or list/set of differential polynomials in R
differential polynomial ring
(optional) name; 'fully' or 'partially'
characterizable differential ideal
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.
R ≔ differential_ring⁡derivations=x,y,ranking=u
q ≔ ux2−4⁢u
P ≔ Rosenfeld_Groebner⁡q,R
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