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

The function belongs_to returns true if q belongs to J. Otherwise, false is returned.

Mathematically, q belongs to J if and only if q vanishes on all the zeros of  J.

The differential polynomial q belongs to J if and only if it belongs to all the components of the characteristic decomposition.

q belongs to a characterizable component  of J if and only if the differential remainder of q by the differential characteristic set defining   is zero.

Characteristic decomposition of radical differential ideal are computed by Rosenfeld_Groebner.

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