test if a differential polynomial belongs to a radical differential ideal
belongs_to (q, J)
radical differential ideal given by a characteristic decomposition.
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 Jj of J if and only if the differential remainder of q by the differential characteristic set defining Jj 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.
R ≔ differential_ring⁡derivations=x,y,ranking=u,v:
p1 ≔ v⁢ux,x−ux:
p2 ≔ ux,y:
p3 ≔ uy,y2−1:
J ≔ Rosenfeld_Groebner⁡p1,p2,p3,R
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