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diffalg[belongs_to] - test if a differential polynomial belongs to a radical differential ideal

Calling Sequence

belongs_to (q, J)

Parameters

q

-

differential polynomial

J

-

radical differential ideal given by a characteristic decomposition.

Description

• 

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.

Examples

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

withdiffalg:

R:=differential_ringderivations=x,y,ranking=u,v:

p1:=v[]ux,xux:

p2:=ux,y:

p3:=uy,y21:

J:=Rosenfeld_Groebnerp1,p2,p3,R

J:=characterizable,characterizable

(1)

belongs_tovy,J1,belongs_tovy,J2,belongs_tovy,J

true,false,false

(2)

belongs_toux,J1,belongs_toux,J2,belongs_toux,J

false,true,false

(3)

belongs_touxvy,J

true

(4)

See Also

diffalg, diffalg(deprecated)/differential_algebra, diffalg(deprecated)/differential_ring, diffalg(deprecated)/differential_sprem, diffalg(deprecated)/reduced_form, diffalg(deprecated)/Rosenfeld_Groebner, diffalg(deprecated)[equations], DifferentialAlgebra[BelongsTo]


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