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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

• 

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.

Examples

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

withdiffalg:

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

R:=PDE_ring

(1)

q:=ux24u[]

q:=ux24u[]

(2)

reducedux3,q,R

false

(3)

reducedux3,q,R,'partially'

true

(4)

P:=Rosenfeld_Groebnerq,R

P:=characterizable,characterizable

(5)

equationsP

ux24u[],u[]

(6)

reducedux,P

true,false

(7)

See Also

diffalg(deprecated), diffalg(deprecated)/differential_algebra, diffalg(deprecated)/Rosenfeld_Groebner, diffalg(deprecated)[equations], diffalg(deprecated)[leader], DifferentialAlgebra[Is]


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