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GCRD

  

find the Greatest Common Right Divisor of 2 differential operators

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

GCRD( f, g, domain)

Parameters

f, g

-

differential operators

domain

-

list containing two names

Description

• 

For operators f and g there exists an operator R such that the solution space of R is the intersection of the solution spaces of f and g. This procedure finds this operator R. Like the gcd for polynomials, this R is a combination R=af+bg for some operators a and b.

• 

The argument domain describes the differential algebra. If this argument is the list Dt,t then the differential operators are notated with the symbols Dt and t. They are viewed as elements of the differential algebra Ct Dt where C is the field of constants.

• 

If the argument domain is omitted then the differential specified by the environment variable _Envdiffopdomain will be used. If this environment variable is not set then the argument domain may not be omitted.

Examples

withDEtools:

GCRDDx4,Dx218x1+2x+3x3,Dx,x

Dx9x2+23x3+2x+1

(1)

See Also

diffop

Ore_algebra/skew_gcdex