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LinearOperators

  

FactoredGCRD

  

return the greatest common right divisor in the completely factored form

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

FactoredGCRD(U, V, x, case)

Parameters

U

-

a completely factored Ore operator

V

-

an Ore operator

x

-

the name of the independent variable

case

-

a parameter indicating the case of the equation ('differential' or 'shift')

Description

• 

Given a completely factored Ore operator U and a non-factored Ore operator V, the LinearOperators[FactoredGCRD] function returns the greatest common right divisor (GCRD) in the completely factored form.

• 

A completely factored Ore operator is an operator that can be factored into a product of factors of degree at most one.

• 

A completely factored Ore operator is represented by a structure that consists of the keyword FactoredOrePoly and a sequence of lists. Each list consists of two elements and describes a first degree factor. The first element provides the zero degree coefficient and the second element provides the first degree coefficient. For example, in the differential case with a differential operator D, FactoredOrePoly([-1, x], [x, 0], [4, x^2], [0, 1]) describes the operator 1+xDxDx2+4D.

• 

An Ore operator is a structure that consists of the keyword OrePoly with a sequence of coefficients starting with the one of degree zero. The coefficients must be rational functions in x. For example, in the differential case with the differential operator D, OrePoly(2/x, x, x+1, 1) represents the operator 2x+xD+x+1D2+D3.

• 

There are routines in the package that convert between Ore operators and the corresponding Maple expressions. See LinearOperators[converters].

Examples

aFactoredOrePoly1,x,3,x

a:=FactoredOrePoly1,x,3,x

(1)

bOrePoly0,0,2x3+4x2,x4

b:=OrePoly0,0,2x3+4x2,x4

(2)

LinearOperators[FactoredGCRD]a,b,x,'differential'

FactoredOrePoly1x,1

(3)

References

  

Abramov, S.A., and Zima, E.V. "Minimal Completely Factorable Annihilators." Proc. ISSAC'97. 1997.

See Also

LinearOperators

LinearOperators[converters]

 


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