LinearOperators - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Factorization and Solving Equations : LinearOperators : LinearOperators/FactoredAnnihilator

LinearOperators

  

FactoredAnnihilator

  

construct completely factorable annihilator

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

FactoredAnnihilator(expr, x, case)

Parameters

expr

-

an algebraic expression

x

-

the name of the independent variable

case

-

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

Description

• 

Given an algebraic expression expr, the LinearOperators[FactoredAnnihilator] function returns a completely factored Ore operator that is an annihilator for expr. That is, applying this operator to expr yields zero. If such an operator does not exist, the function returns 1.

• 

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.

• 

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

• 

To get the completely factorable annihilator, the expression expr must be a d'Alembertian term. The main property of a d'Alembertian term is that it is annihilated by a linear operator that can be written as a composition of operators of the first degree. The set of d'Alembertian terms has a ring structure. The package recognizes some basic d'Alembertian terms and their ring-operation closure terms. The result of the substitution of a rational term for the independent variable in the d'Alembertian term is also a d'Alembertian term.

Examples

exprⅇxx1+x2+1

expr:=ⅇxx1+x2+1

(1)

LLinearOperators[FactoredAnnihilator]expr,x,'differential'

L:=FactoredOrePolyx4+6x22x+3x3x2+x+1x2+1x1,1,1x12,1

(2)

LinearOperators[Apply]L,expr,x,'differential'

0

(3)

References

  

Abramov, S. A., and Zima, E. V. "Minimal Completely Factorable Annihilators." In Proceedings of ISSAC '97, pp. 290-297. Edited by Wolfgang Kuchlin. New York: ACM Press, 1997.

See Also

LinearOperators

LinearOperators[Apply]

LinearOperators[converters]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam