construct the minimal annihilator in the completely factored form
FactoredMinimalAnnihilator(expr, x, case)
name of the independent variable
parameter indicating the case of the equation ('differential' or 'shift')
Given a d'Alembertian term expr, the LinearOperators[FactoredMinimalAnnihilator] function returns a factored Ore operator that is the minimal annihilator in the completely factored form for expr. That is, applying this operator to expr yields zero.
A completely factored Ore operator is an operator that can be factored into a product of linear factors.
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+xD⁡x⁡D⁢x2+4⁡D.
There are routines in the package that convert between Ore operators and the corresponding Maple expressions. See LinearOperators[converters].
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.
expr ≔ x⁢ln⁡x−x+1
L ≔ LinearOperators[FactoredMinimalAnnihilator]⁡expr,x,'differential'
L ≔ FactoredOrePoly⁡−1x−1⁢x,1,−1x,1
expr ≔ Γ⁡n⁢n2
L ≔ LinearOperators[FactoredMinimalAnnihilator]⁡expr,n,'shift'
L ≔ FactoredOrePoly⁡−n2+2⁢n+1n,1
Abramov, S.A., and Zima, E.V. "Minimal Completely Factorable Annihilators." Proc. ISSAC'97. 1997.
Download Help Document
What kind of issue would you like to report? (Optional)
Thank you for submitting feedback on this help document. Your feedback will be used
to improve Maple's help in the future.