Ore_algebra, a Package for Skew Operators - Maple Programming Help

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Ore_algebra, a Package for Skew Operators

Several algorithms for integration and summation have a natural description in terms of linear differential and difference operators, which in turn are well described by skew (or Ore) polynomials. This was the starting point for the Ore_algebra package.





Declaration of an Ore algebra

To work with an Ore algebra, we first have to declare it. The package creates a table that implements and remembers the operations in this algebra. Here is the example of the algebra of linear differential operators in the differential operator Dx with (rational) coefficients in x.




(This is the name of the table.)

Although the usual product in Maple is commutative, we use `*` to denote skew products, with the convention that powers of Dx are on the right.


Multiplication of operators is obtained by the function skew_product.




Remember that in skew algebras of linear operators, factorizations are seldom unique.




An algorithm is also available to compute (one-sided) Groebner bases in Ore algebras. This is demonstrated in the presentation of the Groebner package.


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