Ore_algebra[skew_algebra]  declare an Ore algebra

Calling Sequence


skew_algebra(t_1=l_1,..., t_n=l_n, options)


Parameters


t_i



types of commutation

l_i



lists of indeterminates whose lengths are determined by the corresponding t_i

options



(optional) options described below





Description


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The skew_algebra command declares an Ore algebra and returns a table that can be used by other functions of the Ore_algebra package.


Any pair or commute. The sigma_is are algebra endomorphisms and the delta_is are additive functions that moreover satisfy the following skew Leibniz rule:

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Weyl algebras are a special case of Ore algebras, obtained when all operators are differentiation operators. For more information, see Ore_algebra[Weyl_algebra].

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The lists l_i involve the x_is and d_is, where the names x_i and the d_i may not be assigned. Each list l_i consists of a pseudodifferential indeterminate d_i followed by one or more of the x_js.

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The string t_i represents the type of the pseudoderivative d_i. It is either a predefined type or a userdefined type. Possible commutations are described in Ore_algebra[commutation_rules].

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The sum in Ore algebras is performed by using the `+` of Maple, while the product is performed by the Ore_algebra function skew_product (see the Examples section below).



Examples


The following call declares an Ore algebra built on a differential operator Dx and on a shift operator Sn. It also prepares the use of a function in the coefficients of the polynomials.
>


>


 (1) 
This is the name of a table. Products in the algebra are performed using skew_product.
>


 (2) 
>


 (3) 
>


 (4) 
>


 (5) 
The following declaration, however, is forbidden.
>




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