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OreTools

  

SetOreRing

  

define an Ore polynomial ring

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

SetOreRing(var, 'shift')

SetOreRing(var,q, 'qshift')

SetOreRing(var, 'differential')

SetOreRing(var, algebra_name, 'sigma' = proc1, 'sigma_inverse' = proc2, 'delta' = proc3, 'theta1' = expr)

Parameters

var

-

name; variable

q

-

name; qshift parameter

algebra_name

-

name; algebra to be defined

proc1, proc2, proc3

-

procedures; define algebra

expr

-

Maple expression

Description

• 

The SetOreRing(var, 'shift') calling sequence defines a shift algebra.

• 

The SetOreRing([var, q], 'qshift') calling sequence defines a qshift algebra.

• 

The SetOreRing(var, 'differential') calling sequence defines a differential algebra.

• 

The shift, qshift, and differential algebras are pre-defined. You can use the SetOreRing command to define other Ore polynomial rings. You must specify procedures to compute sigma, sigma_inverse, and delta, and an expression to define theta(1).

  

For a brief review of pseudo-linear algebra (also known as Ore algebra), see OreAlgebra.

Examples

withOreTools:

Define the shift algebra.

ASetOreRingn,'shift'

A:=UnivariateOreRingn,shift

(1)

Define the difference algebra.

B := SetOreRing(n, 'difference',
  'sigma' = proc(p, x) eval(p, x=x+1) end,
  'sigma_inverse' = proc(p, x) eval(p, x=x-1) end,
  'delta' = proc(p, x) eval(p, x=x+1) - p end,
  'theta1' = 0);

B:=UnivariateOreRingn,difference

(2)

See Also

Ore_algebra

OreTools

OreTools/OreAlgebra

OreTools[Properties][Getdelta]

OreTools[Properties][GetRingName]

OreTools[Properties][GetSigma]

OreTools[Properties][GetSigmaInverse]

OreTools[Properties][GetTheta1]

OreTools[Properties][GetVariable]

 


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