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OreTools[SetOreRing] - define an Ore polynomial ring
Calling Sequence
SetOreRing(var, 'shift')
SetOreRing(, '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
Define the shift algebra.
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);
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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