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OreTools[SetOreRing] - define an Ore polynomial ring
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Calling Sequence
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SetOreRing(var, 'shift')
SetOreRing(![[var, q]](/support/helpjp/helpview.aspx?si=7130/file02456/math14.png) , 'qshift')
SetOreRing(var, 'differential')
SetOreRing(var, algebra_name, 'sigma' = proc1, 'sigma_inverse' = proc2, 'delta' = proc3, 'theta1' = expr)
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Parameters
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var
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name; variable
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q
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name; qshift parameter
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algebra_name
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name; algebra to be defined
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proc1, proc2, proc3
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procedures; define algebra
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expr
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Maple expression
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Description
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The SetOreRing(var, 'shift') calling sequence defines a shift algebra.
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The SetOreRing([var, q], 'qshift') calling sequence defines a qshift algebra.
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The SetOreRing(var, 'differential') calling sequence defines a differential algebra.
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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).
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For a brief review of pseudo-linear algebra (also known as Ore algebra), see OreAlgebra.
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Examples
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>
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Define the shift algebra.
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Define the difference algebra.
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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);
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| (2) |
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