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Here is a simple implemention of a recurrence relation operator. It is far from finished, but might serve as a starting point. I experienced the following difficulties:

  • The operator model in Axiom is quite restrictive: all arguments have to be from the same domain. This leads to problems elsewhere, too. I don't think that the following can be justified mathematically:

fricas
sum(k,k=1.0..2.5)

\label{eq1}4.375(1)
Type: Union(Fraction(Polynomial(Float)),...)
  • dummy variables are only supported in a very limited fashion: for the recurrence relation operator it would be good to have also "dummy operators"...

Things to do:

  • a proper operation analogous to sum, rootOf or the like needs to be written. The operation evalRec is just for a start
  • evalRec needs to be speeded up
  • evalADE doesn't really work concerning evaluation

The pamphlet is [rec.spad.pamphlet]? and the source is [rec.spad]?.

Here is an example:

fricas
)lib RECOP
RecurrenceOperator is now explicitly exposed in frame initial RecurrenceOperator will be automatically loaded when needed from /var/aw/var/LatexWiki/RECOP.NRLIB/RECOP dummy := new()$Symbol;
Type: Symbol
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f := operator 'f;
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eq := f(dummy) - f(dummy - 1) - f(dummy - 2);
Type: Expression(Integer)
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r:=evalRec(f, dummy, n, n0, eq, [1,1])$RecurrenceOperator(Integer, Expression Integer)
>> System error: Couldn't load "/var/aw/var/LatexWiki/RECOP.NRLIB/RECOP": file does not exist.




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