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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:


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:

)lib RECOP
)library cannot find the file RECOP. dummy := new()$Symbol;
Type: Symbol
f := operator 'f;
Type: BasicOperator?
eq := f(dummy) - f(dummy - 1) - f(dummy - 2);
Type: Expression(Integer)
r:=evalRec(f, dummy, n, n0, eq, [1,1])$RecurrenceOperator(Integer, Expression Integer)
The function evalRec is not implemented in RecurrenceOperator( Integer,Expression(Integer)) .

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