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:

sum(k,k=1.0..2.5)

(1)

Type: 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

   RecurrenceOperator is now explicitly exposed in frame initial
   RecurrenceOperator will be automatically loaded when needed from
      /var/zope2/var/LatexWiki/RECOP.NRLIB/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)

   >> System error:
   Couldn't load "/var/zope2/var/LatexWiki/RECOP.NRLIB/RECOP": file does not
exist.