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:

(1) -> sum(k,k=1.0..2.5)

(1)

• 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;

f := operator 'f;

eq := f(dummy) - f(dummy - 1) - f(dummy - 2);

r:=evalRec(f, dummy, n, n0, eq, [1,1])$RecurrenceOperator(Integer, Expression Integer)

   The function evalRec is not implemented in RecurrenceOperator(
      Integer,Expression(Integer)) .