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:

axiom
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:

axiom
)lib RECOP

RecurrenceOperator is now explicitly exposed in frame initial RecurrenceOperator will be automatically loaded when needed from /var/zope2/var/LatexWiki/RECOP.NRLIB/code dummy := new()$Symbol;

axiom
f := operator 'f;

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

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

(2)

axiom
[eval(r, n0=k) for k in 0..10]

(3)