Edit detail for RecurrenceRelationOperator revision 1 of 3

changed:
-
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:

\begin{axiom}
sum(k,k=1.0..2.5)
\end{axiom}

  - 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:

\begin{axiom}
)lib 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)
[eval(r, n0=k) for k in 0..10]
\end{axiom}

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)

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:

axiom
)lib RECOP
   )library cannot find the file RECOP.
dummy := new()$Symbol;

Type: Symbol

axiom
f := operator 'f;

Type: BasicOperator?

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

Type: Expression Integer

axiom
r:=evalRec(f, dummy, n, n0, eq, [1,1])$RecurrenceOperator(Integer, Expression Integer)
   Category, domain or package constructor RecurrenceOperator is not 
      available.
[eval(r, n0=k) for k in 0..10]

(2)

Type: List Polynomial Integer