MathAction #336 'binomial$COMBF' is not evaluated consistently

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Consider

axiom

binomial(n,2)

$\label{eq1}{{n^2}- n}\over 2$

(1)

Type: Expression(Integer)

axiom

binomial(n,n-2)

$\label{eq2}{{n^2}- n}\over 2$

(2)

Type: Expression(Integer)

which should, by the definition of the binomial coefficient, give identical results.

The attached patch fixes this.

There is, however, a more fundamental issue to consider: Often, it is desirable that such expressions are not "expanded", but some thought needs to go into this. In my current application (in SPAD), I know a priori that a given ex in EXPR INT (possibly containing binomial coefficients or expressions of the form ) can always be retracted to a FRAC POLY INT. So, in this case, I really need "full" expansion.

I think, MuPAD? and Maple have a convert function for this. In Axiom, it really would be the responsibility of retract/retractIfCan. But that would mean to have at least one other property attached to operators, that tells Axiom how to retract to various domains. I guess that possibly different functions would have to be called for different domains we would like to retract to...

Martin

binomial.patch

Subject: Be Bold !!

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