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Submitted by : (unknown) at: 2007-11-17T22:29:11-08:00 (9 years ago)
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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 (a+b)^5) 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




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