
From:  Ralf HEMMECKE 
Subject:  [Axiomdeveloper] Re: conditionally defined functions 
Date:  Fri, 17 Sep 2004 15:38:06 +0200 
Useragent:  Mozilla/5.0 (X11; U; Linux i686; enUS; rv:1.7) Gecko/20040616 
Hi Martin,
As you might know, I'm experimenting with fixes of the following, superficiallystrange behaviour:(1) > (1/x)::UP(x, FRAC POLY INT) 1 (1)  x Type: UnivariatePolynomial(x,Fraction Polynomial Integer)
Hmm, when I simply type 1/x, I get: 1 (4)  x Type: Fraction Polynomial IntegerSo coercing this into UP(x, FRAC POLY INT) is OK. It only looks a bit strange, because you might want to get an error message telling you that you cannot have x in the denominator.
I made the following experiment: (5) > X := monomial(1,1)$UP(x, FRAC POLY INT) (5) x Type: UnivariatePolynomial(x,Fraction Polynomial Integer) (8) > inv X 1 (8)  x Type: Fraction UnivariatePolynomial(x,Fraction Polynomial Integer) (9) > 1/X 1 (9)  x Type: UnivariatePolynomial(x,Fraction Polynomial Integer) That the types are different is really a bit strange. If I posed the question: Is UP(x, FRAC POLY INT) = FRAC POLY INT ?What would you answer? I am not asking for equality of the domains in AXIOM, but rather what FRAC POLY INT is mathematically.
Ralf
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