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## [Axiom-developer] Re: conditionally defined functions

 From: Ralf HEMMECKE Subject: [Axiom-developer] Re: conditionally defined functions Date: Fri, 17 Sep 2004 15:38:06 +0200 User-agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.7) Gecko/20040616

```Hi Martin,

```
```As you might know, I'm experimenting with fixes of the following, superficially
```
strange 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 Integer

```
So 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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