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## [Axiom-developer] Zero divisors in Expression Integer

 From: Waldek Hebisch Subject: [Axiom-developer] Zero divisors in Expression Integer Date: Thu, 4 Jan 2007 05:47:29 +0100 (CET)

```I have already written that due to incomplte simplification we
may get zero divisors in Expression Integer.  Below an easy
example that multiplication in Expression Integer is nonassociative
(or, if you prefer, a proof that 1 equals 0):

(135) -> c1 := sqrt(2)*sqrt(3*x)+sqrt(6*x)

+--+    +-+ +--+
(135)  \|6x  + \|2 \|3x
Type: Expression Integer
(136) -> c2 := sqrt(2)*sqrt(3*x)-sqrt(6*x)

+--+    +-+ +--+
(136)  - \|6x  + \|2 \|3x
Type: Expression Integer
(137) -> (1/c1)*c1*c2*(1/c2)

(137)  1
Type: Expression Integer
(138) -> (1/c1)*(c1*c2)*(1/c2)

(138)  0
Type: Expression Integer

BTW, a similar looking constant expression throws an error:

(139) -> 1/(sqrt(2)*sqrt(3)+sqrt(6))

>> Error detected within library code:
univariate: denominator is 0 mod p

--
Waldek Hebisch