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[Axiom-math] Gaussian Integers


From: Gabriel Dos Reis
Subject: [Axiom-math] Gaussian Integers
Date: 12 Sep 2006 10:16:18 -0500

Hi,

  I thought Axiom had an algebra support for Gaussian Integers.  It
seems my perception may be wrong...
OK.  

(6) -> unitNormal(3 + 4 * %i)
   (6)  [unit= 1,canonical= 3 + 4%i,associate= 1]
Type: Record(unit: Complex Integer,canonical: Complex Integer,associate: 
Complex Integer)

(7) -> unitNormal(-3 + 4 * %i)
(7) -> 
   (7)  [unit= %i,canonical= 4 + 3%i,associate= - %i]
Type: Record(unit: Complex Integer,canonical: Complex Integer,associate: 
Complex Integer)

 Integer)
(8) -> divide(459 + 9 * %i + 8 - 5 * %i)
   There are no library operations named divide having 1 argument(s) 
      though there are 2 exposed operation(s) and 2 unexposed 
      operation(s) having a different number of arguments. Use HyperDoc
      Browse, or issue
                               )what op divide
      to learn what operations contain " divide " in their names, or 
      issue
                             )display op divide
      to learn more about the available operations.
 
   Cannot find a definition or applicable library operation named 
      divide with argument type(s) 
                               Complex Integer
      
      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
(8) -> factor(83 + 8 * %i)
   Loading /usr/local/axiom/mnt/linux/algebra/GAUSSFAC.o for package 
      GaussianFactorizationPackage 
   Loading /usr/local/axiom/mnt/linux/algebra/MODRING.o for domain 
      ModularRing 
   Loading /usr/local/axiom/mnt/linux/algebra/INTFACT.o for package 
      IntegerFactorizationPackage 
   Loading /usr/local/axiom/mnt/linux/algebra/FR.o for domain Factored 

   (8)  - %i(3 + 20%i)(4 + %i)
                                               Type: Factored Complex Integer


Any idea where the divide() for Gaussian Integers is hiding? (none of
the four  divides seems to be applicable)

-- Gaby




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