[Axiom-developer] Re: non extending category

[root]

.. JetBundleExpression #1 of cat 

(|Join| 
 (|JetBundleFunctionCategory| |#1|)
 (|FunctionSpace| (|Integer|))
 (|AlgebraicallyClosedFunctionSpace| (|Integer|))
 (|TranscendentalFunctionCategory|)
 (|CombinatorialOpsCategory|)
 (|LiouvillianFunctionCategory|)
 (|SpecialFunctionCategory|)

 (CATEGORY |domain| 
   (SIGNATURE |coerce| 
     ($ (|Expression| (|Integer|))))
   (SIGNATURE |coerce| 
     ((|Expression| (|Integer|)) $))
   (SIGNATURE |coerce| 
     ($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))))
   (SIGNATURE |coerce| 
     ($ (|SparseMultivariatePolynomial| (|Expression| (|Integer|)) |#1|)))
   (SIGNATURE |numerJP| 
     ((|SparseMultivariatePolynomial| (|Expression| (|Integer|)) |#1|) $))
   (SIGNATURE |reduce| 
     ($ $))
   (SIGNATURE |function| 
     ($ (|Symbol|) (|List| $) (|NonNegativeInteger|)))))

(IF (|has| (|Integer|) (|IntegralDomain|))
  (PROGN 
    (ATTRIBUTE (|AlgebraicallyClosedFunctionSpace| (|Integer|)))
    (ATTRIBUTE (|TranscendentalFunctionCategory|))
    (ATTRIBUTE (|CombinatorialOpsCategory|))
    (ATTRIBUTE (|LiouvillianFunctionCategory|))
    (ATTRIBUTE (|SpecialFunctionCategory|))
    (SIGNATURE |reduce| 
      ($ $))
    (SIGNATURE |number?|
      ((|Boolean|) $))
    (SIGNATURE |simplifyPower| ($ $ (|Integer|)))

    (IF (|has| (|Integer|) (|GcdDomain|))
       (PROGN
         (SIGNATURE |factorPolynomial|
           ((|Factored| (|SparseUnivariatePolynomial| $))
            (|SparseUnivariatePolynomial| $)))
         (SIGNATURE |squareFreePolynomial|
           ((|Factored| (|SparseUnivariatePolynomial| $)) 
                        (|SparseUnivariatePolynomial| $))))
       |noBranch|)

    (IF (|has| (|Integer|) (|RetractableTo| (|Integer|)))
      (ATTRIBUTE (|RetractableTo| (|AlgebraicNumber|)))
      |noBranch|))
 
 |noBranch|)



join is trying to create a new type that has all of the parents


 (|JetBundleFunctionCategory| |#1|)
 (|FunctionSpace| (|Integer|))
 (|AlgebraicallyClosedFunctionSpace| (|Integer|))
 (|TranscendentalFunctionCategory|)
 (|CombinatorialOpsCategory|)
 (|LiouvillianFunctionCategory|)
 (|SpecialFunctionCategory|)

with this new domain (represented by its signature list).

in addition if the new type HAS certain attributes (the "HAS" conditions)
then the new type will have these additional signatures.

so, simplifying, we are trying to combine types A, B, and C
with a new type D. Type D is represented by its signature list.

if the new type D HAS certain properties (such as being a GCDDomain
then we can add certain additional signatures (like 'factorPolynomial'.

thus if we can do GCDs of the new type
then we can factor polynomials of the new type.

i don't see any error message on the wiki page about 'non-extending
category'

t