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[Axiom-developer] Re: EXPR POLY INT

From: Martin Rubey
Subject: [Axiom-developer] Re: EXPR POLY INT
Date: Tue, 15 Jun 2004 12:33:23 +0000

Dear William,

William Sit writes:

 > So is this a bug? I am not sure, it may be good that the interpreter caught 
 > the
 > ambiguity and it may be bad that the compiler does not. The compiler actually
 > knows how to distinguish POLY INT from EXPR POLY INT even if the SAME symbol 
 > is
 > used, but we (human) will get all confused. Try:
 > )abb package TEST  Test
 > Test():Target==Implementation where
 >   EXPR ==> Expression
 >   POLY ==> Polynomial
 >   INT  ==> Integer
 >   Target ==> with
 >     f1: () -> EXPR POLY INT
 >     f2: () -> POLY INT
 >     f3: () -> EXPR POLY INT
 >     f4: () -> EXPR POLY INT
 >   Implementation ==> add
 >     a:=new()$Symbol
 >     b:=a ::EXPR POLY INT
 >     c:=a :: POLY INT
 >     f1()==b
 >     f2()==c
 >     f3()== (c*b)/b
 >     f4()== f3()/b
 > Note that if you check the signature of /, the compiler "knows" it is legally
 > used and the answer for f4() is c/b, not 1 (which should be the case
 > mathematically).
 Well, I get the fraction %A / %A. I'm not to sure whether the reason for this
 is, that axiom distinguishes the two %A's. I tried to find out why, however, I
 couldn't: in expr.spad, we have the definitions

  K   ==> Kernel %
  MP  ==> SparseMultivariatePolynomial(R, K)
  Rep := Fraction MP

  if R has IntegralDomain then
    x:% / y:%        == reduc(x /$Rep y, commonk(x, y))


    x:MP / y:MP == 
      reduc(x /$Rep y,commonk0(algkernels variables x,algkernels variables y))

When saying f4()$TEST, the former gets called (twice, once for f3 too): The
first time x is %A %A and y is %A and x /$Rep y gives %A / %A, the second time, 
x and y are both %A, and x /$Rep y gives %A / %A.

When I say a::EXPR INT/a, also the former gets called (once, of course),
x and y being a and x /$Rep y gives 1.

However, I was unable to find the definition which gets called for /$Rep. I
tried the definition in Fraction, and some others, to no avail...

More comments later

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