[Axiom-developer] RE: Sets in MonoidRing

[Page, Bill]

Tim,

> 
> Another data point: 
> given:
> 
> > pgr := MonoidRing(Polynomial PrimeField 5, Permutation Integer)
> > p:pgr := 1
> 
> one? p ==> false
> 
> but the answer should be:
> 
> one? p ==> false
> 

I think you meant?

  one? p ==> true

But note that

  a:pgr := 2
  b:pgr := 2
  (a=b)::Boolean

also gives false!

I have seen numerous places in the algebra where
one? was commented out and replaced with or defined
as

 x->(x=1)::Boolean

or equivalent.

> 
> The root of the problem, as I now understand it, is that
> CCL had a builtin, non-Common lisp function called ONEP.
> Clearly this has affected the code. The lsp/ccl source
> tree has the CCL version of the code and I'll have to
> understand what the function ONEP is designed to do and
> add it to the set of common lisp functions.
> 

But doesn't the example above suggest something wrong
with testing for equality?

Is there/was there also a builtin function for zero? Is
equality converted to

  zero? (lhs-rhs)

But presumably equality is/should be a more primative
notion in general.

Cheers,
Bill Page.