Re: [Axiom-developer] indefinites

[Martin Rubey]

William Sit writes:

...

 > Eventually, when this is operational, neither the input nor the output need
 > to use the word "Indefinite" (which is needed only internally: so every
 > declaration without an accompanying assignment will belong to the indefinite
 > domain; an object of the indefinite domain can be "assigned" a value and be
 > "retracted" to the domain, all transparently done. This may suggest a simple
 > method is to put a tag on the object, whether it has been assigned a domain
 > value or not. This would probably work for a while until we want to go to
 > more abstract levels such as computing with indefinites like p+q. The code
 > for the underlying domain will be so messed up with conditionals that it may
 > be wiser to separate the domain from its indefinite version. After all, we
 > separate the domain INT from POLY INT. Fateman has some good suggestions to
 > use lazy evaluation techniques to hold the proliferation of conditionals and
 > handle indefinite loops.
 > 
 > However this is done, the representation of the indefinite integer x will be
 > different from the representation of an integer x that has not been assigned
 > a value (indeed, the latter does not yet have one). This necessary change in
 > representation causes all the operations involving integers to be
 > syntactically invalid on indefinite integers.

I think I agree with this.

A little while ago I thought about how I could make EXPR smarter (in order to
allow for expressions over finite fields) and the idea occurred to me that it
would be "more" correct to have a domain

MY-EXPR [[var1, type1], [var2, type2] ...].

Awful, isn't it?

On the other hand, given the possibility that we could declare variables to be
of some type, this is not so far fetched! In fact, wouldn't this make the
domain EXPR obsolate altogether?

Given x an Indefinite Integer,

2^x*factorial(x)/sqrt(x)

would be an Indefinite AlgebraicNumber, and we could have a modeline

sum(Indefinite AlgebraicNumber, SegmentBinding Indefinite AlgebraicNumber).

Or, given x a Variable

(x^3+2*x^2+x+1)::POLY PF 5

would be a Polynomial, but x an Indefinite PF 5, it would an Indefinite PF 5... 


Is this correct?


It seems, that a domain for transcendental numbers is missing...


Martin