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[Axiom-developer] [#167 Infinite Floats Domain]

From: daly
Subject: [Axiom-developer] [#167 Infinite Floats Domain]
Date: Mon, 13 Jun 2005 09:51:10 -0500




Now that I'm awake the idea is coming back to me. What originally
triggered the thought was that we need a way to compute an answer
to a variable number of decimal places which could be expanded later.
Thus we could compute the coefficients of a polynomial to 3 decimal
places for display but expand them to 200 decimal places when we are
evaluating the polynomial at a point.

The idea was to have a different representation that stored a closure
of the computation, similar to the series mechanism, so we could "continue"
to get more digits at a later time.

This raises the same kind of implementation issue that indefinite
computation raises except that indefinites are symbolic and infinite
precision floats are not.

The issue is that we want to keep the state of a computation in a
form that we can expand. This involves storing functions and 
composition of functions. This would imply that floating point
computations are no longer strictly numeric. So the product of
two infinite floats (INFL) object would be stored in such a way
to keep the original values as well as the result. Ideally we
could stop a computation, store it as a closure, and restart it
when we need more digits.

I have to give some thought to the more general case of a "closure"
based mathematical object that captures the computations. As we push
for more "symbolic" answers this issue keeps appearing.


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