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[Axiom-developer] [#220 'StepThrough' is braindead] (nouveau)

From: kratt6
Subject: [Axiom-developer] [#220 'StepThrough' is braindead] (nouveau)
Date: Sun, 16 Oct 2005 04:30:11 -0500

The 'StepThrough' category provides a function 'init()' which yields an initial 
element of the domain and a function 'nextItem(n)' which produces the element 
after 'n', or '"failed"' if there is no such element.

This sounds quite like an implementation of countable sets. But unfortunately, 
it isn't. The documentation says, that it is not required that all elements of 
the domain are eventually produced.

This given, *any* domain could belong to 'STEP'. Inspecting the domains in 
Axiom we find however, that (nearly) exactly those domains that contain a 
countable number of elements have 'STEP', while, for example 'EXPR' and 'Float' 

I would argue that this should be changed and I will provide an implementation 
shortly. There is little danger of breaking anything, since 'STEP' is only used 
at two different places, namely in 'GENPGCD' and in 'PFBRU'.

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