Maybe a good way to say it is thus:
An algorithm implemented in a program allows no implicit assumptions.
In a case where there are issues with translating an algorithm to
program level, the questions that come to my mind are:
1) Do the implicit assumptions initially made, when made explicit, map
well to the programming environment?
2) Has the space in which the algorithm is known/intended to operate
been well defined?
3) Are the assumptions in fact well understood?
In theory at least, computers ought to be capable of verifying that
human created mathematics is correct. (Somebody correct me if that
isn't true.) Perhaps part of the problem is that a human being faced
with a physical/science problem can make "sane" assumptions where a
computer cannot, or see that a result makes no physical sense and thus
conclude there is a mistake. Making sure the system has enough
information to do the job is often a difficult propositon.
Perhaps a trend toward literate programming such as that being used in
Axiom might be generally better practice for defining algorithms, but I
suspect the extra work involved will limit the appeal to many.
Probably if an idea is reduced to working symbolic computational
algorithms it will be by someone who focuses on that.
--- Richard Fateman <firstname.lastname@example.org> wrote:
> I would not discard the possibility the best most concrete
> of algorithms that you will find will be the programs (e.g.
> Mathematica code), and that the reduction of the papers to
> the code may involve details not present in the papers.
> This opinion is, however, based on general experience and not
> a particular examination of FeynCalc.
> Good luck in any case..
> Axiom-developer mailing list
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