On 12/30/2014 04:44 PM, Bill Page wrote:
I think an alternative is to try to build _automatic_ translators that
convert the base code to mathematical formulation recognizable as
mathematics. I realize that present mathematical notation is not
perfect; but is usable because of 3,000 years of development. Though,
in all honesty, I am speaking from ignorance.
I am inclined more to agree with Waldek here that the SPAD language is
already in principle sufficient as a mathematical notation - for
someone sufficiently motivated to actually want to do mathematics this
way. Translating from one notation to another is only a matter of
temporary convenience. Eventually one needs to become fluent in the
language of implementation. To the extent that this remains
uncomfortable, this is reason and motivation to change the language in
fundamental ways - not just as the level of the notation. To some
extent in systems like Axiom this can be accomplished through
(re-)design of the underlying libraries.
Okay I'll nibble at the bait. I have a current problem that I will
start a page on in the development site. It's neither too hard or too
easy and as far as I can tell a little original; although I can never
tell until the end.
It involves attempts to resolve/equate hypergeometric series
terms/identities; not the standard equation solving techniques (I don't
think). I think I know how to phrase the questions in mathematics; but
I don't know the answers and don't want trial by exhaustion that leaves
no trace of why or how or much of anything. So it's a development
project to test the ease of phrasing standard mathematics in ...
pick a language Aldor or Fricas. And if it can easily be used to test
hypothesis's; I generate a lot and almost all are wrong.
Ray
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