On Mon, Oct 5, 2009 at 11:38 AM, Leo Butler <l.butler at ed.ac.uk> wrote:
> < 1+2.0 => 3.0
> < '(1+2.0) => 3.0
> < '(x+1+2.0) => x+3.0
>
> These examples muddy the water, because they clearly are
> 'simplifications'. There is some arbitrary line that separates a
> 'simplification' from an 'evaluation' (e.g. in your examples above, one
> can say that the '+' function is being evaluated.). I was trying to
> find the line, because it is not where I would naively put it.
The difference is that simplification (in Maxima) is the application
of identities, that is, equations which hold for all values of any
variables involved. I guess this isn't explicitly stated anywhere
in the documentation. Whether or not the identities in questions
actually make something 'simpler' is beside the point (for the
purpose of the definition).
Numerical evaluation of built-in functions fit into this scheme in
the sense that the value of the function must be exactly its
numerical value. (Simplification of gamma function for integer
or half-integer values has the same motivation.)
There is some fuzziness here. E.g. x - x = 0 isn't an identity,
nor is x/x = 1, but Maxima applies them happily.
> < I think this all belongs to a section on simplification in general, which
> < clarifies that x+1+2.0 == "+"(x,1,2.0) and that Maxima applies
> < simplification to all mathematical operators. ?The section should also
> < cross-reference pattern-matching as a way of users' defining simplifying
> < mathematical functions.
>
> Yes, this sounds like an excellent idea. The manual, at the moment,
> suffers from the problem that it is well-nigh impenetrable to
> non-acolytes. This is especially true of the sections on simplification
> and pattern-matching.
True enough about pattern matching, but I'm not sure that there
is any simpler way to describe the behavior of the code.
(I'm not sure which sections you mean by "the sections on
simplification" since there isn't any section specifically about
simplification. This, in itself, is a problem, of course.)
To make the documentation simpler probably requires reworking
the code. I;m not opposed to that btw.
FWIW
Robert Dodier