Hi all,
On Feb 13, 10:09 am, Stan Schymanski <schym...@gmail.com> wrote:
> rjf wrote:
> > If there is an algorithm for simplify_full(), then presumably it could
> > be programmed in Lisp, and incorporated in Maxima.
>
> > You are invited to do so.
>
> > I assume that there are examples for which it doesn't do what you
> > want, and so you could argue that it should do more work.
Sure. I am of course aware that there is no *algorithm* (in the sense
of always terminating in finite time, yielding the correct result) for
deciding whether f>0 for a general expression f, and also it is not
clear what a "simplification" should be.
So, one can't have more than a heuristics. But that's the point: The
better the heuristics, the happier the user --- provided the
heuristics works in a reasonable time. And any good heuristics should
at least catch the obvious cases.
Since Maxima certainly knows sin(x)^2+cos(x)^2 == 1 and various other
identities, it makes sense to try and apply them to f as
simplification rules. There are some rules, some may apply, some not
-- and if the rules are tested in a greedy way (always strictly reduce
the complexity), I guess this step is done in almost no time.
Certainly Maxima does try some rules, before refusing to answer "f>0"?
So, why not add one more easy rule that frequently occurs in real
life? Or does Maxima give up right away when being asked "f>0",
without to try anything?
Best regards
Simon
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