On Mon, Aug 29, 2022 at 09:45:20AM +0800, Qian Yun wrote:
>
> On 8/28/22 21:51, Waldek Hebisch wrote:
> >Another things is "factored expressions". Currently
> >expressions are rational functions of kernels, normalised
> >so that algebraic kernels are reduced by their defining
> >equations. Rational functions are fully expanded.
> >I would like variant where rational functions are
> >partially factored. If you look at Rubi testsuite
> >many epressions are already in factored form.
> >When input as Expression they get expanded.
> >That in many cases leads to much bigger expressions
> >later. At the input in many cases we could restore
> >factored form and take advantage of known factors
> >during computation. Of course, to recognize zero
> >we need to expand. But I feel that there will be
> >net gain.
> >
>
> I have thought about "factored expressions" as well.
> My rough idea is using "paren/box" to prevent expand,
> and adding checks for "paren/box" to expand when needed.
> Do you think this is a viable solution?
Well, peren and box allow keeping factors/terms when
we use Expression as representation. I am not sure
if it would work well for more extensive computations.
One trouble is that our zero test depends on expansion
> Similar to "factored expressions", I think pattern matching,
> integration by part, heuristic algorithm also relies on
> "do not auto expand expression beyond recognition."
Shortest description of Risch algorithm is "integrate by
part when this makes integral simpler, otherwise use
special methods". It depends on having expression
in specific form and keeping it in this form during
computation. So "smart" automatic transformations
are harmful for wide range of computation.
OTOH Risch is insensitve to expansion (except for
cost of computations) while pattern matching
is very sensitive to syntactic form. I must
admit that after experience in FriCAS I am
very sceptical about pattern matching. Namely,
when one wants reliabilty then other methods
usually were simpler.
--
Waldek Hebisch
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