Clark Smith wrote:
> On Wed, 12 Apr 2017 16:43:24 -0700, Richard Fateman wrote:
>
> > On 4/12/2017 12:19 PM, Clark Smith wrote:
> >> Are there any symbolic systems these days that ship with a full
> >> implementation of the Risch algorithm?
> >>
> > 1. Probably not.
> > 2. It is not an algorithm.
> >
> > Why do you ask?
>
> Out of curiosity - I seem to recall that Axiom, when it was
> called Scratchpad, claimed to have a near complete implementation.
"near complete" is very imprecise statement. In particular how
you measure "nearness". Even quite incomplete system may show
good results on simple minded test, so looking at performance
may give too rosy picture. Another point of view is to look
how much code in missing compared to complete implementation.
Currently there is no complete implementation of full algorthm,
so such criteria is hard to apply. For transcendental part
FriCAS has complete implementation (based on Axiom). Axiom
used about 8000 lines of code for integration of which probably
about 4000 lines were specific to algebraic part. So we
can estimate transcendental part at less than 4000 lines.
To get complete implementation in transcendental case
FriCAS added about 2500 lines of code. In the process
Axiom implementation was simplified and about 1000 lines
of code were removed. Some of removed parts were replaced
by new code, but some simplifications would be possible
even without adding new code. So we get somewhat fuzzy estimante
that Axiom had 60-70% of needed code -- I my book missing
30% is fairly incomplete.
Compared to Axiom FriCAS can handle more algebraic cases,
but still there are quite large gaps.
--
Waldek Hebisch
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