Post by MardukPost by Ralf HemmeckeOK, let's try with a being the imaginary unity.
I thought that by default FriCAS assumes that variables are real.
Users requently try to use complex expressions and when possible
FriCAS tries to accomodate this.
Post by Mardukhttps://groups.google.com/d/topic/fricas-devel/jTeaKzcEJgs/discussion
It is surprising that nothing has been done to correct this problem. But
reading that thread
explains why. It is not a matter of mathematics or computer science, but a
matter of sociology.
Well, concerning "nothing has been done" it depends what "this problem"
is. If you mean exact expression appearing in the report, it is
just one of several thousends of possible inputs. If you mean problem
Juanjo raised (better support of special functions), then a lot
happened. In particular FriCAS is now quite good at _indefinite_
integrals with result involving 'erf'. Concerning sociology,
any specific integral could be added via pattern matching (FriCAS
has special pattern matcher for definite integrals), that is
about 40 lines of code. That is great for benchmarketing
(you can show 100% success rate on any small testsuite).
However, if you want comprehensive support in that way you would
need to add hundreds or thousends of integrals meaning several
thoushends of lines of code. Tedious and still it would be
easy to find integrals which are not handled. I prefer
algorithms that handle _all_ functions in given relatively
large class. To put is differently, if I thought that handling
of this specific Gaussian integral is most imporant feature
for FriCAS I would implement it. But fixing via special
cases several such "most imporant features" would soak
all time that I can spent on FriCAS developement and IMO
would result in much weaker system compared to current FriCAS.
Post by MardukTo us physicists, Juanjo in that thread and myself, a CAS should be a tool
that helps us save
time by performing the calculations that come up in our work. But to the
current maintainers of
the big three: Maxima, FriCAS and Reduce, it does not matter that their
programs cannot calculate
Gaussian integrals (all three have failed my tests).
World is not black and white. You write "Gaussian integrals" in
the plural here, so maybe you mean things like (indefinite)
integrate(x^16*exp(-x^2), x)
In the past FriCAS could not do them, now it is handled by
general routine. So it matters. But fixing _one_ definite
integral is not very significant when there are thousends
of similar cases. Now, solutions that handle large classes
take time to develop. IMO seeking general solutions pays
in longer time.
Extra remark about "does not matter": if I would serioulsy
worry about every similar problem/bug I would quickly
end up in a madhouse with serious mental ilness. And
the same applies to other sofware. Mathematica and Maple
are very secretive about their problems, but there are
enough reports to know that they have a lot of problems.
Post by MardukIn the Axiom/FriCAS wiki it is claimed that this CAS boasts the most
complete implementation of the
Risch algorithm. And I am sure that it can calculate thousands of
integrals. But what is the purpose of
having a sophisticated integrator if it cannot calculate the simplest
integrals? In the thread above
Waldek replies: do not use it for calculating integrals you already know.
Seriously?
Read carefuly, it is not what I wrote. Hint: I was discussing possible
_pragmatic_ approches given current FriCAS limitations.
And in this disscussion you were given IMHO reasonable workaround (using
fourth power of parameter), so this problem is not a "killer" in
sense that stops you from doing serious work. Annoying, yes,
so I understand why you are annoyed...
--
Waldek Hebisch
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