>
> OK, let's try with a being the imaginary unity.
>

I thought that by default FriCAS assumes that variables are real. 
 

> Because it is just an operator and a can be anything. 

 
Fair enough. Then one should be able to specify on which domain an operator 
is acting
and abs(a) | a is real should know that a > 0.

I just found out that the exact same question was asked 7 years ago:
https://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.

To 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). 

In 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?

I must say that it is highly disappointing that to this date there is no 
serious free-software alternative to
Mathematica. The three programs mentioned above have been developed for 
about 40-50 years by very
capable computer scientists and mathematicians. Axiom/FriCAS is IMHO the 
best designed of the three, 
it is thoroughly documented and all that effort is wasted because the 
developers do not care for the needs
of the users. Pretty sad.

Marduk

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