implement fricas integrator

[sagetrac-whuss]

The attached patch adds the option algorithm="fricas" to the integrate
command.

CC: @hemmecke

Component: symbolics

Keywords: integrate, fricas

Author: Wilfried Huss, Frédéric Chapoton

Branch/Commit: c5bd849

Reviewer: Burcin Erocal, Ralf Stephan

Issue created by migration from https://trac.sagemath.org/ticket/9427

[sagetrac-whuss]

comment:1

Attachment: trac_9427-fricas-integrate.patch.gz

[burcin]

Changed author from whuss to Wilfried Huss

[burcin]

Reviewer: Burcin Erocal

[burcin]

comment:2

This looks great. Thanks for the quick patch!

I have a few minor comments:

• the conversion of different infinities on line 95-103 should be moved to the _fricas_init_() method of the corresponding classes. Then this would work:

sage: infinity._fricas_init_()
"%plusInfinity"

and we can just do af = a.fricas().

• Similarly, I suggest moving the code for converting the result back to the _sage_() method of the fricas interface.

[sagetrac-whuss]

comment:3

Attachment: fricas_infinity.patch.gz

Replying to @burcin:

• the conversion of different infinities on line 95-103 should be moved to the _fricas_init_() method of the corresponding classes. Then this would work:

sage: infinity._fricas_init_()
"%plusInfinity"

I tried this (see fricas_infinity.patch), but for some reason that I don't understand the output of
fricas_init() changes into something which is not a valid fricas expression.

sage: oo._fricas_init_()
'%plusInfinity'

but

sage: oo._fricas_()
+ infinity

I have no idea what is going on here.

[sagetrac-drkirkby]

comment:4

Is "algorithm" the most appropiate word here? To me, Fricas, Aximom, Maxima etc are software packages, not algorithms. They implement many differerent algorithms.

I'm not a mathmatician, but certainly my mathematical training would never have suggested that Fricas was an algorithm.

I would have thought something like

integrate(f(x), x, use="fricas") 
integrate(f(x), x, software="fricas") 
integrate(f(x), x, method="fricas") 

would be better than

integrate(f(x), x, algorithm="fricas") 

I don't claim any of my choices are optimal, but I think all of them are better than "algorithm".

Dave

[sagetrac-whuss]

comment:5

Replying to @sagetrac-drkirkby:

If I do

sage: search_def('algorithm=')

I get 150 results. So the 'algorithm' convention is widely
used in Sage, I don't think it makes sense to change this
at this point.