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.

[burcin]

comment:6

Replying to @sagetrac-whuss:

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.

This seems to be how fricas prints %plusInfinity. Ralf, can you help us with this?

[hemmecke]

comment:7

Well, not quite right, as http://axiom-wiki.newsynthesis.org/PerCent shows. I've added

)set output algebra on

in order to also show the ascii output. Otherwise mathaction renders tex output of axiom. These things starting with a percent sign are only used for input. What exactly gets printed depends on the ')set output' settings.

[hemmecke]

comment:8

Also look at the exports of OrderedCompletion.
https://github.com/hemmecke/fricas-svn/blob/master/src/algebra/complet.spad.pamphlet#L20
Obviously also 'plusInfinity()' and 'minusInfinity()' could be used as input.

The output is constructed in
https://github.com/hemmecke/fricas-svn/blob/master/src/algebra/complet.spad.pamphlet#L59
How the symbol infinity appears is hidden inside OutputForm and probably deeper.

)set output tex on
(1) -> plusInfinity()      

   (1)   + infinity
$$
+\infty 
\leqno(1)
$$

                                             Type: OrderedCompletion(Integer)

[burcin]

comment:9

So the ascii output for plusInfinity is "+ infinity" and the _fricas_init_() method in attachment: fricas_infinity.patch works as intended.

Wilfried, will you have time to revise the patch? Note that when #9880 is merged (almost) all symbolics patches will need to be rebased.

[videlec]

comment:14

Replying to @sagetrac-drkirkby:

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".

+1 for use, software or library
Moreover, in some situation, when we call the software (fricas, maxima, ...) we might want to feed it with an option algorithm.

Vincent

[fchapoton]

comment:15

I have made a git branch with the attached files, rebased on 6.5.b2

---

New commits:

2b719db	Implement algorithm="fricas" for integration
5db0224	convert infinities to fricas

[fchapoton]

Commit: 5db0224

[fchapoton]

Branch: public/ticket/9427

[rwst]

comment:16

Replying to @videlec:

Moreover, in some situation, when we call the software (fricas, maxima, ...) we might want to feed it with an option algorithm.

First I agreed with this, but now I think it would be easy to allow something like algorithm=fricas-risch, and this would then be more convenient than software=fricas,algorithm=risch. Whereas changing algorithm to software would be annoying as hell.

[rwst]

comment:17

Replying to @burcin:

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

I know this is how Sympy does it but I think such a decision is up to the Fricas developers.

[sagetrac-git]

Changed commit from 5db0224 to c5bd849

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

25820dc	Merge branch 'develop' into t/9427/public/ticket/9427
c5bd849	9427 reviewer's patch: fix doctest

[rwst]

Changed author from Wilfried Huss to Wilfried Huss, Frédéric Chapoton

[rwst]

comment:19

This looks good and tests OK in symbolic and rings.

[rwst]

Changed reviewer from Burcin Erocal to Burcin Erocal, Ralf Stephan

[vbraun]

Changed branch from public/ticket/9427 to c5bd849