sagemath does not translate function('F') to F := operator "F" for fricas interface

[nasser1]

When using algorithm="fricas" in integrate, I defined F as function in sagemath. BUt when the call is made to integrate using fricas, it did not seem to be translated correctly to fricas syntax, which is

F := operator "F"

So fricas was not happy.

>sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.3.rc0, Release Date: 2018-07-08                 │
│ Type "notebook()" for the browser-based notebook interface.        │
│ Type "help()" for help.                                            │
└────────────────────────────────────────────────────────────────────┘
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ Warning: this is a prerelease version, and it may be unstable.     ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
sage: var('x')
x
sage: F=function('F')
sage: integrate(F(x),x,algorithm="fricas")

.....
TypeError: An error occurred when FriCAS evaluated 'F(x)':

The Fricas syntax using Fricas directly is

>fricas
Checking for foreign routines
AXIOM="/usr/lib/fricas/target/x86_64-linux-gnu"
spad-lib="/usr/lib/fricas/target/x86_64-linux-gnu/lib/libspad.so"
                       FriCAS Computer Algebra System 
                            Version: FriCAS 1.3.4
                   Timestamp: Thu Jun 28 08:31:47 CDT 2018
------------------------------------------------------------------- 

(1) -> F := operator "F"

   (1)  F
                                                          Type: BasicOperator
(2) -> integrate(F(x),x)

           x
         ++
   (2)   |   F(%A)d%A
        ++
                                         Type: Union(Expression(Integer),...)

So many such integrals that use generic function such as the above now fail in sagemath when using FriCAS algorithm because it is not translated correctly.

Thank you

--Nasser

CC: @rwst

Component: interfaces

Keywords: integrate, fricas, sagedays@icerm

Author: Martin Rubey

Branch/Commit: aa044c5

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/25838

[mantepse]

comment:2

I will work on this once #25602 is reviewed. It is not hard.

[mantepse]

Branch: u/mantepse/sagemath_does_not_translate_function__f___to_f____operator__f__for_fricas_interface

[mantepse]

Commit: 7802770

[mantepse]

New commits:

c31c7e0	provide FriCAS translations of formal functions and their derivatives
7802770	add doctest

[mantepse]

Author: Martin Rubey

[tscrim]

Changed keywords from integrate, fricas to integrate, fricas, sagedays@icerm

[tscrim]

comment:5

One (trivial, looks like a bad copy/paste) doctest failure here:

    def derivative(self, ex, operator):
        """
        Convert the derivative of ``self`` in FriCAS.

        INPUT:

        - ``ex`` -- a symbolic expression

        - ``operator`` -- operator

        EXAMPLES::

            sage: var('x,y,z')
            (x, y)

Should be (x, y, z).

Otherwise LGTM.

[tscrim]

Reviewer: Travis Scrimshaw

[sagetrac-git]

Changed commit from 7802770 to 0665ead

[sagetrac-git]

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

0665ead

fix trivial omission in doctest

[nbruin]

comment:7

Edge case for naming functions vs. variables:

sage: F=function('f')
sage: f=SR.var('f')
sage: F(f).diff(f).integrate(f)
f(f)

amazingly this actually works with the maxima interface because:

sage: maxima_calculus(F(f))
'f(_SAGE_VAR_f)

[mantepse]

comment:8

I'm not sure what I'm supposed to do. This "works" with FriCAS, too:

sage: F=function('f')
sage: f=SR.var('f')
sage: fricas(F(f)).D(f).integrate(f)
f(f)

Am I missing something? Oh yes, a missing import, fixed.

[sagetrac-git]

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

9a76eb0

fix missing import and add doctest

[sagetrac-git]

Changed commit from 0665ead to 9a76eb0

[nbruin]

comment:10

Replying to @mantepse:

I'm not sure what I'm supposed to do. This "works" with FriCAS, too:
Am I missing something? Oh yes, a missing import, fixed.

OK, then it's fine. I don't have FriCAS installed, so I couldn't check. When I saw F:= operator F I figured some care should be taken to avoid name clashes, but apparently this is taken care of already.

[mantepse]

comment:11

review?

[tscrim]

comment:12

LGTM now, thanks.

[mantepse]

comment:13

Great, many thanks! Once #25602 is reviewed, integration via FriCAS should be useful for quite a variety of integrands!

[vbraun]

comment:14

Merge conflict

[sagetrac-git]

Changed commit from 9a76eb0 to aa044c5

[sagetrac-git]

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

aa044c5

Merge branch 'develop' of git://trac.sagemath.org/sage into t/25838/sagemath_does_not_translate_function__f___to_f____operator__f__for_fricas_interface

[mantepse]

comment:16

trivial rebase

[vbraun]

Changed branch from u/mantepse/sagemath_does_not_translate_function__f___to_f____operator__f__for_fricas_interface to aa044c5