#+TITLE: Tip for exporting Maxima results to LaTeX
#+AUTHOR: Leo Butler
#+OPTIONS: H:3 toc:t num:t tags:nil todo:nil
#+LATEX_CLASS: article
#+LATEX_HEADER: \usepackage{color} \usepackage[margin=2cm]{geometry}
#+LATEX_COMPILER: lualatex
#+PROPERTY: header-args:maxima :eval export :exports results :results raw drawer

* Goal
Generate LaTeX code from Maxima code.

* Setup
** maxima-init.lisp
The command =org-babel-execute:maxima= in =lisp/ob-maxima.el= uses the Maxima command ~batchload~ to execute Maxima code. This is a very tight-lipped loader, so we over-write ~batchload~ with ~batch~. We also ~load~ an init file:

#+name: maxima-init.lisp.org
#+begin_src org :exports code :results replace
,#+name: maxima-init.lisp
,#+begin_src maxima :tangle maxima-init.lisp :exports none
  (defun $batchload (file) (mfuncall '$batch file))
  ($load "./maxima-init.mac")
,#+end_src
#+end_src

On tangling, this produces the ~common-lisp~ output file ~maxima-init.lisp~. It will be pre-loaded into Maxima.

#+RESULTS: maxima-init.lisp.org
#+name: maxima-init.lisp
#+begin_src maxima :tangle maxima-init.lisp :exports none
  (defun $batchload (file) (mfuncall '$batch file))
  ($load "./maxima-init.mac")
#+end_src

** maxima-init.mac
Next, we need to create an init file for Maxima that will provide an output printer that produces @@latex:\LaTeX{}@@ output. One option would be to use the ~imaxima~ printer. Here is another option that uses the ~alt-display~ package.
The code replaces the default printer with ~org_tex_display~. It also sets the ~epilog~ prompt, so that the final ~#+begin_example~ is terminated.

#+name: maxima-init.mac.org
#+begin_src org :exports code :results replace
  ,#+name: maxima-init.mac
  ,#+begin_src maxima :tangle maxima-init.mac :exports none :eval none
  load("alt-display.mac") $
  set_prompt('epilog,printf(false,"~%#+end_example")) $
  define_alt_display(org_tex_display(x),
    block([], 
      printf(true,"#+end_example~%#+begin_export latex~%"),
      printf(true,"\\textcolor{blue}{(\\~a~d)} ",outchar,linenum-1),
      tex(second(x)),
      printf(true,"~&#+end_export~%#+begin_example~%(input) "))) $
  set_alt_display(2,org_tex_display) $
  display2d:true $
  printf(true,"#+begin_example~%(input) ") $
  linenum : 0 $
  ,#+end_src
#+end_src

#+RESULTS: maxima-init.mac.org
#+name: maxima-init.mac
#+begin_src maxima :tangle maxima-init.mac :exports none :eval none
load("alt-display.mac") $
set_prompt('epilog,printf(false,"~%#+end_example")) $
define_alt_display(org_tex_display(x),
  block([], 
    printf(true,"#+end_example~%#+begin_export latex~%"),
    printf(true,"\\textcolor{blue}{(\\~a~d)} ",outchar,linenum-1),
    tex(second(x)),
    printf(true,"~&#+end_export~%#+begin_example~%(input) "))) $
set_alt_display(2,org_tex_display) $
display2d:true $
printf(true,"#+begin_example~%(input) ") $
linenum : 0 $
#+end_src

* An example
Here is an example that computes the partial derivatives of a composite function.

** Org code

#+name: chain-rule.org
#+begin_src org :exports both :results replace
,#+name: chain-rule
,#+begin_src maxima :exports both :cmdline -p ./maxima-init.lisp
  (gradef(f(u,v),f_1(u,v),f_2(u,v)), 'done);
  diff(f(x^2-y^2,x*y),x);
  diff(f(x^2-y^2,x*y),y);
,#+end_src
#+end_src

** Maxima code

#+RESULTS: chain-rule.org

The first line defines the partial derivatives of \(f(u,v)\) with repect to \(u\) and \(v\). The second and third lines compute the partial derivatives of the composite \(f(x²-y²,xy)\).

** Result of evaluation; LaTeX output
The ~batch~ printer echos each input line; it prints the output of
each command line that ends in a semi-colon (=;=). The result of a
line ending in a dollar sign (=$=) is not printed. The
~org_tex_display~ printer wraps each echoed input line in an ~example~
block and prints the output as it would appear in an =imaxima=
session.

#+RESULTS: chain-rule

** Two annoyances
The initial line =read and interpret...= and that final, dangling
input line with ~gnuplot_close()~ are nuisances. They can be easily
suppressed, but that requires patching ~ob-maxima.el~. That's another
story.

* Epilogue
After sending my initial draft to the =Org= mailing list, I received some feedback.
** Eric Fraga's suggestion
:PROPERTIES:
:header-args:maxima: 
:END:

On the mailing list, Eric Fraga suggested adding the prologue/epilogue:

#+begin_example
#+PROPERTY: header-args:maxima :prologue "fpprintprec: 2; linel: 50;"
#+PROPERTY: header-args:maxima :epilogue "for j: 1 thru length(solution) do (\
            print(\"\"), print(\"Solution\", j), \
            print(\"\"), for i: 1 thru length(solution[j]) do grind(solution[j][i]))$"
#+end_example

\normalsize
Let's redo the example above with those settings and incorporating Eric's design that the results need to be collected in the ~solution~ list:

#+name: fraga-example.org
#+begin_src org :exports both :results replace :noweb yes
  ,#+name: chain-rule-redo
  ,#+header: :prologue "fpprintprec: 2; linel: 50;"
  ,#+header: :epilogue "for j: 1 thru length(solution) do (print(\"\"), print(\"Solution\", j), print(\"\"), for i: 1 thru length(solution[j]) do grind(solution[j][i]));"
  ,#+begin_src maxima :exports results :results table
  (gradef(f(u,v),f_1(u,v),f_2(u,v)), 'done);
  fx:diff(f(x^2-y^2,x*y),x);
  fy:diff(f(x^2-y^2,x*y),y);
  solution:[fx,fy];
  ,#+end_src
#+end_src

#+RESULTS: fraga-example.org

Here is the result:

#+RESULTS: chain-rule-redo

** Max Nikulin's idea

Max Nikulin remarked that the ~org~ code in this file contains redundancy. He suggested trying:

#+name: elisp-in-org-in-org
#+begin_src org :exports both :results replace
,#+begin_src elisp :exports results :results silent
  (require 'ob-org)
,#+end_src

,#+name: elisp-in-org
,#+begin_src org :exports both :results replace
  ,,#+name: elisp-block
  ,,#+begin_src elisp :exports results
    '((1 2 3) (4 5 6))
  ,,#+end_src
,#+end_src
#+end_src

The block named ~elisp-in-org~ is exported to:

#+RESULTS: elisp-in-org-in-org

The ~elisp~ code block exports to a named block of =elisp= code.

#+RESULTS: elisp-in-org

That exports to:

#+RESULTS: elisp-block

*** A bug // Feature request
=Org= does a good job of recursively evaluating code blocks, as can be seen by the examples here (Thanks, Max!). But, two things are not done quite correctly:
1. When editing ~org~ code blocks in an indirect buffer, it should be possible to recursively edit a code block. That does not appear to work at the moment.
2. Noweb expansion does not work correctly in combination with recursive evaluation of code blocks. In the ~org~ block named =fraga-example.org=, a noweb reference =<<chain-rule>>= to the Maxima code block =chain-rule= is not expanded correctly (it leaves a blank line).

* How to reproduce the pdf
1. In this =org= file, do ~C-c C-v t~ to tangle the two code blocks.
2. Then, do ~C-c C-e l p~ to export to pdf. Each time you are prompted about evaluating a code block, answer ~y~ or ~yes~.