~bzg/worg

525a1355235c40e7528330daab56b7e9b8be1111 — Leo Butler 1 year, 9 days ago 16ef094
* org-contrib/babel/languages/ob-doc-maxima.org: new header args

* org-contrib/babel/languages/ob-doc-maxima.org: Document the new
header arguments, `:batch' and `:graphics-pkg'.

Show examples with `:batch' that: (1) use Maxima's `:lisp' reader to print
the internal representation of an object as a sexp; (2) reproduce the
output of `batch'-ed input file, including input/output line
labels; (3) typeset Maxima output in LaTeX.

Show examples with `:graphics-pkg' that: (1) create a `gif' graphics
file using `plot'; (2) create an `svg' graphics file using `draw'.

* org-contrib/babel/languages/images/ob-maxima-plot.gif: New file.
* org-contrib/babel/languages/images/ob-maxima-draw.svg: New file.
Both of these files are created in the `:graphics-pkg' examples.
A org-contrib/babel/languages/images/ob-maxima-draw.svg => org-contrib/babel/languages/images/ob-maxima-draw.svg +366 -0
@@ 0,0 1,366 @@
<?xml version="1.0" encoding="utf-8"  standalone="no"?>
<svg 
 width="600" height="500"
 viewBox="0 0 600 500"
 xmlns="http://www.w3.org/2000/svg"
 xmlns:xlink="http://www.w3.org/1999/xlink"
>

<title>Gnuplot</title>
<desc>Produced by GNUPLOT 5.4 patchlevel 4 </desc>

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	<g id="gnuplot_plot_3" ><title>gnuplot_plot_3</title>
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	<g id="gnuplot_plot_4" ><title>gnuplot_plot_4</title>
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A org-contrib/babel/languages/images/ob-maxima-plot.gif => org-contrib/babel/languages/images/ob-maxima-plot.gif +0 -0
M org-contrib/babel/languages/ob-doc-maxima.org => org-contrib/babel/languages/ob-doc-maxima.org +320 -13
@@ 9,6 9,7 @@
#+HTML_LINK_UP:    index.html
#+HTML_LINK_HOME:  https://orgmode.org/worg/
#+EXCLUDE_TAGS: noexport
#+PROPERTY: header-args:org :exports code :results replace

#+name: banner
#+begin_export html


@@ 25,7 26,12 @@
  </div>
#+end_export

* Template Checklist [8/12]                                        :noexport:
#+name: ob-doc-maxima-requires-ob-org
#+begin_src elisp :exports none :results silent
(require 'ob-org)
#+end_src

* Template Checklist [9/12]                                        :noexport:
  - [X] Revise #+TITLE:
  - [X] Indicate #+AUTHOR:
  - [X] Add #+EMAIL:


@@ 37,7 43,7 @@
  - [X] Write an [[Introduction]]
  - [X] Describe [[Requirements and Setup][Requirements and Setup]]
  - [X] Replace "Language" with language name in [[Org Mode Features for Language Source Code Blocks][Org Mode Features for Language Source Code Blocks]]
  - [ ] Describe [[Header Arguments][Header Arguments]]
  - [X] Describe [[Header Arguments][Header Arguments]]
  - [ ] Describe support for [[Sessions]]
  - [ ] Describe [[Result Types][Result Types]]
  - [ ] Describe [[Other]] differences from supported languages


@@ 76,7 82,27 @@ You must activate Maxima by adding a line to

* Org Mode Features for Maxima Source Code Blocks
** Header Arguments
There are no Maxima-specific default header argument values.
There are no Maxima-specific /default/ header arguments.

There are two Maxima-specific header arguments:

- =:batch= :: This can be set to one of Maxima's source-code loaders:
  =batch=, =load= or =batchload=.  The default loader is =batchload=.
- =:graphics-pkg= :: This can set to one of Maxima's graphics
  packages: =draw= or =plot=.  The default package is =plot=.

If a =:file filename.ext= header argument is provided to a Maxima
source block, in conjunction with a =:results graphics file= header
argument, then the graphics device is determined from the file-ending
=ext=. For the =plot= package, the following graphics devices (gnuplot
terminals) are supported:
#+begin_example
png, pdf, ps, svg.
#+end_example
The =draw= package supports these graphics devices:
#+begin_example
png, jpg, gif, eps, svg, pdf.
#+end_example

The header argument, =:cmdline=, can be used to pass command line
arguments to Maxima.


@@ 201,31 227,312 @@ HTML export of the result:
#+RESULTS: tex-maxima
$${{e^ {- x }}\over{x}}$$

*** Toggle inline display of latex code
** The =:batch= header argument
Setting the =:batch= header argument to =batch=:
- allows the use of the =:lisp= reader;
- provides a more verbose output;
- allows one to typeset calculations in LaTeX.

*** An example with the =:lisp= reader
Sample code block:

#+name: batch-maxima.org
#+begin_src org :exports code :results replace
,#+NAME: batch-maxima
,#+HEADER: :batch batch
,#+HEADER: :exports results
,#+HEADER: :results raw
,#+HEADER: :wrap example
,#+BEGIN_SRC maxima
  (assume(z>0), integrate(t^z*exp(-t),t,0,inf));
  :lisp $%
,#+END_SRC
#+end_src

#+RESULTS: batch-maxima.org
#+NAME: batch-maxima
#+HEADER: :batch batch
#+HEADER: :exports results
#+HEADER: :results raw
#+HEADER: :wrap example
#+BEGIN_SRC maxima
  (assume(z>0), integrate(t^z*exp(-t),t,0,inf));
  :lisp $%
#+END_SRC

The first line of input computes the integral \(\int_0^{\infty}
t^z\,e^{-t}\,dt\), assuming that \(z\) is positive.  The second input
line uses the =:lisp= reader to print the internal representation of
that result as a sexp.

HTML export of results:

#+RESULTS: batch-maxima
#+begin_example
(assume(z > 0),integrate(t^z*exp(-t),t,0,inf))
                                 gamma(z + 1)
((%GAMMA SIMP) ((MPLUS SIMP) 1 $Z))
#+end_example

*** An example with line numbering
By default, the command-line option =--very-quiet= is passed to the
Maxima executable; this option suppresses the output of the start-up
banner and input/output labels.  That can be modified by setting
=:cmdline --quiet=, which allows printing of input/output labels.

Sample code block:

#+name: batch-quiet-maxima.org
#+begin_src org :exports code :results replace
,#+NAME: batch-quiet-maxima
,#+HEADER: :batch batch
,#+HEADER: :exports results
,#+HEADER: :results raw
,#+HEADER: :wrap example
,#+HEADER: :cmdline --quiet
,#+BEGIN_SRC maxima
  rat(1/(x+1) + x/(x-1));
,#+END_SRC
#+end_src

#+RESULTS: batch-quiet-maxima.org
#+NAME: batch-quiet-maxima
#+HEADER: :batch batch
#+HEADER: :exports results
#+HEADER: :results raw
#+HEADER: :wrap example
#+HEADER: :cmdline --quiet
#+BEGIN_SRC maxima
  rat(1/(x+1) + x/(x-1));
#+END_SRC

HTML export of results:

#+RESULTS: batch-quiet-maxima
#+begin_example
(%i1) rat(1/(x+1)+x/(x-1))
                                  2
                                 x  + 2 x - 1
(%o1)/R/                         ------------
                                     2
                                    x  - 1
#+end_example

Maxima's default is to print input in linear (or 1d) fashion, while
output is printed in 2d.

*** LaTeX output

To produce LaTeX output for an extended computation, one needs to
set-up a LaTeX printer.  This example uses the ~alt-display~ package
to do that.  To print output as LaTeX, Maxima's 2d printer is replaced
with ~org_tex_display~; to ensure input lines are not echoed, its 1d
printer is replaced with a sink, ~org_no_display~ (see also this
[[batch-note][Note]]).

Tangle this code block (=C-u C-c C-v t=):

#+comment: Ensure the block is evaluated (C-c C-c) after a change.
#+comment: Move to the results block and tangle it (C-u C-c C-v t)
#+name: maxima-initialize.lisp.org
#+begin_src org
,#+NAME: maxima-initialize.lisp
,#+HEADER: :tangle ./maxima-initialize.lisp
,#+HEADER: :exports none
,#+HEADER: :eval none
,#+begin_src maxima
#$(load("alt-display.mac"),
define_alt_display(org_no_display(output_form), ""),
define_alt_display(org_tex_display(output_form),
  block([],
  printf(true,"~&#+begin_example~%(~a~d)~%",outchar,linenum),
  printf(true,"~&#+end_example~%"),
  tex(second(output_form)))),
set_alt_display(2,org_tex_display),
set_alt_display(1,org_no_display));#$
,#+end_src
#+end_src

#+RESULTS: maxima-initialize.lisp.org
#+NAME: maxima-initialize.lisp
#+HEADER: :tangle ./maxima-initialize.lisp
#+HEADER: :exports none
#+HEADER: :eval none
#+begin_src maxima
#$(load("alt-display.mac"),
define_alt_display(org_no_display(output_form), ""),
define_alt_display(org_tex_display(output_form),
  block([],
  printf(true,"~&#+begin_example~%(~a~d)~%",outchar,linenum),
  printf(true,"~&#+end_example~%"),
  tex(second(output_form)))),
set_alt_display(2,org_tex_display),
set_alt_display(1,org_no_display));#$
#+end_src

Next, write a Maxima code block that sets the =:cmdline= header to
read in the initialization code that was just tangled.

#+name: batch-latex-maxima.org
#+begin_src org
,#+NAME: batch-latex-maxima
,#+HEADER: :batch batch
,#+HEADER: :exports results
,#+HEADER: :results raw
,#+HEADER: :wrap maximablock
,#+HEADER: :cmdline --quiet --preload-lisp ./maxima-initialize.lisp
,#+BEGIN_SRC maxima
  (assume(z>0), 'integrate(t^z*exp(-t),t,0,inf) = integrate(t^z*exp(-t),t,0,inf));
  diff(%,z);
,#+END_SRC
#+end_src

#+RESULTS: batch-latex-maxima.org
#+NAME: batch-latex-maxima
#+HEADER: :batch batch
#+HEADER: :exports results
#+HEADER: :results raw
#+HEADER: :wrap maximablock
#+HEADER: :cmdline --quiet --preload-lisp ./maxima-initialize.lisp
#+BEGIN_SRC maxima
  (assume(z>0), 'integrate(t^z*exp(-t),t,0,inf) = integrate(t^z*exp(-t),t,0,inf));
  diff(%,z);
#+END_SRC

HTML export of the results:

#+RESULTS: batch-latex-maxima
#+begin_maximablock
#+begin_example
(%o1)
#+end_example
$$\int_{0}^{\infty }{t^{z}\,e^ {- t }\;dt}=\Gamma\left(z+1\right)$$
#+begin_example
(%o2)
#+end_example
$$\int_{0}^{\infty }{t^{z}\,e^ {- t }\,\log t\;dt}=\psi_{0}(z+1)\,
 \Gamma\left(z+1\right)$$
#+end_maximablock

*** <<batch-note>> Note
Prior to version =5.47=, Maxima could only pre-load a lisp
file; to get around this constraint, the Maxima code is written into a
lisp file, and the =#$= reader macro is used to read the Maxima code.
In versions 5.47 and higher, the Maxima code can be put in a =.mac=
file and pre-loaded without the need for such tricks.

** The =:graphics-pkg= header argument
The =:graphics-pkg= header argument can be set to use either Maxima's
built-in =plot= package (the default), or the =draw= package.

*** The =plot= package
The =plot= package is the default package that provides a simplified
interface to =gnuplot=. Here is an example that creates a =gif= file.

#+name: graphics-pkg--plot.org
#+begin_src org
,#+NAME: graphics-pkg--plot
,#+HEADER: :graphics-pkg plot
,#+HEADER: :file images/ob-maxima-plot.gif
,#+HEADER: :results graphics file
,#+HEADER: :exports both
,#+begin_src maxima
plot2d( sin(x), [x,0,2*%pi]);
,#+end_src
#+end_src

#+RESULTS: graphics-pkg--plot.org
#+NAME: graphics-pkg--plot
#+HEADER: :graphics-pkg plot
#+HEADER: :file images/ob-maxima-plot.gif
#+HEADER: :results graphics file
#+HEADER: :exports both
#+begin_src maxima
plot2d( sin(x), [x,0,2*%pi]);
#+end_src

HTML export of the results:

#+CAPTION: The graph of /sin(x)/ created with =plot=.
#+RESULTS: graphics-pkg--plot
[[file:images/ob-maxima-plot.gif]]

*** The =draw= package
The =draw= package has more features than =plot=, including an
object-oriented interface to several graphics engines, including
=gnuplot=. Here is an example that creates an =svg= file containing
the graph of a discontinuous function.

#+name: graphics-pkg--draw.org
#+begin_src org
,#+NAME: graphics-pkg--draw
,#+HEADER: :graphics-pkg draw
,#+HEADER: :file images/ob-maxima-draw.svg
,#+HEADER: :results graphics file
,#+HEADER: :exports both
,#+begin_src maxima
f(x) := if x>0 then cos(x) else if x<0 then 0;
draw2d(
  line_width=2, grid=true, yrange=[-1.2,1.2],
  explicit(f,x,0,%pi), explicit(f,x,-1,0),
  fill_color=white, ellipse(0,0,0.05,0.05,0,360),
  fill_color=blue , ellipse(0,1,0.05,0.05,0,360));
,#+end_src
#+end_src

#+RESULTS: graphics-pkg--draw.org
#+NAME: graphics-pkg--draw
#+HEADER: :graphics-pkg draw
#+HEADER: :file images/ob-maxima-draw.svg
#+HEADER: :results graphics file
#+HEADER: :exports both
#+begin_src maxima
f(x) := if x>0 then cos(x) else if x<0 then 0;
draw2d(
  line_width=2, grid=true, yrange=[-1.2,1.2],
  explicit(f,x,0,%pi), explicit(f,x,-1,0),
  fill_color=white, ellipse(0,0,0.05,0.05,0,360),
  fill_color=blue , ellipse(0,1,0.05,0.05,0,360));
#+end_src

HTML export of the results:

#+CAPTION: A discontinuous function plotted with =draw=.
#+RESULTS: graphics-pkg--draw
[[file:images/ob-maxima-draw.svg]]

**** Note
Internally, =ob-maxima= uses the function =set_draw_defaults=.
Because this function _overwrites_ the existing defaults, using it in
code blocks with the =:graphics-pkg draw= header argument will cause
the source block evaluation to fail silently.

* Additional Notes

** Toggle inline display of latex code
    Latex code in org mode can be displayed inline by 'C-c C-x
    C-l'. To remove the inline display 'C-c C-c' is used. This is
    described further in the manual [fn:2].
*** Set scale of output
** Set scale of output
    If the inline display of the equations are illegible, the scale
    can be set by customising the variable 'org-format-latex-options',
    by setting the :scale variable to a value >1.
*** Export
    This exports nicely to both html (C-c C-e b) and pdf (C-c C-e
    d). See [fn:3] and [fn:4] in the manual.
*** Noweb expansion
** Export
    This exports nicely to both html (C-c C-e h h) and pdf (C-c C-e l
    p). See [fn:3] and [fn:4] in the manual.
** Noweb expansion
    _NOTE:_ I have not tested this yet, but as Eric Schulte noted on
    the mailing list: "Alternately, if you really want to get fancy
    you could use noweb expansion [fn:5] to insert the results of the
    imaxima code block into a latex code block, and then use the
    existing latex code block functionality to convert the imaxima
    output to images of different types depending on the export
    target."
    target." [fn:6]

*** Footnotes
** Footnotes
[fn:1] (info "(org)Library of Babel")
[fn:2] (info "(org)Previewing LaTeX fragments")
[fn:3] (info "(org)Exporting code blocks")
[fn:4] (info "(org)The export dispatcher")
[fn:5] (info "(org)noweb")


[fn:6] [[https://lists.gnu.org/archive/html/emacs-orgmode/2013-11/msg00893.html][Re: imaxima babel]]