# ---------------- PURPOSE ----------------

# This document illustrates how to mix human and math dialects
# conditionally in a Org file.

# ---------------- README ----------------

# Ingest all the Emacs Lisp blocks before export.

# In other words, with cursor inside the Emacs Lisps block do a
# ~M-x org-babel-execute-src-block~ or a ~C-c C-c~

# ---------------- CONFIGURE EXPORT ----------------

# Common setup for all backends

#+setupfile: setup.org

#+begin_src emacs-lisp :exports results :results none
(defun add-includes-for-current-backend ()
  (let ((setupfile (format "setup-%s.org" org-export-current-backend)))
    (when (file-readable-p setupfile)
      (format "#+setupfile: %s" setupfile))))
#+end_src

# Include a setup file specific to each target format.
#+MACRO: add-includes-for-current-backend (eval (add-includes-for-current-backend))

# Each backend has it's own setup.  For example, when exporting to
# ODT, include ~setup-odt.org~.  But when exporting to HTML or LaTeX
# do nothing.

{{{add-includes-for-current-backend}}}

# ---------------- INFORMATIONAL ----------------

#+MACRO: printbackend (eval (upcase (symbol-name org-export-current-backend)))

# ---------------- CONDITIONAL INCLUSION OF SPAN OF TEXT ----------------

#+begin_src emacs-lisp :exports results :results none
(defun current-backend-is-one-of (backends)
  (member (symbol-name org-export-current-backend) (split-string backends ":")))
#+end_src

# Include Starmath or LaTeX according as the target format is ODT or non-ODT.
#+MACRO: starmath-or-latex-full (eval (if (current-backend-is-one-of "odt") $1 $2))

# Same as ~starmath-or-latex-full~ but encloses them in `\(' and '\)'.
#+MACRO: starmath-or-latex (eval (format "\\(%s\\)" (if (current-backend-is-one-of "odt") $1 $2)))

# Functionally same as ~starmath-or-latex-full~, but for /human/ languages.
#+MACRO: english-or-tamil (eval (if (current-backend-is-one-of "odt") $1 $2))

# ---------------- TEXT CONTENT BEGINS HERE ----------------

#+begin_center
/(You are viewing this document in {{{printbackend}}} format)/
#+end_center

Hello {{{english-or-tamil(நண்பனே!, my friend!)}}}

:ENGLISH:
How are you?
:END:

:TAMIL:
நீ எப்படி இருக்கிறாய்?
:END:

:ENGLISH:
You asked me for some help with Euler's Identity. There is a very helpful article about this on
Wikipedia.  Here is an extract from the Wikipedia page.
:END:

:TAMIL:
Euler's Identity தொடர்பாக என்னிடம் உதவி கேட்டாய். விக்கிபீடியாவில் இதைப் பற்றி மிகவும் பயனுள்ள கட்டுரை
Hope this helpsஉள்ளது. விக்கிபீடியா கட்டுரைலிருந்து எடுக்கப்பட்ட ஒரு பகுதியை இங்கே இணைத்துள்ளேன்.
:END:

:ENGLISH:
Hope this helps.
:END:

:TAMIL:
இது உனக்கு உதவும் என நம்புகிறேன்.
:END:

:ENGLISH:
Kind regards,
:END:

:TAMIL:
அன்புடன்,
:END:

/Emacksnotes/

----------------

#+begin_center
_*On Euler's Identity*_
#+end_center

# STRATEGY 1: Replicate the paragraphs while replacing the text spans.  You can see an example in
# the following paragraph.
#
# Enable preview with ~M-x org-latex-preview~ (or ~C-c C-x C-l~).
# Starmath has no preview.  So, it is "broken".

:STARMATH:
Euler's identity asserts that ${func e}^{i %pi}$  is equal to −1.
:END:

:LATEX:
Euler's identity asserts that $\mathrm{e}^{i\pi }$ is equal to −1.
:END:

# STRATEGY 2: Retain the paragraph, but conditionally pick the text spans using a macro.  You can
# see an example in the following paragraph.

The expression {{{starmath-or-latex({func e}^{i %pi},\mathrm{e}^{i\pi})}}} is a special case of the
expression {{{starmath-or-latex({func e}^{z},\mathrm{e}^{z})}}}, where $z$ is any complex number.

# The problem with STRATEGY 2 is that Org mode doesn't recognize latex fragments within a macro.
# You can see what I mean if you do ~M-x org-latex-preview~ (or ~C-c C-x C-l~)

In general {{{starmath-or-latex-full(\({func e}^{z}\),\(\mathrm{e}^{z}\))}}} is defined for complex $z$ by
extending one of the definitions of the exponential function from real exponents to complex
exponents. One such definition is:

# LaTeX Equations that are NOT inlined doesn't pose a problem when it comes to previewing.
# There is no preview for Starmath fragments.

:STARMATH:
$${func e}^{z} =  lim from{n -> infinity} ({  1 + z over n })^{ n }$$
:END:

:LATEX:
$$\mathrm{e}^{z}=\lim _{n\rightarrow \infty }\left(1+\frac{z}{n}\right)^{n}$$
:END:

Euler's identity therefore states that the limit, as n approaches infinity, of
{{{starmath-or-latex(({ 1 + {i %pi} wideslash n })^{ n},\left(1+\frac{i\pi }{n}\right)^{n})}}} is
equal to −1.

Euler's identity is a special case of Euler's formula, which states that for any real number x,

# I wish there was a way to selectively fold only some named drawers, much like there is a way to
# selectively export only some named drawers.  If such an option were available, I would happily
# fold away the STARTMATH drawers and hide the visual clutter like so:

:STARMATH:
$${func e}^{i x} `=` cos( x ) ` + ` i ` sin( x )$$
:END:

:LATEX:
$$\mathrm{e}^{ix}\ =\ \cos (x)\ +\ i\ \sin (x)$$
:END:

where the inputs of the trigonometric functions sine and cosine are given in radians.

In particular, when {{{starmath-or-latex(x = π,x=\pi )}}},

:STARMATH:
$${func e}^{i %pi} `=` cos %pi  ` + ` i ` sin %pi $$
:END:

:LATEX:
$$\mathrm{e}^{i\pi }\ =\ \cos \pi \ +\ i\ \sin \pi $$
:END:

Since {{{starmath-or-latex(cos %pi `=` -1,\cos \pi =-1)}}} and {{{starmath-or-latex(sin %pi `=` 0,\sin \pi =0)}}}
it follows that

:STARMATH:
$${func e}^{i %pi} = -1$$
:END:

:LATEX:
$$\mathrm{e}^{i\pi }=-1$$
:END:

which yields Euler's identity

:STARMATH:
$${func e}^{i %pi} + 1 = 0$$
:END:

:LATEX:
$$\mathrm{e}^{i\pi }+1=0$$
:END: