LaTeXML Test

This LaTeXML test reproduces math examples from https://latexml.mathweb.org/editor
The equations in the first table came originally from http://www.mathjax.org/demos/tex-samples/, which no longer exists.

Equations

	Source	Temml
The Lorenz Equations
1	\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned}	$\begin{aligned} \dot{x} & = σ (y - x) \\ \dot{y} & = ρ x - y - x z \\ \dot{z} & = - β z + x y \end{aligned}$
The Cauchy-Schwarz Inequality
2	\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \	${(\sum_{k = 1}^{n} a_{k} b_{k})}^{2} \leq (\sum_{k = 1}^{n} a_{k}^{2}) (\sum_{k = 1}^{n} b_{k}^{2})$
A Cross Product Formula
3	\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix}	$𝐕_{1} \times 𝐕_{2} = \| \begin{array}{ccc} 𝐢 & 𝐣 & 𝐤 \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{array} \|$
The probability of getting $k$ heads when flipping $n$ coins is:
4	P(E) = {n \choose k} p^k (1-p)^{ n-k} \	$P (E) = (\binom{n}{k}) p^{k} (1 - p)^{n - k}$
An Identity of Ramanujan
5	\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}- \phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } }	$\frac{1}{(\sqrt{ϕ \sqrt{5}} - ϕ) e^{\frac{2}{5} π}} = 1 + \frac{e^{- 2 π}}{1 + \frac{e^{- 4 π}}{1 + \frac{e^{- 6 π}}{1 + \frac{e^{- 8 π}}{1 + \dots}}}}$
A Rogers-Ramanujan Identity
6	1 + \frac{q^2}{(1-q)}+ \frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1} {(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for} \|q\|<1.	$1 + \frac{q^{2}}{(1 - q)} + \frac{q^{6}}{(1 - q) (1 - q^{2})} + \dots = \prod_{j = 0}^{\infty} \frac{1}{(1 - q^{5 j + 2}) (1 - q^{5 j + 3})}, for \| q \| < 1 .$
Maxwell's Equations
7	\begin{aligned} \nabla \times \vec{\mathbf{B}} -\\, \frac1c\, \frac{\partial\vec{ \mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{ \mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} \	$\begin{aligned} \nabla \times \vec{𝐁} - \frac{1}{c} \frac{\partial \vec{𝐄}}{\partial t} & = \frac{4 π}{c} \vec{𝐣} \\ \nabla \cdot \vec{𝐄} & = 4 π ρ \\ \nabla \times \vec{𝐄} + \frac{1}{c} \frac{\partial \vec{𝐁}}{\partial t} & = \vec{𝟎} \\ \nabla \cdot \vec{𝐁} & = 0 \end{aligned}$

Boxes

Source	Temml
`\raisebox{0pt}[0pt][0pt]{\Large%` `\textbf{Aaaa\raisebox{-0.3ex}{a}%` `\raisebox{-0.7ex}{aa}\raisebox{-1.2ex}{r}%` `\raisebox{-2.2ex}{g}\raisebox{-4.5ex}{h}}}`	$𝐀𝐚𝐚𝐚 𝐚 𝐚 𝐚 𝐫 𝐠 𝐡$

Unicode

The tests below come from https://latexml.mathweb.org/editor
They got them from https://trac.edgewall.org/wiki/TracUnicode
I have no idea what these lines say.

All the Unicode characters are written inside \text{}.

Language	Temml
Arabic	$\frac{تراك يقوم بحفظ كل الكلمات باستخدام صيغة}{2}$
Bulgarian	$\frac{Българският език работи ли?}{2}$
Česky	$\frac{Čeština v kódování UTF-8, žádný problém.}{2}$
Chinese (Traditional)	$\frac{繁體中文, 漢字測試}{2}$
Chinese (Simplified)	$\frac{简体中文，汉字测试}{2}$
Croatian	$(\begin{array}{l} Ako podržava srpski i slovenski mora podržavati \\ i Hrvatski - čćžšđ ČĆŽŠĐ \end{array})$
English	$\frac{Yes indeed, Trac supports English. Fully.}{2}$
Français	$\frac{Il est possible d’écrire en Français : à, ç, û, \dots}{2}$
German	$(\begin{array}{l} Trac-Wiki muß auch deutsche Umlaute richtig anzeigen: \\ ö, ä, ü, Ä, Ö, Ü; und das scharfe ß \end{array})$
Greek	$\frac{Τα Ελληνικά υποστηρίζονται επαρκώς επίσης.}{2}$
Hebrew	$\frac{אני יכול לאכול זכוכית וזה לא מזיק לי}{2}$
Hindi	$\frac{अब हिन्दी में।}{2}$
Hungarian	$\frac{Árvíztűrő tükörfúrógép}{2}$
Icelandic	$\frac{Ævar sagði við ömmu sína: Sjáðu hvað ég er stór!}{2}$
Japanese	$\frac{漢字ひらがなカタカナﾊﾝｶｸｶﾅ日本語試験}{2}$
Korean	$\frac{이번에는 한글로 써보겠습니다. 잘 보이나요? 한글}{2}$
Latvian	$\frac{Latviešu valoda arī strādā!}{2}$
Lithuanian	$(\begin{array}{l} Sudalyvaukime ir mes. Ar veikia lietuviškos raidės? \\ ąčęėįšųūž ĄČĘĖĮŠŲŪŽ Žinoma, kad veikia :) Kas tie mes? \end{array})$
Persian (Farsi)	$(\begin{array}{l} ولی امکان نوشتن مستقیم فارسی نیست چون حالت متن از راست به چپ و جود \\ این یک متن فارسی است ندارد برای فارسی نوشتن باید از HTML استفاده کنید. \end{array})$
Polish	$(\begin{array}{l} Pchnąć w tę łódź jeża lub osiem skrzyń fig; \\ Nocna gżegżółka zawsze dzienną przekuka. \end{array})$
Portuguese	$(\begin{array}{l} É possível guardar caracteres especias da língua portuguesa, \\ incluindo o símbolo da moeda européia ’€’, trema ’ü’, crase ’à’, agudos ’áéíóú’, \\ circunflexos ’âêô’, til ’ãõ’, cedilha ’ç’, ordinais ’ªº’, grau ’°¹²³’. \end{array})$
Russian	$\frac{(Проверка русского языка: кажется работает... И буква "ё" есть...}{2}$
Serbian	$(\begin{array}{l} Podržan, uprkos činjenici da se za njegovo \\ pisanje koriste чак два алфабета. \end{array})$
Slovenian	$\frac{Ta suhi škafec pušča vodo že od nekdaj!}{2}$
Spanish	$(\begin{array}{l} Esto es un pequeño texto en Español, \\ donde el veloz murciélago hindú comía cardlllo y kiwi \end{array})$
Swedish	$\frac{Räven raskar över isen med luva på.}{2}$
Thai	$\frac{Trac แสดงภาษาไทยได้อย่างถูกต้อง!}{2}$
Ukrainian	$\frac{Перевірка української мови...}{2}$
Urdu	$\frac{ٹریک اردو بھی سپورٹ کرتا ہے۔}{2}$
Vietnamese	$\frac{Viết tiếng Việt cũng được.}{2}$