MathJax reference

What a treasure trove! This page prioritizes what I tend to use or find interesting, mostly in the context of this Obsidian vault. The most complete and useful reference page I've seen is One Mathematical Cat, though sadly it's covers an old version (v2 versus the current, v4). The current docs are at MathJax.org, but show no examples.

However, be warned that MathJax doesn't support all of TeX.

Introduction

• For inline formulas, enclose the MathJax expression in $…$.
  • For displayed formulas, use $$…$$.
• Most symbol macros are words prefaced with a backslash, like \frac, and need a space to delimit them. Examples throughout.
• Groups of symbols. Macros apply only to the next "group", one or more characters surrounded by curly braces {…}.
  • For example, with superscript ^, if you did x^10, you'd get a surprise: $x^{1}0$!
  • But x^{10} gives what you probably want: $x^{10}$.
  • Braces can also allow you to "double up" a few macros, ex. x^{2^{n}} to get $x^{2^n}$.

Math

Text

• For plain text as in business formulas, use \text{after-effect} for normal words → $\text{after-effect}$, versus $after-effect$.
  • Spaces are tricky — MathJax sometimes collapses or ignores them. Use \, \: \; \quad \qquad gives whitespace in increasing amounts: $ab,ab,ab,ab,ab,ab$.
    • Use ~ for a non-breaking space.
    • Use \! for a negative thin space to mimic ligatures, like this: \rm a\!e → $\mathrm{a}\mathrm{e}$.
  • Use \dots for ellipses like this… "$a_1,a_2,\dots$".
    • \ldots for horizontal dots on the line: $\dots$
    • \cdots for horizontal dots above the line: $\cdots$
    • \vdots for vertical dots: $⋮$
    • \ddots for diagonal dots: $\ddots$
    • See \def below if you want ascending diagonal dots.
  • \dagger and \ddagger are $†,‡$.
• Unicode is available via the pre-loaded unicode extension, \unicode{x2156} → $\text{⅖}$.
• For Greek letters, use \alpha $\alpha$, \beta, …, \omega.
  • For uppercase letters, use \Gamma $\mathrm{\Gamma }$, \Delta, …, \Omega. Ones like Alpha and Beta that look like their Roman equivalents don't have macros. Many letters have italicized variants, like \varGamma $\Gamma$.
  • Some Greek letters have variant forms:
    • \epsilon $ϵ$ vs. \varepsilon $\epsilon$
    • \kappa $\kappa$ vs. \varkappa $\varkappa$
    • \phi $\varphi$ vs. \varphi $\phi$
    • \pi $\pi$ vs. \varpi $\varpi$
    • \rho $\rho$ vs. \varrho $\varrho$
    • \sigma $\sigma$ vs. \varsigma $\varsigma$
    • \theta $\theta$ vs. \vartheta $\vartheta$
    • \digamma $ϝ$
• Special typefaces.
  • Blackboard bold, for sets: \mathbb{N} \mathbb{Z}_p → $\mathbb{N},{\mathbb{Z}}_p$
  • Boldface, \mathbf {a,A} → $\mathbf{a}\mathbf{,}\mathbf{A}$
  • Calligraphy, \mathcal {A,B} → $\mathcal{A}\mathcal{,}\mathcal{B}$
  • Fraktur, \mathfrak {a,A} → $\mathfrak{a}\mathfrak{,}\mathfrak{A}$
  • Roman, \mathrm {a,A} → $\mathrm{a},\mathrm{A}$
  • Script, \mathscr {a,A} → $\mathcal{a}\mathcal{,}\mathcal{A}$
    • Lowercase l is \ell → $\ell$.
  • To turn these on to the end of the block, remove "math", ex: \scr hello → $\mathcal{h}\mathcal{e}\mathcal{l}\mathcal{l}\mathcal{o}$.
• Card suits: \spadesuit → $\mathrm{♠}$, also $\mathrm{♣},\mathrm{♡},\mathrm{♢}$.

Font sizes

• \displaystyle is ${\displaystyle \int f^{-1}(x-x_a)dx}$, suitable for separate blocks but not inline
• \textstyle is $\int f^{-1}(x-x_a)dx$, normal use, the default
• \scriptstyle is $\int f^{-1}(x-x_a)dx$
• \scriptscriptstyle is $\int f^{-1}(x-x_a)dx$

For individual items, these adjustments increase the size incrementally: \big, \Big, \bigg, \Bigg. \Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr) yields:

Common symbols

• Delimiters.
  • You can use normal symbols like | / ([{ }]).
    • There's \backslash, though, because \ is reserved for macros.
    • \vert is an alternative for |; \Vert and \parallel both yield $\Vert$.
      • You'll find a few other cases of two macros that render the same, where \Vert is typesetting, but \parallel has semantic meaning.
  • Angle brackets: \langle S \rangle → $⟨S⟩$.
  • Use \left and \right to expand delimiters to fit larger macros like \dfrac, such as:
    • \left| \dfrac xy \right| for $\left|{\displaystyle \frac{x}{y}}\right|$, versus $|\frac{x}{y}|$.
    • \left(\dfrac{x}{x-1}\right) → $\left({\displaystyle \frac{x}{x-1}}\right)$
  • Floor and ceiling: \lfloor x\rfloor → $\lfloor x\rfloor$, \lceil x\rceil → $\lceil x\rceil$.
  • \llcorner \lrcorner \ulcorner \urcorner gives $⌞,⌟,⌜,⌝$
• For superscripts and subscripts, use ^ and _. For example, x_i^2 is $x_i^2$.
• Text decoration.
  • Absolute value: |x| or \vert \frac xy \vert → $|x|,|\frac{x}{y}|$.
  • Vector: \vec a → $\overrightarrow{a}$
    • \overleftarrow{abc} \overrightarrow{abc} → $\overleftarrow{abc},\overrightarrow{abc}$
  • Over-line for line segments, repeating decimals: \overline {AB} makes $\overline{AB}$
  • Estimated value, cross-product: \hat a for $\hat{a}$, \widehat {ab} for $\widehat{ab}$, \widetilde{abc}for $\widetilde{abc}$
  • Conjugates: \overline{x} n^{\overline{m}} → $\bar{x},n^{\bar{m}}$
  • n^{\underline{m}} → $n^{\underset{―}{m}}$
• Arrows.
  • \to \rightarrow \Rightarrow \implies \mapsto makes $\to ,\to ,\Rightarrow ,⟹,\mapsto$
  • \gets \leftarrow \Leftarrow \impliedby yields $\leftarrow ,\leftarrow ,\Leftarrow ,⟸$
  • \leftrightarrow \iff for $\leftrightarrow ,⟺$
  • \uparrow \Uparrow for $\uparrow ,\Uparrow$
  • \downarrow \Downarrow for $\downarrow ,\Downarrow$
  • \nearrow \nwarrow \searrow \swarrow are $\nearrow ,\nwarrow ,\searrow ,\swarrow$
• Proofs.
  • \therefore x, \because y → $\therefore x,\because y$
  • QED, use \blacksquare \Box to end a proof → $◼,◻$`

Operations and other symbols

• Equals is just plain =, \neq is $\ne$.
• Inequalities. \lt \gt \le \ge \neq \ll \gg $<,>,\le ,\ge ,\ne ,\ll ,\gg$.
  • There's an "n" form of most of these for negation, ex. \nleq $\nleqq$
  • You can use \not to put a slash through almost anything: \not\lt $\nless$, but it often looks bad.
  • Preceder and successor: \prec \succ $\prec ,\succ$
• Approximates. \approx \sim \simeq \cong $\approx ,\sim ,\simeq ,\cong$
• Equivalence. \equiv \lhd $\equiv ,⊲$
  • Let operators: \triangleq \overset{def}=, \mathrel{:=} → $\triangleq ,\stackrel{def}{=},:=$
  • Proportions: \propto $\propto$
• Binary operations. \times \div \pm \mp \sqrt x $\times ,÷,\pm ,\mp ,\sqrt{x}$.
  • \sqrt[3]{x} is the cube root, and so on → $\sqrt[3]{x}$
  • x \cdot y is a centered dot → $x\cdot y$
  • \star \ast \oplus \otimes \circ \bullet \Box → $\star ,\ast ,\oplus ,\otimes ,\circ ,\bullet ,◻$
• Fractions. x/y works → $x/y$.
  • \frac 25 applies to the next two items → $\frac{2}{5}$.
    • Use braces for grouping: \frac{a+1}{b+1} is $\frac{a+1}{b+1}$.
  • If both numerator and denominator need grouping, you may prefer \over, which splits the group it's in: {x+1\over y+1} is $\frac{x+1}{y+1}$.
  • Use \dfrac to display the letters normal size in a block, but considered improper when used inline:
    • \dfrac{V_1}{n_1} = \frac{V_2}{n_2} → ${\displaystyle \frac{V_1}{n_1}}=\frac{V_2}{n_2}$
• Trigonometric and other named functions are normally set in Roman font, use \lim, \log, \sin and the like to make these: $lim,\log ,\sin$.
  • For "mod", you have a few choices: \bmod, \mod, and \pmod: $3mod2,3\mathrm{mod}2,3(\mathrm{mod}2)$. bmod is "binary mod", spaced as an operator.
  • Nonstandard function names can be set with \operatorname{foo}(x) → $\mathrm{foo}(x)$.
  • Use \mathrm otherwise, as for Euler's constant \mathrm{e} → $\mathrm{e}$.
• Infinity is \infty $\mathrm{\infty }$, and also a few Hebrew letters like \aleph_0 → ${\mathrm{\aleph }}_0$.
• Sums and integrals. \sum and \int, ex. \sum_{i=0}^n i^2 yields $\sum _{i=0}^n{i}^2$.
  • Integral: \int, \int_a^b f(x) → ${\int }_a^{b}f(x)$
  • Limit: \lim, \lim_{n\to \infty} → $\underset{n\to \mathrm{\infty }}{lim}$.
  • Product: \prod_{i=1}^n a_i → $\prod _{i=1}^n{a}_i$
  • Similar to \dfrac, \displaystyle can expand these in text blocks, see #Font sizes:
    • \displaystyle \lim_{n\to \infty} \sum_{i=1}^n f(x_i)\,\Delta x_i = \int_a^b f(x) \, \mathrm{d}x\ → ${\displaystyle \underset{n\to \mathrm{\infty }}{lim}\sum _{i=1}^{n}f(x_i)\mathrm{\Delta }{x}_i={\int }_a^{b}f(x)\mathrm{d}x}$
    • Note that we're not using the #Physics extension for derivative support here.
• Other Calculus operations.
  • Derivative. Lagrange's notation f' → $f^{\prime }$
    • or Newton's \dot x $\dot{x}$ and \ddot x $\ddot{x}$
    • or Leibniz's \frac{\mathrm{d}y}{\mathrm{d}x} $\frac{\mathrm{d}y}{\mathrm{d}x}$, but see #Physics below.
      • Partials: \frac{\partial f}{\partial x_i} $\frac{\partial f}{\partial x_i}$
  • Gradient. \boldsymbol{\nabla} → $\mathbf{\nabla }$
• Set operations.
  • \cup \cap \setminus \triangle \complement_A $\cup ,\cap ,\setminus ,\mathrm{△},{\complement }_A$
    • $A\mathrm{△}B$ is the set of items that belong to exactly one of $A$ and $B$.
    • Also \lor and \land for join and meet operations: $\vee ,\wedge$.
  • \subset \subseteq \subsetneq $\subset ,\subseteq ,⊊$
  • \supset \supseteq \supsetneq $\supset ,\supseteq ,⊋$
  • \in \notin $\in ,\notin$
    • Such that: :, | or \ni $\ni$
  • \emptyset \varnothing $\mathrm{\varnothing },\varnothing$
• Combinatorial notation.
  • {n+1 \choose 2k} and \binom{n+1}{2k} both yield $(\genfrac{}{}{0ex}{}{n+1}{2k})$
    • \binom n{k_1, k_2, \ldots, k_m} → ${\displaystyle (\genfrac{}{}{0ex}{}{n}{k_1,k_2,\dots ,k_m})}$
  • Factorial: $n!$ is $n!$
  • Sterling numbers:
    • \left[{n \atop k}\right] → $\left[\genfrac{}{}{0ex}{}{n}{k}\right]$
    • \left\{\begin{matrix} n \\ k \end{matrix}\right\} → $\left\{\begin{array}{c}n\\ k\end{array}\right\}$
• Logic.
  • \land \lor \lnot $\wedge ,\vee ,\mathrm{\neg }$
  • Exclusive or (XOR): A \veebar B → $A⊻B$
  • \forall \exists \vdash \vDash $\mathrm{\forall },\mathrm{\exists },⊢,\models$
  • True, false: \top \bot → $\mathrm{\top }\mathrm{\perp }$
  • Uniqueness: \exists! x → $\mathrm{\exists }!x$

Alignment

% inserts a comment lasting till the next newline.

% quadratic formula
ax^2 + bx + c = 0  % standard format

renders as:

Right align over multiple lines using align, aligned, or align* via \begin and \end, like so:

\begin{align}
x^2 + 2x + 1 = 0 \\
(x+1)^2 &= 0
\end{align}

An align environment is a table-like structure, with & (ampersand) as a column separator and \\ as a row separator. If you want to include whitespace use \phantom{item}, where item is the expression that has equivalent spacing. Here, we use them together to align equals signs:

\begin{align}
15&=5+4+3+2+1\\
-5+15&=\phantom{5+{}}4+3+2+1\\
-4-5+15&=\phantom{5+4+{}}3+2+1\\
-3-4-5+15&=\phantom{5+4+3+{}}2+1\\
-2-3-4-5+15&=\phantom{5+4+3+2+{}}1\\
\end{align}

The first expression in each line of an align block is right justified, then the expression within each subsequent 'column' alternates between being left-justified and right-justified. So, a 'column' in each line will be right-justified if it is preceded by an even number (0, 2, 4…) of ampersands, and it will be left-justified if preceded by an odd number (1, 3, …) of ampersands.

Thus, you can do achieve multi-column layouts, too, using && instead of &:

\begin{align}
5+4+3+2+1&&5+4+3+2+1\\
4+3+2+1&&4+3+2+1\\
\vdots&&\vdots\\
1&&1
\end{align}

Matrices

These are always at display height.

• With parentheses: \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}: $\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)$.
• With brackets, it's bmatrix instead: $\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$.

More complex example:

\begin{pmatrix}
 &  Bob & Alice \\
Bob & 0 & 1 \\
Alice & 1 & 0
\end{pmatrix}

Grouping braces

Try \begin{cases}2x+y=1\\3x-y=1\end{cases} to get:

or this:

|x|=\begin{cases}
x & \text{if }x>0 \\
-x & \text{if }x<0
\end{cases}

to get:

This shows under- and over-braces, and also the use of \quad to put items side by side: \underbrace{ (a,b,\ldots,z) }_{26} \quad \overbrace{ (a,b,\ldots,z) }^{26}:

Cancel lines

Obsidian has imported the cancel macros, letting you write:

• \cancel: A diagonal line rising to the right
• \bcancel: A diagonal line falling to the right
• \xcancel: An 'X'
• \cancelto: A single-headed arrow rising to the right, with a value indicated at the end of the arrow

Example: \dfrac{x^\bcancel{3}}{\cancel{x^2}} = x → ${\displaystyle \frac{x^{\bcancel{3}}}{\cancel{x^2}}}=x$

Custom macros

If all this isn't enough, you can define your own macros with \def:

\def\iddots{
  {\kern3mu\raise1mu{.}\kern3mu\raise6mu{.}\kern3mu\raise12mu{.}}}
% … then later on the page
\iddots

yields:

Enclosures

Obsidian has also imported enclosure for you, so you can do:

• \enclose{longdiv}{x^2+5} → .
• \enclose{actuarial}{2x} → $\overline{2x\hspace{.2em}|}$
• A_1\enclose{phasorangle}{\theta_1} → $A_1\phase{{\theta }_1}$
• ^3\enclose{radical}{x^6} = x^2 → ${}^3\sqrt{x^6}=x^2$
• \enclose{box}{x = 1 \pm 3} → $\boxed{x=1\pm 3}$
• \enclose{roundedbox}{y = {1\over x}} → $\boxed{y=\frac{1}{x}}$
• \enclose{circle}{f(x)=x^2} → $\overline{)f(x)=x^2}$
  • You may need to play with the spacing using ~, see \enclose{circle}{~~~~f(x)=x^2\phantom{x^2\over 1}} → $\overline{)f(x)=x^2\phantom{\frac{x^2}{1}}}$
• left, right, top, bottom
  • \enclose{bottom}{x+y}\cdots\enclose{right}{x\over y} → $\underline{x+y}\cdots \overline{)\frac{x}{y}}$
• updiagonalstrike, downdiagonalstrike, verticalstrike, horizontalstrike
  • \enclose{circle updiagonalstrike}{a+b^2\over c+d} → $\cancel{\frac{a+b^2}{c+d}}$, also illustrating that enclosures can be combined

Color

MathJax has already imported color!

It supports the standard colors and the 68 dvips color names:

• \color (redefinition, becoming a to-end-of-scope modifier, takes RGB)
  • \definecolor{clay}{rgb}{0.8,0.32,0.0} defines a color "clay" for later use $$
  • this\color{clay}{and}that → $thisandthat$, note it's lasts until the end of the line
  • Use \textcolor for finer control, this\textcolor{Apricot}{and}that, $thisandthat$
• \colorbox, set the background color, as shown above with \colorbox{lightgray}{\color{white}{white}}
  • \fcolorbox, similar, but with a frame: \fcolorbox{lime}{lightgray}{\color{white}{white}} → $\text{white}$

There's a separate bbox package that lets you do \bbox[10px,cyan]{a+b} to include CSS padding like this: $a+b$. You can really go bananas: \bbox[lightblue,5px,border-style: solid; border-color:greenyellow; border-width: 4px]{x+y} → $x+y$

Physics

To import physics, you need to put \require{physics} $\text{require}physics$ before your MathJax expression somewhere on the page. It's not enabled by default because it overwrites a number of standard macros!

However, it gives you Physics items like:

• Derivative: \dd or \diffd → $\text{dd}$, such as $\text{dd}x$. In practice, you'll want to preface these expressions with \, to insert a space.
  • \dv does "fractions" like \dv{x} → $\text{dv}x$ and \dv{y}{x} → $\text{dv}yx$.
  • \pdv for partials, \pdv{y}{x} → $\text{pdv}yx$
    • Use \partial for complicated stuff, like $\frac{{\partial }^{2}u}{\partial x^2}$

You may need other symbols, but these are defined elsewhere. For example, \hbar → $\hslash$ for Planck's constant.

Chemistry

Obsidian already includes mhchem for Chemistry which gives you:

• Chemical expressions \ce, from formulas to diagram.
  • ^ is an up arrow, not shown
• Physical unit \pu, used for typesetting scientific expressions, units and measures.
  • Note, \pu is MathJax specific. The equivalent for LaTeX is siunitx.

\begin{array}{c}
\ce{\phantom{H_3}CH_3}\\% phantom to get the bond aligned with the C
| \\
\ce{CH_3-C-CH_3}\\
| \\
\ce{Cl}
\end{array}

There also exist packages like hpstatement and rsphrase, for official hazard statements and precautionary statements. For example, \rsphrase{S2} would yield "Keep out of the reach of children".

2D reaction networks

Since Obsidian has imported AMScd, you can also create 2D reaction networks! mhchem is also supported, but you have to apply it to each item in the grid. See the Chemistry Stack Exchange for more.

Arrows