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# KaTeX and MathJax Comparison Demo

Page by Murray Bourne, IntMath.com. Last updated: 29 Apr 2020

This page demonstrates the processing and loading times for a reasonably complex page while using KaTeX, MathJax v2.7 and MathJax v3. All 3 processors handle all the expressions on this page.

Processed by KaTeX Process with MathJax 2.7 Process with MathJax 3

## Timings: Page processed with KaTeX

 Process KaTeX 0 ms DOMContentLoaded 0 ms Fonts loaded 0 ms Page complete 0 ms

"Fonts loaded" is determined using document.fonts.onloadingdone.

"Page complete" is the window.onload event.

### Repeating fractions

\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} \equiv 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }

### Summation notation

\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 of a Series

I broke up the next two examples into separate lines so it behaves better on a mobile phone. That's why they include \displaystyle.

\displaystyle\sum_{i=1}^{k+1}i
\displaystyle= \left(\sum_{i=1}^{k}i\right) +(k+1)
\displaystyle= \frac{k(k+1)}{2}+k+1
\displaystyle= \frac{k(k+1)+2(k+1)}{2}
\displaystyle= \frac{(k+1)(k+2)}{2}
\displaystyle= \frac{(k+1)((k+1)+1)}{2}

### Product notation

\displaystyle 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \displaystyle \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \displaystyle\text{ for }\lvert q\rvert < 1.

### Inline math

And here is some in-line math: k_{n+1} = n^2 + k_n^2 - k_{n-1}, followed by some more text.

Inline math uses

<span class="math">...</span>

rather than a div.

### Greek Letters

\Gamma\ \Delta\ \Theta\ \Lambda\ \Xi\ \Pi\ \Sigma\ \Upsilon\ \Phi\ \Psi\ \Omega

\alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi \ \omicron\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega\ \varepsilon\ \vartheta\ \varpi\ \varrho\ \varsigma\ \varphi

### Arrows

\gets\ \to\ \leftarrow\ \rightarrow\ \uparrow\ \Uparrow\ \downarrow\ \Downarrow\ \updownarrow\ \Updownarrow
\Leftarrow\ \Rightarrow\ \leftrightarrow\ \Leftrightarrow\ \mapsto\ \hookleftarrow
\leftharpoonup\ \leftharpoondown\ \rightleftharpoons\ \longleftarrow\ \Longleftarrow\ \longrightarrow
\Longrightarrow\ \longleftrightarrow\ \Longleftrightarrow\ \longmapsto\ \hookrightarrow\ \rightharpoonup
\rightharpoondown\ \leadsto\ \nearrow\ \searrow\ \swarrow\ \nwarrow

### Symbols

\surd\ \barwedge\ \veebar\ \odot\ \oplus\ \otimes\ \oslash\ \circledcirc\ \boxdot\ \bigtriangleup
\bigtriangledown\ \dagger\ \diamond\ \star\ \triangleleft\ \triangleright\ \angle\ \infty\ \prime\ \triangle

### Calculus

\int u \frac{dv}{dx}\,dx=uv-\int \frac{du}{dx}v\,dx
f(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x}
\oint \vec{F} \cdot d\vec{s}=0

### Lorenz Equations

\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned}

### Cross Product

This works in KaTeX, but the separation of fractions in this environment is not so good.

\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}

Here's a workaround: make the fractions smaller with an extra class that targets the spans with "mfrac" class (makes no difference in the MathJax case):

\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}

### Accents

\hat{x}\ \vec{x}\ \ddot{x}

### Stretchy brackets

\left(\frac{x^2}{y^3}\right)

### Evaluation at limits

\left.\frac{x^3}{3}\right|_0^1

### Case definitions

f(n) = \begin{cases} \frac{n}{2}, & \text{if } n\text{ is even} \\ 3n+1, & \text{if } n\text{ is odd} \end{cases}

### Maxwell's Equations

\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}

These equations are quite cramped. We can add vertical spacing using (for example) [1em] after each line break (\\). as you can see here:

\begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\[1em] \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\[0.5em] \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\[1em] \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}

### Statistics

Definition of combination:

\frac{n!}{k!(n-k)!} = {^n}C_k
{n \choose k}

### Fractions on fractions

\frac{\frac{1}{x}+\frac{1}{y}}{y-z}

### n-th root

\sqrt[n]{1+x+x^2+x^3+\ldots}

### Matrices

\begin{pmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33} \end{pmatrix}
\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}

### Punctuation

f(x) = \sqrt{1+x} \quad (x \ge -1)
f(x) \sim x^2 \quad (x\to\infty)

Now with punctuation:

f(x) = \sqrt{1+x}, \quad x \ge -1
f(x) \sim x^2, \quad x\to\infty
\mathcal L_{\mathcal T}(\vec{\lambda}) = \sum_{(\mathbf{x},\mathbf{s})\in \mathcal T} \log P(\mathbf{s}\mid\mathbf{x}) - \sum_{i=1}^m \frac{\lambda_i^2}{2\sigma^2}
S (\omega)=\frac{\alpha g^2}{\omega^5} \, e ^{[-0.74\bigl\{\frac{\omega U_\omega 19.5}{g}\bigr\}^{-4}]}

## Only one instance of math?

Say you only have a limited number of math items on a page. You can use KaTeX by simply calling

katex.render

with a TeX expression and a DOM element to render into, as follows:

...

This example is independent of the loop that KaTeX goes through for other math on this page.

### Generating HTML on the server

To generate HTML on the server, you can use "katex.renderToString", as follows:

...

## Try again?

Processed by KaTeX Process with MathJax 2.7 Process with MathJax 3

## Background and explanation

Read more about KaTeX and the examples above here:

KaTeX â€“ a new way to display math on the Web

See also: ASCIIMathML, KaTeX and MathJax Demo