Mozilla Tests

Differentials
\bigg(\frac{\partial^2} {\partial x^2} + \frac {\partial^2}{\partial y^2} \bigg){\big\lvert\varphi (x+iy)\big\rvert}^2 | (∂2∂x 2+∂2∂y 2)|φ(x+i y)|2
Environments
f(x) = \begin{cases}1/3 & \text{if }0 \le x \le 1; \\ 2/3 & \text{if }3\le x \le 4;\\ 0 &\text{elsewhere.} \end{cases} | f(x)={1/3 if 0≤x≤1;2/3 if 3≤x≤4;0 elsewhere.
\begin{pmatrix} \begin{pmatrix}a&b\\c&d \end{pmatrix} & \begin{pmatrix}e&f\\g&h \end{pmatrix} \\ 0 & \begin{pmatrix}i&j\\k&l \end{pmatrix} \end{pmatrix} | ((a b c d)(e f g h)0(i j k l))
\det\begin{vmatrix} c_0&c_1&c_2&\dots& c_n\\ c_1 & c_2 & c_3 & \dots & c_{n+1}\\ c_2 & c_3 & c_4 &\dots & c_{n+2}\\ \vdots &\vdots&\vdots & &\vdots \\c_n & c_{n+1} & c_{n+2} &\dots&c_{2n} \end{vmatrix} > 0 | det⁡|c 0 c 1 c 2⋯c n c 1 c 2 c 3⋯c n+1 c 2 c 3 c 4⋯c n+2⋮⋮⋮⋮c n c n+1 c n+2⋯c 2 n|>0
Everything
\sum_{p\text{ prime}} f(p)=\int_{t>1} f(t)d\pi(t) | ∑p prime f(p)=∫t>1 f(t)d π(t)
\lim_{n \to +\infty} \frac{\sqrt{2\pi n}}{n!} \genfrac (){}{}n{e}^n = 1 | lim n→+∞⁡2 π n n!(n e)n=1
\det(A) = \sum_{\sigma \in S_n} \epsilon(\sigma) \prod_{i=1}^n a_{i, \sigma_i} | det⁡(A)=∑σ∈S n ϵ(σ)∏i=1 n a i,σ i
Fractions
\frac{x+y^2}{k+1} | x+y 2 k+1
x+y^\frac{2}{k + 1} | x+y 2 k+1
\frac{a}{b/2} | a b/2
a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3 + \cfrac{1}{a_4}}}} | a 0+1 a 1+1 a 2+1 a 3+1 a 4
a_0+\frac{1}{a_1+\frac{1}{a_2+\frac{1}{a_3+ \frac{1}{a_4}}}} | a 0+1 a 1+1 a 2+1 a 3+1 a 4
\binom{p}{2} x^2 y^{p-2} - \frac{1}{1-x} \frac{1}{1-x^2} | (p 2)x 2 y p−2−1 1−x 1 1−x 2
Integrals
\int_1^x \frac{dt}{t} | ∫1 x d t t
\int\!\!\!\int_D dx,dy | ∫∫D d x,d y
Over Under Braces
\overbrace{x +\cdots + x} ^{k \text{ times}} | x+⋯+x⏞k times
{\underbrace{\overbrace{ \mathstrut a,\dots,a}^{k ,a\rq\text{s}}, \overbrace{ \mathstrut b,\dots,b}^{l, b\rq\text{s}}}_{k+l \text{ elements}}} | height="0.7em" />a,…,a⏞k,a′s, height="0.7em" />b,…,b⏞l,b′s⏟k+l elements
Roots
\sqrt{1+\sqrt{1+\sqrt{1+ \sqrt{1+\sqrt{1+\sqrt{1+ \sqrt{1+x}}}}}}} | 1+1+1+1+1+1+1+x
Scripts
x^2y^2 | x 2 y 2
_2F_3 | 2 F 3
x^{2y} | x 2 y
2^{2^{2^x}} | 2 2 2 x
y_{x^2} | y x 2
y_{x_2} | y x 2
x_{92}^{31415} + \pi | x 92 31415+π
x_{y^a_b}^{z^c_d} | x y b a z d c
y_3''' | y 3′′′
Summations
\sum_{\genfrac{}{}{0mu}{2}{0 \le i \le m}{0 < j < n}} P(i, j) | ∑0≤i≤m 0<j<n P(i,j)
\sum_{i=1}^p \sum_{j=1}^q \sum_{k=1}^r a_{ij}b_{jk}c_{ki} | ∑i=1 p∑j=1 q∑k=1 r a i j b j k c k i