John Preston
7.3 KiB
LaTeX in Markdown — Ultimate Test File
This document tests every common (and uncommon) way LaTeX appears in Markdown rendering.
1. Basic Inline Math
Single variable: x, y, \alpha, \beta, \pi.
In a sentence: The famous identity e^{i\pi} + 1 = 0 connects five fundamental constants.
Multiple inline: We have a = 1, b = 2, and c = a + b = 3.
Inline with operators: f(x) = x^2 + 2x - 1 evaluated at x = 3 gives f(3) = 14.
Greek letters: \alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \iota, \kappa, \lambda, \mu, \nu, \xi, \pi, \rho, \sigma, \tau, \upsilon, \phi, \chi, \psi, \omega.
Capital Greek: \Gamma, \Delta, \Theta, \Lambda, \Xi, \Pi, \Sigma, \Upsilon, \Phi, \Psi.
2. Display Math
Standard display:
E = mc^2
The quadratic formula:
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Euler's identity:
e^{i\pi} + 1 = 0
3. Fractions, Roots, and Powers
Inline fractions: \frac{1}{2}, \frac{a+b}{c-d}, \frac{x^2}{y^3}.
Nested fractions: \frac{1}{1 + \frac{1}{1 + \frac{1}{x}}}.
Display fraction:
\frac{\partial f}{\partial x} = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
Roots: \sqrt{2}, \sqrt[3]{27}, \sqrt[n]{x^n} = x.
Display roots:
\sqrt{1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + \cdots}}}} = \varphi
Powers and subscripts: x^2, x_i, x_i^2, x^{i+j}, x_{i,j}^{2k}.
4. Sums, Products, Integrals, Limits
Inline: \sum_{i=1}^{n} i, \prod_{i=1}^{n} i, \int_0^1 x \, dx, \lim_{x \to 0} \frac{\sin x}{x}.
Display sum:
\sum_{i=1}^{n} i = \frac{n(n+1)}{2}
Display product:
\prod_{p \text{ prime}} \frac{1}{1 - p^{-s}} = \sum_{n=1}^{\infty} \frac{1}{n^s}
Definite integral:
\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi}
Double integral:
\iint_D f(x, y) \, dA
Contour integral:
\oint_C \mathbf{F} \cdot d\mathbf{r} = \iint_S (\nabla \times \mathbf{F}) \cdot d\mathbf{S}
Limits:
\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e
5. Matrices and Arrays
Plain matrix:
\begin{matrix}
a & b \\
c & d
\end{matrix}
Parenthesized:
\begin{pmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{pmatrix}
Bracketed:
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
Determinant (vertical bars):
\begin{vmatrix}
a & b \\
c & d
\end{vmatrix} = ad - bc
Double bars (norm):
\begin{Vmatrix}
v_1 \\
v_2
\end{Vmatrix}
Curly braces:
\begin{Bmatrix}
x \\
y
\end{Bmatrix}
6. Cases and Piecewise Functions
f(x) = \begin{cases}
x^2 & \text{if } x \geq 0 \\
-x^2 & \text{if } x < 0
\end{cases}
\text{sgn}(x) = \begin{cases}
1 & x > 0 \\
0 & x = 0 \\
-1 & x < 0
\end{cases}
7. Aligned Equations
\begin{aligned}
(a + b)^2 &= a^2 + 2ab + b^2 \\
(a - b)^2 &= a^2 - 2ab + b^2 \\
(a + b)(a - b) &= a^2 - b^2
\end{aligned}
Multi-step derivation:
\begin{aligned}
\nabla \times (\nabla \times \mathbf{A}) &= \nabla(\nabla \cdot \mathbf{A}) - \nabla^2 \mathbf{A} \\
&= \nabla(\nabla \cdot \mathbf{A}) - \Delta \mathbf{A}
\end{aligned}
8. Operators and Symbols
Logic: \land, \lor, \neg, \implies, \iff, \forall, \exists, \nexists.
Set theory: \in, \notin, \subset, \subseteq, \supset, \supseteq, \cup, \cap, \emptyset, \setminus.
Comparison: <, >, \leq, \geq, \neq, \approx, \equiv, \sim, \simeq, \cong, \propto.
Arrows: \to, \gets, \leftrightarrow, \Rightarrow, \Leftarrow, \Leftrightarrow, \mapsto, \hookrightarrow.
Misc: \infty, \partial, \nabla, \pm, \mp, \times, \div, \cdot, \circ, \star, \ast.
Number sets: \mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}, \mathbb{C}, \mathbb{H}, \mathbb{F}_p.
9. Functions and Operators
Trig: \sin x, \cos x, \tan x, \csc x, \sec x, \cot x.
Inverse trig: \arcsin x, \arccos x, \arctan x.
Hyperbolic: \sinh x, \cosh x, \tanh x.
Logs: \log x, \ln x, \log_2 x, \log_{10} x.
Other: \exp x, \min, \max, \sup, \inf, \arg\min, \arg\max, \det, \dim, \ker, \deg, \gcd, \lim, \limsup, \liminf.
10. Accents and Decorations
Bar: \bar{x}, \overline{ABC}.
Hat: \hat{x}, \widehat{xyz}.
Tilde: \tilde{x}, \widetilde{xyz}.
Vector: \vec{v}, \overrightarrow{AB}.
Dot: \dot{x}, \ddot{x}, \dddot{x}.
Bold/script: \mathbf{v}, \mathbf{0}, \boldsymbol{\alpha}, \mathcal{L}, \mathfrak{g}, \mathscr{F}.
11. Probability and Statistics
Expected value: \mathbb{E}[X] = \int_{-\infty}^{\infty} x f(x) \, dx.
Variance: \text{Var}(X) = \mathbb{E}[(X - \mu)^2].
Normal distribution:
f(x \mid \mu, \sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)
Bayes' theorem:
P(A \mid B) = \frac{P(B \mid A) \, P(A)}{P(B)}
12. Edge Cases and Common Pitfalls
Dollar signs as currency (should NOT render as math)
The shirt costs $20 and the pants cost $30. Together: $50.
Dollar signs near math
I have $5 in my pocket, not 5x + 3 dollars.
Underscores in inline math vs Markdown
Variables like x_1, x_2, x_3 should render correctly without triggering italic.
Backslashes in text
Use \frac{a}{b} to write \frac{a}{b}.
Math inside lists
- First item with math:
a^2 + b^2 = c^2 - Second with display:
\int_0^\infty e^{-x} \, dx = 1 - Third with fraction:
\frac{p}{q}
Math inside blockquotes
The Cauchy-Schwarz inequality:
\left(\sum_{i=1}^n a_i b_i\right)^2 \leq \left(\sum_{i=1}^n a_i^2\right)\left(\sum_{i=1}^n b_i^2\right)
Math in tables
| Function | Derivative | Integral |
|---|---|---|
x^n |
nx^{n-1} |
\frac{x^{n+1}}{n+1} |
e^x |
e^x |
e^x |
\sin x |
\cos x |
-\cos x |
\ln x |
\frac{1}{x} |
x \ln x - x |
Math in headers
The equation ax^2 + bx + c = 0
Bold and italic with math
Bold text with E = mc^2 inline.
Italic with \pi \approx 3.14 inline.
Code blocks should NOT render math
This is a code block: $x^2 + y^2 = z^2$ — should be literal.
Inline code: $x^2$ — also literal.
Escaped dollar signs
To write a literal dollar sign: $100 or $x^2$.
13. Long and Complex Expressions
Maxwell's equations:
\begin{aligned}
\nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\
\nabla \cdot \mathbf{B} &= 0 \\
\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\
\nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}
\end{aligned}
Schrödinger equation:
i\hbar \frac{\partial}{\partial t} \Psi(\mathbf{r}, t) = \left[-\frac{\hbar^2}{2m} \nabla^2 + V(\mathbf{r}, t)\right] \Psi(\mathbf{r}, t)
Einstein field equations:
R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}
Fourier transform:
\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x) \, e^{-2\pi i x \xi} \, dx
14. Spacing Tests
No space: a+b, a-b, a=b.
Thin space: a\,b.
Medium space: a\:b.
Thick space: a\;b.
Quad: a\quad b.
Double quad: a\qquad b.
Negative space: a\!b.
15. Stretchy Delimiters
\left( \frac{a}{b} \right), \quad \left[ \frac{a}{b} \right], \quad \left\{ \frac{a}{b} \right\}, \quad \left| \frac{a}{b} \right|, \quad \left\| \frac{a}{b} \right\|
\left( \sum_{i=1}^{n} \frac{x_i^2}{\sqrt{1 + x_i^4}} \right)^{1/2}