Rendering LaTeX Math

LCOJ supports rendering LaTeX math formulas in problem statements, so formulas look clean and professional.

Note:

• This feature is optional
• This guide covers bare metal installs
• With Docker, you need to set up Mathoid separately on the host or in another container

Installing Mathoid

Mathoid is a service that renders LaTeX formulas as images.

Step 1: Install Node.js

curl -sL https://deb.nodesource.com/setup_18.x | sudo -E bash -
apt install nodejs

Step 2: Install Mathoid

git clone https://github.com/wikimedia/mathoid.git
cd mathoid
npm install

Step 3: Run Mathoid

node server.js

By default, Mathoid runs on localhost:10044.

Configuring LCOJ

Add to local_settings.py:

# Mathoid URL
MATHOID_URL = 'http://localhost:10044'

# Cache directory for rendered formula images
# Must be writable by both Mathoid and nginx
MATHOID_CACHE_ROOT = '/home/lcoj/mathoid_cache'

# URL for accessing the cache over the web
# Example: /home/lcoj/mathoid_cache/abc.png -> luyencode.net/mathoid/abc.png
MATHOID_CACHE_URL = '//luyencode.net/mathoid/'

Configure Nginx

Add to your nginx config file:

location /mathoid/ {
    alias /home/lcoj/mathoid_cache/;
    expires 1y;
    add_header Cache-Control "public, immutable";
}

Create the cache directory

mkdir -p /home/lcoj/mathoid_cache
chown www-data:www-data /home/lcoj/mathoid_cache
chmod 755 /home/lcoj/mathoid_cache

Restart

Docker:

docker compose restart site nginx

Bare metal:

supervisorctl restart site
service nginx reload

Using Math in Problem Statements

Inline math

Use ~...~ for small formulas within a line:

Given two integers ~a~ and ~b~ ~(1 \le a, b \le 10^9)~.

Renders as: Given two integers a and b (1 ≤ a, b ≤ 10⁹).

Display math

Use $...$ for large formulas on their own line:

The Fibonacci sequence is defined as:

$F(n) = \begin{cases} 
0, & \text{if } n = 0 \\ 
1, & \text{if } n = 1 \\ 
F(n-2) + F(n-1), & \text{if } n \ge 2 
\end{cases}$

Full example

# Fibonacci Sequence

The Fibonacci sequence is a well-known sequence defined as:

$F(n) = \begin{cases} 
0, & \text{if } n = 0 \\ 
1, & \text{if } n = 1 \\ 
F(n-2) + F(n-1), & \text{if } n \ge 2 
\end{cases}$

Given an integer ~N~ ~(1 \le N \le 10^{19})~, find the ~N~-th Fibonacci number
modulo ~1\,000\,000\,007~ ~(= 10^9 + 7)~.

**Note:** For 30% of the points, ~1 \le N \le 1\,000\,000~.

Common LaTeX Symbols

Operators

~a + b~          # Addition
~a - b~          # Subtraction
~a \times b~     # Multiplication
~a \div b~       # Division
~a \le b~        # Less than or equal to
~a \ge b~        # Greater than or equal to
~a \ne b~        # Not equal to
~a \equiv b~     # Congruent to

Fractions

~\frac{a}{b}~    # Fraction a/b

Superscripts and subscripts

~a^2~            # a to the power of 2
~a_i~            # a subscript i
~a^{10}~         # a to the power of 10
~a_{i,j}~        # a subscript i,j

Sums and products

~\sum_{i=1}^{n} a_i~     # Sum
~\prod_{i=1}^{n} a_i~    # Product

Roots

~\sqrt{x}~       # Square root
~\sqrt[3]{x}~    # Cube root

Special symbols

~\infty~         # Infinity
~\pi~            # Pi
~\log n~         # Logarithm
~\ln n~          # Natural logarithm
~\lfloor x \rfloor~  # Floor
~\lceil x \rceil~    # Ceiling

Troubleshooting

Formulas do not render:

• Check that Mathoid is running: curl http://localhost:10044
• Check the MATHOID_URL setting
• Check the Mathoid logs

Images do not load:

• Check the nginx configuration
• Check the cache directory permissions
• Check MATHOID_CACHE_URL

Formulas render incorrectly:

• Check the LaTeX syntax
• Test it in an online LaTeX editor

Optimization

Cache

Mathoid caches rendered formulas automatically. You do not need to clear the cache manually.

Performance

If you have many formulas, we recommend that you:

• Give Mathoid more memory
• Use a CDN for the cache directory
• Tune nginx caching

Running Mathoid with Supervisor

Create the file /etc/supervisor/conf.d/mathoid.conf:

[program:mathoid]
command=/usr/bin/node /path/to/mathoid/server.js
directory=/path/to/mathoid
user=mathoid
autostart=true
autorestart=true
redirect_stderr=true
stdout_logfile=/var/log/mathoid.log

Start it:

supervisorctl update
supervisorctl start mathoid