# LaTeX, Maths, and Code

### 5 August, 2020

This blog supports code syntax highlighting through prism-react-renderer and the usage of $\LaTeX$ via gatsby-remark-katex

However $\KaTeX$ (the library used to render) $\LaTeX$ will crash your development environment if it encounters a symbol it is unfamiliar with. Make sure you test your posts locally before publishing the site to a production server.

To learn more about implementing $\LaTeX$ in markdown, check out the documentation here

# $\LaTeX$ Examples

Consider the following list of k a's and l b's:

$\{\underbrace{% \overbrace{a,\ldots, a}^{k\ a's}, \overbrace{b,\ldots, b}^{l\ b's}} _{k+l\ \mathrm{elements}} \}$

Look further at this wild equation:

$\frac{\pm \left|\begin{array}{ccc} x_1-x_2 & y_1-y_2 \\ l_1 & m_1 \end{array}\right|} {\sqrt{\left|\begin{array}{cc}l_1&m_1\\ l_2&m_2\end{array}\right|^2 + \left|\begin{array}{cc}m_1&n_1\\ n_1&l_1\end{array}\right|^2}}$

# Code Examples

### Quotient and remainder of a pair of numbers in c++

#include <iostream>
using namespace std;

int main()
{
int divisor, dividend, quotient, remainder;

cout << "Enter dividend: ";
cin >> dividend;

cout << "Enter divisor: ";
cin >> divisor;

quotient = dividend / divisor;
remainder = dividend % divisor;

cout << "Quotient = " << quotient << endl;
cout << "Remainder = " << remainder;

return 0;
}


### Sieve of Eratosthenes implemented in Python

def countPrimes_sieve_of_eratosthenes(self, n: int) -> int:
if n < 2:
return 0

marked = set()
seive = [i for i in range(1, n)]
skip = 2
while skip * skip < n:
if skip not in marked:
marked.update(seive[2 * skip - 1 :: skip])
skip += 1

return len(seive) - len(marked) - 1