# mathtools
mathtools is a program for computing various mathematical results that would be
tedious to compute by hand.

## Why?
Obviously, libraries, software packages, and websites exist for these sort of
calculations, but there are tradeoffs with any approach. Rather than needing to
write a script, use a REPL, or load a webpage, this allows for an approach more
like standard CLI utilities such as [GNU
factor](https://www.gnu.org/software/coreutils/factor).

Generally, I've opted to implement routines for problems that are best solved
with *algorithms*, rather than *formulas*. For instance, the quadratic formula,
while useful, is basically plug and chug, and thus isn't implemented here. On
the other hand, determining whether a number is prime is a little more tedious
to do by hand, so it's provided as a routine.

## Available routines
Available routines include:
* convergents of a periodic continued fraction
* solving systems of linear congruences with the Chinese remainder theorem
* discrete logarithm
* greatest common divisor
* primality testing
* Jacobi symbol
* modular inverse
* modular square root
* multiplicative order
* integer partitions
* solving Pell equations
* primitive root modulo n
* area of a simple polygon from vertex coordinates
* sieves for totient function, divisor function, Mobius function, and more
* repetend of the continued fraction of a square root
* Stirling numbers
* summatory functions