Contents

# Integer Factorization

## Divisibility Poset

by William Stein

## Factor Trees

by William Stein

More complicated demonstration using Mathematica: http://demonstrations.wolfram.com/FactorTrees/

## Factoring an Integer

by Timothy Clemans

Sage implementation of the Mathematica demonstration of the same name. http://demonstrations.wolfram.com/FactoringAnInteger/

# Prime Numbers

## Illustrating the prime number theorem

by William Stein

## Prime Spiral - Square FIXME

by David Runde

## Prime Spiral - Polar

by David Runde

Needs fix for show_factors

# Modular Forms

## Computing modular forms

by William Stein

## Computing the cuspidal subgroup

by William Stein

ncols not working

## A Charpoly and Hecke Operator Graph

by William Stein

# Modular Arithmetic

## Quadratic Residue Table FIXME

by Emily Kirkman

## Cubic Residue Table FIXME

by Emily Kirkman

# Cyclotomic Fields

## Gauss and Jacobi Sums in Complex Plane

by Emily Kirkman

## Exhaustive Jacobi Plotter

by Emily Kirkman

# Elliptic Curves

## Adding points on an elliptic curve

by David MÃ¸ller Hansen

## Plotting an elliptic curve over a finite field

# Cryptography

## The Diffie-Hellman Key Exchange Protocol

by Timothy Clemans and William Stein

# Other

## Continued Fraction Plotter

by William Stein

crows not working

## Computing Generalized Bernoulli Numbers

by William Stein (Sage-2.10.3)

## Fundamental Domains of SL_2(ZZ)

by Robert Miller

# Multiple Zeta Values

by Akhilesh P.

## Computing Multiple Zeta values

### Word Input

### Composition Input

## Program to Compute Integer Relation between Multiple Zeta Values

## Word to composition

## Composition to Word

## Dual of a Word

## Shuffle product of two Words

## Shuffle Regularization at 0

## Shuffle Regularization at 1