Sage Interactions - Number Theory

• Integer Factorization
  • Divisibility Poset
  • Factor Trees
  • Factoring an Integer
• Prime Numbers
  • Illustrating the prime number theorem
  • Prime Spiral - Square FIXME
  • Prime Spiral - Polar
• Modular Forms
  • Computing modular forms
  • Computing the cuspidal subgroup
  • A Charpoly and Hecke Operator Graph
• Modular Arithmetic
  • Quadratic Residue Table FIXME
  • Cubic Residue Table FIXME
• Cyclotomic Fields
  • Gauss and Jacobi Sums in Complex Plane
  • Exhaustive Jacobi Plotter
• Elliptic Curves
  • Adding points on an elliptic curve
  • Plotting an elliptic curve over a finite field
• Cryptography
  • The Diffie-Hellman Key Exchange Protocol
• Other
  • Continued Fraction Plotter
  • Computing Generalized Bernoulli Numbers
  • Fundamental Domains of SL_2(ZZ)
• Multiple Zeta Values
  • 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