Internals

This section covers the developers-only documentation, i.e part of the API that may be changed anytime by anyone.

• Internals of the Polynomial Manipulation Module
  • Manipulation of sparse, distributed polynomials
  • Polynomial factorization algorithms
  • Gröbner basis algorithms
  • Algebraic number fields
  • Factorization over algebraic number fields
  • Modular GCD
  • Heuristic GCD
  • Further tools
  • Undocumented
• The Gruntz Algorithm
• Details on the Hypergeometric Function Expansion
  • Hypergeometric Function Expansion Algorithm
  • Meijer G-Functions of Finite Confluence
  • Extending The Hypergeometric Tables
  • Implemented Hypergeometric Formulae
• Computing Integrals using Meijer G-Functions
  • Overview
  • Polar Numbers and Branched Functions
  • Representing Branched Functions on the Argand Plane
  • Table Lookups and Inverse Mellin Transforms
  • Applying the Integral Theorems
  • The G-Function Integration Theorems
  • The Inverse Laplace Transform of a G-function
  • Implemented G-Function Formulae
• Numerical evaluation
  • Floating-point numbers
  • Accuracy and error handling
  • Sums and integrals
  • Numerical simplification
  • uFuncify