Internals

• Internals of the Polynomial Manipulation Module
  • Level One
  • Level Zero
  • Exceptions
  • Reference
  • Undocumented
• The Gruntz Algorithm
  • Notes
  • References
• Details on the Hypergeometric Function Expansion
  • Hypergeometric Function Expansion Algorithm
  • Meijer G-Functions of Finite Confluence
  • Extending The Hypergeometric Tables
  • Implemented Hypergeometric Formulae
  • References
• 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
  • Conditions of Convergence for Integral (1)
  • Conditions of Convergence for Integral (2)
• The Inverse Laplace Transform of a G-function
  • How to compute the integral
  • When this computation is valid
  • When the integral exists
• Implemented G-Function Formulae
• Numerical evaluation
  • Basics
  • Floating-point numbers
  • Accuracy and error handling
  • Sums and integrals
  • Numerical simplification
• Numeric Computation
  • Subs/evalf
  • Lambdify
  • uFuncify
  • Theano
  • So Which Should I Use?
• Term rewriting
  • Expanding
  • Common Subexpression Detection and Collection