Generic rings : detailed table of contents

• gr.h – generic structures and their elements
  • Introduction
    • Parents and elements
    • Parent and element types
    • Error handling
    • Predicates
  • Context operations
  • Element operations
    • Memory management
    • Random elements
    • Input, output and string conversion
    • Assignment and conversions
    • Special values
    • Basic properties
    • Arithmetic
    • Division
    • Powering
    • Square roots
    • Greatest common divisors
    • Factorization
    • Fractions
    • Integer and complex parts
    • Infinities and extended values
    • Ordering methods
    • Enclosure and interval methods
    • Finite field methods
• gr.h (continued) – implementing rings
  • Example
  • Method table
  • Placeholder and trivial methods
  • Required methods
  • Testing rings
• gr.h (continued) – builtin domains and types
  • Coercions
  • Domain properties
  • Groups
  • Basic rings and fields
  • Residue rings and finite fields
  • Number fields and algebraic numbers
  • Real and complex numbers
  • Extended number sets
  • Floating-point arithmetic
  • Vectors
  • Matrices
  • Polynomial rings
  • Power series
  • Fraction fields
  • Symbolic expressions
• gr_special.h – special arithmetic and transcendental functions
  • Mathematical constants
  • Elementary functions
  • Factorials and gamma functions
  • Combinatorial numbers
  • Error function and exponential integrals
  • Orthogonal polynomials
  • Bessel, Airy and Coulomb functions
  • Hypergeometric functions
  • Riemann zeta, polylogarithms and Dirichlet L-functions
  • Elliptic integrals
  • Elliptic, modular and theta functions
• gr_vec.h – vectors over generic rings
  • Types and basic operations
  • Arithmetic
  • Sums and products
  • Dot products
  • Sorting and searching
  • Other functions
• gr_mat.h – dense matrices over generic rings
  • Type compatibility
  • Types, macros and constants
  • Memory management
  • Window matrices
  • Input and output
  • Comparisons
  • Assignment and special values
  • Basic row, column and entry operations
  • Entrywise operations
  • Norms
  • Arithmetic
  • Diagonal and triangular matrices
  • Gaussian elimination
  • Solving
  • Determinant and trace
  • Rank
  • Row echelon form
  • Nullspace
  • Inverse and adjugate
  • Characteristic polynomial
  • Minimal polynomial
  • Companion matrix
  • Similarity transformations
  • Eigenvalues
  • Jordan decomposition
  • Matrix functions
  • Hessenberg form
  • Random matrices
  • Special matrices
  • Helper functions for reduction
  • Test functions
• gr_poly.h – dense univariate polynomials over generic rings
  • Supported coefficient domains
  • Type compatibility
  • Weak normalization
  • Types, macros and constants
  • Memory management
  • Basic manipulation
  • Arithmetic
  • Powering
  • Shifting
  • Scalar division
  • Division with remainder
  • Division with remainder with full precomputed inverse
  • Power series division
  • Exact division
  • Square roots
  • Evaluation
  • Multipoint evaluation and interpolation
  • Composition
  • Power series composition and reversion
  • Derivative and integral
  • Monic polynomials
  • GCD
  • Resultant
  • Squarefree factorization
  • Roots
  • Power series special functions
  • Modular arithmetic and composition
  • Test functions
• gr_mpoly.h – sparse multivariate polynomials over generic rings
  • Types, macros and constants
  • Context object methods
  • Memory management
  • Basic manipulation
  • Generators
  • Conversions
  • Comparisons
  • Random generation
  • Input and output
  • Coefficient and exponent access
  • Arithmetic
  • Other operations
  • Container operations