hex
hex
Table of Contents
1.
HexBasic: shared dependency-free utilities
2.
HexTruncatedSeries: power series to a fixed precision
3.
HexArith: low-level arithmetic foundations
4.
HexModular: Chinese remaindering and rational reconstruction
5.
HexPrimality: certified primality at scale
6.
HexECPP: proving primality with elliptic curves
7.
HexPoly: normalized dense polynomials
8.
HexPolyFast: fast dense polynomials
9.
HexMvPoly: executable sparse multivariate polynomials
10.
HexSparsePoly: sparse univariate polynomials
11.
HexModArith: machine-word modular arithmetic
12.
HexPolyFp: prime-field dense polynomials
13.
HexPolyZ: integer dense polynomials
14.
HexGFqRing: executable Fₚ quotient ring
15.
HexHensel: executable Hensel lifting
16.
HexRoots: certified complex-root isolation
17.
HexRealRoots: certified real-root isolation
18.
HexRCF: a decision procedure for univariate real arithmetic
19.
HexMatrix: dense matrices and arithmetic
20.
HexRowReduce: Gauss-Jordan reduction, span, and nullspace
21.
HexBerlekamp: factorization over finite fields
22.
HexGF2: packed GF(2) polynomials and GF(2ⁿ) fields
23.
HexGFqField: executable GF(pⁿ)
24.
HexConway: verified Conway-polynomial lookup
25.
HexGFq: canonical finite-field constructors
26.
HexDeterminant: the Leibniz determinant and cofactor theory
27.
HexBareiss: the fraction-free determinant
28.
HexResultant: subresultants and discriminants
29.
HexGramSchmidt: Gram-Schmidt orthogonalization
30.
HexLLL: lattice basis reduction
31.
HexBerlekampZassenhaus: factorization over the integers
32.
factor_poly
and
irreducibility
: certified factoring
33.
HexNumberField: exact algebraic numbers
34.
HexNumberFieldTower: successive algebraic extensions
35.
HexPermGroup: computing with permutation groups
36.
HexGraphIso: coloured graph canonical labelling
37.
The
nauty
canonical labelling algorithm
38.
Tutorials
39.
Draft sections for unreleased libraries
8.
HexPolyFast: fast dense polynomials
8.1.
Introduction
8.2.
Multiplication plans
8.3.
Division by Newton iteration
8.4.
The half-gcd algorithm
8.5.
Many points at once
8.6.
Padé approximation
8.7.
Costs
8.8.
Proofs and Mathlib
8.9.
Cross-references
←
7.9. Cross-references
8.1. Introduction
→
8. HexPolyFast: fast dense polynomials
🔗
8.1.
Introduction
8.2.
Multiplication plans
8.3.
Division by Newton iteration
8.4.
The half-gcd algorithm
8.5.
Many points at once
8.6.
Padé approximation
8.7.
Costs
8.8.
Proofs and Mathlib
8.9.
Cross-references
←
7.9. Cross-references
8.1. Introduction
→