hex
hex
Table of Contents
1.
HexBasic: shared dependency-free utilities
2.
HexArith: low-level arithmetic foundations
3.
HexPrimality: certified primality at scale
4.
HexPoly: normalized dense polynomials
5.
HexMvPoly: executable sparse multivariate polynomials
6.
HexSparsePoly: sparse univariate polynomials
7.
HexModArith: machine-word modular arithmetic
8.
HexPolyFp: prime-field dense polynomials
9.
HexPolyZ: integer dense polynomials
10.
HexGFqRing: executable Fₚ quotient ring
11.
HexHensel: executable Hensel lifting
12.
HexRoots: certified complex-root isolation
13.
HexRealRoots: certified real-root isolation
14.
HexRCF: a decision procedure for univariate real arithmetic
15.
HexMatrix: dense matrices and arithmetic
16.
HexRowReduce: Gauss-Jordan reduction, span, and nullspace
17.
HexBerlekamp: factorization over finite fields
18.
HexGF2: packed GF(2) polynomials and GF(2ⁿ) fields
19.
HexGFqField: executable GF(pⁿ)
20.
HexConway: verified Conway-polynomial lookup
21.
HexGFq: canonical finite-field constructors
22.
HexDeterminant: the Leibniz determinant and cofactor theory
23.
HexBareiss: the fraction-free determinant
24.
HexResultant: subresultants and discriminants
25.
HexGramSchmidt: Gram-Schmidt orthogonalization
26.
HexLLL: lattice basis reduction
27.
HexBerlekampZassenhaus: factorization over the integers
28.
factor_poly
and
irreducibility
: certified factoring
29.
HexNumberField: exact algebraic numbers
30.
HexNumberFieldTower: successive algebraic extensions
31.
HexPermGroup: checked finite permutation groups
32.
HexGraphIso: coloured graph canonical labelling
33.
The
nauty
canonical labelling algorithm
34.
Tutorials
35.
Draft sections for unreleased libraries
9.
HexPolyZ: integer dense polynomials
9.1.
Introduction
9.2.
Integer polynomial type
9.3.
Content and primitive part
9.4.
Congruence for Hensel lifting
9.5.
Content multiplicativity
9.6.
The Mignotte coefficient bound
9.7.
Key correctness theorems
9.8.
The Mathlib correspondence
9.9.
Cross-references
←
8.7. Cross-references
9.1. Introduction
→
9. HexPolyZ: integer dense polynomials
🔗
9.1.
Introduction
9.2.
Integer polynomial type
9.3.
Content and primitive part
9.4.
Congruence for Hensel lifting
9.5.
Content multiplicativity
9.6.
The Mignotte coefficient bound
9.7.
Key correctness theorems
9.8.
The Mathlib correspondence
9.9.
Cross-references
←
8.7. Cross-references
9.1. Introduction
→