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cf_hnf.h
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1/* emacs edit mode for this file is -*- C++ -*- */
2#ifndef CF_HNF_H
3#define CF_HNF_H
4
5/*BEGINPUBLIC*/
6
7/**
8 *
9 * The input matrix A is square matrix of integers
10 * output: the Hermite Normal Form of A; that is,
11 * the unique m x m matrix whose rows span L, such that
12 *
13 * - lower triangular,
14 * - the diagonal entries are positive,
15 * - any entry below the diagonal is a non-negative number
16 * strictly less than the diagonal entry in its column.
17 *
18 * @note: uses NTL
19 *
20**/
21
23
24/**
25 * performs LLL reduction.
26 *
27 * B is an m x n matrix, viewed as m rows of n-vectors. m may be less
28 * than, equal to, or greater than n, and the rows need not be
29 * linearly independent. B is transformed into an LLL-reduced basis,
30 * and the return value is the rank r of B. The first m-r rows of B
31 * are zero.
32 *
33 * More specifically, elementary row transformations are performed on
34 * B so that the non-zero rows of new-B form an LLL-reduced basis
35 * for the lattice spanned by the rows of old-B.
36 * The default reduction parameter is delta=3/4, which means
37 * that the squared length of the first non-zero basis vector
38 * is no more than 2^{r-1} times that of the shortest vector in
39 * the lattice.
40 *
41 * @note: uses NTL or FLINT
42**/
43
45
46/*ENDPUBLIC*/
47
48#endif
CFMatrix *FACTORY_PUBLIC cf_HNF(CFMatrix &A)
The input matrix A is square matrix of integers output: the Hermite Normal Form of A; that is,...
Definition: cf_hnf.cc:44
CFMatrix *FACTORY_PUBLIC cf_LLL(CFMatrix &A)
performs LLL reduction.
Definition: cf_hnf.cc:66
#define FACTORY_PUBLIC
Definition: globaldefs.h:25
#define A
Definition: sirandom.c:24