My Project
Loading...
Searching...
No Matches
lattice.h
Go to the documentation of this file.
1#ifndef LATTICE_HPP
2#define LATTICE_HPP
3
4// Algorithms based on chapter 2.6 of
5// "A course in computational algebraic numbertheory" by Henry Cohen
6class lattice {
7
8 private:
9
10 //array of basisvectors
12
13 //gram matrix of the lattice
15
16 //size of basis
17 int n;
18
19 //length of basisvectors
20 int m;
21
23
24 //constant for LLL
25 number c;
26
27 //array of basisvectors of LLL-basis
29
30 //for LLL, see Cohen 2.6.3
32
33 //array of B_i, see Cohen 2.6.3
34 number * B;
35
36 //for LLL, see Cohen 2.6.3
38
39 //for LLL, see Cohen 2.6.3
41
42 //for integral LLL, see Cohen 2.6.7
43 number * d;
44
45 //rank of the lattice
46 int rank;
47
48 //if true transformation matrix H will be computed
50
51 //true if basisvectors should be considered independent
53
54 //true if gram matrix is integral
56
57 //triangular matrix for enumeration
59
60 //testing element for enumeration
62
63 //bond for x_i in enumeration
64 number * bound;
65
66 //coef for output
68
69
70// int precision;
71
72
73
74 //for LLL, see Cohen 2.6.3
75 inline void RED(int k, int l);
76
77 //for LLL, see Cohen 2.6.3
78 inline void SWAP(int k, int k_max);
79
80 //for MLLL, see Cohen 2.6.8
81 inline void SWAPG(int k, int k_max);
82
83 //for LLL, see Cohen 2.6.3
84 inline bool gram_schmidt(int k);
85
86 //for MLLL, see Cohen 2.6.8
87 inline void gram_schmidt_MLLL(int k);
88
89// inline void INSERT(int k, int i);
90// inline bool gram_matrix(int k);
91
92 inline void compute_gram_matrix();
93
94 inline number enumerate_get_next();
95
96 inline bool quadratic_supplement();
97
98 inline void increase_x(int index);
99 inline number check_bound(int index);
100
101 public:
102
103 //constructor creates new lattice spanned by columns of b
105
106 //destructor
107 ~lattice();
108
109 //LLL with c=3/4
110 bool LLL();
111
112 bool LLL(number& c);
113
115
117
119
120 bigintmat * enumerate_all(number a);
121
122 bigintmat * enumerate_next(number a, bigintmat * x);
123
124 bigintmat * enumerate_next(number a);
125
127
129
130// void set_precision(int a);
131
132};
133
134
135//NOTE: could be moved to bigintmat
136inline number scalarproduct(bigintmat * a, bigintmat * b);
137
138//minkowski
139bigintmat * minkowksi(bigintmat ** elementarray,int size_elementarray, number * poly,int deg, coeffs coef, int precision);
140bool IsReal(number a, coeffs coef);
141bool ImagGreaterZero(number a, coeffs coef);
142number squareroot(number a, coeffs coef, int iteration);// iteration in Heron algorithm
143
144#endif
int l
Definition: cfEzgcd.cc:100
int k
Definition: cfEzgcd.cc:99
CanonicalForm b
Definition: cfModGcd.cc:4103
Matrices of numbers.
Definition: bigintmat.h:51
Definition: lattice.h:6
bool quadratic_supplement()
Definition: lattice.cc:775
bigintmat * my
Definition: lattice.h:40
int m
Definition: lattice.h:20
~lattice()
Definition: lattice.cc:90
bool integral
Definition: lattice.h:55
void SWAP(int k, int k_max)
Definition: lattice.cc:315
void SWAPG(int k, int k_max)
Definition: lattice.cc:357
int rank
Definition: lattice.h:46
bigintmat * H
Definition: lattice.h:37
bool trans_matrix
Definition: lattice.h:49
void increase_x(int index)
Definition: lattice.cc:841
bigintmat * get_transformation_matrix()
Definition: lattice.cc:890
number * B
Definition: lattice.h:34
bool independentVectors
Definition: lattice.h:52
bigintmat ** basis
Definition: lattice.h:11
bigintmat * get_basis()
Definition: lattice.cc:874
void compute_gram_matrix()
Definition: lattice.cc:828
bigintmat * enumerate_all(number a)
Definition: lattice.cc:507
bigintmat * gram_matrix
Definition: lattice.h:14
number enumerate_get_next()
Definition: lattice.cc:718
number c
Definition: lattice.h:25
coeffs out_coef
Definition: lattice.h:67
bool LLL()
Definition: lattice.cc:133
int n
Definition: lattice.h:17
number check_bound(int index)
Definition: lattice.cc:855
coeffs coef
Definition: lattice.h:22
number * bound
Definition: lattice.h:64
bool gram_schmidt(int k)
Definition: lattice.cc:430
bigintmat * enumerate_next()
Definition: lattice.cc:691
void gram_schmidt_MLLL(int k)
Definition: lattice.cc:454
bigintmat * Q
Definition: lattice.h:58
bigintmat * x
Definition: lattice.h:61
void RED(int k, int l)
Definition: lattice.cc:276
bigintmat ** b_star
Definition: lattice.h:31
bigintmat ** b
Definition: lattice.h:28
bigintmat * get_reduced_basis()
Definition: lattice.cc:882
number * d
Definition: lattice.h:43
bool IsReal(number a, coeffs coef)
Definition: lattice.cc:1097
number scalarproduct(bigintmat *a, bigintmat *b)
Definition: lattice.cc:915
bigintmat * minkowksi(bigintmat **elementarray, int size_elementarray, number *poly, int deg, coeffs coef, int precision)
Definition: lattice.cc:948
number squareroot(number a, coeffs coef, int iteration)
Definition: lattice.cc:1111
bool ImagGreaterZero(number a, coeffs coef)
Definition: lattice.cc:1104
The main handler for Singular numbers which are suitable for Singular polynomials.
static int index(p_Length length, p_Ord ord)
Definition: p_Procs_Impl.h:592