/**************************************************************************\
MODULE: mat_GF2
SUMMARY:
Defines the class mat_GF2.
\**************************************************************************/
#include <NTL/matrix.h>
#include <NTL/vec_vec_GF2.h>
typedef Mat<GF2> mat_GF2; // backward compatibility
void conv(mat_GF2& X, const vec_vec_GF2& A);
mat_GF2 to_mat_GF2(const vec_vec_GF2& A);
// convert a vector of vec_GF2's to a matrix
// procedural arithmetic routines:
void add(mat_GF2& X, const mat_GF2& A, const mat_GF2& B);
// X = A + B
void sub(mat_GF2& X, const mat_GF2& A, const mat_GF2& B);
// X = A - B = A + B
void negate(mat_GF2& X, const mat_GF2& A);
// X = -A = A
void mul(mat_GF2& X, const mat_GF2& A, const mat_GF2& B);
// X = A * B
void mul(vec_GF2& x, const mat_GF2& A, const vec_GF2& b);
// x = A * b
void mul(vec_GF2& x, const vec_GF2& a, const mat_GF2& B);
// x = a * B
void mul(mat_GF2& X, const mat_GF2& A, GF2 b);
void mul(mat_GF2& X, const mat_GF2& A, long b);
// X = A * b
void mul(mat_GF2& X, GF2 a, const mat_GF2& B);
void mul(mat_GF2& X, long a, const mat_GF2& B);
// X = a * B
void determinant(GF2& d, const mat_GF2& A);
GF2 determinant(const mat_GF2& A);
// d = determinant of A
void transpose(mat_GF2& X, const mat_GF2& A);
mat_GF2 transpose(const mat_GF2& A);
// X = transpose of A
void solve(GF2& d, vec_GF2& x, const mat_GF2& A, const vec_GF2& b);
// A is an n x n matrix, b is a length n vector. Computes d = determinant(A).
// If d != 0, solves x*A = b.
void solve(GF2& d, const mat_GF2& A, vec_GF2& x, const vec_GF2& b);
// A is an n x n matrix, b is a length n vector. Computes d = determinant(A).
// If d != 0, solves A*x = b (so x and b are treated as a column vectors).
void inv(GF2& d, mat_GF2& X, const mat_GF2& A);
// A is an n x n matrix. Computes d = det(A). If d != 0,
// computes X = A^{-1}.
void sqr(mat_GF2& X, const mat_GF2& A);
mat_GF2 sqr(const mat_GF2& A);
// X = A*A
void inv(mat_GF2& X, const mat_GF2& A);
mat_GF2 inv(const mat_GF2& A);
// X = A^{-1}; error is raised if A is singular
void power(mat_GF2& X, const mat_GF2& A, const ZZ& e);
mat_GF2 power(const mat_GF2& A, const ZZ& e);
void power(mat_GF2& X, const mat_GF2& A, long e);
mat_GF2 power(const mat_GF2& A, long e);
// X = A^e; e may be negative (in which case A must be nonsingular).
void ident(mat_GF2& X, long n);
mat_GF2 ident_mat_GF2(long n);
// X = n x n identity matrix
long IsIdent(const mat_GF2& A, long n);
// test if A is n x n identity matrix
void diag(mat_GF2& X, long n, GF2 d);
mat_GF2 diag(long n, GF2 d);
// X = n x n diagonal matrix with diagonal element d
long IsDiag(const mat_GF2& A, long n, long d);
// test if X is an n x n diagonal matrix with diagonal element (d mod 2)
long gauss(mat_GF2& M);
long gauss(mat_GF2& M, long w);
// Performs unitary row operations so as to bring M into row echelon
// form. If the optional argument w is supplied, stops when first w
// columns are in echelon form. The return value is the rank (or the
// rank of the first w columns).
void image(mat_GF2& X, const mat_GF2& A);
// The rows of X are computed as basis of A's row space. X is is row
// echelon form
void kernel(mat_GF2& X, const mat_GF2& A);
// Computes a basis for the kernel of the map x -> x*A. where x is a
// row vector.
// miscellaneous:
void clear(mat_GF2& X);
// X = 0 (dimension unchanged)
long IsZero(const mat_GF2& A);
// test if A is the zero matrix (any dimension)
// arithmetic operator notation:
mat_GF2 operator+(const mat_GF2& a, const mat_GF2& b);
mat_GF2 operator-(const mat_GF2& a, const mat_GF2& b);
mat_GF2 operator*(const mat_GF2& a, const mat_GF2& b);
mat_GF2 operator-(const mat_GF2& a);
// matrix/scalar multiplication:
mat_GF2 operator*(const mat_GF2& a, GF2 b);
mat_GF2 operator*(const mat_GF2& a, long b);
mat_GF2 operator*(GF2 a, const mat_GF2& b);
mat_GF2 operator*(long a, const mat_GF2& b);
// matrix/vector multiplication:
vec_GF2 operator*(const mat_GF2& a, const vec_GF2& b);
vec_GF2 operator*(const vec_GF2& a, const mat_GF2& b);
// assignment operator notation:
mat_GF2& operator+=(mat_GF2& x, const mat_GF2& a);
mat_GF2& operator-=(mat_GF2& x, const mat_GF2& a);
mat_GF2& operator*=(mat_GF2& x, const mat_GF2& a);
mat_GF2& operator*=(mat_GF2& x, GF2 a);
mat_GF2& operator*=(mat_GF2& x, long a);
vec_GF2& operator*=(vec_GF2& x, const mat_GF2& a);