/**************************************************************************\

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)


void random(mat_GF2& x, long n, long m);  // x = random n x m matrix
mat_GF2 random_mat_GF2(long n, long m);

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);