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

MODULE: mat_GF2E

SUMMARY:

Defines the class mat_GF2E.

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


#include <NTL/matrix.h>
#include <NTL/vec_vec_GF2E.h>


typedef Mat<GF2E> mat_GF2E; // backward compatibility


void add(mat_GF2E& X, const mat_GF2E& A, const mat_GF2E& B); 
// X = A + B

void sub(mat_GF2E& X, const mat_GF2E& A, const mat_GF2E& B); 
// X = A - B = A + B

void negate(mat_GF2E& X, const mat_GF2E& A); 
// X = - A  = A

void mul(mat_GF2E& X, const mat_GF2E& A, const mat_GF2E& B); 
// X = A * B

void mul(vec_GF2E& x, const mat_GF2E& A, const vec_GF2E& b); 
// x = A * b

void mul(vec_GF2E& x, const vec_GF2E& a, const mat_GF2E& B); 
// x = a * B

void mul(mat_GF2E& X, const mat_GF2E& A, const GF2E& b);
void mul(mat_GF2E& X, const mat_GF2E& A, GF2 b);
void mul(mat_GF2E& X, const mat_GF2E& A, long b);
// X = A * b

void mul(mat_GF2E& X, const GF2E& a, const mat_GF2E& B);
void mul(mat_GF2E& X, GF2 a, const mat_GF2E& B);
void mul(mat_GF2E& X, long a, const mat_GF2E& B);
// X = a * B



void determinant(GF2E& d, const mat_GF2E& A);
GF2E determinant(const mat_GF2E& a);
// d = determinant(A)


void transpose(mat_GF2E& X, const mat_GF2E& A);
mat_GF2E transpose(const mat_GF2E& A);
// X = transpose of A

void solve(GF2E& d, vec_GF2E& x, const mat_GF2E& A, const vec_GF2E& 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(GF2E& d, const mat_GF2E& A, vec_GF2E& x, const vec_GF2E& 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(GF2E& d, mat_GF2E& X, const mat_GF2E& A);
// A is an n x n matrix.  Computes d = determinant(A).  If d != 0,
// computes X = A^{-1}.

void sqr(mat_GF2E& X, const mat_GF2E& A);
mat_GF2E sqr(const mat_GF2E& A);
// X = A*A   

void inv(mat_GF2E& X, const mat_GF2E& A);
mat_GF2E inv(const mat_GF2E& A);
// X = A^{-1}; error is raised if A is  singular

void power(mat_GF2E& X, const mat_GF2E& A, const ZZ& e);
mat_GF2E power(const mat_GF2E& A, const ZZ& e);

void power(mat_GF2E& X, const mat_GF2E& A, long e);
mat_GF2E power(const mat_GF2E& A, long e);
// X = A^e; e may be negative (in which case A must be nonsingular).


void ident(mat_GF2E& X, long n);
mat_GF2E ident_mat_GF2E(long n);
// X = n x n identity matrix

long IsIdent(const mat_GF2E& A, long n);
// test if A is the n x n identity matrix

void diag(mat_GF2E& X, long n, const GF2E& d);
mat_GF2E diag(long n, const GF2E& d);
// X = n x n diagonal matrix with d on diagonal

long IsDiag(const mat_GF2E& A, long n, const GF2E& d);
// test if X is an  n x n diagonal matrix with d on diagonal



void random(mat_GF2E& x, long n, long m);  // x = random n x m matrix
mat_GF2E random_mat_GF2E(long n, long m);



long gauss(mat_GF2E& M);
long gauss(mat_GF2E& 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_GF2E& X, const mat_GF2E& A);
// The rows of X are computed as basis of A's row space.  X is is row
// echelon form

void kernel(mat_GF2E& X, const mat_GF2E& A);
// Computes a basis for the kernel of the map x -> x*A. where x is a
// row vector.




// miscellaneous:

void clear(mat_GF2E& a);
// x = 0 (dimension unchanged)

long IsZero(const mat_GF2E& a);
// test if a is the zero matrix (any dimension)


// operator notation:

mat_GF2E operator+(const mat_GF2E& a, const mat_GF2E& b);
mat_GF2E operator-(const mat_GF2E& a, const mat_GF2E& b);
mat_GF2E operator*(const mat_GF2E& a, const mat_GF2E& b);

mat_GF2E operator-(const mat_GF2E& a);


// matrix/scalar multiplication:

mat_GF2E operator*(const mat_GF2E& a, const GF2E& b);
mat_GF2E operator*(const mat_GF2E& a, GF2 b);
mat_GF2E operator*(const mat_GF2E& a, long b);

mat_GF2E operator*(const GF2E& a, const mat_GF2E& b);
mat_GF2E operator*(GF2 a, const mat_GF2E& b);
mat_GF2E operator*(long a, const mat_GF2E& b);

// matrix/vector multiplication:

vec_GF2E operator*(const mat_GF2E& a, const vec_GF2E& b);

vec_GF2E operator*(const vec_GF2E& a, const mat_GF2E& b);


// assignment operator notation:

mat_GF2E& operator+=(mat_GF2E& x, const mat_GF2E& a);
mat_GF2E& operator-=(mat_GF2E& x, const mat_GF2E& a);
mat_GF2E& operator*=(mat_GF2E& x, const mat_GF2E& a);

mat_GF2E& operator*=(mat_GF2E& x, const GF2E& a);
mat_GF2E& operator*=(mat_GF2E& x, GF2 a);
mat_GF2E& operator*=(mat_GF2E& x, long a);

vec_GF2E& operator*=(vec_GF2E& x, const mat_GF2E& a);


