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/**************************************************************************\
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
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);