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

    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);