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

MODULE: mat_zz_p

SUMMARY:

Defines the class mat_zz_p.

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


#include <NTL/matrix.h>
#include "vec_vec_zz_p.h"


typedef Mat<zz_p> mat_zz_p; // backward compatibility

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

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

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

void mul(vec_zz_p& x, const mat_zz_p& A, const vec_zz_p& b);
// x = A * b

void mul(vec_zz_p& x, const vec_zz_p& a, const mat_zz_p& B);
// x = a * B

void mul(mat_zz_p& X, const mat_zz_p& A, zz_p b);
void mul(mat_zz_p& X, const mat_zz_p& A, long b);
// X = A * b

void mul(mat_zz_p& X, zz_p a, const mat_zz_p& B);
void mul(mat_zz_p& X, long a, const mat_zz_p& B);
// X = a * B


void determinant(zz_p& d, const mat_zz_p& A);
zz_p determinant(const mat_zz_p& a);
// d = determinant(A)


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

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

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

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

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

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


void ident(mat_zz_p& X, long n);
mat_zz_p ident_mat_zz_p(long n);
// X = n x n identity matrix

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

void diag(mat_zz_p& X, long n, zz_p d);
mat_zz_p diag(long n, zz_p d);
// X = n x n diagonal matrix with d on diagonal

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



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

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



// miscellaneous:

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

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


// operator notation:

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

mat_zz_p operator-(const mat_zz_p& a);


// matrix/scalar multiplication:

mat_zz_p operator*(const mat_zz_p& a, zz_p b);
mat_zz_p operator*(const mat_zz_p& a, long b);

mat_zz_p operator*(zz_p a, const mat_zz_p& b);
mat_zz_p operator*(long a, const mat_zz_p& b);


// matrix/vector multiplication:

vec_zz_p operator*(const mat_zz_p& a, const vec_zz_p& b);

vec_zz_p operator*(const vec_zz_p& a, const mat_zz_p& b);


// assignment operator notation:

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

mat_zz_p& operator*=(mat_zz_p& x, zz_p a);
mat_zz_p& operator*=(mat_zz_p& x, long a);

vec_zz_p& operator*=(vec_zz_p& x, const mat_zz_p& a);