/Volumes/unix-files/u/ntl-new/ntl-6.1.0/doc/mat_lzz_p.cpp.html

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