/**************************************************************************\MODULE: mat_ZZSUMMARY:Defines the class mat_ZZ.\**************************************************************************/#include <NTL/matrix.h>#include <NTL/vec_vec_ZZ.h>NTL_matrix_decl(ZZ,vec_ZZ,vec_vec_ZZ,mat_ZZ)NTL_io_matrix_decl(ZZ,vec_ZZ,vec_vec_ZZ,mat_ZZ)NTL_eq_matrix_decl(ZZ,vec_ZZ,vec_vec_ZZ,mat_ZZ)void add(mat_ZZ& X, const mat_ZZ& A, const mat_ZZ& B); // X = A + Bvoid sub(mat_ZZ& X, const mat_ZZ& A, const mat_ZZ& B); // X = A - Bvoid negate(mat_ZZ& X, const mat_ZZ& A); // X = - Avoid mul(mat_ZZ& X, const mat_ZZ& A, const mat_ZZ& B); // X = A * Bvoid mul(vec_ZZ& x, const mat_ZZ& A, const vec_ZZ& b); // x = A * bvoid mul(vec_ZZ& x, const vec_ZZ& a, const mat_ZZ& B); // x = a * Bvoid mul(mat_ZZ& X, const mat_ZZ& A, const ZZ& b);void mul(mat_ZZ& X, const mat_ZZ& A, long b);// X = A * bvoid mul(mat_ZZ& X, const ZZ& a, const mat_ZZ& B);void mul(mat_ZZ& X, long a, const mat_ZZ& B);// X = a * Bvoid determinant(ZZ& d, const mat_ZZ& A, long deterministic=0);ZZ determinant(const mat_ZZ& a, long deterministic=0);// d = determinant(A).  If !deterministic, a randomized strategy may// be used that errs with probability at most 2^{-80}.void solve(ZZ& d, vec_ZZ& x,           const mat_ZZ& A, const vec_ZZ& b,           long deterministic=0)// computes d = determinant(A) and solves x*A = b*d if d != 0; A must// be a square matrix and have compatible dimensions with b.  If// !deterministic, the computation of d may use a randomized strategy// that errs with probability 2^{-80}.void solve1(ZZ& d, vec_ZZ& x, const mat_ZZ& A, const vec_ZZ& b);// A must be a square matrix.// If A is singular, this routine sets d = 0 and returns.// Otherwise, it computes d, x such that x*A == b*d, // such that d > 0 and minimal.// Note that d is a positive divisor of the determinant,// and is not in general equal to the determinant.// The routine is deterministic, and uses either a Hensel lifting// strategy.// For backward compatability, there is also a routine called// HenselSolve1 that simply calls solve1.void inv(ZZ& d, mat_ZZ& X, const mat_ZZ& A, long deterministic=0);// computes d = determinant(A) and solves X*A = I*d if d != 0; A must// be a square matrix.  If !deterministic, the computation of d may// use a randomized strategy that errs with probability 2^{-80}.// NOTE:  See LLL.txt for routines that compute the kernel and// image of an integer matrix.// NOTE: See HNF.txt for a routine that computes Hermite Normal Forms.void sqr(mat_ZZ& X, const mat_ZZ& A);mat_ZZ sqr(const mat_ZZ& A);// X = A*A   void inv(mat_ZZ& X, const mat_ZZ& A);mat_ZZ inv(const mat_ZZ& A);// X = A^{-1}; error is raised if |det(A)| != 1.void power(mat_ZZ& X, const mat_ZZ& A, const ZZ& e);mat_ZZ power(const mat_ZZ& A, const ZZ& e);void power(mat_ZZ& X, const mat_ZZ& A, long e);mat_ZZ power(const mat_ZZ& A, long e);// X = A^e; e may be negative (in which case A must be nonsingular).void ident(mat_ZZ& X, long n); mat_ZZ ident_mat_ZZ(long n); // X = n x n identity matrixlong IsIdent(const mat_ZZ& A, long n);// test if A is the n x n identity matrixvoid diag(mat_ZZ& X, long n, const ZZ& d);mat_ZZ diag(long n, const ZZ& d);// X = n x n diagonal matrix with d on diagonallong IsDiag(const mat_ZZ& A, long n, const ZZ& d);// test if X is an  n x n diagonal matrix with d on diagonalvoid transpose(mat_ZZ& X, const mat_ZZ& A);mat_ZZ transpose(const mat_ZZ& A);// X = transpose of Along CRT(mat_ZZ& a, ZZ& prod, const mat_zz_p& A);// Incremental Chinese Remaindering: If p is the current zz_p modulus with// (p, prod) = 1; Computes a' such that a' = a mod prod and a' = A mod p,// with coefficients in the interval (-p*prod/2, p*prod/2]; // Sets a := a', prod := p*prod, and returns 1 if a's value changed.// miscellaneous:void clear(mat_ZZ& a);// x = 0 (dimension unchanged)long IsZero(const mat_ZZ& a);// test if a is the zero matrix (any dimension)// operator notation:mat_ZZ operator+(const mat_ZZ& a, const mat_ZZ& b);mat_ZZ operator-(const mat_ZZ& a, const mat_ZZ& b);mat_ZZ operator*(const mat_ZZ& a, const mat_ZZ& b);mat_ZZ operator-(const mat_ZZ& a);// matrix/scalar multiplication:mat_ZZ operator*(const mat_ZZ& a, const ZZ& b);mat_ZZ operator*(const mat_ZZ& a, long b);mat_ZZ operator*(const ZZ& a, const mat_ZZ& b);mat_ZZ operator*(long a, const mat_ZZ& b);// matrix/vector multiplication:vec_ZZ operator*(const mat_ZZ& a, const vec_ZZ& b);vec_ZZ operator*(const vec_ZZ& a, const mat_ZZ& b);// assignment operator notation:mat_ZZ& operator+=(mat_ZZ& x, const mat_ZZ& a);mat_ZZ& operator-=(mat_ZZ& x, const mat_ZZ& a);mat_ZZ& operator*=(mat_ZZ& x, const mat_ZZ& a);mat_ZZ& operator*=(mat_ZZ& x, const ZZ& a);mat_ZZ& operator*=(mat_ZZ& x, long a);vec_ZZ& operator*=(vec_ZZ& x, const mat_ZZ& a);