/**************************************************************************\ MODULE: mat_ZZ_p SUMMARY: Defines the class mat_ZZ_p. \**************************************************************************/ #include #include typedef Mat 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 negate(mat_ZZ_p& X, const mat_ZZ_p& A); // X = - A 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, const 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, const 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 solve(zz_p& d, const mat_zz_p& A, vec_zz_p& x, 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 A*x = b (so x and b are treated as a column vectors). 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, const ZZ_p& d); mat_ZZ_p diag(long n, const ZZ_p& d); // X = n x n diagonal matrix with d on diagonal long IsDiag(const mat_ZZ_p& A, long n, const ZZ_p& d); // test if X is an n x n diagonal matrix with d on diagonal void random(mat_ZZ_p& x, long n, long m); // x = random n x m matrix mat_ZZ_p random_mat_ZZ_p(long n, long m); 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, const ZZ_p& b); mat_ZZ_p operator*(const mat_ZZ_p& a, long b); mat_ZZ_p operator*(const 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, const 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);