void mul(vec_zz_pE& x, const vec_zz_pE& a, long b_in) { NTL_zz_pRegister(b); b = b_in; long n = a.length(); x.SetLength(n); long i; for (i = 0; i < n; i++) mul(x[i], a[i], b); }
void sub(vec_zz_pE& x, const vec_zz_pE& a, const vec_zz_pE& b) { long n = a.length(); if (b.length() != n) LogicError("vector sub: dimension mismatch"); x.SetLength(n); long i; for (i = 0; i < n; i++) sub(x[i], a[i], b[i]); }
void convert(vec_zz_pE& X, const vector<ZZX>& A) { long n = A.size(); zz_pX tmp; X.SetLength(n); for (long i = 0; i < n; i++) { conv(tmp, A[i]); conv(X[i], tmp); } }
void VectorCopy(vec_zz_pE& x, const vec_zz_pE& a, long n) { if (n < 0) Error("VectorCopy: negative length"); if (NTL_OVERFLOW(n, 1, 0)) Error("overflow in VectorCopy"); long m = min(n, a.length()); x.SetLength(n); long i; for (i = 0; i < m; i++) x[i] = a[i]; for (i = m; i < n; i++) clear(x[i]); }
namespaceanon void mul_aux(vec_zz_pE& x, const vec_zz_pE& a, const mat_zz_pE& B) { long n = B.NumRows(); long l = B.NumCols(); if (n != a.length()) Error("matrix mul: dimension mismatch"); x.SetLength(l); long i, k; zz_pX acc, tmp; for (i = 1; i <= l; i++) { clear(acc); for (k = 1; k <= n; k++) { mul(tmp, rep(a(k)), rep(B(k,i))); add(acc, acc, tmp); } conv(x(i), acc); } }
namespaceanon void mul_aux(vec_zz_pE& x, const mat_zz_pE& A, const vec_zz_pE& b) { long n = A.NumRows(); long l = A.NumCols(); if (l != b.length()) Error("matrix mul: dimension mismatch"); x.SetLength(n); long i, k; zz_pX acc, tmp; for (i = 1; i <= n; i++) { clear(acc); for (k = 1; k <= l; k++) { mul(tmp, rep(A(i,k)), rep(b(k))); add(acc, acc, tmp); } conv(x(i), acc); } }
void solve(zz_pE& d, vec_zz_pE& X, const mat_zz_pE& A, const vec_zz_pE& b) { long n = A.NumRows(); if (A.NumCols() != n) Error("solve: nonsquare matrix"); if (b.length() != n) Error("solve: dimension mismatch"); if (n == 0) { set(d); X.SetLength(0); return; } long i, j, k, pos; zz_pX t1, t2; zz_pX *x, *y; const zz_pXModulus& p = zz_pE::modulus(); vec_zz_pX *M = newNTL_NEW_OP vec_zz_pX[n]; for (i = 0; i < n; i++) { M[i].SetLength(n+1); for (j = 0; j < n; j++) { M[i][j].rep.SetMaxLength(2*deg(p)-1); M[i][j] = rep(A[j][i]); } M[i][n].rep.SetMaxLength(2*deg(p)-1); M[i][n] = rep(b[i]); } zz_pX det; set(det); for (k = 0; k < n; k++) { pos = -1; for (i = k; i < n; i++) { rem(t1, M[i][k], p); M[i][k] = t1; if (pos == -1 && !IsZero(t1)) { pos = i; } } if (pos != -1) { if (k != pos) { swap(M[pos], M[k]); negate(det, det); } MulMod(det, det, M[k][k], p); // make M[k, k] == -1 mod p, and make row k reduced InvMod(t1, M[k][k], p); negate(t1, t1); for (j = k+1; j <= n; j++) { rem(t2, M[k][j], p); MulMod(M[k][j], t2, t1, p); } for (i = k+1; i < n; i++) { // M[i] = M[i] + M[k]*M[i,k] t1 = M[i][k]; // this is already reduced x = M[i].elts() + (k+1); y = M[k].elts() + (k+1); for (j = k+1; j <= n; j++, x++, y++) { // *x = *x + (*y)*t1 mul(t2, *y, t1); add(*x, *x, t2); } } } else { clear(d); goto done; } } X.SetLength(n); for (i = n-1; i >= 0; i--) { clear(t1); for (j = i+1; j < n; j++) { mul(t2, rep(X[j]), M[i][j]); add(t1, t1, t2); } sub(t1, t1, M[i][n]); conv(X[i], t1); } conv(d, det); done: delete[] M; }