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 = NTL_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;
}
