void power(mat_ZZ_p& X, const mat_ZZ_p& A, const ZZ& e)
{
if (A.NumRows() != A.NumCols()) Error("power: non-square matrix");
if (e == 0) {
ident(X, A.NumRows());
return;
}
mat_ZZ_p T1, T2;
long i, k;
k = NumBits(e);
T1 = A;
for (i = k-2; i >= 0; i--) {
sqr(T2, T1);
if (bit(e, i))
mul(T1, T2, A);
else
T1 = T2;
}
if (e < 0)
inv(X, T1);
else
X = T1;
}
void to_mat_ZZ_p_crt_rep(mat_ZZ_p_crt_rep& X, const mat_ZZ_p& A)
{
long n = A.NumRows();
long m = A.NumCols();
const MatPrime_crt_helper& H = get_MatPrime_crt_helper_info();
long nprimes = H.GetNumPrimes();
if (NTL_OVERFLOW(nprimes, CRT_BLK, 0))
ResourceError("overflow"); // this is pretty academic
X.rep.SetLength(nprimes);
for (long k = 0; k < nprimes; k++) X.rep[k].SetDims(n, m);
ZZ_pContext context;
context.save();
bool seq = (double(n)*double(m)*H.GetCost() < PAR_THRESH);
// FIXME: right now, we just partition the rows, but if
// #cols > #rows, we should perhaps partition the cols
NTL_GEXEC_RANGE(seq, n, first, last)
NTL_IMPORT(n)
NTL_IMPORT(m)
NTL_IMPORT(nprimes)
context.restore();
MatPrime_crt_helper_scratch scratch;
Vec<MatPrime_residue_t> remainders_store;
remainders_store.SetLength(nprimes*CRT_BLK);
MatPrime_residue_t *remainders = remainders_store.elts();
for (long i = first; i < last; i++) {
const ZZ_p *a = A[i].elts();
long jj = 0;
for (; jj <= m-CRT_BLK; jj += CRT_BLK) {
for (long j = 0; j < CRT_BLK; j++)
reduce(H, rep(a[jj+j]), remainders + j*nprimes, scratch);
for (long k = 0; k < nprimes; k++) {
MatPrime_residue_t *x = X.rep[k][i].elts();
for (long j = 0; j < CRT_BLK; j++)
x[jj+j] = remainders[j*nprimes+k];
}
}
if (jj < m) {
for (long j = 0; j < m-jj; j++)
reduce(H, rep(a[jj+j]), remainders + j*nprimes, scratch);
for (long k = 0; k < nprimes; k++) {
MatPrime_residue_t *x = X.rep[k][i].elts();
for (long j = 0; j < m-jj; j++)
x[jj+j] = remainders[j*nprimes+k];
}
}
}
NTL_GEXEC_RANGE_END
}
void mul_aux(mat_ZZ_p& X, const mat_ZZ_p& A, const mat_ZZ_p& B)
{
long n = A.NumRows();
long l = A.NumCols();
long m = B.NumCols();
if (l != B.NumRows())
Error("matrix mul: dimension mismatch");
X.SetDims(n, m);
long i, j, k;
ZZ acc, tmp;
for (i = 1; i <= n; i++) {
for (j = 1; j <= m; j++) {
clear(acc);
for(k = 1; k <= l; k++) {
mul(tmp, rep(A(i,k)), rep(B(k,j)));
add(acc, acc, tmp);
}
conv(X(i,j), acc);
}
}
}
void transpose(mat_ZZ_p& X, const mat_ZZ_p& A)
{
long n = A.NumRows();
long m = A.NumCols();
long i, j;
if (&X == & A) {
if (n == m)
for (i = 1; i <= n; i++)
for (j = i+1; j <= n; j++)
swap(X(i, j), X(j, i));
else {
mat_ZZ_p tmp;
tmp.SetDims(m, n);
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
tmp(j, i) = A(i, j);
X.kill();
X = tmp;
}
}
else {
X.SetDims(m, n);
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
X(j, i) = A(i, j);
}
}
void negate(mat_ZZ_p& X, const mat_ZZ_p& A)
{
long n = A.NumRows();
long m = A.NumCols();
X.SetDims(n, m);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
negate(X(i,j), A(i,j));
}
void mul(mat_ZZ_p& X, const mat_ZZ_p& A, const mat_ZZ_p& B)
{
long n = A.NumRows();
long l = A.NumCols();
long m = B.NumCols();
if (l != B.NumRows()) LogicError("matrix mul: dimension mismatch");
if (NTL_USE_MM_MATMUL && n >= 24 && l >= 24 && m >= 24)
multi_modular_mul(X, A, B);
else
plain_mul(X, A, B);
}
void mul(mat_ZZ_p& X, const mat_ZZ_p& A, long b_in)
{
NTL_ZZ_pRegister(b);
b = b_in;
long n = A.NumRows();
long m = A.NumCols();
X.SetDims(n, m);
long i, j;
for (i = 0; i < n; i++)
for (j = 0; j < m; j++)
mul(X[i][j], A[i][j], b);
}
void sub(mat_ZZ_p& X, const mat_ZZ_p& A, const mat_ZZ_p& B)
{
long n = A.NumRows();
long m = A.NumCols();
if (B.NumRows() != n || B.NumCols() != m)
Error("matrix sub: dimension mismatch");
X.SetDims(n, m);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
sub(X(i,j), A(i,j), B(i,j));
}
void clear(mat_ZZ_p& x)
{
long n = x.NumRows();
long i;
for (i = 0; i < n; i++)
clear(x[i]);
}
void multi_modular_mul(mat_ZZ_p& X, const mat_ZZ_p& A, const mat_ZZ_p& B)
{
long l = A.NumCols();
if (l != B.NumRows())
LogicError("matrix mul: dimension mismatch");
if (l > NTL_MatPrimeLimit)
ResourceError("matrix mul: dimension too large");
mat_ZZ_p_crt_rep x, a, b;
to_mat_ZZ_p_crt_rep(a, A);
to_mat_ZZ_p_crt_rep(b, B);
mul(x, a, b);
from_mat_ZZ_p_crt_rep(x, X);
}
NTL_START_IMPL
void add(mat_ZZ_p& X, const mat_ZZ_p& A, const mat_ZZ_p& B)
{
long n = A.NumRows();
long m = A.NumCols();
if (B.NumRows() != n || B.NumCols() != m)
LogicError("matrix add: dimension mismatch");
X.SetDims(n, m);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
add(X(i,j), A(i,j), B(i,j));
}
long IsDiag(const mat_ZZ_p& A, long n, const ZZ_p& d)
{
if (A.NumRows() != n || A.NumCols() != n)
return 0;
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
if (i != j) {
if (!IsZero(A(i, j))) return 0;
}
else {
if (A(i, j) != d) return 0;
}
return 1;
}
long IsIdent(const mat_ZZ_p& A, long n)
{
if (A.NumRows() != n || A.NumCols() != n)
return 0;
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
if (i != j) {
if (!IsZero(A(i, j))) return 0;
}
else {
if (!IsOne(A(i, j))) return 0;
}
return 1;
}
void mul(vec_ZZ_p& x, const mat_ZZ_p& A, const vec_ZZ_p& b)
{
if (&b == &x || A.position1(x) != -1) {
vec_ZZ_p tmp;
mul_aux(tmp, A, b);
x = tmp;
}
else
mul_aux(x, A, b);
}
void conv(mat_ZZ_p& x, const mat_ZZ& a)
{
long n = a.NumRows();
long m = a.NumCols();
long i;
x.SetDims(n, m);
for (i = 0; i < n; i++)
conv(x[i], a[i]);
}
void plain_mul_transpose_aux(mat_ZZ_p& X, const mat_ZZ_p& A, const mat_ZZ_p& B)
{
long n = A.NumRows();
long l = A.NumCols();
long m = B.NumRows();
if (l != B.NumCols())
LogicError("matrix mul: dimension mismatch");
X.SetDims(n, m);
ZZ_pContext context;
context.save();
long sz = ZZ_p::ModulusSize();
bool seq = (double(n)*double(l)*double(m)*double(sz)*double(sz) < PAR_THRESH);
NTL_GEXEC_RANGE(seq, m, first, last)
NTL_IMPORT(n)
NTL_IMPORT(l)
NTL_IMPORT(m)
context.restore();
long i, j, k;
ZZ acc, tmp;
for (j = first; j < last; j++) {
const ZZ_p *B_col = B[j].elts();
for (i = 0; i < n; i++) {
clear(acc);
for (k = 0; k < l; k++) {
mul(tmp, rep(A[i][k]), rep(B_col[k]));
add(acc, acc, tmp);
}
conv(X[i][j], acc);
}
}
NTL_GEXEC_RANGE_END
}
long IsZero(const mat_ZZ_p& a)
{
long n = a.NumRows();
long i;
for (i = 0; i < n; i++)
if (!IsZero(a[i]))
return 0;
return 1;
}
void ident(mat_ZZ_p& X, long n)
{
X.SetDims(n, n);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
if (i == j)
set(X(i, j));
else
clear(X(i, j));
}
void Testbench::initMatrix(mat_ZZ_p & m, int int_size) {
ZZ_p n;
n.init(to_ZZ("56563749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995"));
switch (int_size) {
case 64:
n = to_ZZ_p(to_ZZ("9999999999999999995"));
break;
case 128:
n = to_ZZ_p(to_ZZ("99993749237498237498237493299999999995"));
break;
case 256:
n = to_ZZ_p(to_ZZ("99993749237498237498237493299999937129873912873981273129842343242399999799995"));
break;
case 512:
n = to_ZZ_p(to_ZZ("9999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995"));
break;
case 1024:
n = to_ZZ_p(to_ZZ("99993749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995"));
break;
case 2048:
n = to_ZZ_p(to_ZZ("9999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995"));
break;
case 4096:
n = to_ZZ_p(to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
break;
case 8192:
n = to_ZZ_p(to_ZZ("9999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995999937492374982374982374932999999371298739128739812731298423432423999997999959999374923749823749823749329999993712987391287398127312984234324239999979999599993749237498237498237493299999937129873912873981273129842343242399999799995"));
break;
default:
n = to_ZZ_p(to_ZZ("9999999999999999995"));
break;
}
for (int i = 1; i <= m.NumRows(); i++) {
for (int j = 1; j <= m.NumCols(); j++) {
m(i,j) = n;
}
}
}
void diag(mat_ZZ_p& X, long n, const ZZ_p& d_in)
{
ZZ_p d = d_in;
X.SetDims(n, n);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
if (i == j)
X(i, j) = d;
else
clear(X(i, j));
}
static
void mul_aux(vec_ZZ_p& x, const mat_ZZ_p& A, const vec_ZZ_p& 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 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);
}
}
static
void mul_aux(vec_ZZ_p& x, const vec_ZZ_p& a, const mat_ZZ_p& 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 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);
}
}
long NumCols() const
{
return body.NumCols();
}
static
void solve_impl(ZZ_p& d, vec_ZZ_p& X, const mat_ZZ_p& A, const vec_ZZ_p& b, bool trans)
{
long n = A.NumRows();
if (A.NumCols() != n)
LogicError("solve: nonsquare matrix");
if (b.length() != n)
LogicError("solve: dimension mismatch");
if (n == 0) {
set(d);
X.SetLength(0);
return;
}
long i, j, k, pos;
ZZ t1, t2;
ZZ *x, *y;
const ZZ& p = ZZ_p::modulus();
vec_ZZVec M;
sqr(t1, p);
mul(t1, t1, n);
M.SetLength(n);
for (i = 0; i < n; i++) {
M[i].SetSize(n+1, t1.size());
if (trans)
for (j = 0; j < n; j++) M[i][j] = rep(A[j][i]);
else
for (j = 0; j < n; j++) M[i][j] = rep(A[i][j]);
M[i][n] = rep(b[i]);
}
ZZ 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]);
NegateMod(det, det, p);
}
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);
NegateMod(t1, t1, p);
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);
return;
}
}
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);
}
NTL_START_IMPL
void CharPoly(ZZ_pX& f, const mat_ZZ_p& M)
{
long n = M.NumRows();
if (M.NumCols() != n)
Error("CharPoly: nonsquare matrix");
if (n == 0) {
set(f);
return;
}
ZZ_p t;
if (n == 1) {
SetX(f);
negate(t, M(1, 1));
SetCoeff(f, 0, t);
return;
}
mat_ZZ_p H;
H = M;
long i, j, m;
ZZ_p u, t1;
for (m = 2; m <= n-1; m++) {
i = m;
while (i <= n && IsZero(H(i, m-1)))
i++;
if (i <= n) {
t = H(i, m-1);
if (i > m) {
swap(H(i), H(m));
// swap columns i and m
for (j = 1; j <= n; j++)
swap(H(j, i), H(j, m));
}
for (i = m+1; i <= n; i++) {
div(u, H(i, m-1), t);
for (j = m; j <= n; j++) {
mul(t1, u, H(m, j));
sub(H(i, j), H(i, j), t1);
}
for (j = 1; j <= n; j++) {
mul(t1, u, H(j, i));
add(H(j, m), H(j, m), t1);
}
}
}
}
vec_ZZ_pX F;
F.SetLength(n+1);
ZZ_pX T;
T.SetMaxLength(n);
set(F[0]);
for (m = 1; m <= n; m++) {
LeftShift(F[m], F[m-1], 1);
mul(T, F[m-1], H(m, m));
sub(F[m], F[m], T);
set(t);
for (i = 1; i <= m-1; i++) {
mul(t, t, H(m-i+1, m-i));
mul(t1, t, H(m-i, m));
mul(T, F[m-i-1], t1);
sub(F[m], F[m], T);
}
}
f = F[n];
}
void kernel(mat_ZZ_p& X, const mat_ZZ_p& A)
{
long m = A.NumRows();
long n = A.NumCols();
mat_ZZ_p M;
long r;
transpose(M, A);
r = gauss(M);
X.SetDims(m-r, m);
long i, j, k, s;
ZZ t1, t2;
ZZ_p T3;
vec_long D;
D.SetLength(m);
for (j = 0; j < m; j++) D[j] = -1;
vec_ZZ_p inverses;
inverses.SetLength(m);
j = -1;
for (i = 0; i < r; i++) {
do {
j++;
} while (IsZero(M[i][j]));
D[j] = i;
inv(inverses[j], M[i][j]);
}
for (k = 0; k < m-r; k++) {
vec_ZZ_p& v = X[k];
long pos = 0;
for (j = m-1; j >= 0; j--) {
if (D[j] == -1) {
if (pos == k)
set(v[j]);
else
clear(v[j]);
pos++;
}
else {
i = D[j];
clear(t1);
for (s = j+1; s < m; s++) {
mul(t2, rep(v[s]), rep(M[i][s]));
add(t1, t1, t2);
}
conv(T3, t1);
mul(T3, T3, inverses[j]);
negate(v[j], T3);
}
}
}
}
long gauss(mat_ZZ_p& M)
{
return gauss(M, M.NumCols());
}
long gauss(mat_ZZ_p& M_in, long w)
{
long k, l;
long i, j;
long pos;
ZZ t1, t2, t3;
ZZ *x, *y;
long n = M_in.NumRows();
long m = M_in.NumCols();
if (w < 0 || w > m)
Error("gauss: bad args");
const ZZ& p = ZZ_p::modulus();
vec_ZZVec M;
sqr(t1, p);
mul(t1, t1, n);
M.SetLength(n);
for (i = 0; i < n; i++) {
M[i].SetSize(m, t1.size());
for (j = 0; j < m; j++) {
M[i][j] = rep(M_in[i][j]);
}
}
l = 0;
for (k = 0; k < w && l < n; k++) {
pos = -1;
for (i = l; i < n; i++) {
rem(t1, M[i][k], p);
M[i][k] = t1;
if (pos == -1 && !IsZero(t1)) {
pos = i;
}
}
if (pos != -1) {
swap(M[pos], M[l]);
InvMod(t3, M[l][k], p);
NegateMod(t3, t3, p);
for (j = k+1; j < m; j++) {
rem(M[l][j], M[l][j], p);
}
for (i = l+1; i < n; i++) {
// M[i] = M[i] + M[l]*M[i,k]*t3
MulMod(t1, M[i][k], t3, p);
clear(M[i][k]);
x = M[i].elts() + (k+1);
y = M[l].elts() + (k+1);
for (j = k+1; j < m; j++, x++, y++) {
// *x = *x + (*y)*t1
mul(t2, *y, t1);
add(t2, t2, *x);
*x = t2;
}
}
l++;
}
}
for (i = 0; i < n; i++)
for (j = 0; j < m; j++)
conv(M_in[i][j], M[i][j]);
return l;
}
void inv(ZZ_p& d, mat_ZZ_p& X, const mat_ZZ_p& A)
{
long n = A.NumRows();
if (A.NumCols() != n)
Error("inv: nonsquare matrix");
if (n == 0) {
set(d);
X.SetDims(0, 0);
return;
}
long i, j, k, pos;
ZZ t1, t2;
ZZ *x, *y;
const ZZ& p = ZZ_p::modulus();
vec_ZZVec M;
sqr(t1, p);
mul(t1, t1, n);
M.SetLength(n);
for (i = 0; i < n; i++) {
M[i].SetSize(2*n, t1.size());
for (j = 0; j < n; j++) {
M[i][j] = rep(A[i][j]);
clear(M[i][n+j]);
}
set(M[i][n+i]);
}
ZZ 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]);
NegateMod(det, det, p);
}
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);
NegateMod(t1, t1, p);
for (j = k+1; j < 2*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 < 2*n; j++, x++, y++) {
// *x = *x + (*y)*t1
mul(t2, *y, t1);
add(*x, *x, t2);
}
}
}
else {
clear(d);
return;
}
}
X.SetDims(n, n);
for (k = 0; k < n; k++) {
for (i = n-1; i >= 0; i--) {
clear(t1);
for (j = i+1; j < n; j++) {
mul(t2, rep(X[j][k]), M[i][j]);
add(t1, t1, t2);
}
sub(t1, t1, M[i][n+k]);
conv(X[i][k], t1);
}
}
conv(d, det);
}
void determinant(ZZ_p& d, const mat_ZZ_p& M_in)
{
long k, n;
long i, j;
long pos;
ZZ t1, t2;
ZZ *x, *y;
const ZZ& p = ZZ_p::modulus();
n = M_in.NumRows();
if (M_in.NumCols() != n)
Error("determinant: nonsquare matrix");
if (n == 0) {
set(d);
return;
}
vec_ZZVec M;
sqr(t1, p);
mul(t1, t1, n);
M.SetLength(n);
for (i = 0; i < n; i++) {
M[i].SetSize(n, t1.size());
for (j = 0; j < n; j++)
M[i][j] = rep(M_in[i][j]);
}
ZZ 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]);
NegateMod(det, det, p);
}
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);
NegateMod(t1, t1, p);
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);
return;
}
}
conv(d, det);
}
