void
nmod_poly_mat_det(nmod_poly_t det, const nmod_poly_mat_t A)
{
slong n = A->r;
if (n == 0)
{
nmod_poly_one(det);
}
else if (n == 1)
{
nmod_poly_set(det, nmod_poly_mat_entry(A, 0, 0));
}
else if (n == 2)
{
nmod_poly_t tmp;
nmod_poly_init(tmp, nmod_poly_mat_modulus(A));
nmod_poly_mul(det, nmod_poly_mat_entry(A, 0, 0),
nmod_poly_mat_entry(A, 1, 1));
nmod_poly_mul(tmp, nmod_poly_mat_entry(A, 0, 1),
nmod_poly_mat_entry(A, 1, 0));
nmod_poly_sub(det, det, tmp);
nmod_poly_clear(tmp);
}
else if (n < 15) /* should be entry sensitive too */
{
nmod_poly_mat_det_fflu(det, A);
}
else
{
nmod_poly_mat_det_interpolate(det, A);
}
}
long
nmod_poly_mat_nullspace(nmod_poly_mat_t res, const nmod_poly_mat_t mat)
{
long i, j, k, m, n, rank, nullity;
long * pivots;
long * nonpivots;
nmod_poly_mat_t tmp;
nmod_poly_t den;
m = mat->r;
n = mat->c;
nmod_poly_init(den, nmod_poly_mat_modulus(mat));
nmod_poly_mat_init_set(tmp, mat);
rank = nmod_poly_mat_rref(tmp, den, NULL, tmp);
nullity = n - rank;
nmod_poly_mat_zero(res);
if (rank == 0)
{
for (i = 0; i < nullity; i++)
nmod_poly_one(res->rows[i] + i);
}
else if (nullity)
{
pivots = flint_malloc(rank * sizeof(long));
nonpivots = flint_malloc(nullity * sizeof(long));
for (i = j = k = 0; i < rank; i++)
{
while (nmod_poly_is_zero(tmp->rows[i] + j))
{
nonpivots[k] = j;
k++;
j++;
}
pivots[i] = j;
j++;
}
while (k < nullity)
{
nonpivots[k] = j;
k++;
j++;
}
nmod_poly_set(den, tmp->rows[0] + pivots[0]);
for (i = 0; i < nullity; i++)
{
for (j = 0; j < rank; j++)
nmod_poly_set(res->rows[pivots[j]] + i,
tmp->rows[j] + nonpivots[i]);
nmod_poly_neg(res->rows[nonpivots[i]] + i, den);
}
flint_free(pivots);
flint_free(nonpivots);
}
nmod_poly_clear(den);
nmod_poly_mat_clear(tmp);
return nullity;
}
void
nmod_poly_xgcd_hgcd(nmod_poly_t G, nmod_poly_t S, nmod_poly_t T,
const nmod_poly_t A, const nmod_poly_t B)
{
if (A->length < B->length)
{
nmod_poly_xgcd_hgcd(G, T, S, B, A);
}
else /* lenA >= lenB >= 0 */
{
const slong lenA = A->length, lenB = B->length;
mp_limb_t inv;
if (lenA == 0) /* lenA = lenB = 0 */
{
nmod_poly_zero(G);
nmod_poly_zero(S);
nmod_poly_zero(T);
}
else if (lenB == 0) /* lenA > lenB = 0 */
{
inv = n_invmod(A->coeffs[lenA - 1], A->mod.n);
nmod_poly_scalar_mul_nmod(G, A, inv);
nmod_poly_zero(T);
nmod_poly_set_coeff_ui(S, 0, inv);
S->length = 1;
}
else if (lenB == 1) /* lenA >= lenB = 1 */
{
nmod_poly_fit_length(T, 1);
T->length = 1;
T->coeffs[0] = n_invmod(B->coeffs[0], A->mod.n);
nmod_poly_one(G);
nmod_poly_zero(S);
}
else /* lenA >= lenB >= 2 */
{
mp_ptr g, s, t;
slong lenG;
if (G == A || G == B)
{
g = _nmod_vec_init(FLINT_MIN(lenA, lenB));
}
else
{
nmod_poly_fit_length(G, FLINT_MIN(lenA, lenB));
g = G->coeffs;
}
if (S == A || S == B)
{
s = _nmod_vec_init(FLINT_MAX(lenB - 1, 2));
}
else
{
nmod_poly_fit_length(S, FLINT_MAX(lenB - 1, 2));
s = S->coeffs;
}
if (T == A || T == B)
{
t = _nmod_vec_init(FLINT_MAX(lenA - 1, 2));
}
else
{
nmod_poly_fit_length(T, FLINT_MAX(lenA - 1, 2));
t = T->coeffs;
}
if (lenA >= lenB)
lenG = _nmod_poly_xgcd_hgcd(g, s, t, A->coeffs, lenA,
B->coeffs, lenB, A->mod);
else
lenG = _nmod_poly_xgcd_hgcd(g, t, s, B->coeffs, lenB,
A->coeffs, lenA, A->mod);
if (G == A || G == B)
{
flint_free(G->coeffs);
G->coeffs = g;
G->alloc = FLINT_MIN(lenA, lenB);
}
if (S == A || S == B)
{
flint_free(S->coeffs);
S->coeffs = s;
S->alloc = FLINT_MAX(lenB - 1, 2);
}
if (T == A || T == B)
{
flint_free(T->coeffs);
T->coeffs = t;
T->alloc = FLINT_MAX(lenA - 1, 2);
}
G->length = lenG;
S->length = FLINT_MAX(lenB - lenG, 1);
T->length = FLINT_MAX(lenA - lenG, 1);
MPN_NORM(S->coeffs, S->length);
MPN_NORM(T->coeffs, T->length);
if (G->coeffs[lenG - 1] != 1)
{
inv = n_invmod(G->coeffs[lenG - 1], A->mod.n);
nmod_poly_scalar_mul_nmod(G, G, inv);
nmod_poly_scalar_mul_nmod(S, S, inv);
nmod_poly_scalar_mul_nmod(T, T, inv);
}
}
}
}
int
nmod_poly_mat_inv(nmod_poly_mat_t Ainv, nmod_poly_t den,
const nmod_poly_mat_t A)
{
slong n = nmod_poly_mat_nrows(A);
if (n == 0)
{
nmod_poly_one(den);
return 1;
}
else if (n == 1)
{
nmod_poly_set(den, E(A, 0, 0));
nmod_poly_one(E(Ainv, 0, 0));
return !nmod_poly_is_zero(den);
}
else if (n == 2)
{
nmod_poly_mat_det(den, A);
if (nmod_poly_is_zero(den))
{
return 0;
}
else if (Ainv == A)
{
nmod_poly_swap(E(A, 0, 0), E(A, 1, 1));
nmod_poly_neg(E(A, 0, 1), E(A, 0, 1));
nmod_poly_neg(E(A, 1, 0), E(A, 1, 0));
return 1;
}
else
{
nmod_poly_set(E(Ainv, 0, 0), E(A, 1, 1));
nmod_poly_set(E(Ainv, 1, 1), E(A, 0, 0));
nmod_poly_neg(E(Ainv, 0, 1), E(A, 0, 1));
nmod_poly_neg(E(Ainv, 1, 0), E(A, 1, 0));
return 1;
}
}
else
{
nmod_poly_mat_t LU, I;
slong * perm;
int result;
perm = _perm_init(n);
nmod_poly_mat_init_set(LU, A);
result = (nmod_poly_mat_fflu(LU, den, perm, LU, 1) == n);
if (result)
{
nmod_poly_mat_init(I, n, n, nmod_poly_mat_modulus(A));
nmod_poly_mat_one(I);
nmod_poly_mat_solve_fflu_precomp(Ainv, perm, LU, I);
nmod_poly_mat_clear(I);
}
else
nmod_poly_zero(den);
if (_perm_parity(perm, n))
{
nmod_poly_mat_neg(Ainv, Ainv);
nmod_poly_neg(den, den);
}
_perm_clear(perm);
nmod_poly_mat_clear(LU);
return result;
}
}
