int
fmpz_poly_sqrt_classical(fmpz_poly_t b, const fmpz_poly_t a)
{
long blen, len = a->length;
int result;
if (len % 2 == 0)
{
fmpz_poly_zero(b);
return len == 0;
}
if (b == a)
{
fmpz_poly_t tmp;
fmpz_poly_init(tmp);
result = fmpz_poly_sqrt(tmp, a);
fmpz_poly_swap(b, tmp);
fmpz_poly_clear(tmp);
return result;
}
blen = len / 2 + 1;
fmpz_poly_fit_length(b, blen);
_fmpz_poly_set_length(b, blen);
result = _fmpz_poly_sqrt_classical(b->coeffs, a->coeffs, len);
if (!result)
_fmpz_poly_set_length(b, 0);
return result;
}
void
fmpz_poly_mulhigh_classical(fmpz_poly_t res,
const fmpz_poly_t poly1, const fmpz_poly_t poly2,
long start)
{
long len_out = poly1->length + poly2->length - 1;
if (poly1->length == 0 || poly2->length == 0 || start >= len_out)
{
fmpz_poly_zero(res);
return;
}
if (res == poly1 || res == poly2)
{
fmpz_poly_t temp;
fmpz_poly_init2(temp, len_out);
_fmpz_poly_mulhigh_classical(temp->coeffs, poly1->coeffs,
poly1->length, poly2->coeffs,
poly2->length, start);
fmpz_poly_swap(res, temp);
fmpz_poly_clear(temp);
}
else
{
fmpz_poly_fit_length(res, len_out);
_fmpz_poly_mulhigh_classical(res->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length, start);
}
_fmpz_poly_set_length(res, len_out);
}
void
fmpz_poly_mullow_classical(fmpz_poly_t res, const fmpz_poly_t poly1,
const fmpz_poly_t poly2, long n)
{
long len_out;
if (poly1->length == 0 || poly2->length == 0 || n == 0)
{
fmpz_poly_zero(res);
return;
}
len_out = poly1->length + poly2->length - 1;
if (n > len_out)
n = len_out;
if (res == poly1 || res == poly2)
{
fmpz_poly_t t;
fmpz_poly_init2(t, n);
_fmpz_poly_mullow_classical(t->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length, n);
fmpz_poly_swap(res, t);
fmpz_poly_clear(t);
}
else
{
fmpz_poly_fit_length(res, n);
_fmpz_poly_mullow_classical(res->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length, n);
}
_fmpz_poly_set_length(res, n);
_fmpz_poly_normalise(res);
}
void fmpz_poly_sqr_classical(fmpz_poly_t rop, const fmpz_poly_t op)
{
long len;
if (op->length == 0)
{
fmpz_poly_zero(rop);
return;
}
len = 2 * op->length - 1;
if (rop == op)
{
fmpz_poly_t t;
fmpz_poly_init2(t, len);
_fmpz_poly_sqr_classical(t->coeffs, op->coeffs, op->length);
fmpz_poly_swap(rop, t);
fmpz_poly_clear(t);
}
else
{
fmpz_poly_fit_length(rop, len);
_fmpz_poly_sqr_classical(rop->coeffs, op->coeffs, op->length);
}
_fmpz_poly_set_length(rop, len);
}
void
fmpz_poly_mulmid_classical(fmpz_poly_t res,
const fmpz_poly_t poly1, const fmpz_poly_t poly2)
{
slong len_out;
if (poly1->length == 0 || poly2->length == 0)
{
fmpz_poly_zero(res);
return;
}
len_out = poly1->length - poly2->length + 1;
if (res == poly1 || res == poly2)
{
fmpz_poly_t temp;
fmpz_poly_init2(temp, len_out);
_fmpz_poly_mulmid_classical(temp->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length);
fmpz_poly_swap(res, temp);
fmpz_poly_clear(temp);
}
else
{
fmpz_poly_fit_length(res, len_out);
_fmpz_poly_mulmid_classical(res->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length);
}
_fmpz_poly_set_length(res, len_out);
_fmpz_poly_normalise(res);
}
void fmpz_poly_sqrlow(fmpz_poly_t res, const fmpz_poly_t poly, long n)
{
const long len = poly->length;
if (len == 0 || n == 0)
{
fmpz_poly_zero(res);
return;
}
if (res == poly)
{
fmpz_poly_t t;
fmpz_poly_init2(t, n);
fmpz_poly_sqrlow(t, poly, n);
fmpz_poly_swap(res, t);
fmpz_poly_clear(t);
return;
}
n = FLINT_MIN(2 * len - 1, n);
fmpz_poly_fit_length(res, n);
_fmpz_poly_sqrlow(res->coeffs, poly->coeffs, len, n);
_fmpz_poly_set_length(res, n);
_fmpz_poly_normalise(res);
}
void
fmpz_poly_mullow_KS(fmpz_poly_t res,
const fmpz_poly_t poly1, const fmpz_poly_t poly2, long n)
{
const long len1 = poly1->length;
const long len2 = poly2->length;
if (len1 == 0 || len2 == 0 || n == 0)
{
fmpz_poly_zero(res);
return;
}
if (res == poly1 || res == poly2)
{
fmpz_poly_t t;
fmpz_poly_init2(t, n);
fmpz_poly_mullow_KS(t, poly1, poly2, n);
fmpz_poly_swap(res, t);
fmpz_poly_clear(t);
return;
}
fmpz_poly_fit_length(res, n);
if (len1 >= len2)
_fmpz_poly_mullow_KS(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, n);
else
_fmpz_poly_mullow_KS(res->coeffs, poly2->coeffs, len2,
poly1->coeffs, len1, n);
_fmpz_poly_set_length(res, n);
_fmpz_poly_normalise(res);
}
void
fmpz_poly_revert_series_lagrange(fmpz_poly_t Qinv,
const fmpz_poly_t Q, slong n)
{
fmpz *Qcopy;
int Qalloc;
slong Qlen = Q->length;
if (Qlen < 2 || !fmpz_is_zero(Q->coeffs) || !fmpz_is_pm1(Q->coeffs + 1))
{
flint_printf("Exception (fmpz_poly_revert_series_lagrange). Input must have \n"
"zero constant term and +1 or -1 as coefficient of x^1.\n");
abort();
}
if (Qlen >= n)
{
Qcopy = Q->coeffs;
Qalloc = 0;
}
else
{
slong i;
Qcopy = (fmpz *) flint_malloc(n * sizeof(fmpz));
for (i = 0; i < Qlen; i++)
Qcopy[i] = Q->coeffs[i];
for ( ; i < n; i++)
Qcopy[i] = 0;
Qalloc = 1;
}
if (Qinv != Q)
{
fmpz_poly_fit_length(Qinv, n);
_fmpz_poly_revert_series_lagrange(Qinv->coeffs, Qcopy, n);
}
else
{
fmpz_poly_t t;
fmpz_poly_init2(t, n);
_fmpz_poly_revert_series_lagrange(t->coeffs, Qcopy, n);
fmpz_poly_swap(Qinv, t);
fmpz_poly_clear(t);
}
_fmpz_poly_set_length(Qinv, n);
_fmpz_poly_normalise(Qinv);
if (Qalloc)
flint_free(Qcopy);
}
void
fmpz_poly_compose_series(fmpz_poly_t res,
const fmpz_poly_t poly1, const fmpz_poly_t poly2, long n)
{
long len1 = poly1->length;
long len2 = poly2->length;
long lenr;
if (len2 != 0 && !fmpz_is_zero(poly2->coeffs))
{
printf("exception: fmpz_poly_compose_series: inner polynomial "
"must have zero constant term\n");
abort();
}
if (len1 == 0 || n == 0)
{
fmpz_poly_zero(res);
return;
}
if (len2 == 0 || len1 == 1)
{
fmpz_poly_set_fmpz(res, poly1->coeffs);
return;
}
lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
len1 = FLINT_MIN(len1, lenr);
len2 = FLINT_MIN(len2, lenr);
if ((res != poly1) && (res != poly2))
{
fmpz_poly_fit_length(res, lenr);
_fmpz_poly_compose_series(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr);
_fmpz_poly_set_length(res, lenr);
_fmpz_poly_normalise(res);
}
else
{
fmpz_poly_t t;
fmpz_poly_init2(t, lenr);
_fmpz_poly_compose_series(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr);
_fmpz_poly_set_length(t, lenr);
_fmpz_poly_normalise(t);
fmpz_poly_swap(res, t);
fmpz_poly_clear(t);
}
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("swap....");
fflush(stdout);
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_poly_t a, b, c;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(c);
fmpz_poly_randtest(a, state, n_randint(state, 100), 200);
fmpz_poly_randtest(b, state, n_randint(state, 100), 200);
fmpz_poly_set(c, b);
fmpz_poly_swap(a, b);
result = (fmpz_poly_equal(a, c));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_poly_print(a), flint_printf("\n\n");
fmpz_poly_print(b), flint_printf("\n\n");
fmpz_poly_print(c), flint_printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void
fmpz_poly_pow_multinomial(fmpz_poly_t res, const fmpz_poly_t poly, ulong e)
{
const long len = poly->length;
long rlen;
if ((len < 2) | (e < 3UL))
{
if (e == 0UL)
fmpz_poly_set_ui(res, 1);
else if (len == 0)
fmpz_poly_zero(res);
else if (len == 1)
{
fmpz_poly_fit_length(res, 1);
fmpz_pow_ui(res->coeffs, poly->coeffs, e);
_fmpz_poly_set_length(res, 1);
}
else if (e == 1UL)
fmpz_poly_set(res, poly);
else /* e == 2UL */
fmpz_poly_sqr(res, poly);
return;
}
rlen = (long) e * (len - 1) + 1;
if (res != poly)
{
fmpz_poly_fit_length(res, rlen);
_fmpz_poly_pow_multinomial(res->coeffs, poly->coeffs, len, e);
_fmpz_poly_set_length(res, rlen);
}
else
{
fmpz_poly_t t;
fmpz_poly_init2(t, rlen);
_fmpz_poly_pow_multinomial(t->coeffs, poly->coeffs, len, e);
_fmpz_poly_set_length(t, rlen);
fmpz_poly_swap(res, t);
fmpz_poly_clear(t);
}
}
void
fmpz_poly_pow_binomial(fmpz_poly_t res, const fmpz_poly_t poly, ulong e)
{
const long len = poly->length;
long rlen;
if (len != 2)
{
printf("Exception: poly->length not equal to 2 in fmpz_poly_pow_binomial\n");
abort();
}
if (e < 3UL)
{
if (e == 0UL)
fmpz_poly_set_ui(res, 1UL);
else if (e == 1UL)
fmpz_poly_set(res, poly);
else /* e == 2UL */
fmpz_poly_sqr(res, poly);
return;
}
rlen = (long) e + 1;
if (res != poly)
{
fmpz_poly_fit_length(res, rlen);
_fmpz_poly_set_length(res, rlen);
_fmpz_poly_pow_binomial(res->coeffs, poly->coeffs, e);
}
else
{
fmpz_poly_t t;
fmpz_poly_init2(t, rlen);
_fmpz_poly_set_length(t, rlen);
_fmpz_poly_pow_binomial(t->coeffs, poly->coeffs, e);
fmpz_poly_swap(res, t);
fmpz_poly_clear(t);
}
}
void
fmpz_poly_compose_divconquer(fmpz_poly_t res,
const fmpz_poly_t poly1, const fmpz_poly_t poly2)
{
const long len1 = poly1->length;
const long len2 = poly2->length;
long lenr;
if (len1 == 0)
{
fmpz_poly_zero(res);
return;
}
if (len1 == 1 || len2 == 0)
{
fmpz_poly_set_fmpz(res, poly1->coeffs);
return;
}
lenr = (len1 - 1) * (len2 - 1) + 1;
if (res != poly1 && res != poly2)
{
fmpz_poly_fit_length(res, lenr);
_fmpz_poly_compose_divconquer(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2);
_fmpz_poly_set_length(res, lenr);
_fmpz_poly_normalise(res);
}
else
{
fmpz_poly_t t;
fmpz_poly_init2(t, lenr);
_fmpz_poly_compose_divconquer(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2);
_fmpz_poly_set_length(t, lenr);
_fmpz_poly_normalise(t);
fmpz_poly_swap(res, t);
fmpz_poly_clear(t);
}
}
void
fmpz_poly_divrem_divconquer(fmpz_poly_t Q, fmpz_poly_t R,
const fmpz_poly_t A, const fmpz_poly_t B)
{
const long lenA = A->length;
const long lenB = B->length;
fmpz_poly_t tQ, tR;
fmpz *q, *r;
if (lenB == 0)
{
printf("Exception: division by zero in fmpz_poly_divrem_divconquer\n");
abort();
}
if (lenA < lenB)
{
fmpz_poly_set(R, A);
fmpz_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
fmpz_poly_init2(tQ, lenA - lenB + 1);
q = tQ->coeffs;
}
else
{
fmpz_poly_fit_length(Q, lenA - lenB + 1);
q = Q->coeffs;
}
if (R == A || R == B)
{
fmpz_poly_init2(tR, lenA);
r = tR->coeffs;
}
else
{
fmpz_poly_fit_length(R, lenA);
r = R->coeffs;
}
_fmpz_poly_divrem_divconquer(q, r, A->coeffs, lenA, B->coeffs, lenB);
if (Q == A || Q == B)
{
_fmpz_poly_set_length(tQ, lenA - lenB + 1);
fmpz_poly_swap(tQ, Q);
fmpz_poly_clear(tQ);
}
else
_fmpz_poly_set_length(Q, lenA - lenB + 1);
if (R == A || R == B)
{
_fmpz_poly_set_length(tR, lenA);
fmpz_poly_swap(tR, R);
fmpz_poly_clear(tR);
}
else
_fmpz_poly_set_length(R, lenA);
_fmpz_poly_normalise(Q);
_fmpz_poly_normalise(R);
}
bool
poly_inverse_poly_q(fmpz_poly_t Fq,
const fmpz_poly_t a,
const ntru_params *params)
{
bool retval = false;
int k = 0,
j = 0;
fmpz *b_last;
fmpz_poly_t a_tmp,
b,
c,
f,
g;
/* general initialization of temp variables */
fmpz_poly_init(b);
fmpz_poly_set_coeff_ui(b, 0, 1);
fmpz_poly_init(c);
fmpz_poly_init(f);
fmpz_poly_set(f, a);
/* set g(x) = x^N − 1 */
fmpz_poly_init(g);
fmpz_poly_set_coeff_si(g, 0, -1);
fmpz_poly_set_coeff_si(g, params->N, 1);
/* avoid side effects */
fmpz_poly_init(a_tmp);
fmpz_poly_set(a_tmp, a);
fmpz_poly_zero(Fq);
while (1) {
while (fmpz_poly_get_coeff_ptr(f, 0) &&
fmpz_is_zero(fmpz_poly_get_coeff_ptr(f, 0))) {
for (uint32_t i = 1; i <= params->N; i++) {
fmpz *f_coeff = fmpz_poly_get_coeff_ptr(f, i);
fmpz *c_coeff = fmpz_poly_get_coeff_ptr(c, params->N - i);
/* f(x) = f(x) / x */
fmpz_poly_set_coeff_fmpz_n(f, i - 1,
f_coeff);
/* c(x) = c(x) * x */
fmpz_poly_set_coeff_fmpz_n(c, params->N + 1 - i,
c_coeff);
}
fmpz_poly_set_coeff_si(f, params->N, 0);
fmpz_poly_set_coeff_si(c, 0, 0);
k++;
if (fmpz_poly_degree(f) == -1)
goto cleanup;
}
if (fmpz_poly_is_zero(g) == 1)
goto cleanup;
if (fmpz_poly_degree(f) == 0)
break;
if (fmpz_poly_degree(f) < fmpz_poly_degree(g)) {
fmpz_poly_swap(f, g);
fmpz_poly_swap(b, c);
}
fmpz_poly_add(f, g, f);
fmpz_poly_mod_unsigned(f, 2);
fmpz_poly_add(b, c, b);
fmpz_poly_mod_unsigned(b, 2);
}
k = k % params->N;
b_last = fmpz_poly_get_coeff_ptr(b, params->N);
if (fmpz_cmp_si_n(b_last, 0))
goto cleanup;
/* Fq(x) = x^(N-k) * b(x) */
for (int i = params->N - 1; i >= 0; i--) {
fmpz *b_i;
j = i - k;
if (j < 0)
j = j + params->N;
b_i = fmpz_poly_get_coeff_ptr(b, i);
fmpz_poly_set_coeff_fmpz_n(Fq, j, b_i);
}
poly_mod2_to_modq(Fq, a_tmp, params);
/* check if the f * Fq = 1 (mod p) condition holds true */
fmpz_poly_set(a_tmp, a);
poly_starmultiply(a_tmp, a_tmp, Fq, params, params->q);
if (fmpz_poly_is_one(a_tmp))
retval = true;
else
fmpz_poly_zero(Fq);
cleanup:
fmpz_poly_clear(a_tmp);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
fmpz_poly_clear(f);
fmpz_poly_clear(g);
return retval;
}
bool
poly_inverse_poly_p(fmpz_poly_t Fp,
const fmpz_poly_t a,
const ntru_params *params)
{
bool retval = false;
int k = 0,
j = 0;
fmpz *b_last;
fmpz_poly_t a_tmp,
b,
c,
f,
g;
/* general initialization of temp variables */
fmpz_poly_init(b);
fmpz_poly_set_coeff_ui(b, 0, 1);
fmpz_poly_init(c);
fmpz_poly_init(f);
fmpz_poly_set(f, a);
/* set g(x) = x^N − 1 */
fmpz_poly_init(g);
fmpz_poly_set_coeff_si(g, 0, -1);
fmpz_poly_set_coeff_si(g, params->N, 1);
/* avoid side effects */
fmpz_poly_init(a_tmp);
fmpz_poly_set(a_tmp, a);
fmpz_poly_zero(Fp);
while (1) {
while (fmpz_poly_get_coeff_ptr(f, 0) &&
fmpz_is_zero(fmpz_poly_get_coeff_ptr(f, 0))) {
for (uint32_t i = 1; i <= params->N; i++) {
fmpz *f_coeff = fmpz_poly_get_coeff_ptr(f, i);
fmpz *c_coeff = fmpz_poly_get_coeff_ptr(c, params->N - i);
/* f(x) = f(x) / x */
fmpz_poly_set_coeff_fmpz_n(f, i - 1,
f_coeff);
/* c(x) = c(x) * x */
fmpz_poly_set_coeff_fmpz_n(c, params->N + 1 - i,
c_coeff);
}
fmpz_poly_set_coeff_si(f, params->N, 0);
fmpz_poly_set_coeff_si(c, 0, 0);
k++;
if (fmpz_poly_degree(f) == -1)
goto cleanup;
}
if (fmpz_poly_is_zero(g) == 1)
goto cleanup;
if (fmpz_poly_degree(f) == 0)
break;
if (fmpz_poly_degree(f) < fmpz_poly_degree(g)) {
/* exchange f and g and exchange b and c */
fmpz_poly_swap(f, g);
fmpz_poly_swap(b, c);
}
{
fmpz_poly_t c_tmp,
g_tmp;
fmpz_t u,
mp_tmp;
fmpz_init(u);
fmpz_zero(u);
fmpz_init_set(mp_tmp, fmpz_poly_get_coeff_ptr(f, 0));
fmpz_poly_init(g_tmp);
fmpz_poly_set(g_tmp, g);
fmpz_poly_init(c_tmp);
fmpz_poly_set(c_tmp, c);
/* u = f[0] * g[0]^(-1) mod p */
/* = (f[0] mod p) * (g[0] inverse mod p) mod p */
fmpz_invmod_ui(u,
fmpz_poly_get_coeff_ptr(g, 0),
params->p);
fmpz_mod_ui(mp_tmp, mp_tmp, params->p);
fmpz_mul(u, mp_tmp, u);
fmpz_mod_ui(u, u, params->p);
/* f = f - u * g mod p */
fmpz_poly_scalar_mul_fmpz(g_tmp, g_tmp, u);
fmpz_poly_sub(f, f, g_tmp);
fmpz_poly_mod_unsigned(f, params->p);
/* b = b - u * c mod p */
fmpz_poly_scalar_mul_fmpz(c_tmp, c_tmp, u);
fmpz_poly_sub(b, b, c_tmp);
fmpz_poly_mod_unsigned(b, params->p);
fmpz_clear(u);
fmpz_poly_clear(g_tmp);
fmpz_poly_clear(c_tmp);
}
}
k = k % params->N;
b_last = fmpz_poly_get_coeff_ptr(b, params->N);
if (fmpz_cmp_si_n(b_last, 0))
goto cleanup;
/* Fp(x) = x^(N-k) * b(x) */
for (int i = params->N - 1; i >= 0; i--) {
fmpz *b_i;
/* b(X) = f[0]^(-1) * b(X) (mod p) */
{
fmpz_t mp_tmp;
fmpz_init(mp_tmp);
fmpz_invmod_ui(mp_tmp,
fmpz_poly_get_coeff_ptr(f, 0),
params->p);
if (fmpz_poly_get_coeff_ptr(b, i)) {
fmpz_mul(fmpz_poly_get_coeff_ptr(b, i),
fmpz_poly_get_coeff_ptr(b, i),
mp_tmp);
fmpz_mod_ui(fmpz_poly_get_coeff_ptr(b, i),
fmpz_poly_get_coeff_ptr(b, i),
params->p);
}
}
j = i - k;
if (j < 0)
j = j + params->N;
b_i = fmpz_poly_get_coeff_ptr(b, i);
fmpz_poly_set_coeff_fmpz_n(Fp, j, b_i);
}
/* check if the f * Fp = 1 (mod p) condition holds true */
fmpz_poly_set(a_tmp, a);
poly_starmultiply(a_tmp, a_tmp, Fp, params, params->p);
if (fmpz_poly_is_one(a_tmp))
retval = true;
else
fmpz_poly_zero(Fp);
cleanup:
fmpz_poly_clear(a_tmp);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
fmpz_poly_clear(f);
fmpz_poly_clear(g);
return retval;
}
int
fmpz_poly_gcd_heuristic(fmpz_poly_t res,
const fmpz_poly_t poly1, const fmpz_poly_t poly2)
{
const long len1 = poly1->length;
const long len2 = poly2->length;
long rlen;
int done = 0;
if (len1 == 0)
{
if (len2 == 0)
fmpz_poly_zero(res);
else
{
if (fmpz_sgn(poly2->coeffs + (len2 - 1)) > 0)
fmpz_poly_set(res, poly2);
else
fmpz_poly_neg(res, poly2);
}
return 1;
}
else
{
if (len2 == 0)
{
if (fmpz_sgn(poly1->coeffs + (len1 - 1)) > 0)
fmpz_poly_set(res, poly1);
else
fmpz_poly_neg(res, poly1);
return 1;
}
}
rlen = FLINT_MIN(len1, len2);
if (res == poly1 || res == poly2)
{
fmpz_poly_t temp;
fmpz_poly_init2(temp, rlen);
if (len1 >= len2)
done = _fmpz_poly_gcd_heuristic(temp->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2);
else
done = _fmpz_poly_gcd_heuristic(temp->coeffs, poly2->coeffs, len2,
poly1->coeffs, len1);
fmpz_poly_swap(temp, res);
fmpz_poly_clear(temp);
}
else
{
fmpz_poly_fit_length(res, rlen);
if (len1 >= len2)
done = _fmpz_poly_gcd_heuristic(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2);
else
done = _fmpz_poly_gcd_heuristic(res->coeffs, poly2->coeffs, len2,
poly1->coeffs, len1);
}
if (done)
{
_fmpz_poly_set_length(res, rlen);
_fmpz_poly_normalise(res);
}
return done;
}
int
fmpz_poly_mat_inv(fmpz_poly_mat_t Ainv, fmpz_poly_t den,
const fmpz_poly_mat_t A)
{
long n = fmpz_poly_mat_nrows(A);
if (n == 0)
{
fmpz_poly_one(den);
return 1;
}
else if (n == 1)
{
fmpz_poly_set(den, E(A, 0, 0));
fmpz_poly_one(E(Ainv, 0, 0));
return !fmpz_poly_is_zero(den);
}
else if (n == 2)
{
fmpz_poly_mat_det(den, A);
if (fmpz_poly_is_zero(den))
{
return 0;
}
else if (Ainv == A)
{
fmpz_poly_swap(E(A, 0, 0), E(A, 1, 1));
fmpz_poly_neg(E(A, 0, 1), E(A, 0, 1));
fmpz_poly_neg(E(A, 1, 0), E(A, 1, 0));
return 1;
}
else
{
fmpz_poly_set(E(Ainv, 0, 0), E(A, 1, 1));
fmpz_poly_set(E(Ainv, 1, 1), E(A, 0, 0));
fmpz_poly_neg(E(Ainv, 0, 1), E(A, 0, 1));
fmpz_poly_neg(E(Ainv, 1, 0), E(A, 1, 0));
return 1;
}
}
else
{
fmpz_poly_mat_t LU, I;
long * perm;
int result;
perm = _perm_init(n);
fmpz_poly_mat_init_set(LU, A);
result = (fmpz_poly_mat_fflu(LU, den, perm, LU, 1) == n);
if (result)
{
fmpz_poly_mat_init(I, n, n);
fmpz_poly_mat_one(I);
fmpz_poly_mat_solve_fflu_precomp(Ainv, perm, LU, I);
fmpz_poly_mat_clear(I);
}
else
fmpz_poly_zero(den);
if (_perm_parity(perm, n))
{
fmpz_poly_mat_neg(Ainv, Ainv);
fmpz_poly_neg(den, den);
}
_perm_clear(perm);
fmpz_poly_mat_clear(LU);
return result;
}
}
void frob(const mpoly_t P, const ctx_t ctxFracQt,
const qadic_t t1, const qadic_ctx_t Qq,
prec_t *prec, const prec_t *prec_in,
int verbose)
{
const padic_ctx_struct *Qp = &Qq->pctx;
const fmpz *p = Qp->p;
const long a = qadic_ctx_degree(Qq);
const long n = P->n - 1;
const long d = mpoly_degree(P, -1, ctxFracQt);
const long b = gmc_basis_size(n, d);
long i, j, k;
/* Diagonal fibre */
padic_mat_t F0;
/* Gauss--Manin Connection */
mat_t M;
mon_t *bR, *bC;
fmpz_poly_t r;
/* Local solution */
fmpz_poly_mat_t C, Cinv;
long vC, vCinv;
/* Frobenius */
fmpz_poly_mat_t F;
long vF;
fmpz_poly_mat_t F1;
long vF1;
fmpz_poly_t cp;
clock_t c0, c1;
double c;
if (verbose)
{
printf("Input:\n");
printf(" P = "), mpoly_print(P, ctxFracQt), printf("\n");
printf(" p = "), fmpz_print(p), printf("\n");
printf(" t1 = "), qadic_print_pretty(t1, Qq), printf("\n");
printf("\n");
fflush(stdout);
}
/* Step 1 {M, r} *********************************************************/
c0 = clock();
mat_init(M, b, b, ctxFracQt);
fmpz_poly_init(r);
gmc_compute(M, &bR, &bC, P, ctxFracQt);
{
fmpz_poly_t t;
fmpz_poly_init(t);
fmpz_poly_set_ui(r, 1);
for (i = 0; i < M->m; i++)
for (j = 0; j < M->n; j++)
{
fmpz_poly_lcm(t, r, fmpz_poly_q_denref(
(fmpz_poly_q_struct *) mat_entry(M, i, j, ctxFracQt)));
fmpz_poly_swap(r, t);
}
fmpz_poly_clear(t);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Gauss-Manin connection:\n");
printf(" r(t) = "), fmpz_poly_print_pretty(r, "t"), printf("\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
{
qadic_t t;
qadic_init2(t, 1);
fmpz_poly_evaluate_qadic(t, r, t1, Qq);
if (qadic_is_zero(t))
{
printf("Exception (deformation_frob).\n");
printf("The resultant r evaluates to zero (mod p) at t1.\n");
abort();
}
qadic_clear(t);
}
/* Precisions ************************************************************/
if (prec_in != NULL)
{
*prec = *prec_in;
}
else
{
deformation_precisions(prec, p, a, n, d, fmpz_poly_degree(r));
}
if (verbose)
{
printf("Precisions:\n");
printf(" N0 = %ld\n", prec->N0);
printf(" N1 = %ld\n", prec->N1);
printf(" N2 = %ld\n", prec->N2);
printf(" N3 = %ld\n", prec->N3);
printf(" N3i = %ld\n", prec->N3i);
printf(" N3w = %ld\n", prec->N3w);
printf(" N3iw = %ld\n", prec->N3iw);
printf(" N4 = %ld\n", prec->N4);
printf(" m = %ld\n", prec->m);
printf(" K = %ld\n", prec->K);
printf(" r = %ld\n", prec->r);
printf(" s = %ld\n", prec->s);
printf("\n");
fflush(stdout);
}
/* Initialisation ********************************************************/
padic_mat_init2(F0, b, b, prec->N4);
fmpz_poly_mat_init(C, b, b);
fmpz_poly_mat_init(Cinv, b, b);
fmpz_poly_mat_init(F, b, b);
vF = 0;
fmpz_poly_mat_init(F1, b, b);
vF1 = 0;
fmpz_poly_init(cp);
/* Step 2 {F0} ***********************************************************/
{
padic_ctx_t pctx_F0;
fmpz *t;
padic_ctx_init(pctx_F0, p, FLINT_MIN(prec->N4 - 10, 0), prec->N4, PADIC_VAL_UNIT);
t = _fmpz_vec_init(n + 1);
c0 = clock();
mpoly_diagonal_fibre(t, P, ctxFracQt);
diagfrob(F0, t, n, d, prec->N4, pctx_F0, 0);
padic_mat_transpose(F0, F0);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Diagonal fibre:\n");
printf(" P(0) = {"), _fmpz_vec_print(t, n + 1), printf("}\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
_fmpz_vec_clear(t, n + 1);
padic_ctx_clear(pctx_F0);
}
/* Step 3 {C, Cinv} ******************************************************/
/*
Compute C as a matrix over Z_p[[t]]. A is the same but as a series
of matrices over Z_p. Mt is the matrix -M^t, and Cinv is C^{-1}^t,
the local solution of the differential equation replacing M by Mt.
*/
c0 = clock();
{
const long K = prec->K;
padic_mat_struct *A;
gmde_solve(&A, K, p, prec->N3, prec->N3w, M, ctxFracQt);
gmde_convert_soln(C, &vC, A, K, p);
for(i = 0; i < K; i++)
padic_mat_clear(A + i);
free(A);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Local solution:\n");
printf(" Time for C = %f\n", c);
fflush(stdout);
}
c0 = clock();
{
const long K = (prec->K + (*p) - 1) / (*p);
mat_t Mt;
padic_mat_struct *Ainv;
mat_init(Mt, b, b, ctxFracQt);
mat_transpose(Mt, M, ctxFracQt);
mat_neg(Mt, Mt, ctxFracQt);
gmde_solve(&Ainv, K, p, prec->N3i, prec->N3iw, Mt, ctxFracQt);
gmde_convert_soln(Cinv, &vCinv, Ainv, K, p);
fmpz_poly_mat_transpose(Cinv, Cinv);
fmpz_poly_mat_compose_pow(Cinv, Cinv, *p);
for(i = 0; i < K; i++)
padic_mat_clear(Ainv + i);
free(Ainv);
mat_clear(Mt, ctxFracQt);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf(" Time for C^{-1} = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 4 {F(t) := C(t) F(0) C(t^p)^{-1}} ********************************/
/*
Computes the product C(t) F(0) C(t^p)^{-1} modulo (p^{N_2}, t^K).
This is done by first computing the unit part of the product
exactly over the integers modulo t^K.
*/
c0 = clock();
{
fmpz_t pN;
fmpz_poly_mat_t T;
fmpz_init(pN);
fmpz_poly_mat_init(T, b, b);
for (i = 0; i < b; i++)
{
/* Find the unique k s.t. F0(i,k) is non-zero */
for (k = 0; k < b; k++)
if (!fmpz_is_zero(padic_mat_entry(F0, i, k)))
break;
if (k == b)
{
printf("Exception (frob). F0 is singular.\n\n");
abort();
}
for (j = 0; j < b; j++)
{
fmpz_poly_scalar_mul_fmpz(fmpz_poly_mat_entry(T, i, j),
fmpz_poly_mat_entry(Cinv, k, j),
padic_mat_entry(F0, i, k));
}
}
fmpz_poly_mat_mul(F, C, T);
fmpz_poly_mat_truncate(F, prec->K);
vF = vC + padic_mat_val(F0) + vCinv;
/* Canonicalise (F, vF) */
{
long v = fmpz_poly_mat_ord_p(F, p);
if (v == LONG_MAX)
{
printf("ERROR (deformation_frob). F(t) == 0.\n");
abort();
}
else if (v > 0)
{
fmpz_pow_ui(pN, p, v);
fmpz_poly_mat_scalar_divexact_fmpz(F, F, pN);
vF = vF + v;
}
}
/* Reduce (F, vF) modulo p^{N2} */
fmpz_pow_ui(pN, p, prec->N2 - vF);
fmpz_poly_mat_scalar_mod_fmpz(F, F, pN);
fmpz_clear(pN);
fmpz_poly_mat_clear(T);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Matrix for F(t):\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 5 {G = r(t)^m F(t)} **********************************************/
c0 = clock();
{
fmpz_t pN;
fmpz_poly_t t;
fmpz_init(pN);
fmpz_poly_init(t);
fmpz_pow_ui(pN, p, prec->N2 - vF);
/* Compute r(t)^m mod p^{N2-vF} */
if (prec->denR == NULL)
{
fmpz_mod_poly_t _t;
fmpz_mod_poly_init(_t, pN);
fmpz_mod_poly_set_fmpz_poly(_t, r);
fmpz_mod_poly_pow(_t, _t, prec->m);
fmpz_mod_poly_get_fmpz_poly(t, _t);
fmpz_mod_poly_clear(_t);
}
else
{
/* TODO: We don't really need a copy */
fmpz_poly_set(t, prec->denR);
}
fmpz_poly_mat_scalar_mul_fmpz_poly(F, F, t);
fmpz_poly_mat_scalar_mod_fmpz(F, F, pN);
/* TODO: This should not be necessary? */
fmpz_poly_mat_truncate(F, prec->K);
fmpz_clear(pN);
fmpz_poly_clear(t);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Analytic continuation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Steps 6 and 7 *********************************************************/
if (a == 1)
{
/* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/
c0 = clock();
{
const long N = prec->N2 - vF;
fmpz_t f, g, t, pN;
fmpz_init(f);
fmpz_init(g);
fmpz_init(t);
fmpz_init(pN);
fmpz_pow_ui(pN, p, N);
/* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */
_padic_teichmuller(f, t1->coeffs + 0, p, N);
if (prec->denR == NULL)
{
_fmpz_mod_poly_evaluate_fmpz(g, r->coeffs, r->length, f, pN);
fmpz_powm_ui(t, g, prec->m, pN);
}
else
{
_fmpz_mod_poly_evaluate_fmpz(t, prec->denR->coeffs, prec->denR->length, f, pN);
}
_padic_inv(g, t, p, N);
/* F1 := g G(\hat{t_1}) */
for (i = 0; i < b; i++)
for (j = 0; j < b; j++)
{
const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j);
const long len = poly->length;
if (len == 0)
{
fmpz_poly_zero(fmpz_poly_mat_entry(F1, i, j));
}
else
{
fmpz_poly_fit_length(fmpz_poly_mat_entry(F1, i, j), 1);
_fmpz_mod_poly_evaluate_fmpz(t, poly->coeffs, len, f, pN);
fmpz_mul(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, g, t);
fmpz_mod(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0,
fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, pN);
_fmpz_poly_set_length(fmpz_poly_mat_entry(F1, i, j), 1);
_fmpz_poly_normalise(fmpz_poly_mat_entry(F1, i, j));
}
}
vF1 = vF;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(f);
fmpz_clear(g);
fmpz_clear(t);
fmpz_clear(pN);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Evaluation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
}
else
{
/* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/
c0 = clock();
{
const long N = prec->N2 - vF;
fmpz_t pN;
fmpz *f, *g, *t;
fmpz_init(pN);
f = _fmpz_vec_init(a);
g = _fmpz_vec_init(2 * a - 1);
t = _fmpz_vec_init(2 * a - 1);
fmpz_pow_ui(pN, p, N);
/* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */
_qadic_teichmuller(f, t1->coeffs, t1->length, Qq->a, Qq->j, Qq->len, p, N);
if (prec->denR == NULL)
{
fmpz_t e;
fmpz_init_set_ui(e, prec->m);
_fmpz_mod_poly_compose_smod(g, r->coeffs, r->length, f, a,
Qq->a, Qq->j, Qq->len, pN);
_qadic_pow(t, g, a, e, Qq->a, Qq->j, Qq->len, pN);
fmpz_clear(e);
}
else
{
_fmpz_mod_poly_reduce(prec->denR->coeffs, prec->denR->length, Qq->a, Qq->j, Qq->len, pN);
_fmpz_poly_normalise(prec->denR);
_fmpz_mod_poly_compose_smod(t, prec->denR->coeffs, prec->denR->length, f, a,
Qq->a, Qq->j, Qq->len, pN);
}
_qadic_inv(g, t, a, Qq->a, Qq->j, Qq->len, p, N);
/* F1 := g G(\hat{t_1}) */
for (i = 0; i < b; i++)
for (j = 0; j < b; j++)
{
const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j);
const long len = poly->length;
fmpz_poly_struct *poly2 = fmpz_poly_mat_entry(F1, i, j);
if (len == 0)
{
fmpz_poly_zero(poly2);
}
else
{
_fmpz_mod_poly_compose_smod(t, poly->coeffs, len, f, a,
Qq->a, Qq->j, Qq->len, pN);
fmpz_poly_fit_length(poly2, 2 * a - 1);
_fmpz_poly_mul(poly2->coeffs, g, a, t, a);
_fmpz_mod_poly_reduce(poly2->coeffs, 2 * a - 1, Qq->a, Qq->j, Qq->len, pN);
_fmpz_poly_set_length(poly2, a);
_fmpz_poly_normalise(poly2);
}
}
/* Now the matrix for p^{-1} F_p at t=t_1 is (F1, vF1). */
vF1 = vF;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(pN);
_fmpz_vec_clear(f, a);
_fmpz_vec_clear(g, 2 * a - 1);
_fmpz_vec_clear(t, 2 * a - 1);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Evaluation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 7 {Norm} *****************************************************/
/*
Computes the matrix for $q^{-1} F_q$ at $t = t_1$ as the
product $F \sigma(F) \dotsm \sigma^{a-1}(F)$ up appropriate
transpositions because our convention of columns vs rows is
the opposite of that used by Gerkmann.
Note that, in any case, transpositions do not affect
the characteristic polynomial.
*/
c0 = clock();
{
const long N = prec->N1 - a * vF1;
fmpz_t pN;
fmpz_poly_mat_t T;
fmpz_init(pN);
fmpz_poly_mat_init(T, b, b);
fmpz_pow_ui(pN, p, N);
fmpz_poly_mat_frobenius(T, F1, 1, p, N, Qq);
_qadic_mat_mul(F1, F1, T, pN, Qq);
for (i = 2; i < a; i++)
{
fmpz_poly_mat_frobenius(T, T, 1, p, N, Qq);
_qadic_mat_mul(F1, F1, T, pN, Qq);
}
vF1 = a * vF1;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(pN);
fmpz_poly_mat_clear(T);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Norm:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
}
/* Step 8 {Reverse characteristic polynomial} ****************************/
c0 = clock();
deformation_revcharpoly(cp, F1, vF1, n, d, prec->N0, prec->r, prec->s, Qq);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Reverse characteristic polynomial:\n");
printf(" p(T) = "), fmpz_poly_print_pretty(cp, "T"), printf("\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Clean up **************************************************************/
padic_mat_clear(F0);
mat_clear(M, ctxFracQt);
free(bR);
free(bC);
fmpz_poly_clear(r);
fmpz_poly_mat_clear(C);
fmpz_poly_mat_clear(Cinv);
fmpz_poly_mat_clear(F);
fmpz_poly_mat_clear(F1);
fmpz_poly_clear(cp);
}
