void _fmpq_poly_scalar_mul_fmpz(fmpz * rpoly, fmpz_t rden,
const fmpz * poly, const fmpz_t den, long len,
const fmpz_t c)
{
fmpz_t gcd; /* GCD( den, c ) */
if (fmpz_is_zero(c))
{
_fmpz_vec_zero(rpoly, len);
fmpz_one(rden);
return;
}
fmpz_init(gcd);
fmpz_one(gcd);
if (*c != 1L)
fmpz_gcd(gcd, c, den);
if (*gcd == 1L)
{
_fmpz_vec_scalar_mul_fmpz(rpoly, poly, len, c);
fmpz_set(rden, den);
}
else
{
fmpz_t c2;
fmpz_init(c2);
fmpz_divexact(c2, c, gcd);
_fmpz_vec_scalar_mul_fmpz(rpoly, poly, len, c2);
fmpz_divexact(rden, den, gcd);
fmpz_clear(c2);
}
fmpz_clear(gcd);
}
void
fmpq_poly_compose(fmpq_poly_t res,
const fmpq_poly_t poly1, const fmpq_poly_t poly2)
{
const long len1 = poly1->length;
const long len2 = poly2->length;
long lenr;
if (len1 == 0L)
{
fmpq_poly_zero(res);
return;
}
if (len1 == 1L || len2 == 0L)
{
fmpq_poly_fit_length(res, 1);
fmpz_set(res->coeffs, poly1->coeffs);
fmpz_set(res->den, poly1->den);
{
fmpz_t d;
fmpz_init(d);
fmpz_gcd(d, res->coeffs, res->den);
if (*d != 1L)
{
fmpz_divexact(res->coeffs, res->coeffs, d);
fmpz_divexact(res->den, res->den, d);
}
fmpz_clear(d);
}
_fmpq_poly_set_length(res, 1);
_fmpq_poly_normalise(res);
return;
}
lenr = (len1 - 1L) * (len2 - 1L) + 1L;
if ((res != poly1) && (res != poly2))
{
fmpq_poly_fit_length(res, lenr);
_fmpq_poly_compose(res->coeffs, res->den,
poly1->coeffs, poly1->den, len1,
poly2->coeffs, poly2->den, len2);
_fmpq_poly_set_length(res, lenr);
_fmpq_poly_normalise(res);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, lenr);
_fmpq_poly_compose(t->coeffs, t->den,
poly1->coeffs, poly1->den, len1,
poly2->coeffs, poly2->den, len2);
_fmpq_poly_set_length(t, lenr);
_fmpq_poly_normalise(t);
fmpq_poly_swap(res, t);
fmpq_poly_clear(t);
}
}
void _fmpq_poly_canonicalise(fmpz * poly, fmpz_t den, slong len)
{
if (*den == WORD(1))
return;
if (*den == WORD(-1))
{
_fmpz_vec_neg(poly, poly, len);
fmpz_one(den);
}
else if (len == 0)
{
fmpz_one(den);
}
else
{
fmpz_t gcd;
fmpz_init(gcd);
_fmpz_vec_content(gcd, poly, len);
if (*gcd != WORD(1))
fmpz_gcd(gcd, gcd, den);
if (fmpz_sgn(den) < 0)
fmpz_neg(gcd, gcd);
if (*gcd != WORD(1))
{
_fmpz_vec_scalar_divexact_fmpz(poly, poly, len, gcd);
fmpz_divexact(den, den, gcd);
}
fmpz_clear(gcd);
}
}
static void
_padic_log_bsplit(fmpz_t z, const fmpz_t y, long v, const fmpz_t p, long N)
{
fmpz_t P, B, T;
long n;
if (fmpz_fits_si(p))
n = _padic_log_bound(v, N, fmpz_get_si(p));
else
n = (N - 1) / v;
n = FLINT_MAX(n, 2);
fmpz_init(P);
fmpz_init(B);
fmpz_init(T);
_padic_log_bsplit_series(P, B, T, y, 1, n);
n = fmpz_remove(B, B, p);
fmpz_pow_ui(P, p, n);
fmpz_divexact(T, T, P);
_padic_inv(B, B, p, N);
fmpz_mul(z, T, B);
fmpz_clear(P);
fmpz_clear(B);
fmpz_clear(T);
}
void
fmpz_mat_solve_fflu_precomp(fmpz_mat_t X,
const long * perm,
const fmpz_mat_t FFLU, const fmpz_mat_t B)
{
fmpz_t T;
long i, j, k, m, n;
n = X->r;
m = X->c;
fmpz_init(T);
fmpz_mat_set_perm(X, perm, B);
for (k = 0; k < m; k++)
{
/* Fraction-free forward substitution */
for (i = 0; i < n - 1; i++)
{
for (j = i + 1; j < n; j++)
{
fmpz_mul(XX(j, k), XX(j, k), LU(i, i));
fmpz_mul(T, LU(j, i), XX(i, k));
fmpz_sub(XX(j, k), XX(j, k), T);
if (i > 0)
fmpz_divexact(XX(j, k), XX(j, k), LU(i-1, i-1));
}
}
/* Fraction-free back substitution */
for (i = n - 2; i >= 0; i--)
{
fmpz_mul(XX(i, k), XX(i, k), LU(n-1, n-1));
for (j = i + 1; j < n; j++)
{
fmpz_mul(T, XX(j, k), LU(i, j));
fmpz_sub(XX(i, k), XX(i, k), T);
}
fmpz_divexact(XX(i, k), XX(i, k), LU(i, i));
}
}
fmpz_clear(T);
}
void fmpz_poly_q_scalar_mul_si(fmpz_poly_q_t rop, const fmpz_poly_q_t op, long x)
{
fmpz_t cont, fx, gcd;
if (fmpz_poly_q_is_zero(op) || (x == 0))
{
fmpz_poly_q_zero(rop);
return;
}
if (x == 1)
{
fmpz_poly_q_set(rop, op);
return;
}
fmpz_init(cont);
fmpz_poly_content(cont, op->den);
if (fmpz_is_one(cont))
{
fmpz_poly_scalar_mul_si(rop->num, op->num, x);
fmpz_poly_set(rop->den, op->den);
fmpz_clear(cont);
return;
}
fmpz_init(fx);
fmpz_init(gcd);
fmpz_set_si(fx, x);
fmpz_gcd(gcd, cont, fx);
if (fmpz_is_one(gcd))
{
fmpz_poly_scalar_mul_si(rop->num, op->num, x);
fmpz_poly_set(rop->den, op->den);
}
else
{
fmpz_divexact(fx, fx, gcd);
fmpz_poly_scalar_mul_fmpz(rop->num, op->num, fx);
fmpz_poly_scalar_divexact_fmpz(rop->den, op->den, gcd);
}
fmpz_clear(cont);
fmpz_clear(fx);
fmpz_clear(gcd);
}
void
_fmpq_mat_get_fmpz_mat_rowwise(fmpz_mat_struct ** num, fmpz * den,
const fmpq_mat_struct ** mat, slong n)
{
fmpz_t t, lcm;
slong i, j, k;
if (fmpq_mat_is_empty(mat[0]))
return;
fmpz_init(t);
fmpz_init(lcm);
for (i = 0; i < mat[0]->r; i++)
{
/* Compute common denominator of row */
fmpz_set(lcm, fmpq_mat_entry_den(mat[0], i, 0));
for (k = 0; k < n; k++)
for (j = (k == 0); j < mat[k]->c; j++)
fmpz_lcm(lcm, lcm, fmpq_mat_entry_den(mat[k], i, j));
if (den != NULL)
fmpz_set(den + i, lcm);
for (k = 0; k < n; k++)
{
/* Rescale numerators in row */
if (fmpz_is_one(lcm))
{
for (j = 0; j < mat[k]->c; j++)
fmpz_set(fmpz_mat_entry(num[k], i, j),
fmpq_mat_entry_num(mat[k], i, j));
}
else
{
for (j = 0; j < mat[k]->c; j++)
{
fmpz_divexact(t, lcm, fmpq_mat_entry_den(mat[k], i, j));
fmpz_mul(fmpz_mat_entry(num[k], i, j),
fmpq_mat_entry_num(mat[k], i, j), t);
}
}
}
}
fmpz_clear(t);
fmpz_clear(lcm);
}
void
_fmpz_poly_pow_multinomial(fmpz * res, const fmpz * poly, long len, ulong e)
{
long k, low, rlen;
fmpz_t d, t;
fmpz * P;
rlen = (long) e * (len - 1L) + 1L;
_fmpz_vec_zero(res, rlen);
for (low = 0L; poly[low] == 0L; low++) ;
if (low == 0L)
{
P = (fmpz *) poly;
}
else
{
P = (fmpz *) poly + low;
len -= low;
res += (long) e * low;
rlen -= (long) e * low;
}
fmpz_init(d);
fmpz_init(t);
fmpz_pow_ui(res, P, e);
for (k = 1; k < rlen; k++)
{
long i, u = -k;
for (i = 1; i <= FLINT_MIN(k, len - 1); i++)
{
fmpz_mul(t, P + i, res + (k - i));
u += (long) e + 1;
if (u >= 0)
fmpz_addmul_ui(res + k, t, (ulong) u);
else
fmpz_submul_ui(res + k, t, - ((ulong) u));
}
fmpz_add(d, d, P);
fmpz_divexact(res + k, res + k, d);
}
fmpz_clear(d);
fmpz_clear(t);
}
static void
_set_vec(fmpz * rnum, fmpz_t den,
const fmpz * xnum, const fmpz * xden, slong len)
{
slong j;
fmpz_t t;
fmpz_init(t);
fmpz_one(den);
for (j = 0; j < len; j++)
fmpz_lcm(den, den, xden + j);
for (j = 0; j < len; j++)
{
fmpz_divexact(t, den, xden + j);
fmpz_mul(rnum + j, xnum + j, t);
}
fmpz_clear(t);
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("div_basecase....");
fflush(stdout);
flint_randinit(state);
/* Compare to divrem_basecase */
for (i = 0; i < 5000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, q, q2, r2;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(q, p);
fmpz_mod_poly_init(q2, p);
fmpz_mod_poly_init(r2, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1);
{
fmpz_t d;
fmpz *leadB = fmpz_mod_poly_lead(b);
fmpz_init(d);
fmpz_gcd(d, p, leadB);
while (!fmpz_is_one(d))
{
fmpz_divexact(leadB, leadB, d);
fmpz_gcd(d, p, leadB);
}
fmpz_clear(d);
}
fmpz_mod_poly_div_basecase(q, a, b);
fmpz_mod_poly_divrem_basecase(q2, r2, a, b);
result = (fmpz_mod_poly_equal(q, q2));
if (!result)
{
printf("FAIL:\n");
printf("p = "), fmpz_print(p), printf("\n\n");
printf("a = "), fmpz_mod_poly_print(a), printf("\n\n");
printf("b = "), fmpz_mod_poly_print(b), printf("\n\n");
printf("q = "), fmpz_mod_poly_print(q), printf("\n\n");
printf("q2 = "), fmpz_mod_poly_print(q2), printf("\n\n");
printf("r2 = "), fmpz_mod_poly_print(r2), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(q);
fmpz_mod_poly_clear(q2);
fmpz_mod_poly_clear(r2);
fmpz_clear(p);
}
/* Alias a and q */
for (i = 0; i < 500; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, q;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(q, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1);
{
fmpz_t d;
fmpz *leadB = fmpz_mod_poly_lead(b);
fmpz_init(d);
fmpz_gcd(d, p, leadB);
while (!fmpz_is_one(d))
{
fmpz_divexact(leadB, leadB, d);
fmpz_gcd(d, p, leadB);
}
fmpz_clear(d);
}
fmpz_mod_poly_div_basecase(q, a, b);
fmpz_mod_poly_div_basecase(a, a, b);
result = (fmpz_mod_poly_equal(q, a));
if (!result)
{
printf("FAIL:\n");
printf("p = "), fmpz_print(p), printf("\n\n");
printf("a = "), fmpz_mod_poly_print(a), printf("\n\n");
printf("b = "), fmpz_mod_poly_print(b), printf("\n\n");
printf("q = "), fmpz_mod_poly_print(q), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(q);
fmpz_clear(p);
}
/* Alias b and q */
for (i = 0; i < 500; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, q;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(q, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1);
{
fmpz_t d;
fmpz *leadB = fmpz_mod_poly_lead(b);
fmpz_init(d);
fmpz_gcd(d, p, leadB);
while (!fmpz_is_one(d))
{
fmpz_divexact(leadB, leadB, d);
fmpz_gcd(d, p, leadB);
}
fmpz_clear(d);
}
fmpz_mod_poly_div_basecase(q, a, b);
fmpz_mod_poly_div_basecase(b, a, b);
result = (fmpz_mod_poly_equal(q, b));
if (!result)
{
printf("FAIL:\n");
printf("p = "), fmpz_print(p), printf("\n\n");
printf("a = "), fmpz_mod_poly_print(a), printf("\n\n");
printf("b = "), fmpz_mod_poly_print(b), printf("\n\n");
printf("q = "), fmpz_mod_poly_print(q), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(q);
fmpz_clear(p);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("divexact....");
fflush(stdout);
for (i = 0; i < 10000 * flint_test_multiplier(); i++)
{
fmpz_t a, b, c;
mpz_t d, e, f, g;
fmpz_init(a);
fmpz_init(b);
fmpz_init(c);
mpz_init(d);
mpz_init(e);
mpz_init(f);
mpz_init(g);
fmpz_randtest(a, state, 200);
fmpz_randtest_not_zero(b, state, 200);
fmpz_mul(c, a, b);
fmpz_get_mpz(d, b);
fmpz_get_mpz(e, c);
fmpz_divexact(a, c, b);
mpz_divexact(f, e, d);
fmpz_get_mpz(g, a);
result = (mpz_cmp(f, g) == 0);
if (!result)
{
flint_printf("FAIL:\n");
gmp_printf("d = %Zd, e = %Zd, f = %Zd, g = %Zd\n", d, e, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(c);
mpz_clear(d);
mpz_clear(e);
mpz_clear(f);
mpz_clear(g);
}
/* Check aliasing of a and b */
for (i = 0; i < 10000 * flint_test_multiplier(); i++)
{
fmpz_t a, c;
mpz_t d, f, g;
fmpz_init(a);
fmpz_init(c);
mpz_init(d);
mpz_init(f);
mpz_init(g);
fmpz_randtest_not_zero(a, state, 200);
fmpz_get_mpz(d, a);
fmpz_divexact(c, a, a);
mpz_divexact(f, d, d);
fmpz_get_mpz(g, c);
result = (mpz_cmp(f, g) == 0);
if (!result)
{
flint_printf("FAIL:\n");
gmp_printf("d = %Zd, f = %Zd, g = %Zd\n", d, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(c);
mpz_clear(d);
mpz_clear(f);
mpz_clear(g);
}
/* Test aliasing of a and c */
for (i = 0; i < 10000 * flint_test_multiplier(); i++)
{
fmpz_t a, b, c;
mpz_t d, e, f, g;
fmpz_init(a);
fmpz_init(b);
fmpz_init(c);
mpz_init(d);
mpz_init(e);
mpz_init(f);
mpz_init(g);
fmpz_randtest(a, state, 200);
fmpz_randtest_not_zero(b, state, 200);
fmpz_mul(c, a, b);
fmpz_get_mpz(d, c);
fmpz_get_mpz(e, b);
fmpz_divexact(c, c, b);
mpz_divexact(f, d, e);
fmpz_get_mpz(g, c);
result = (mpz_cmp(f, g) == 0);
if (!result)
{
flint_printf("FAIL:\n");
gmp_printf("d = %Zd, e = %Zd, f = %Zd, g = %Zd\n", d, e, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(c);
mpz_clear(d);
mpz_clear(e);
mpz_clear(f);
mpz_clear(g);
}
/* Test aliasing of b and c */
for (i = 0; i < 10000 * flint_test_multiplier(); i++)
{
fmpz_t a, b, c;
mpz_t d, e, f, g;
fmpz_init(a);
fmpz_init(b);
fmpz_init(c);
mpz_init(d);
mpz_init(e);
mpz_init(f);
mpz_init(g);
fmpz_randtest(a, state, 200);
fmpz_randtest_not_zero(b, state, 200);
fmpz_mul(c, a, b);
fmpz_get_mpz(d, c);
fmpz_get_mpz(e, b);
fmpz_divexact(b, c, b);
mpz_divexact(f, d, e);
fmpz_get_mpz(g, b);
result = (mpz_cmp(f, g) == 0);
if (!result)
{
flint_printf("FAIL:\n");
gmp_printf("d = %Zd, e = %Zd, f = %Zd, g = %Zd\n", d, e, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(c);
mpz_clear(d);
mpz_clear(e);
mpz_clear(f);
mpz_clear(g);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void
_fmpz_poly_resultant(fmpz_t res, const fmpz * poly1, long len1,
const fmpz * poly2, long len2)
{
if (len2 == 1)
{
fmpz_pow_ui(res, poly2, len1 - 1);
}
else
{
fmpz_t a, b, g, h, t;
fmpz *A, *B, *W;
const long alloc = len1 + len2;
long sgn = 1;
fmpz_init(a);
fmpz_init(b);
fmpz_init(g);
fmpz_init(h);
fmpz_init(t);
A = W = _fmpz_vec_init(alloc);
B = W + len1;
_fmpz_poly_content(a, poly1, len1);
_fmpz_poly_content(b, poly2, len2);
_fmpz_vec_scalar_divexact_fmpz(A, poly1, len1, a);
_fmpz_vec_scalar_divexact_fmpz(B, poly2, len2, b);
fmpz_set_ui(g, 1);
fmpz_set_ui(h, 1);
fmpz_pow_ui(a, a, len2 - 1);
fmpz_pow_ui(b, b, len1 - 1);
fmpz_mul(t, a, b);
do
{
const long d = len1 - len2;
if (!(len1 & 1L) & !(len2 & 1L))
sgn = -sgn;
_fmpz_poly_pseudo_rem_cohen(A, A, len1, B, len2);
for (len1--; len1 >= 0 && !A[len1]; len1--) ;
len1++;
if (len1 == 0)
{
fmpz_zero(res);
goto cleanup;
}
{
fmpz * T;
long len;
T = A, A = B, B = T;
len = len1, len1 = len2, len2 = len;
}
fmpz_pow_ui(a, h, d);
fmpz_mul(b, g, a);
_fmpz_vec_scalar_divexact_fmpz(B, B, len2, b);
fmpz_pow_ui(g, A + (len1 - 1), d);
fmpz_mul(b, h, g);
fmpz_divexact(h, b, a);
fmpz_set(g, A + (len1 - 1));
} while (len2 > 1);
fmpz_pow_ui(g, h, len1 - 1);
fmpz_pow_ui(b, B + (len2 - 1), len1 - 1);
fmpz_mul(a, h, b);
fmpz_divexact(h, a, g);
fmpz_mul(res, t, h);
if (sgn < 0)
fmpz_neg(res, res);
cleanup:
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(g);
fmpz_clear(h);
fmpz_clear(t);
_fmpz_vec_clear(W, alloc);
}
}
void
fmpz_holonomic_get_nth_fmpq(fmpq_t res, const fmpz_holonomic_t op, const fmpq * initial, long n0, long n)
{
long r = fmpz_holonomic_order(op);
if (r == 0)
{
fmpq_zero(res);
return;
}
else if (n < n0)
{
printf("not implemented\n");
abort();
}
else if (n - n0 < r)
{
fmpq_set(res, initial + n - n0);
return;
}
else
{
fmpz_mat_t M;
long i;
fmpz_t Q;
fmpz_mat_init(M, r, r);
fmpz_init(Q);
fmpz_holonomic_forward_fmpz_mat(M, Q, op, n0, n - n0 - r + 1);
{
fmpz_t g, t;
fmpz_init(g);
fmpz_init(t);
fmpz_one(g);
for (i = 0; i < r; i++)
fmpz_lcm(g, g, fmpq_denref(initial + i));
fmpz_divexact(t, g, fmpq_denref(initial + 0));
fmpz_mul(t, t, fmpq_numref(initial + 0));
fmpz_mul(fmpz_mat_entry(M, r - 1, 0), fmpz_mat_entry(M, r - 1, 0), t);
for (i = 1; i < r; i++)
{
fmpz_divexact(t, g, fmpq_denref(initial + i));
fmpz_mul(t, t, fmpq_numref(initial + i));
fmpz_addmul(fmpz_mat_entry(M, r - 1, 0), fmpz_mat_entry(M, r - 1, i), t);
}
fmpz_set(fmpq_numref(res), fmpz_mat_entry(M, r - 1, 0));
fmpz_mul(fmpq_denref(res), Q, g);
fmpq_canonicalise(res);
fmpz_clear(g);
fmpz_clear(t);
}
fmpz_mat_clear(M);
fmpz_clear(Q);
}
}
void
_fmpq_sub(fmpz_t rnum, fmpz_t rden, const fmpz_t p, const fmpz_t q,
const fmpz_t r, const fmpz_t s)
{
fmpz_t g, a, b, t, u;
/* Same denominator */
if (fmpz_equal(q, s))
{
fmpz_sub(rnum, p, r);
/* Both are integers */
if (fmpz_is_one(q))
{
fmpz_set(rden, q);
}
else
{
fmpz_init(g);
fmpz_gcd(g, rnum, q);
if (fmpz_is_one(g))
{
fmpz_set(rden, q);
}
else
{
fmpz_divexact(rnum, rnum, g);
fmpz_divexact(rden, q, g);
}
fmpz_clear(g);
}
return;
}
/* p/q is an integer */
if (fmpz_is_one(q))
{
fmpz_init(t);
fmpz_mul(t, p, s);
fmpz_sub(rnum, t, r);
fmpz_set(rden, s);
fmpz_clear(t);
return;
}
/* r/s is an integer */
if (fmpz_is_one(s))
{
fmpz_init(t);
fmpz_mul(t, r, q);
fmpz_sub(rnum, p, t);
fmpz_set(rden, q);
fmpz_clear(t);
return;
}
fmpz_init(g);
fmpz_gcd(g, q, s);
if (fmpz_is_one(g))
{
fmpz_init(t);
fmpz_init(u);
fmpz_mul(t, p, s);
fmpz_mul(u, q, r);
fmpz_sub(rnum, t, u);
fmpz_mul(rden, q, s);
fmpz_clear(t);
fmpz_clear(u);
}
else
{
fmpz_init(a);
fmpz_init(b);
fmpz_init(t);
fmpz_init(u);
fmpz_divexact(a, q, g);
fmpz_divexact(b, s, g);
fmpz_mul(t, p, b);
fmpz_mul(u, r, a);
fmpz_sub(rnum, t, u);
fmpz_gcd(t, rnum, g);
if (fmpz_is_one(t))
{
fmpz_mul(rden, q, b);
}
else
{
fmpz_divexact(rnum, rnum, t);
fmpz_divexact(g, q, t);
fmpz_mul(rden, g, b);
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(t);
fmpz_clear(u);
}
fmpz_clear(g);
}
void eis_series(fmpz_poly_t *eis, ulong k, ulong prec)
{
ulong i, p, ee, p_pow, ind;
fmpz_t last, last_m1, mult, fp, t_coeff, term, term_m1;
long bern_fac[15] = {0, 0, 0, 0, 240, 0, -504, 0, 480, 0, -264, 0, 0, 0, -24};
// Now, we compute the eisenstein series
// First, compute primes by sieving.
// allocate memory for the array.
/*
char *primes;
primes = calloc(prec + 1, sizeof(char));
for(i = 0; i <= prec; i++) {
primes[i] = 1;
}
primes[0] = 0;
primes[1] = 0;
p = 2;
while(p*p <= prec) {
j = p*p;
while(j <= prec) {
primes[j] = 0;
j += p;
}
p += 1;
while(primes[p] != 1)
p += 1;
}
*/
// Now, create the eisenstein series.
// We build up each coefficient using the multiplicative properties of the
// divisor sum function.
fmpz_poly_set_coeff_si(*eis, 0, 1);
for(i = 1; i <= prec; i++)
fmpz_poly_set_coeff_si(*eis, i, bern_fac[k]);
fmpz_init(last);
fmpz_init(last_m1);
fmpz_init(mult);
fmpz_init(fp);
fmpz_init(t_coeff);
fmpz_init(term);
fmpz_init(term_m1);
ee = k - 1;
p = 2;
while(p <= prec) {
p_pow = p;
fmpz_set_ui(fp, p);
fmpz_pow_ui(mult, fp, ee);
fmpz_pow_ui(term, mult, 2);
fmpz_set(last, mult);
while(p_pow <= prec) {
ind = p_pow;
fmpz_sub_ui(term_m1, term, 1);
fmpz_sub_ui(last_m1, last, 1);
while(ind <= prec) {
fmpz_poly_get_coeff_fmpz(t_coeff, *eis, ind);
fmpz_mul(t_coeff, t_coeff, term_m1);
fmpz_divexact(t_coeff, t_coeff, last_m1);
fmpz_poly_set_coeff_fmpz(*eis, ind, t_coeff);
ind += p_pow;
}
p_pow *= p;
fmpz_set(last, term);
fmpz_mul(term, term, mult);
}
p = n_nextprime(p, 1);
}
fmpz_clear(last);
fmpz_clear(last_m1);
fmpz_clear(mult);
fmpz_clear(fp);
fmpz_clear(t_coeff);
fmpz_clear(term);
fmpz_clear(term_m1);
}
void nf_elem_rep_mat_fmpz_mat_den(fmpz_mat_t res, fmpz_t den, const nf_elem_t a, const nf_t nf)
{
if (nf->flag & NF_LINEAR)
{
fmpz_set(fmpz_mat_entry(res, 0, 0), LNF_ELEM_NUMREF(a));
fmpz_set(den, LNF_ELEM_DENREF(a));
}
else if (nf->flag & NF_QUADRATIC)
{
nf_elem_t t;
const fmpz * const anum = QNF_ELEM_NUMREF(a);
const fmpz * const aden = QNF_ELEM_DENREF(a);
fmpz * const tnum = QNF_ELEM_NUMREF(t);
fmpz * const tden = QNF_ELEM_DENREF(t);
nf_elem_init(t, nf);
nf_elem_mul_gen(t, a, nf);
if (fmpz_equal(tden, aden))
{
fmpz_set(fmpz_mat_entry(res, 0, 0), anum);
fmpz_set(fmpz_mat_entry(res, 0, 1), anum + 1);
fmpz_set(fmpz_mat_entry(res, 1, 0), tnum);
fmpz_set(fmpz_mat_entry(res, 1, 1), tnum + 1);
fmpz_set(den, tden);
}
else
{
fmpz_lcm(den, tden, aden);
fmpz_divexact(fmpz_mat_entry(res, 0, 0), den, aden);
fmpz_mul(fmpz_mat_entry(res, 0, 1), anum + 1, fmpz_mat_entry(res, 0, 0));
fmpz_mul(fmpz_mat_entry(res, 0, 0), anum, fmpz_mat_entry(res, 0, 0));
fmpz_divexact(fmpz_mat_entry(res, 1, 0), den, tden);
fmpz_mul(fmpz_mat_entry(res, 1, 1), tnum + 1, fmpz_mat_entry(res, 1, 0));
fmpz_mul(fmpz_mat_entry(res, 1, 0), tnum, fmpz_mat_entry(res, 1, 0));
}
nf_elem_clear(t, nf);
}
else
{
slong i, j;
nf_elem_t t;
slong d = fmpq_poly_degree(nf->pol);
nf_elem_init(t, nf);
nf_elem_set(t, a, nf);
if (NF_ELEM(a)->length == 0)
{
fmpz_mat_zero(res);
fmpz_one(den);
}
else if (NF_ELEM(a)->length == 1)
{
fmpz_mat_zero(res);
for (i = 0; i <= d - 1; i++)
{
fmpz_set(fmpz_mat_entry(res, i, i), fmpq_poly_numref(NF_ELEM(a)));
}
fmpz_set(den, fmpq_poly_denref(NF_ELEM(a)));
}
else
{
/* Special case if defining polynomial is monic and integral and the element also has trivial denominator */
if (nf->flag & NF_MONIC && fmpz_is_one(fmpq_poly_denref(nf->pol)) && fmpz_is_one(fmpq_poly_denref(NF_ELEM(a))))
{
fmpz_one(den);
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, 0, i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, 0, i));
for (j = 1; j <= d - NF_ELEM(a)->length; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i < j; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, j + i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = j + NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
}
for (j = d - NF_ELEM(a)->length + 1; j <= d - 1; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i <= d - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, i), fmpq_poly_numref(NF_ELEM(t)) + i);
}
}
else
{
/* Now the general case. For 0 <= j < d - 2 we store the
* denominator for row j at res[d - 1, j]. At the end we
* divide the lcm of all of them by the corresponding
* denominator of the row to get the correct multiplier for
* row.
*/
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, 0, i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, 0, i));
fmpz_set(fmpz_mat_entry(res, d - 1, 0), fmpq_poly_denref(NF_ELEM(a)));
for (j = 1; j <= d - NF_ELEM(a)->length; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i < j; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, j + i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = j + NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
fmpz_set(fmpz_mat_entry(res, d - 1, j), fmpq_poly_denref(NF_ELEM(a)));
}
for (j = d - NF_ELEM(a)->length + 1; j <= d - 2; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i <= d - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, i), fmpq_poly_numref(NF_ELEM(t)) + i);
fmpz_set(fmpz_mat_entry(res, d - 1, j), fmpq_poly_denref(NF_ELEM(t)));
}
nf_elem_mul_gen(t, t, nf);
/* Now compute the correct denominator */
fmpz_set(fmpz_mat_entry(res, d - 1, d - 1), fmpq_poly_denref(NF_ELEM(t)));
fmpz_set(den, fmpq_poly_denref(NF_ELEM(t)));
for (j = 0; j <= d - 2; j++)
fmpz_lcm(den, den, fmpz_mat_entry(res, d - 1, j));
for (j = 0; j <= d - 2; j++)
{
if (!fmpz_equal(den, fmpz_mat_entry(res, d - 1, j)))
{
fmpz_divexact(fmpz_mat_entry(res, d - 1, j), den, fmpz_mat_entry(res, d - 1, j));
for (i = 0; i <= d - 1; i++)
fmpz_mul(fmpz_mat_entry(res, j, i), fmpz_mat_entry(res, j, i), fmpz_mat_entry(res, d - 1, j));
}
}
if (fmpz_equal(den, fmpz_mat_entry(res, d - 1, d - 1)))
{
for (i = 0; i < d; i++)
fmpz_set(fmpz_mat_entry(res, d - 1, i), fmpq_poly_numref(NF_ELEM(t)) + i);
}
else
{
fmpz_divexact(fmpz_mat_entry(res, d - 1, d - 1), den, fmpq_poly_denref(NF_ELEM(t)));
for (i = 0; i < d; i++)
fmpz_mul(fmpz_mat_entry(res, d - 1, i), fmpq_poly_numref(NF_ELEM(t)) + i, fmpz_mat_entry(res, d - 1, d - 1));
}
}
}
nf_elem_clear(t, nf);
}
}
void
_fmpq_mul(fmpz_t rnum, fmpz_t rden, const fmpz_t op1num, const fmpz_t op1den,
const fmpz_t op2num, const fmpz_t op2den)
{
/* Common special cases: squaring, same denominator (e.g. both integers) */
if (((op1num == op2num) && (op1den == op2den)) ||
fmpz_equal(op1den, op2den))
{
fmpz_mul(rnum, op1num, op2num);
fmpz_mul(rden, op1den, op2den);
}
/* Exactly one argument is an integer */
else if (fmpz_is_one(op1den))
{
fmpz_t t, x;
fmpz_init(t);
fmpz_init(x);
fmpz_gcd(t, op1num, op2den);
fmpz_divexact(x, op1num, t);
fmpz_mul(rnum, x, op2num);
fmpz_divexact(t, op2den, t);
fmpz_mul(rden, op1den, t);
fmpz_clear(t);
fmpz_clear(x);
}
else if (fmpz_is_one(op2den))
{
fmpz_t t, x;
fmpz_init(t);
fmpz_init(x);
fmpz_gcd(t, op2num, op1den);
fmpz_divexact(x, op2num, t);
fmpz_mul(rnum, x, op1num);
fmpz_divexact(t, op1den, t);
fmpz_mul(rden, op2den, t);
fmpz_clear(t);
fmpz_clear(x);
}
else
{
fmpz_t t, u, x, y;
fmpz_init(t);
fmpz_init(u);
fmpz_init(x);
fmpz_init(y);
fmpz_gcd(t, op1num, op2den);
fmpz_gcd(u, op1den, op2num);
fmpz_divexact(x, op1num, t);
fmpz_divexact(y, op2num, u);
fmpz_mul(rnum, x, y);
fmpz_divexact(x, op1den, u);
fmpz_divexact(y, op2den, t);
fmpz_mul(rden, x, y);
fmpz_clear(t);
fmpz_clear(u);
fmpz_clear(x);
fmpz_clear(y);
}
}
void precompute_muex(fmpz **mu, long M,
const long **C, const long *lenC,
const fmpz *a, long n, long p, long N)
{
const long ve = (p == 2) ? M / 4 + 1 : M / (p * (p - 1)) + 1;
fmpz_t P, pNe, pe;
fmpz_t apow, f, g, h;
fmpz *nu;
long *v;
long i, j;
fmpz_init_set_ui(P, p);
fmpz_init(pNe);
fmpz_init(pe);
fmpz_pow_ui(pNe, P, N + ve);
fmpz_pow_ui(pe, P, ve);
fmpz_init(apow);
fmpz_init(f);
fmpz_init(g);
fmpz_init(h);
/* Precompute $(l!)^{-1}$ */
nu = _fmpz_vec_init(M + 1);
v = malloc((M + 1) * sizeof(long));
{
long *D, lenD = 0, k = 0;
for (i = 0; i <= n; i++)
lenD += lenC[i];
D = malloc(lenD * sizeof(long));
for (i = 0; i <= n; i++)
for (j = 0; j < lenC[i]; j++)
D[k++] = C[i][j];
_remove_duplicates(D, &lenD);
_sort(D, lenD);
precompute_nu(nu, v, M, D, lenD, p, N + ve);
free(D);
}
for (i = 0; i <= n; i++)
{
long m = -1, quo, idx, w;
fmpz *z;
/* Set apow = a[i]^{-(p-1)} mod p^N */
fmpz_invmod(apow, a + i, pNe);
fmpz_powm_ui(apow, apow, p - 1, pNe);
/*
Run over all relevant m in [0, M].
Note that lenC[i] > 0 for all i.
*/
for (quo = 0; m <= M; quo++)
{
for (idx = 0; idx < lenC[i]; idx++)
{
m = quo * p + C[i][idx];
if (m > M)
break;
/*
Note that $\mu_m$ is equal to
$\sum_{k=0}^{\floor{m/p}} p^{\floor{m/p}-k}\nu_{m-pk}\nu_k$
where $\nu_i$ denotes the number with unit part nu[i]
and valuation v[i].
*/
w = (p == 2) ? (3 * m) / 4 - (m == 3 || m == 7) : m / p;
z = mu[i] + lenC[i] * quo + idx;
fmpz_zero(z);
fmpz_one(h);
for (j = 0; j <= m / p; j++)
{
fmpz_pow_ui(f, P, ve + w - j + v[m - p*j] + v[j]);
fmpz_mul(g, nu + (m - p*j), nu + j);
fmpz_mul(f, f, g);
fmpz_mul(f, f, h);
fmpz_add(z, z, f);
fmpz_mod(z, z, pNe);
/* Set h = a[i]^{- (j+1)(p-1)} mod p^{N+e} */
fmpz_mul(h, h, apow);
fmpz_mod(h, h, pNe);
}
fmpz_divexact(z, z, pe);
}
}
}
fmpz_clear(P);
fmpz_clear(pNe);
fmpz_clear(pe);
fmpz_clear(apow);
fmpz_clear(f);
fmpz_clear(g);
fmpz_clear(h);
_fmpz_vec_clear(nu, M + 1);
free(v);
}
void _nf_elem_sub_qf(nf_elem_t a, const nf_elem_t b,
const nf_elem_t c, const nf_t nf, int can)
{
fmpz_t d;
const fmpz * const bnum = QNF_ELEM_NUMREF(b);
const fmpz * const bden = QNF_ELEM_DENREF(b);
const fmpz * const cnum = QNF_ELEM_NUMREF(c);
const fmpz * const cden = QNF_ELEM_DENREF(c);
fmpz * const anum = QNF_ELEM_NUMREF(a);
fmpz * const aden = QNF_ELEM_DENREF(a);
fmpz_init(d);
fmpz_one(d);
if (fmpz_equal(bden, cden))
{
fmpz_sub(anum, bnum, cnum);
fmpz_sub(anum + 1, bnum + 1, cnum + 1);
fmpz_sub(anum + 2, bnum + 2, cnum + 2);
fmpz_set(aden, bden);
if (can && !fmpz_is_one(aden))
{
fmpz_gcd(d, anum, anum + 1);
fmpz_gcd(d, d, anum + 2);
if (!fmpz_is_one(d))
{
fmpz_gcd(d, d, aden);
if (!fmpz_is_one(d))
{
fmpz_divexact(anum, anum, d);
fmpz_divexact(anum + 1, anum + 1, d);
fmpz_divexact(anum + 2, anum + 2, d);
fmpz_divexact(aden, aden, d);
}
}
}
fmpz_clear(d);
return;
}
if (!fmpz_is_one(bden) && !fmpz_is_one(cden))
fmpz_gcd(d, bden, cden);
if (fmpz_is_one(d))
{
fmpz_mul(anum, bnum, cden);
fmpz_mul(anum + 1, bnum + 1, cden);
fmpz_mul(anum + 2, bnum + 2, cden);
fmpz_submul(anum, cnum, bden);
fmpz_submul(anum + 1, cnum + 1, bden);
fmpz_submul(anum + 2, cnum + 2, bden);
fmpz_mul(aden, bden, cden);
} else
{
fmpz_t bden1;
fmpz_t cden1;
fmpz_init(bden1);
fmpz_init(cden1);
fmpz_divexact(bden1, bden, d);
fmpz_divexact(cden1, cden, d);
fmpz_mul(anum, bnum, cden1);
fmpz_mul(anum + 1, bnum + 1, cden1);
fmpz_mul(anum + 2, bnum + 2, cden1);
fmpz_submul(anum, cnum, bden1);
fmpz_submul(anum + 1, cnum + 1, bden1);
fmpz_submul(anum + 2, cnum + 2, bden1);
if (fmpz_is_zero(anum) && fmpz_is_zero(anum + 1) && fmpz_is_zero(anum + 2))
fmpz_one(aden);
else
{
if (can)
{
fmpz_t e;
fmpz_init(e);
fmpz_gcd(e, anum, anum + 1);
fmpz_gcd(e, e, anum + 2);
if (!fmpz_is_one(e))
fmpz_gcd(e, e, d);
if (fmpz_is_one(e))
fmpz_mul(aden, bden, cden1);
else
{
fmpz_divexact(anum, anum, e);
fmpz_divexact(anum + 1, anum + 1, e);
fmpz_divexact(anum + 2, anum + 2, e);
fmpz_divexact(bden1, bden, e);
fmpz_mul(aden, bden1, cden1);
}
fmpz_clear(e);
} else
fmpz_mul(aden, bden, cden1);
}
fmpz_clear(bden1);
fmpz_clear(cden1);
}
fmpz_clear(d);
}
void _fmpz_poly_signature(long * r1, long * r2, fmpz * poly, long len)
{
fmpz *A, *B, *f, *g, *h, *w;
long lenA, lenB;
int s, t;
if (len <= 2)
{
*r1 = (len == 2);
*r2 = 0;
return;
}
w = _fmpz_vec_init(2 * len + 2);
A = w;
B = w + len;
lenA = len;
lenB = lenA - 1;
f = w + 2 * len - 1;
g = w + 2 * len;
h = w + 2 * len + 1;
_fmpz_poly_primitive_part(A, poly, lenA);
_fmpz_poly_derivative(B, A, lenA);
_fmpz_poly_primitive_part(B, B, lenB);
fmpz_one(g);
fmpz_one(h);
s = 1;
t = (lenA & 1L) ? -s : s;
*r1 = 1;
while (1)
{
long delta = lenA - lenB;
int sgnA;
_fmpz_poly_pseudo_rem_cohen(A, A, lenA, B, lenB);
lenA = lenB;
FMPZ_VEC_NORM(A, lenA);
if (lenA == 0)
{
printf("Exception: non-squarefree polynomial detected in fmpz_poly_signature\n");
_fmpz_vec_clear(w, 2 * len + 2);
abort();
}
if ((fmpz_sgn(B + (lenB - 1)) > 0) || (delta & 1L))
_fmpz_vec_neg(A, A, lenA);
sgnA = fmpz_sgn(A + (lenA - 1));
if (sgnA != s)
{
s = -s;
(*r1)--;
}
if (sgnA != ((lenA & 1L) ? t : -t))
{
t = -t;
(*r1)++;
}
if (lenA == 1)
{
*r2 = ((len - 1) - *r1) / 2;
_fmpz_vec_clear(w, 2 * len + 2);
return;
}
else
{
{
fmpz * temp = A;
A = B;
B = temp;
}
{
long temp = lenA;
lenA = lenB;
lenB = temp;
}
if (delta == 1)
{
fmpz_mul(f, g, h);
_fmpz_vec_scalar_divexact_fmpz(B, B, lenB, f);
fmpz_set(g, A + (lenA - 1));
fmpz_set(h, g);
}
else
{
fmpz_pow_ui(f, h, delta);
fmpz_mul(f, f, g);
_fmpz_vec_scalar_divexact_fmpz(B, B, lenB, f);
fmpz_pow_ui(f, h, delta - 1);
fmpz_pow_ui(g, A + (lenA - 1), delta);
fmpz_divexact(h, g, f);
fmpz_set(g, A + (lenA - 1));
}
}
}
}
void
fmpq_poly_compose_series_horner(fmpq_poly_t res,
const fmpq_poly_t poly1, const fmpq_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: fmpq_poly_compose_series_horner: inner polynomial "
"must have zero constant term\n");
abort();
}
if (len1 == 0 || n == 0)
{
fmpq_poly_zero(res);
return;
}
if (len2 == 0 || len1 == 1)
{
fmpq_poly_fit_length(res, 1);
fmpz_set(res->coeffs, poly1->coeffs);
fmpz_set(res->den, poly1->den);
{
fmpz_t d;
fmpz_init(d);
fmpz_gcd(d, res->coeffs, res->den);
if (!fmpz_is_one(d))
{
fmpz_divexact(res->coeffs, res->coeffs, d);
fmpz_divexact(res->den, res->den, d);
}
fmpz_clear(d);
}
_fmpq_poly_set_length(res, 1);
_fmpq_poly_normalise(res);
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))
{
fmpq_poly_fit_length(res, lenr);
_fmpq_poly_compose_series_horner(res->coeffs, res->den,
poly1->coeffs, poly1->den, len1,
poly2->coeffs, poly2->den, len2, lenr);
_fmpq_poly_set_length(res, lenr);
_fmpq_poly_normalise(res);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, lenr);
_fmpq_poly_compose_series_horner(t->coeffs, t->den,
poly1->coeffs, poly1->den, len1,
poly2->coeffs, poly2->den, len2, lenr);
_fmpq_poly_set_length(t, lenr);
_fmpq_poly_normalise(t);
fmpq_poly_swap(res, t);
fmpq_poly_clear(t);
}
}
static void
__ramanujan_even_common_denom(fmpz * num, fmpz * den, long start, long n)
{
fmpz_t t, c, d, cden;
long j, k, m, mcase;
int prodsize;
if (start >= n)
return;
fmpz_init(t);
fmpz_init(c);
fmpz_init(d);
fmpz_init(cden);
/* Common denominator */
fmpz_primorial(cden, n + 1);
start += start % 2;
/* Convert initial values to common denominator */
for (k = 0; k < start; k += 2)
{
fmpz_divexact(t, cden, den + k);
fmpz_mul(num + k, num + k, t);
}
/* Ramanujan's recursive formula */
for (m = start; m < n; m += 2)
{
mcase = m % 6;
fmpz_mul_ui(num + m, cden, m + 3UL);
fmpz_divexact_ui(num + m, num + m, 3UL);
if (mcase == 4)
{
fmpz_neg(num + m, num + m);
fmpz_divexact_ui(num + m, num + m, 2UL);
}
/* All factors are strictly smaller than m + 4; choose prodsize such
that (m + 4)^prodsize fits in a signed long. */
{
#if FLINT64
if (m < 1444L) prodsize = 6;
else if (m < 2097148L) prodsize = 3;
else if (m < 3037000495L) prodsize = 2; /* not very likely... */
else abort();
#else
if (m < 32L) prodsize = 6;
else if (m < 1286L) prodsize = 3;
else if (m < 46336L) prodsize = 2;
else abort();
#endif
}
/* c = t = binomial(m+3, m) */
fmpz_set_ui(t, m + 1UL);
fmpz_mul_ui(t, t, m + 2UL);
fmpz_mul_ui(t, t, m + 3UL);
fmpz_divexact_ui(t, t, 6UL);
fmpz_set(c, t);
for (j = 6; j <= m; j += 6)
{
long r = m - j;
/* c = binomial(m+3, m-j); */
switch (prodsize)
{
case 2:
fmpz_mul_ui(c, c, (r+6)*(r+5));
fmpz_mul_ui(c, c, (r+4)*(r+3));
fmpz_mul_ui(c, c, (r+2)*(r+1));
fmpz_set_ui(d, (j+0)*(j+3));
fmpz_mul_ui(d, d, (j-2)*(j+2));
fmpz_mul_ui(d, d, (j-1)*(j+1));
fmpz_divexact(c, c, d);
break;
case 3:
fmpz_mul_ui(c, c, (r+6)*(r+5)*(r+4));
fmpz_mul_ui(c, c, (r+3)*(r+2)*(r+1));
fmpz_set_ui(d, (j+0)*(j+3)*(j-2));
fmpz_mul_ui(d, d, (j+2)*(j-1)*(j+1));
fmpz_divexact(c, c, d);
break;
case 6:
fmpz_mul_ui(c, c, (r+6)*(r+5)*(r+4)*(r+3)*(r+2)*(r+1));
fmpz_divexact_ui(c, c, (j+0)*(j+3)*(j-2)*(j+2)*(j-1)*(j+1));
break;
}
fmpz_submul(num + m, c, num + (m - j));
}
fmpz_divexact(num + m, num + m, t);
}
/* Convert to separate denominators */
for (k = 0; k < n; k += 2)
{
bernoulli_number_denom(den + k, k);
fmpz_divexact(t, cden, den + k);
fmpz_divexact(num + k, num + k, t);
}
fmpz_clear(t);
fmpz_clear(c);
fmpz_clear(d);
fmpz_clear(cden);
}
void _fmpq_poly_scalar_div_mpq(fmpz * rpoly, fmpz_t rden,
const fmpz * poly, const fmpz_t den, long len,
const fmpz_t r, const fmpz_t s)
{
fmpz_t gcd1; /* GCD( poly, r ) */
fmpz_t gcd2; /* GCD( s, den ) */
fmpz_init(gcd1);
fmpz_init(gcd2);
fmpz_set_ui(gcd1, 1);
fmpz_set_ui(gcd2, 1);
if (*r != 1L)
{
_fmpz_vec_content(gcd1, poly, len);
if (*gcd1 != 1L)
fmpz_gcd(gcd1, gcd1, r);
}
if (*den != 1L && *s != 1L)
fmpz_gcd(gcd2, s, den);
if (*gcd1 == 1L)
{
if (*gcd2 == 1L)
{
_fmpz_vec_scalar_mul_fmpz(rpoly, poly, len, s);
fmpz_mul(rden, den, r);
}
else
{
fmpz_t s2;
fmpz_init(s2);
fmpz_divexact(s2, s, gcd2);
_fmpz_vec_scalar_mul_fmpz(rpoly, poly, len, s2);
fmpz_divexact(rden, den, gcd2);
fmpz_mul(rden, rden, r);
fmpz_clear(s2);
}
}
else
{
fmpz_t r2;
fmpz_init(r2);
fmpz_divexact(r2, r, gcd1);
if (*gcd2 == 1L)
{
_fmpz_vec_scalar_divexact_fmpz(rpoly, poly, len, gcd1);
_fmpz_vec_scalar_mul_fmpz(rpoly, rpoly, len, s);
fmpz_mul(rden, den, r2);
}
else
{
fmpz_t s2;
fmpz_init(s2);
fmpz_divexact(s2, s, gcd2);
_fmpz_vec_scalar_divexact_fmpz(rpoly, poly, len, gcd1);
_fmpz_vec_scalar_mul_fmpz(rpoly, rpoly, len, s2);
fmpz_divexact(rden, den, gcd2);
fmpz_mul(rden, rden, r2);
fmpz_clear(s2);
}
fmpz_clear(r2);
}
if (_fmpz_vec_is_zero(rpoly, len))
fmpz_set_ui(rden, 1);
if (fmpz_sgn(rden) < 0)
{
_fmpz_vec_neg(rpoly, rpoly, len);
fmpz_neg(rden, rden);
}
fmpz_clear(gcd1);
fmpz_clear(gcd2);
}
char * _padic_get_str(char * str, const padic_t op, const padic_ctx_t ctx)
{
const fmpz * u = padic_unit(op);
const long v = padic_val(op);
if (fmpz_is_zero(u))
{
if (!str)
{
str = flint_malloc(2);
}
str[0] = '0';
str[1] = '\0';
return str;
}
if (ctx->mode == PADIC_TERSE)
{
if (v == 0)
{
str = fmpz_get_str(str, 10, u);
}
else if (v > 0)
{
fmpz_t t;
fmpz_init(t);
fmpz_pow_ui(t, ctx->p, v);
fmpz_mul(t, t, u);
str = fmpz_get_str(str, 10, t);
fmpz_clear(t);
}
else /* v < 0 */
{
fmpz_t t;
fmpz_init(t);
fmpz_pow_ui(t, ctx->p, -v);
str = _fmpq_get_str(str, 10, u, t);
fmpz_clear(t);
}
}
else if (ctx->mode == PADIC_SERIES)
{
char *s;
fmpz_t x;
fmpz_t d;
long j, N;
if (fmpz_sgn(u) < 0)
{
printf("ERROR (_padic_get_str). u < 0 in SERIES mode.\n");
abort();
}
N = fmpz_clog(u, ctx->p) + v;
if (!str)
{
long b = (N - v) * (2 * fmpz_sizeinbase(ctx->p, 10)
+ z_sizeinbase(FLINT_MAX(FLINT_ABS(v), FLINT_ABS(N)), 10)
+ 5) + 1;
str = flint_malloc(b);
if (!str)
{
printf("ERROR (_padic_get_str). Memory allocation failed.\n");
abort();
}
}
s = str;
fmpz_init(d);
fmpz_init(x);
fmpz_set(x, u);
/* Unroll first step */
j = 0;
{
fmpz_mod(d, x, ctx->p); /* d = u mod p^{j+1} */
fmpz_sub(x, x, d); /* x = x - d */
fmpz_divexact(x, x, ctx->p); /* x = x / p */
if (!fmpz_is_zero(d))
{
if (j + v != 0)
{
fmpz_get_str(s, 10, d);
while (*++s != '\0') ;
*s++ = '*';
fmpz_get_str(s, 10, ctx->p);
while (*++s != '\0') ;
*s++ = '^';
sprintf(s, "%ld", j + v);
while (*++s != '\0') ;
}
else
{
fmpz_get_str(s, 10, d);
while (*++s != '\0') ;
}
}
j++;
}
for ( ; !fmpz_is_zero(x); j++)
{
fmpz_mod(d, x, ctx->p); /* d = u mod p^{j+1} */
fmpz_sub(x, x, d); /* x = x - d */
fmpz_divexact(x, x, ctx->p); /* x = x / p */
if (!fmpz_is_zero(d))
{
if (j + v != 0)
{
*s++ = ' ';
*s++ = '+';
*s++ = ' ';
fmpz_get_str(s, 10, d);
while (*++s != '\0') ;
*s++ = '*';
fmpz_get_str(s, 10, ctx->p);
while (*++s != '\0') ;
*s++ = '^';
sprintf(s, "%ld", j + v);
while (*++s != '\0') ;
}
else
{
*s++ = ' ';
*s++ = '+';
*s++ = ' ';
fmpz_get_str(s, 10, d);
while (*++s != '\0') ;
}
}
}
fmpz_clear(x);
fmpz_clear(d);
}
else /* ctx->mode == PADIC_VAL_UNIT */
{
if (!str)
{
long b = fmpz_sizeinbase(u, 10) + fmpz_sizeinbase(ctx->p, 10)
+ z_sizeinbase(v, 10) + 4;
str = flint_malloc(b);
if (!str)
{
printf("ERROR (_padic_get_str). Memory allocation failed.\n");
abort();
}
}
if (v == 0)
{
str = fmpz_get_str(str, 10, u);
}
else if (v == 1)
{
char *s = str;
fmpz_get_str(s, 10, u);
while (*++s != '\0') ;
*s++ = '*';
fmpz_get_str(s, 10, ctx->p);
}
else
{
char *s = str;
fmpz_get_str(s, 10, u);
while (*++s != '\0') ;
*s++ = '*';
fmpz_get_str(s, 10, ctx->p);
while (*++s != '\0') ;
*s++ = '^';
sprintf(s, "%ld", v);
}
}
return str;
}
void
_qseive(const mp_limb_t n, const mp_limb_t B)
{
nmod_sparse_mat_t M;
mp_limb_t quad, *quads, *xs, x, i = 0, j, piB = n_prime_pi(B);
const mp_limb_t * ps = n_primes_arr_readonly(piB + 2);
const double * pinvs = n_prime_inverses_arr_readonly(piB + 2);
mzd_t *K;
/* init */
quads = (mp_limb_t *)malloc((piB + 1)*sizeof(mp_limb_t *));
xs = (mp_limb_t *)malloc((piB + 1)*sizeof(mp_limb_t *));
K = mzd_init(piB + 1, 1);
nmod_sparse_mat_init(M, piB + 1, piB + 1, 2);
printf("init done\n");
printf("using %ld primes\n", piB);
/* seive */
for (x = n_sqrt(n), i = 0; i <= piB; x++)
{
quad = x*x - n;
if (quad == 0)
continue;
for (j = 0; j < piB; j++)
n_remove2_precomp(&quad, ps[j], pinvs[j]);
if (quad == 1) /* was B-smooth */
{
quads[i] = x*x - n;
quad = x*x - n;
for (j = 0; j < piB; j++)
{
if (n_remove2_precomp(&quad, ps[j], pinvs[j]) % 2)
_nmod_sparse_mat_set_entry(M, j, i, M->row_supports[j], 1);
}
xs[i] = x;
i++;
}
}
printf("data collection done\n");
n_cleanup_primes();
_bw(K, M, 1, 2, 7, 7);
printf("procesing complete\n");
mzd_print(K);
int done = 0;
for (j = 0; !done; j++)
{
fmpz_t a, b, diff, N;
fmpz_init_set_ui(a, 1);
fmpz_init_set_ui(b, 1);
fmpz_init_set_ui(N, n);
fmpz_init(diff);
for (i = 0; i < piB; i++)
{
if (mzd_read_bit(K, i, j))
{
fmpz_mul_ui(a, a, xs[i]);
fmpz_mul_ui(b, b, quads[i]);
}
}
assert(fmpz_is_square(b));
fmpz_sqrt(b, b);
if (fmpz_mod_ui(a, a, n) != fmpz_mod_ui(b, b, n) && fmpz_mod_ui(a, a, n) != n - fmpz_mod_ui(b, b, n))
{
done = 1;
fmpz_print(a);
printf("\n");
fmpz_print(b);
printf("\n");
fmpz_sub(diff, a, b);
fmpz_gcd(a, diff, N);
fmpz_divexact(b, N, a);
fmpz_print(a);
printf("\n");
fmpz_print(b);
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(N);
fmpz_clear(diff);
}
/* cleanup */
free(quads);
free(xs);
mzd_free(K);
nmod_sparse_mat_clear(M);
return;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("divrem_f....");
fflush(stdout);
/* Check q*b + r = a when gcd(lead(B),p) = 1, no aliasing */
for (i = 0; i < 5000; i++)
{
fmpz_t f, p;
fmpz_mod_poly_t a, b, q, r, t;
fmpz_init(f);
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(q, p);
fmpz_mod_poly_init(r, p);
fmpz_mod_poly_init(t, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1);
{
fmpz_t d;
fmpz *leadB = fmpz_mod_poly_lead(b);
fmpz_init(d);
fmpz_gcd(d, p, leadB);
while (!fmpz_is_one(d))
{
fmpz_divexact(leadB, leadB, d);
fmpz_gcd(d, p, leadB);
}
fmpz_clear(d);
}
fmpz_mod_poly_divrem_f(f, q, r, a, b);
fmpz_mod_poly_mul(t, q, b);
fmpz_mod_poly_add(t, t, r);
result = (fmpz_is_one(f) && fmpz_mod_poly_equal(a, t));
if (!result)
{
flint_printf("FAIL (divrem):\n");
flint_printf("p = "), fmpz_print(p), flint_printf("\n\n");
flint_printf("f = "), fmpz_print(f), flint_printf("\n\n");
flint_printf("a = "), fmpz_mod_poly_print(a), flint_printf("\n\n");
flint_printf("b = "), fmpz_mod_poly_print(b), flint_printf("\n\n");
flint_printf("q = "), fmpz_mod_poly_print(q), flint_printf("\n\n");
flint_printf("r = "), fmpz_mod_poly_print(r), flint_printf("\n\n");
flint_printf("t = "), fmpz_mod_poly_print(t), flint_printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(q);
fmpz_mod_poly_clear(r);
fmpz_mod_poly_clear(t);
fmpz_clear(f);
fmpz_clear(p);
}
/* Check f | p when gcd(lead(B),p) > 1 */
for (i = 0; i < 5000; i++)
{
fmpz_t f, p, q1, q2;
fmpz_mod_poly_t a, b, q, r, t;
fmpz_init(f);
fmpz_init(p);
fmpz_init(q1);
fmpz_init(q2);
fmpz_randtest_unsigned(q1, state, 2 * FLINT_BITS);
fmpz_randtest_unsigned(q2, state, 2 * FLINT_BITS);
fmpz_add_ui(q1, q1, 2);
fmpz_add_ui(q2, q2, 2);
fmpz_mul(p, q1, q2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(q, p);
fmpz_mod_poly_init(r, p);
fmpz_mod_poly_init(t, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1);
{
fmpz_t d;
fmpz *leadB = fmpz_mod_poly_lead(b);
fmpz_init(d);
fmpz_gcd(d, p, leadB);
if (fmpz_is_one(d))
fmpz_set(leadB, q1);
fmpz_clear(d);
}
fmpz_mod_poly_divrem_f(f, q, r, a, b);
fmpz_mod_poly_mul(t, q, b);
fmpz_mod_poly_add(t, t, r);
result = (fmpz_cmp_ui(f, 1) > 0 && fmpz_cmp(f, p) < 0 && fmpz_divisible(p, f));
if (!result)
{
flint_printf("FAIL (factor):\n");
flint_printf("p = "), fmpz_print(p), flint_printf("\n\n");
flint_printf("f = "), fmpz_print(f), flint_printf("\n\n");
flint_printf("q1 = "), fmpz_print(q1), flint_printf("\n\n");
flint_printf("q2 = "), fmpz_print(q2), flint_printf("\n\n");
flint_printf("a = "), fmpz_mod_poly_print(a), flint_printf("\n\n");
flint_printf("b = "), fmpz_mod_poly_print(b), flint_printf("\n\n");
flint_printf("q = "), fmpz_mod_poly_print(q), flint_printf("\n\n");
flint_printf("r = "), fmpz_mod_poly_print(r), flint_printf("\n\n");
flint_printf("t = "), fmpz_mod_poly_print(t), flint_printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(q);
fmpz_mod_poly_clear(r);
fmpz_mod_poly_clear(t);
fmpz_clear(f);
fmpz_clear(p);
fmpz_clear(q1);
fmpz_clear(q2);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void
_fmpq_poly_interpolate_fmpz_vec(fmpz * poly, fmpz_t den,
const fmpz * xs, const fmpz * ys, long n)
{
fmpz *P, *Q, *w;
fmpz_t t;
long i, j;
/* Constant */
if (n == 1)
{
fmpz_set(poly, ys);
fmpz_one(den);
return;
}
/* Linear */
if (n == 2)
{
fmpz_sub(den, xs, xs + 1);
fmpz_sub(poly + 1, ys, ys + 1);
fmpz_mul(poly, xs, ys + 1);
fmpz_submul(poly, xs + 1, ys);
return;
}
fmpz_init(t);
P = _fmpz_vec_init(n + 1);
Q = _fmpz_vec_init(n);
w = _fmpz_vec_init(n);
/* P = (x-x[0])*(x-x[1])*...*(x-x[n-1]) */
_fmpz_poly_product_roots_fmpz_vec(P, xs, n);
/* Weights */
for (i = 0; i < n; i++)
{
fmpz_one(w + i);
for (j = 0; j < n; j++)
{
if (i != j)
{
fmpz_sub(t, xs + i, xs + j);
fmpz_mul(w + i, w + i, t);
}
}
}
_fmpz_vec_zero(poly, n);
_fmpz_vec_lcm(den, w, n);
for (i = 0; i < n; i++)
{
/* Q = P / (x - x[i]) */
_fmpz_poly_div_root(Q, P, n + 1, xs + i);
/* result += Q * weight(i) */
fmpz_divexact(t, den, w + i);
fmpz_mul(t, t, ys + i);
_fmpz_vec_scalar_addmul_fmpz(poly, Q, n, t);
}
_fmpz_vec_clear(P, n + 1);
_fmpz_vec_clear(Q, n);
_fmpz_vec_clear(w, n);
fmpz_clear(t);
}
