void fmpz_poly_hensel_lift_without_inverse(fmpz_poly_t Gout, fmpz_poly_t Hout,
const fmpz_poly_t f, const fmpz_poly_t g, const fmpz_poly_t h,
const fmpz_poly_t a, const fmpz_poly_t b,
const fmpz_t p, const fmpz_t p1)
{
fmpz_poly_fit_length(Gout, g->length);
fmpz_poly_fit_length(Hout, h->length);
_fmpz_poly_set_length(Gout, g->length);
_fmpz_poly_set_length(Hout, h->length);
_fmpz_poly_hensel_lift_without_inverse(Gout->coeffs, Hout->coeffs,
f->coeffs, f->length, g->coeffs, g->length, h->coeffs, h->length,
a->coeffs, a->length, b->coeffs, b->length, p, p1);
}
void
fmpz_poly_bit_unpack_unsigned(fmpz_poly_t poly, const fmpz_t f,
mp_bitcnt_t bit_size)
{
slong len;
mpz_t tmp;
if (fmpz_sgn(f) < 0)
{
flint_printf("Exception (fmpz_poly_bit_unpack_unsigned). Expected an unsigned value.\n");
abort();
}
if (bit_size == 0 || fmpz_is_zero(f))
{
fmpz_poly_zero(poly);
return;
}
len = (fmpz_bits(f) + bit_size - 1) / bit_size;
mpz_init2(tmp, bit_size*len);
flint_mpn_zero(tmp->_mp_d, tmp->_mp_alloc);
fmpz_get_mpz(tmp, f);
fmpz_poly_fit_length(poly, len);
_fmpz_poly_bit_unpack_unsigned(poly->coeffs, len, tmp->_mp_d, bit_size);
_fmpz_poly_set_length(poly, len);
_fmpz_poly_normalise(poly);
mpz_clear(tmp);
}
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);
}
int padic_poly_get_fmpz_poly(fmpz_poly_t rop, const padic_poly_t op,
const padic_ctx_t ctx)
{
const slong len = op->length;
if (op->val < 0)
{
return 0;
}
if (padic_poly_is_zero(op))
{
fmpz_poly_zero(rop);
return 1;
}
fmpz_poly_fit_length(rop, len);
_fmpz_poly_set_length(rop, len);
if (op->val == 0)
{
_fmpz_vec_set(rop->coeffs, op->coeffs, len);
}
else /* op->val > 0 */
{
fmpz_t pow;
fmpz_init(pow);
fmpz_pow_ui(pow, ctx->p, op->val);
_fmpz_vec_scalar_mul_fmpz(rop->coeffs, op->coeffs, len, pow);
fmpz_clear(pow);
}
return 1;
}
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_mul_karatsuba(fmpz_poly_t res,
const fmpz_poly_t poly1, const fmpz_poly_t poly2)
{
long len_out;
if ((poly1->length == 0) || (poly2->length == 0))
{
fmpz_poly_zero(res);
return;
}
len_out = poly1->length + poly2->length - 1;
fmpz_poly_fit_length(res, len_out);
if (poly1->length >= poly2->length)
_fmpz_poly_mul_karatsuba(res->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length);
else
_fmpz_poly_mul_karatsuba(res->coeffs, poly2->coeffs, poly2->length,
poly1->coeffs, poly1->length);
_fmpz_poly_set_length(res, len_out);
}
/* x^n+1 */
void
pol_xn1(fmpz_poly_t poly, ulong n)
{
fmpz_poly_fit_length(poly, n + 1);
fmpz_poly_set_coeff_si(poly, 0, 1);
fmpz_poly_set_coeff_si(poly, n, 1);
}
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_scalar_mul_ui(fmpz_poly_t poly1, const fmpz_poly_t poly2, ulong x)
{
long i;
/* Either scalar or input poly is zero */
if ((x == 0) || (poly2->length == 0))
{
fmpz_poly_zero(poly1);
return;
}
/* Special case, multiply by 1 */
if (x == 1)
{
fmpz_poly_set(poly1, poly2);
return;
}
fmpz_poly_fit_length(poly1, poly2->length);
for (i = 0; i < poly2->length; i++)
fmpz_mul_ui(poly1->coeffs + i, poly2->coeffs + i, x);
_fmpz_poly_set_length(poly1, poly2->length);
}
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_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_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_set_ui(fmpz_poly_t poly, ulong c)
{
if (c == UWORD(0))
fmpz_poly_zero(poly);
else
{
fmpz_poly_fit_length(poly, 1);
fmpz_set_ui(poly->coeffs, c);
_fmpz_poly_set_length(poly, 1);
}
}
/*
Applies the operator $\sigma^e$ to all elements in the matrix \code{op},
setting the corresponding elements in \code{rop} to the results.
*/
static
void fmpz_poly_mat_frobenius(fmpz_poly_mat_t B,
const fmpz_poly_mat_t A, long e,
const fmpz_t p, long N, const qadic_ctx_t ctx)
{
const long d = qadic_ctx_degree(ctx);
e = e % d;
if (e < 0)
e += d;
if (e == 0)
{
fmpz_t pN;
fmpz_init(pN);
fmpz_pow_ui(pN, p, N);
fmpz_poly_mat_scalar_mod_fmpz(B, A, pN);
fmpz_clear(pN);
}
else
{
long i, j;
fmpz *t = _fmpz_vec_init(2 * d - 1);
for (i = 0; i < B->r; i++)
for (j = 0; j < B->c; j++)
{
const fmpz_poly_struct *a = fmpz_poly_mat_entry(A, i, j);
fmpz_poly_struct *b = fmpz_poly_mat_entry(B, i, j);
if (a->length == 0)
{
fmpz_poly_zero(b);
}
else
{
_qadic_frobenius(t, a->coeffs, a->length, e,
ctx->a, ctx->j, ctx->len, p, N);
fmpz_poly_fit_length(b, d);
_fmpz_vec_set(b->coeffs, t, d);
_fmpz_poly_set_length(b, d);
_fmpz_poly_normalise(b);
}
}
_fmpz_vec_clear(t, 2 * d - 1);
}
}
void
fmpz_poly_randtest_unsigned(fmpz_poly_t f, flint_rand_t state,
long len, mp_bitcnt_t bits)
{
long i;
fmpz_poly_fit_length(f, len);
for (i = 0; i < len; i++)
fmpz_randtest_unsigned(f->coeffs + i, state, bits);
_fmpz_poly_set_length(f, len);
_fmpz_poly_normalise(f);
}
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);
}
}
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_sub(fmpz_poly_t res, const fmpz_poly_t poly1,
const fmpz_poly_t poly2)
{
slong max = FLINT_MAX(poly1->length, poly2->length);
fmpz_poly_fit_length(res, max);
_fmpz_poly_sub(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs,
poly2->length);
_fmpz_poly_set_length(res, max);
_fmpz_poly_normalise(res); /* there may have been cancellation */
}
void
fmpz_poly_scalar_mul_2exp(fmpz_poly_t poly1, const fmpz_poly_t poly2,
ulong exp)
{
if (poly2->length == 0)
{
fmpz_poly_zero(poly1);
return;
}
fmpz_poly_fit_length(poly1, poly2->length);
_fmpz_vec_scalar_mul_2exp(poly1->coeffs, poly2->coeffs, poly2->length, exp);
_fmpz_poly_set_length(poly1, poly2->length);
}
void
fq_sub(fq_t rop, const fq_t op1, const fq_t op2, const fq_ctx_t ctx)
{
slong max = FLINT_MAX(op1->length, op2->length);
fmpz_poly_fit_length(rop, max);
_fmpz_mod_poly_sub(rop->coeffs,
op1->coeffs, op1->length, op2->coeffs, op2->length,
fq_ctx_prime(ctx));
_fmpz_poly_set_length(rop, max);
_fmpz_poly_normalise(rop);
}
void
fmpz_poly_set_coeff_si(fmpz_poly_t poly, long n, long x)
{
fmpz_poly_fit_length(poly, n + 1);
if (n + 1 > poly->length) /* insert zeroes between end of poly and new coeff if needed */
{
mpn_zero((mp_ptr) (poly->coeffs + poly->length), n - poly->length);
poly->length = n + 1;
}
fmpz_set_si(poly->coeffs + n, x);
_fmpz_poly_normalise(poly); /* we may have set leading coefficient to zero */
}
void
fmpz_poly_scalar_mul_fmpz(fmpz_poly_t poly1, const fmpz_poly_t poly2,
const fmpz_t x)
{
/* Either scalar or input poly is zero */
if ((*x == 0) || (poly2->length == 0))
{
fmpz_poly_zero(poly1);
return;
}
fmpz_poly_fit_length(poly1, poly2->length);
_fmpz_vec_scalar_mul_fmpz(poly1->coeffs, poly2->coeffs, poly2->length, x);
_fmpz_poly_set_length(poly1, poly2->length);
}
void
arith_cos_minpoly(fmpz_poly_t poly, ulong n)
{
if (n == 0)
{
fmpz_poly_set_ui(poly, UWORD(1));
}
else
{
slong d = (n <= 2) ? 1 : n_euler_phi(n) / 2;
fmpz_poly_fit_length(poly, d + 1);
_arith_cos_minpoly(poly->coeffs, d, n);
_fmpz_poly_set_length(poly, d + 1);
}
}
static
void fmpz_poly_compose_pow(fmpz_poly_t rop, const fmpz_poly_t op, long k)
{
const long len = op->length;
const long lenr = (len - 1) * k + 1;
if (len == 0)
{
fmpz_poly_zero(rop);
}
else
{
fmpz_poly_fit_length(rop, lenr);
_fmpz_poly_compose_pow(rop->coeffs, op->coeffs, len, k);
_fmpz_poly_set_length(rop, lenr);
}
}
void
fmpz_poly_scalar_divexact_fmpz(fmpz_poly_t poly1, const fmpz_poly_t poly2,
const fmpz_t x)
{
if (fmpz_is_zero(x))
{
printf("Exception: division by zero in fmpz_poly_scalar_divexact_fmpz\n");
abort();
}
if (poly2->length == 0)
{
fmpz_poly_zero(poly1);
return;
}
fmpz_poly_fit_length(poly1, poly2->length);
_fmpz_vec_scalar_divexact_fmpz(poly1->coeffs, poly2->coeffs, poly2->length, x);
_fmpz_poly_set_length(poly1, poly2->length);
}
void
fmpz_poly_scalar_fdiv_ui(fmpz_poly_t poly1, const fmpz_poly_t poly2,
ulong x)
{
if (x == 0)
{
flint_printf("Exception (fmpz_poly_scalar_fdiv_ui). Division by zero.\n");
abort();
}
if (poly2->length == 0)
{
fmpz_poly_zero(poly1);
return;
}
fmpz_poly_fit_length(poly1, poly2->length);
_fmpz_vec_scalar_fdiv_q_ui(poly1->coeffs, poly2->coeffs, poly2->length, x);
_fmpz_poly_set_length(poly1, poly2->length);
}
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);
}
}