void
fmpz_mat_solve_cramer(fmpz * x, fmpz_t den, const fmpz_mat_t A, const fmpz * b)
{
long dim = A->r;
switch (dim)
{
case 0:
fmpz_set_ui(den, 1UL);
break;
case 1:
fmpz_set(den, A->rows[0]);
fmpz_set(x, b);
break;
case 2:
_fmpz_mat_solve_cramer_2x2(x, den, A->rows, b);
break;
case 3:
_fmpz_mat_solve_cramer_3x3(x, den, A->rows, b);
break;
default:
printf("Exception: fmpz_mat_solve_cramer: dim > 3 not implemented");
abort();
}
}
void
fmpq_mat_mul_fmpz_mat(fmpq_mat_t C, const fmpq_mat_t A, const fmpz_mat_t B)
{
slong i, j;
fmpz_mat_t Aclear;
fmpz_mat_t Cclear;
fmpz * Aden;
fmpz_mat_init(Aclear, A->r, A->c);
fmpz_mat_init(Cclear, A->r, B->c);
Aden = _fmpz_vec_init(A->r);
fmpq_mat_get_fmpz_mat_rowwise(Aclear, Aden, A);
fmpz_mat_mul(Cclear, Aclear, B);
for (i = 0; i < C->r; i++)
{
for (j = 0; j < C->c; j++)
{
fmpz_set(fmpq_mat_entry_num(C, i, j), fmpz_mat_entry(Cclear, i, j));
fmpz_set(fmpq_mat_entry_den(C, i, j), Aden + i);
fmpq_canonicalise(fmpq_mat_entry(C, i, j));
}
}
fmpz_mat_clear(Aclear);
fmpz_mat_clear(Cclear);
_fmpz_vec_clear(Aden, A->r);
}
void _fmpz_mod_poly_evaluate_fmpz(fmpz_t res, const fmpz *poly, slong len,
const fmpz_t a, const fmpz_t p)
{
if (len == 0)
{
fmpz_zero(res);
}
else if (len == 1 || fmpz_is_zero(a))
{
fmpz_set(res, poly);
}
else
{
slong i = len - 1;
fmpz_t t;
fmpz_init(t);
fmpz_set(res, poly + i);
for (i = len - 2; i >= 0; i--)
{
fmpz_mul(t, res, a);
fmpz_mod(t, t, p);
fmpz_add(res, poly + i, t);
}
fmpz_clear(t);
if (fmpz_cmpabs(res, p) >= 0)
fmpz_sub(res, res, p);
}
}
void
_fmpz_poly_evaluate_horner_fmpz(fmpz_t res, const fmpz * f, long len,
const fmpz_t a)
{
if (len == 0)
{
fmpz_zero(res);
}
else if (len == 1 || fmpz_is_zero(a))
{
fmpz_set(res, f);
}
else
{
long i = len - 1;
fmpz_t t;
fmpz_init(t);
fmpz_set(res, f + i);
for (i = len - 2; i >= 0; i--)
{
fmpz_mul(t, res, a);
fmpz_add(res, f + i, t);
}
fmpz_clear(t);
}
}
static
void _fmpz_poly_compose_pow(fmpz *rop, const fmpz *op, long len, long k)
{
if (k == 1)
{
if (rop != op)
{
_fmpz_vec_set(rop, op, len);
}
}
else if (len == 1)
{
fmpz_set(rop, op);
}
else
{
long i, j, h;
for (i = len - 1, j = (len - 1) * k ; i >= 0; i--, j -= k)
{
fmpz_set(rop + j, op + i);
if (i != 0)
for (h = 1; h < k; h++)
fmpz_zero(rop + (j - h));
}
}
}
void __fmpz_multi_CRT_sign(fmpz_t output, fmpz_t input, fmpz_comb_t comb)
{
unsigned long n = comb->n;
if (n == 0L)
{
if (input[0] == 0L)
{
fmpz_set_ui(output, 0L);
return;
}
unsigned long p = comb->primes[0];
if ((p - input[1]) < input[1]) fmpz_set_si(output, (long) (input[1] - p));
else fmpz_set_ui(output, input[1]);
return;
}
fmpz_t temp = fmpz_init(fmpz_size(comb->comb[n-1][0]) + 1);
fmpz_sub(temp, input, comb->comb[comb->n - 1][0]);
if (fmpz_cmpabs(temp, input) <= 0L) fmpz_set(output, temp);
else fmpz_set(output, input);
fmpz_clear(temp);
return;
}
void
_fmpq_poly_compose_series_horner(fmpz * res, fmpz_t den, const fmpz * poly1,
const fmpz_t den1, long len1, const fmpz * poly2,
const fmpz_t den2, long len2, long n)
{
if (fmpz_is_one(den2))
{
_fmpz_poly_compose_series(res, poly1, len1, poly2, len2, n);
fmpz_set(den, den1);
_fmpq_poly_canonicalise(res, den, n);
}
else if (n == 1)
{
fmpz_set(res, poly1);
fmpz_set(den, den1);
_fmpq_poly_canonicalise(res, den, 1);
}
else
{
long i = len1 - 1;
long lenr;
fmpz_t tden;
fmpz * t = _fmpz_vec_init(n);
fmpz_init(tden);
_fmpz_vec_zero(res, n);
lenr = len2;
_fmpq_poly_scalar_mul_fmpz(res, den, poly2, den2, len2, poly1 + i);
_fmpq_poly_scalar_div_fmpz(res, den, res, den, len2, den1);
i--;
_fmpq_poly_add(res, den, res, den, len2, poly1 + i, den1, 1);
_fmpq_poly_canonicalise(res, den, lenr);
while (i > 0)
{
i--;
if (lenr + len2 - 1 < n)
{
_fmpq_poly_mul(t, tden, res, den, lenr, poly2, den2, len2);
lenr = lenr + len2 - 1;
}
else
{
_fmpq_poly_mullow(t, tden, res, den, lenr,
poly2, den2, len2, n);
lenr = n;
}
_fmpq_poly_canonicalise(t, tden, lenr);
_fmpq_poly_add(res, den, t, tden, lenr, poly1 + i, den1, 1);
}
_fmpq_poly_canonicalise(res, den, n);
_fmpz_vec_clear(t, n);
fmpz_clear(tden);
}
}
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
bernoulli_rev_init(bernoulli_rev_t iter, ulong nmax)
{
long j;
fmpz_t t;
fmprb_t x;
int round1, round2;
long wp;
nmax -= (nmax % 2);
iter->n = nmax;
iter->alloc = 0;
if (nmax < BERNOULLI_REV_MIN)
return;
iter->prec = wp = global_prec(nmax);
iter->max_power = zeta_terms(nmax, iter->prec);
iter->alloc = iter->max_power + 1;
iter->powers = _fmpz_vec_init(iter->alloc);
fmpz_init(iter->pow_error);
fmprb_init(iter->prefactor);
fmprb_init(iter->two_pi_squared);
fmprb_init(x);
fmpz_init(t);
/* precompute powers */
for (j = 3; j <= iter->max_power; j += 2)
{
fmprb_ui_pow_ui(x, j, nmax, power_prec(j, nmax, wp));
fmprb_ui_div(x, 1UL, x, power_prec(j, nmax, wp));
round1 = fmpr_get_fmpz_fixed_si(t, fmprb_midref(x), -wp);
fmpz_set(iter->powers + j, t);
/* error: the radius, plus two roundings */
round2 = fmpr_get_fmpz_fixed_si(t, fmprb_radref(x), -wp);
fmpz_add_ui(t, t, (round1 != 0) + (round2 != 0));
if (fmpz_cmp(iter->pow_error, t) < 0)
fmpz_set(iter->pow_error, t);
}
/* precompute (2pi)^2 and 2*(n!)/(2pi)^n */
fmprb_fac_ui(iter->prefactor, nmax, wp);
fmprb_mul_2exp_si(iter->prefactor, iter->prefactor, 1);
fmprb_const_pi(x, wp);
fmprb_mul_2exp_si(x, x, 1);
fmprb_mul(iter->two_pi_squared, x, x, wp);
fmprb_pow_ui(x, iter->two_pi_squared, nmax / 2, wp);
fmprb_div(iter->prefactor, iter->prefactor, x, wp);
fmpz_clear(t);
fmprb_clear(x);
}
slong
fmpr_add_naive(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd)
{
slong shift, xsize, ysize;
if (fmpr_is_special(x) || fmpr_is_special(y))
{
return _fmpr_add_special(z, x, y, prec, rnd);
}
shift = _fmpz_sub_small(fmpr_expref(x), fmpr_expref(y));
if (shift == 0)
{
fmpz_add(fmpr_manref(z), fmpr_manref(x), fmpr_manref(y));
fmpz_set(fmpr_expref(z), fmpr_expref(x));
}
else if (shift > 0)
{
ysize = _fmpz_size(fmpr_manref(y)) * FLINT_BITS;
/* x and y do not overlap */
if (shift > ysize && prec != FMPR_PREC_EXACT)
{
/* y does not overlap with result */
if (ysize + prec - (slong) fmpz_bits(fmpr_manref(x)) < shift)
{
return _fmpr_add_eps(z, x, fmpz_sgn(fmpr_manref(y)), prec, rnd);
}
}
fmpz_add_mul2exp(fmpr_manref(z), fmpr_manref(y), fmpr_manref(x), shift);
fmpz_set(fmpr_expref(z), fmpr_expref(y));
}
else
{
shift = -shift;
xsize = _fmpz_size(fmpr_manref(x)) * FLINT_BITS;
/* x and y do not overlap */
if (shift > xsize && prec != FMPR_PREC_EXACT)
{
/* y does not overlap with result */
if (xsize + prec - (slong) fmpz_bits(fmpr_manref(y)) < shift)
{
return _fmpr_add_eps(z, y, fmpz_sgn(fmpr_manref(x)), prec, rnd);
}
}
fmpz_add_mul2exp(fmpr_manref(z), fmpr_manref(x), fmpr_manref(y), shift);
fmpz_set(fmpr_expref(z), fmpr_expref(x));
}
return _fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, rnd);
}
void
_padic_log_balanced(fmpz_t z, const fmpz_t y, long v, const fmpz_t p, long N)
{
fmpz_t pv, pN, r, t, u;
long val;
padic_inv_t S;
fmpz_init(pv);
fmpz_init(pN);
fmpz_init(r);
fmpz_init(t);
fmpz_init(u);
_padic_inv_precompute(S, p, N);
fmpz_set(t, y);
fmpz_set(pv, p);
fmpz_pow_ui(pN, p, N);
fmpz_zero(z);
val = 1;
/*
TODO: Abort earlier if larger than $p^N$, possible
with variable precision?
*/
while (!fmpz_is_zero(t))
{
fmpz_mul(pv, pv, pv);
fmpz_fdiv_qr(t, r, t, pv);
if (!fmpz_is_zero(t))
{
fmpz_mul(t, t, pv);
fmpz_add_ui(u, r, 1);
_padic_inv_precomp(u, u, S);
fmpz_mul(t, t, u);
fmpz_mod(t, t, pN);
}
if (!fmpz_is_zero(r))
{
fmpz_neg(r, r);
_padic_log_bsplit(r, r, val, p, N);
fmpz_sub(z, z, r);
}
val *= 2;
}
fmpz_clear(pv);
fmpz_clear(pN);
fmpz_clear(r);
fmpz_clear(t);
fmpz_clear(u);
_padic_inv_clear(S);
}
void
_fmpq_bsplit_sum_abpq(fmpz_t P, fmpz_t Q, fmpz_t B, fmpz_t T,
const fmpq * ab, const fmpq * pq, long n1, long n2)
{
if (n2 - n1 <= 0)
{
fmpz_zero(P);
fmpz_one(Q);
}
else if (n2 - n1 == 1)
{
fmpz_set(P, fmpq_numref(pq + n1));
fmpz_set(Q, fmpq_denref(pq + n1));
fmpz_set(B, fmpq_denref(ab + n1));
fmpz_mul(T, P, fmpq_numref(ab + n1));
}
else
{
long m = (n1 + n2) / 2;
fmpz_t P2, Q2, B2, T2;
fmpz_init(P2);
fmpz_init(Q2);
fmpz_init(B2);
fmpz_init(T2);
_fmpq_bsplit_sum_abpq(P, Q, B, T, ab, pq, n1, m);
_fmpq_bsplit_sum_abpq(P2, Q2, B2, T2, ab, pq, m, n2);
if (!fmpz_is_one(B2))
fmpz_mul(T, T, B2);
fmpz_mul(T, T, Q2);
if (!fmpz_is_one(B))
fmpz_mul(T2, T2, B);
fmpz_mul(T2, T2, P);
fmpz_add(T, T, T2);
fmpz_mul(P, P, P2);
fmpz_mul(Q, Q, Q2);
fmpz_mul(B, B, B2);
fmpz_clear(P2);
fmpz_clear(Q2);
fmpz_clear(B2);
fmpz_clear(T2);
}
}
void _fmpz_ramanujan_tau(fmpz_t res, fmpz_factor_t factors)
{
fmpz_poly_t poly;
fmpz_t tau_p, p_11, next, this, prev;
long k, r;
ulong max_prime;
max_prime = 1UL;
for (k = 0; k < factors->length; k++)
{
/* TODO: handle overflow properly */
max_prime = FLINT_MAX(max_prime, fmpz_get_ui(factors->p + k));
}
fmpz_poly_init(poly);
fmpz_poly_ramanujan_tau(poly, max_prime + 1);
fmpz_set_ui(res, 1);
fmpz_init(tau_p);
fmpz_init(p_11);
fmpz_init(next);
fmpz_init(this);
fmpz_init(prev);
for (k = 0; k < factors->length; k++)
{
ulong p = fmpz_get_ui(factors->p + k);
fmpz_set(tau_p, poly->coeffs + p);
fmpz_set_ui(p_11, p);
fmpz_pow_ui(p_11, p_11, 11);
fmpz_set_ui(prev, 1);
fmpz_set(this, tau_p);
for (r = 1; r < fmpz_get_ui(factors->exp + k); r++)
{
fmpz_mul(next, tau_p, this);
fmpz_submul(next, p_11, prev);
fmpz_set(prev, this);
fmpz_set(this, next);
}
fmpz_mul(res, res, this);
}
fmpz_clear(tau_p);
fmpz_clear(p_11);
fmpz_clear(next);
fmpz_clear(this);
fmpz_clear(prev);
fmpz_poly_clear(poly);
}
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 _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);
}
// truncated multiplication for fmpz
void fmpz_mul_trunc(fmpz_t res, fmpz_t a, fmpz_t b, unsigned long trunc)
{
unsigned long sizea = FLINT_MIN(fmpz_size(a), trunc);
unsigned long sizeb = FLINT_MIN(fmpz_size(b), trunc);
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
if ((sizea == 0) || (sizeb == 0)) {
res[0] = 0;
return;
}
if (trunc >= sizea + sizeb) {
mp_limb_t mslimb;
if (sizea >= sizeb) mslimb = F_mpn_mul(res+1, a+1, sizea, b+1, sizeb);
else mslimb = F_mpn_mul(res+1, b+1, sizeb, a+1, sizea);
res[0] = sizea + sizeb - (mslimb == 0);
} else {
mp_limb_t mslimb;
fmpz_t temp = flint_stack_alloc(sizea + sizeb + 1);
if (sizea >= sizeb) mslimb = F_mpn_mul_trunc(temp+1, a+1, sizea, b+1, sizeb, trunc);
else mslimb = F_mpn_mul_trunc(temp+1, b+1, sizeb, a+1, sizea, trunc);
temp[0] = trunc;
if (UNLIKELY(!mslimb))
__fmpz_normalise(temp); // normalise if most significant limb == 0
fmpz_set(res, temp);
flint_stack_release();
}
if ((long) (a[0] ^ b[0]) < 0L) res[0] = -res[0];
}
void fmpz_div_2exp(fmpz_t output, fmpz_t x, unsigned long exp)
{
unsigned long limbs = (exp >> FLINT_LG_BITS_PER_LIMB);
unsigned long bits = (exp & (FLINT_BITS - 1));
if ((x[0] == 0) || (limbs >= FLINT_ABS(x[0])))
{
output[0] = 0L;
return;
}
if (bits)
{
fmpz_t temp = fmpz_init(FLINT_ABS(x[0]) - limbs);
mpn_rshift(temp + 1, x + limbs + 1, FLINT_ABS(x[0]) - limbs, bits);
if ((long) x[0] >= 0L) temp[0] = x[0] - limbs;
else temp[0] = limbs + x[0];
NORM(temp);
fmpz_set(output, temp);
fmpz_clear(temp);
} else
{
F_mpn_copy(output + 1, x + limbs + 1, FLINT_ABS(x[0]) - limbs);
if ((long) x[0] >= 0L) output[0] = x[0] - limbs;
else output[0] = limbs + x[0];
}
}
static
void fmpz_poly_mat_get_fmpz_mat(fmpz_mat_t B, const fmpz_poly_mat_t A)
{
long i, j;
if (!(A->r == B->r && A->c == B->c))
{
printf("ERROR (fmpz_poly_mat_get_fmpz_mat). Incompatible dimensions.\n");
abort();
}
for (i = 0; i < A->r; i++)
for (j = 0; j < A->c; j++)
{
const fmpz_poly_struct *poly = fmpz_poly_mat_entry(A, i, j);
const long len = poly->length;
if (len == 0)
{
fmpz_zero(fmpz_mat_entry(B, i, j));
}
else if (len == 1)
{
fmpz_set(fmpz_mat_entry(B, i, j), poly->coeffs + 0);
}
else
{
printf("ERROR (fmpz_poly_mat_get_fmpz_mat).\n");
printf("A contains a polynomial of length greater than 1.\n");
abort();
}
}
}
void
_fmpq_poly_compose(fmpz * res, fmpz_t den, const fmpz * poly1, const fmpz_t den1,
long len1, const fmpz * poly2, const fmpz_t den2, long len2)
{
if (*den2 == 1L)
{
_fmpz_poly_compose(res, poly1, len1, poly2, len2);
fmpz_set(den, den1);
_fmpq_poly_canonicalise(res, den, (len1 - 1L) * (len2 - 1L) + 1L);
}
else
{
fmpz_t one;
fmpz * v = _fmpz_vec_init(len1);
fmpz_init(one);
fmpz_one(one);
_fmpq_poly_rescale(v, den, poly1, den1, len1, one, den2);
_fmpz_poly_compose(res, v, len1, poly2, len2);
_fmpq_poly_canonicalise(res, den, (len1 - 1L) * (len2 - 1L) + 1L);
fmpz_clear(one);
_fmpz_vec_clear(v, len1);
}
}
int
fmpz_mat_randpermdiag(fmpz_mat_t mat, flint_rand_t state,
const fmpz * diag, long n)
{
int parity;
long i;
long * rows;
long * cols;
rows = malloc(sizeof(long) * mat->r);
cols = malloc(sizeof(long) * mat->c);
for (i = 0; i < mat->r; i++) rows[i] = i;
for (i = 0; i < mat->c; i++) cols[i] = i;
parity = shuffle(rows, state, mat->r);
parity ^= shuffle(cols, state, mat->c);
fmpz_mat_zero(mat);
for (i = 0; i < n; i++)
fmpz_set(&mat->rows[rows[i]][cols[i]], &diag[i]);
free(rows);
free(cols);
return parity;
}
void
_fmpz_holonomic_eval_companion_matrix_fmpz(fmpz_mat_t M, fmpz_t Q,
const fmpz_holonomic_t op, long n)
{
fmpz_t c;
long r = fmpz_holonomic_order(op);
long i, j;
fmpz_init(c);
fmpz_set_si(c, n);
fmpz_poly_evaluate_fmpz(Q, op->coeffs + r, c);
for (i = 0; i < r - 1; i++)
{
for (j = 0; j < r; j++)
{
if (i + 1 == j)
fmpz_set(M->rows[i] + j, Q);
else
fmpz_zero(M->rows[i] + j);
}
}
for (j = 0; j < r; j++)
{
fmpz_poly_evaluate_fmpz(M->rows[r - 1] + j, op->coeffs + j, c);
fmpz_neg(M->rows[r - 1] + j, M->rows[r - 1] + j);
}
fmpz_clear(c);
}
void fmpq_poly_get_slice(fmpq_poly_t rop, const fmpq_poly_t op, long i, long j)
{
i = FLINT_MAX(i, 0);
j = FLINT_MIN(j, op->length);
if (i < j)
{
long k;
if (rop == op)
{
for (k = 0; k < i; k++)
fmpz_zero(rop->coeffs + k);
for (k = j; k < rop->length; k++)
fmpz_zero(rop->coeffs + k);
fmpq_poly_canonicalise(rop);
}
else
{
fmpq_poly_fit_length(rop, j);
_fmpq_poly_set_length(rop, j);
_fmpz_vec_set(rop->coeffs + i, op->coeffs + i, j - i);
fmpz_set(rop->den, op->den);
fmpq_poly_canonicalise(rop);
}
}
else
{
fmpq_poly_zero(rop);
}
}
int
fmpz_mat_solve_cramer(fmpz_mat_t X, fmpz_t den,
const fmpz_mat_t A, const fmpz_mat_t B)
{
long i, dim = fmpz_mat_nrows(A);
if (dim == 0)
{
fmpz_one(den);
return 1;
}
else if (dim == 1)
{
fmpz_set(den, fmpz_mat_entry(A, 0, 0));
if (fmpz_is_zero(den))
return 0;
if (!fmpz_mat_is_empty(B))
_fmpz_vec_set(X->rows[0], B->rows[0], fmpz_mat_ncols(B));
return 1;
}
else if (dim == 2)
{
fmpz_t t, u;
_fmpz_mat_det_cofactor_2x2(den, A->rows);
if (fmpz_is_zero(den))
return 0;
fmpz_init(t);
fmpz_init(u);
for (i = 0; i < fmpz_mat_ncols(B); i++)
{
fmpz_mul (t, fmpz_mat_entry(A, 1, 1), fmpz_mat_entry(B, 0, i));
fmpz_submul(t, fmpz_mat_entry(A, 0, 1), fmpz_mat_entry(B, 1, i));
fmpz_mul (u, fmpz_mat_entry(A, 0, 0), fmpz_mat_entry(B, 1, i));
fmpz_submul(u, fmpz_mat_entry(A, 1, 0), fmpz_mat_entry(B, 0, i));
fmpz_swap(fmpz_mat_entry(X, 0, i), t);
fmpz_swap(fmpz_mat_entry(X, 1, i), u);
}
fmpz_clear(t);
fmpz_clear(u);
return 1;
}
else if (dim == 3)
{
return _fmpz_mat_solve_cramer_3x3(X, den, A, B);
}
else
{
printf("Exception: fmpz_mat_solve_cramer: dim > 3 not implemented");
abort();
}
}
void
fmpr_get_fmpq(fmpq_t y, const fmpr_t x)
{
if (fmpr_is_zero(x))
{
fmpq_zero(y);
}
else if (fmpr_is_special(x) || COEFF_IS_MPZ(*fmpr_expref(x)))
{
printf("exception: fmpr_get_fmpq: cannot convert to rational\n");
abort();
}
else
{
long exp = *fmpr_expref(x);
fmpz_set_ui(fmpq_denref(y), 1UL);
if (exp >= 0)
{
fmpz_mul_2exp(fmpq_numref(y), fmpr_manref(x), exp);
}
else
{
fmpz_set(fmpq_numref(y), fmpr_manref(x));
fmpz_mul_2exp(fmpq_denref(y), fmpq_denref(y), -exp);
}
}
}
void _fmpq_poly_scalar_mul_ui(fmpz * rpoly, fmpz_t rden,
const fmpz * poly, const fmpz_t den, slong len,
ulong c)
{
fmpz_t gcd; /* GCD( den, c ) */
if (c == 0)
{
_fmpz_vec_zero(rpoly, len);
fmpz_one(rden);
return;
}
fmpz_init(gcd);
fmpz_set_ui(gcd, c);
fmpz_gcd(gcd, gcd, den);
if (*gcd == WORD(1))
{
_fmpz_vec_scalar_mul_ui(rpoly, poly, len, c);
fmpz_set(rden, den);
}
else
{
ulong gcd2 = fmpz_get_ui(gcd);
ulong c2 = c / gcd2;
_fmpz_vec_scalar_mul_ui(rpoly, poly, len, c2);
fmpz_fdiv_q_ui(rden, den, gcd2);
}
fmpz_clear(gcd);
}
void
_fmpz_poly_revert_series_lagrange(fmpz * Qinv, const fmpz * Q, slong n)
{
slong i;
fmpz *R, *S, *T, *tmp;
if (n <= 2)
{
_fmpz_vec_set(Qinv, Q, n);
return;
}
R = _fmpz_vec_init(n - 1);
S = _fmpz_vec_init(n - 1);
T = _fmpz_vec_init(n - 1);
fmpz_zero(Qinv);
fmpz_set(Qinv + 1, Q + 1);
_fmpz_poly_inv_series(R, Q + 1, n - 1);
_fmpz_vec_set(S, R, n - 1);
for (i = 2; i < n; i++)
{
_fmpz_poly_mullow(T, S, n - 1, R, n - 1, n - 1);
fmpz_divexact_ui(Qinv + i, T + i - 1, i);
tmp = S; S = T; T = tmp;
}
_fmpz_vec_clear(R, n - 1);
_fmpz_vec_clear(S, n - 1);
_fmpz_vec_clear(T, n - 1);
}
void
_fmpz_mat_inv_2x2(fmpz ** b, fmpz_t den, fmpz ** const a)
{
fmpz_t tmp;
_fmpz_mat_det_cofactor_2x2(den, a);
fmpz_neg(&b[0][1], &a[0][1]);
fmpz_neg(&b[1][0], &a[1][0]);
fmpz_init(tmp);
fmpz_set(tmp, &a[0][0]);
fmpz_set(&b[0][0], &a[1][1]);
fmpz_set(&b[1][1], tmp);
fmpz_clear(tmp);
}
int
fmpz_mat_inv(fmpz_mat_t B, fmpz_t den, const fmpz_mat_t A)
{
long dim = A->r;
if (dim == 0)
{
fmpz_one(den);
return 1;
}
else if (dim == 1)
{
fmpz_set(den, A->entries);
fmpz_one(B->entries);
return !fmpz_is_zero(den);
}
else if (dim == 2)
{
_fmpz_mat_inv_2x2(B->rows, den, A->rows);
return !fmpz_is_zero(den);
}
else
{
fmpz_mat_t I;
long i;
int success;
fmpz_mat_init(I, dim, dim);
for (i = 0; i < dim; i++)
fmpz_one(fmpz_mat_entry(I, i, i));
success = fmpz_mat_solve_fflu(B, den, A, I);
fmpz_mat_clear(I);
return success;
}
}
void _fmpq_poly_scalar_div_ui(fmpz * rpoly, fmpz_t rden, const fmpz * poly,
const fmpz_t den, long len, ulong c)
{
if (c == 1UL)
{
if (rpoly != poly)
_fmpz_vec_set(rpoly, poly, len);
fmpz_set(rden, den);
}
else
{
fmpz_t d, fc;
ulong ud;
fmpz_init(d);
fmpz_init(fc);
_fmpz_vec_content(d, poly, len);
fmpz_set_ui(fc, c);
fmpz_gcd(d, d, fc);
ud = fmpz_get_ui(d); /* gcd of d and c fits into a ulong */
_fmpz_vec_scalar_divexact_ui(rpoly, poly, len, ud);
fmpz_mul_ui(rden, den, c / ud);
fmpz_clear(d);
fmpz_clear(fc);
}
}
void padic_ctx_init(padic_ctx_t ctx, const fmpz_t p, long N,
enum padic_print_mode mode)
{
fmpz_init(ctx->p);
fmpz_set(ctx->p, p);
ctx->N = N;
ctx->pinv = (!COEFF_IS_MPZ(*p)) ? n_precompute_inverse(fmpz_get_ui(p)) : 0;
if (N > 0)
{
long i, len;
ctx->min = FLINT_MAX(1, N - 10);
ctx->max = N + 10;
len = ctx->max - ctx->min;
ctx->pow = _fmpz_vec_init(len);
fmpz_pow_ui(ctx->pow, p, ctx->min);
for (i = 1; i < len; i++)
fmpz_mul(ctx->pow + i, ctx->pow + (i - 1), p);
}
else
{
ctx->min = 0;
ctx->max = 0;
ctx->pow = NULL;
}
ctx->mode = mode;
}