int
fmpq_poly_set_str(fmpq_poly_t poly, const char * str)
{
int ans;
long len;
len = atol(str);
if (len < 0)
return -1;
if (len == 0)
{
fmpq_poly_zero(poly);
return 0;
}
fmpq_poly_fit_length(poly, len);
ans = _fmpq_poly_set_str(poly->coeffs, poly->den, str);
if (ans == 0)
{
_fmpq_poly_set_length(poly, len);
_fmpq_poly_normalise(poly);
}
else
{
_fmpz_vec_zero(poly->coeffs, len);
fmpz_set_ui(poly->den, 1);
_fmpq_poly_set_length(poly, 0);
}
return ans;
}
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_set_coeff_mpz(fmpq_poly_t poly, long n, const mpz_t x)
{
long len = poly->length;
const int replace = (n < len && !fmpz_is_zero(poly->coeffs + n));
if (!replace && mpz_sgn(x) == 0)
return;
if (n + 1 > len)
{
fmpq_poly_fit_length(poly, n + 1);
_fmpq_poly_set_length(poly, n + 1);
mpn_zero((mp_ptr) poly->coeffs + len, (n + 1) - len);
}
if (*poly->den == 1L)
{
fmpz_set_mpz(poly->coeffs + n, x);
if (replace)
_fmpq_poly_normalise(poly);
}
else
{
fmpz_set_mpz(poly->coeffs + n, x);
fmpz_mul(poly->coeffs + n, poly->coeffs + n, poly->den);
if (replace)
fmpq_poly_canonicalise(poly);
}
}
void
_nf_elem_mod_fmpz(nf_elem_t res, const nf_elem_t a, const fmpz_t mod, const nf_t nf)
{
if (nf_elem_is_zero(a, nf))
{
nf_elem_zero(res, nf);
return;
}
if (nf->flag & NF_LINEAR)
{
fmpz_mod(LNF_ELEM_NUMREF(res), LNF_ELEM_NUMREF(a), mod);
fmpz_one(LNF_ELEM_DENREF(res));
}
else if (nf->flag & NF_QUADRATIC)
{
_fmpz_vec_scalar_mod_fmpz(QNF_ELEM_NUMREF(res), QNF_ELEM_NUMREF(a), 3, mod);
fmpz_one(QNF_ELEM_DENREF(res));
}
else
{
fmpq_poly_fit_length(NF_ELEM(res), fmpq_poly_length(NF_ELEM(a)));
_fmpq_poly_set_length(NF_ELEM(res), fmpq_poly_length(NF_ELEM(a)));
_fmpz_vec_scalar_mod_fmpz(NF_ELEM(res)->coeffs, NF_ELEM(a)->coeffs, fmpq_poly_length(NF_ELEM(a)), mod);
fmpz_one(NF_ELEM_DENREF(res));
}
nf_elem_canonicalise(res, nf);
}
void fmpq_poly_scalar_div_mpq(fmpq_poly_t rop, const fmpq_poly_t op, const mpq_t c)
{
fmpz_t r, s;
if (mpq_sgn(c) == 0)
{
printf("Exception: division by zero in fmpq_poly_scalar_div_mpq\n");
abort();
}
if (fmpq_poly_is_zero(op))
{
fmpq_poly_zero(rop);
return;
}
fmpq_poly_fit_length(rop, op->length);
_fmpq_poly_set_length(rop, op->length);
fmpz_init(r);
fmpz_init(s);
fmpz_set_mpz(r, mpq_numref(c));
fmpz_set_mpz(s, mpq_denref(c));
_fmpq_poly_scalar_div_mpq(rop->coeffs, rop->den,
op->coeffs, op->den, op->length, r, s);
fmpz_clear(r);
fmpz_clear(s);
}
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);
}
}
void fmpq_poly_exp_series(fmpq_poly_t res, const fmpq_poly_t poly, long n)
{
fmpz *copy;
int alloc;
if (poly->length == 0)
{
fmpq_poly_set_ui(res, 1UL);
return;
}
if (!fmpz_is_zero(poly->coeffs))
{
printf("Exception: fmpq_poly_exp_series: constant term != 0");
abort();
}
if (n < 2)
{
if (n == 0) fmpq_poly_zero(res);
if (n == 1) fmpq_poly_set_ui(res, 1UL);
return;
}
if (poly->length >= n)
{
copy = poly->coeffs;
alloc = 0;
}
else
{
long i;
copy = (fmpz *) flint_malloc(n * sizeof(fmpz));
for (i = 0; i < poly->length; i++)
copy[i] = poly->coeffs[i];
for ( ; i < n; i++)
copy[i] = 0;
alloc = 1;
}
if (res != poly)
{
fmpq_poly_fit_length(res, n);
_fmpq_poly_exp_series(res->coeffs, res->den, copy, poly->den, n);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, n);
_fmpq_poly_exp_series(t->coeffs, t->den, copy, poly->den, n);
fmpq_poly_swap(res, t);
fmpq_poly_clear(t);
}
_fmpq_poly_set_length(res, n);
_fmpq_poly_normalise(res);
if (alloc)
flint_free(copy);
}
void
fmpq_poly_revert_series(fmpq_poly_t res,
const fmpq_poly_t poly, long n)
{
fmpz *copy;
int alloc;
if (poly->length < 2 || !fmpz_is_zero(poly->coeffs)
|| fmpz_is_zero(poly->coeffs + 1))
{
printf("exception: fmpq_poly_revert_series: input must have "
"zero constant term and nonzero coefficient of x^1");
abort();
}
if (n < 2)
{
fmpq_poly_zero(res);
return;
}
if (poly->length >= n)
{
copy = poly->coeffs;
alloc = 0;
}
else
{
long i;
copy = (fmpz *) flint_malloc(n * sizeof(fmpz));
for (i = 0; i < poly->length; i++)
copy[i] = poly->coeffs[i];
for ( ; i < n; i++)
copy[i] = 0;
alloc = 1;
}
if (res != poly)
{
fmpq_poly_fit_length(res, n);
_fmpq_poly_revert_series(res->coeffs,
res->den, copy, poly->den, n);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, n);
_fmpq_poly_revert_series(t->coeffs,
t->den, copy, poly->den, n);
fmpq_poly_swap(res, t);
fmpq_poly_clear(t);
}
_fmpq_poly_set_length(res, n);
_fmpq_poly_normalise(res);
if (alloc)
flint_free(copy);
}
void fmpq_poly_set_ui(fmpq_poly_t poly, ulong x)
{
fmpq_poly_fit_length(poly, 1);
fmpz_set_ui(poly->coeffs, x);
fmpz_one(poly->den);
_fmpq_poly_set_length(poly, 1);
_fmpq_poly_normalise(poly);
}
void fmpq_poly_set_array_mpq(fmpq_poly_t poly, const mpq_t * a, long n)
{
if (n == 0)
fmpq_poly_zero(poly);
else
{
fmpq_poly_fit_length(poly, n);
_fmpq_poly_set_array_mpq(poly->coeffs, poly->den, a, n);
_fmpq_poly_set_length(poly, n);
_fmpq_poly_normalise(poly);
}
}
void fmpq_poly_sqrt_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n)
{
fmpz *copy;
int alloc;
if (poly->length < 1 || !fmpz_equal(poly->coeffs, poly->den))
{
flint_printf("Exception (fmpq_poly_sqrt_series). Constant term != 1.\n");
abort();
}
if (n < 1)
{
fmpq_poly_zero(res);
return;
}
if (poly->length >= n)
{
copy = poly->coeffs;
alloc = 0;
}
else
{
slong i;
copy = (fmpz *) flint_malloc(n * sizeof(fmpz));
for (i = 0; i < poly->length; i++)
copy[i] = poly->coeffs[i];
for ( ; i < n; i++)
copy[i] = 0;
alloc = 1;
}
if (res != poly)
{
fmpq_poly_fit_length(res, n);
_fmpq_poly_sqrt_series(res->coeffs, res->den, copy, poly->den, n);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, n);
_fmpq_poly_sqrt_series(t->coeffs, t->den, copy, poly->den, n);
fmpq_poly_swap(res, t);
fmpq_poly_clear(t);
}
_fmpq_poly_set_length(res, n);
fmpq_poly_canonicalise(res);
if (alloc)
flint_free(copy);
}
void fmpq_poly_derivative(fmpq_poly_t res, const fmpq_poly_t poly)
{
slong len = poly->length;
if (len < 2)
{
fmpq_poly_zero(res);
return;
}
fmpq_poly_fit_length(res, len - 1);
_fmpq_poly_derivative(res->coeffs, res->den, poly->coeffs, poly->den, len);
_fmpq_poly_set_length(res, len - 1);
}
void fmpq_poly_integral(fmpq_poly_t res, const fmpq_poly_t poly)
{
slong len = poly->length;
if (len == 0)
{
fmpq_poly_zero(res);
return;
}
fmpq_poly_fit_length(res, len + 1);
_fmpq_poly_integral(res->coeffs, res->den, poly->coeffs, poly->den, len + 1);
_fmpq_poly_set_length(res, len + 1);
}
void fmpq_poly_neg(fmpq_poly_t poly1, const fmpq_poly_t poly2)
{
if (poly1 == poly2)
{
_fmpz_vec_neg(poly1->coeffs, poly2->coeffs, poly2->length);
}
else
{
fmpq_poly_fit_length(poly1, poly2->length);
_fmpz_vec_neg(poly1->coeffs, poly2->coeffs, poly2->length);
_fmpq_poly_set_length(poly1, poly2->length);
fmpz_set(poly1->den, poly2->den);
}
}
void fmpq_poly_scalar_mul_fmpz(fmpq_poly_t rop, const fmpq_poly_t op, const fmpz_t c)
{
if (fmpz_is_zero(c) || fmpq_poly_is_zero(op))
{
fmpq_poly_zero(rop);
return;
}
fmpq_poly_fit_length(rop, op->length);
_fmpq_poly_set_length(rop, op->length);
_fmpq_poly_scalar_mul_fmpz(rop->coeffs, rop->den,
op->coeffs, op->den, op->length, c);
}
void fmpq_poly_scalar_mul_ui(fmpq_poly_t rop, const fmpq_poly_t op, ulong c)
{
if (c == 0 || fmpq_poly_is_zero(op))
{
fmpq_poly_zero(rop);
return;
}
fmpq_poly_fit_length(rop, op->length);
_fmpq_poly_set_length(rop, op->length);
_fmpq_poly_scalar_mul_ui(rop->coeffs, rop->den,
op->coeffs, op->den, op->length, c);
}
void fmpq_poly_primitive_part(fmpq_poly_t res, const fmpq_poly_t poly)
{
const long len = poly->length;
if (len == 0)
{
fmpq_poly_zero(res);
}
else
{
fmpq_poly_fit_length(res, len);
_fmpq_poly_set_length(res, len);
_fmpq_poly_primitive_part(res->coeffs, res->den,
poly->coeffs, poly->den, len);
}
}
void fmpq_poly_reverse(fmpq_poly_t res, const fmpq_poly_t poly, slong n)
{
slong len = FLINT_MIN(n, poly->length);
if (len == 0)
{
fmpq_poly_zero(res);
return;
}
fmpq_poly_fit_length(res, n);
_fmpz_poly_reverse(res->coeffs, poly->coeffs, len, n);
fmpz_set(res->den, poly->den);
_fmpq_poly_set_length(res, n);
fmpq_poly_canonicalise(res);
}
void random_fmpq_poly(fmpq_poly_t pol, flint_rand_t state, slong length)
{
fmpz * arr;
slong i;
fmpq_poly_fit_length(pol, length);
arr = fmpq_poly_numref(pol);
for (i = 0; i < length; i++)
fmpz_randbits(arr + i, state, BITS);
fmpz_randbits(fmpq_poly_denref(pol), state, BITS);
_fmpq_poly_set_length(pol, length);
_fmpq_poly_normalise(pol);
fmpq_poly_canonicalise(pol);
}
void fmpq_poly_scalar_div_ui(fmpq_poly_t rop, const fmpq_poly_t op, ulong c)
{
if (c == 0UL)
{
printf("Exception: division by zero in fmpq_poly_scalar_div_ui\n");
abort();
}
if (fmpq_poly_is_zero(op))
{
fmpq_poly_zero(rop);
return;
}
fmpq_poly_fit_length(rop, op->length);
_fmpq_poly_set_length(rop, op->length);
_fmpq_poly_scalar_div_ui(rop->coeffs, rop->den,
op->coeffs, op->den, op->length, c);
}
void
fmpq_poly_interpolate_fmpz_vec(fmpq_poly_t poly,
const fmpz * xs, const fmpz * ys, long n)
{
if (n == 0)
{
fmpq_poly_zero(poly);
}
else if (n == 1)
{
fmpq_poly_set_fmpz(poly, ys);
}
else
{
fmpq_poly_fit_length(poly, n);
_fmpq_poly_interpolate_fmpz_vec(poly->coeffs, poly->den, xs, ys, n);
_fmpq_poly_set_length(poly, n);
fmpq_poly_canonicalise(poly);
}
}
void fmpq_poly_div(fmpq_poly_t Q,
const fmpq_poly_t poly1, const fmpq_poly_t poly2)
{
long lenA, lenB, lenQ;
if (fmpq_poly_is_zero(poly2))
{
printf("Exception: division by zero in fmpq_poly_div\n");
abort();
}
if (poly1->length < poly2->length)
{
fmpq_poly_zero(Q);
return;
}
/* Deal with aliasing */
if (Q == poly1 || Q == poly2)
{
fmpq_poly_t tempQ;
fmpq_poly_init(tempQ);
fmpq_poly_div(tempQ, poly1, poly2);
fmpq_poly_swap(Q, tempQ);
fmpq_poly_clear(tempQ);
return;
}
lenA = poly1->length;
lenB = poly2->length;
lenQ = lenA - lenB + 1;
fmpq_poly_fit_length(Q, lenQ);
_fmpq_poly_div(Q->coeffs, Q->den,
poly1->coeffs, poly1->den, poly1->length,
poly2->coeffs, poly2->den, poly2->length);
_fmpq_poly_set_length(Q, lenQ);
}
void fmpq_poly_inv_series_newton(fmpq_poly_t Qinv, const fmpq_poly_t Q, long n)
{
fmpz *copy;
int alloc;
if (Q->length >= n)
{
copy = Q->coeffs;
alloc = 0;
}
else
{
long i;
copy = (fmpz *) flint_malloc(n * sizeof(fmpz));
for (i = 0; i < Q->length; i++)
copy[i] = Q->coeffs[i];
for ( ; i < n; i++)
copy[i] = 0;
alloc = 1;
}
if (Qinv != Q)
{
fmpq_poly_fit_length(Qinv, n);
_fmpq_poly_inv_series_newton(Qinv->coeffs, Qinv->den, copy, Q->den, n);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, n);
_fmpq_poly_inv_series_newton(t->coeffs, t->den, copy, Q->den, n);
fmpq_poly_swap(Qinv, t);
fmpq_poly_clear(t);
}
_fmpq_poly_set_length(Qinv, n);
fmpq_poly_canonicalise(Qinv);
if (alloc)
flint_free(copy);
}
void
fmpq_poly_log_series(fmpq_poly_t res, const fmpq_poly_t f, long n)
{
fmpz * f_coeffs;
long flen = f->length;
if (flen < 1 || !fmpz_equal(f->coeffs, f->den))
{
printf("Exception: fmpq_poly_log_series: constant term != 1\n");
abort();
}
if (flen == 1 || n < 2)
{
fmpq_poly_zero(res);
return;
}
fmpq_poly_fit_length(res, n);
if (flen < n)
{
f_coeffs = _fmpz_vec_init(n);
_fmpz_vec_set(f_coeffs, f->coeffs, flen);
}
else
{
f_coeffs = f->coeffs;
}
_fmpq_poly_log_series(res->coeffs, res->den, f_coeffs, f->den, n);
if (flen < n)
{
_fmpz_vec_clear(f_coeffs, n);
}
_fmpq_poly_set_length(res, n);
_fmpq_poly_normalise(res);
}
void fmpq_poly_scalar_div_fmpq(fmpq_poly_t rop, const fmpq_poly_t op, const fmpq_t c)
{
if (fmpq_is_zero(c))
{
flint_printf("Exception (fmpq_poly_scalar_div_fmpq). Division by zero.\n");
abort();
}
if (fmpq_poly_is_zero(op))
{
fmpq_poly_zero(rop);
}
else
{
fmpq_poly_fit_length(rop, op->length);
_fmpq_poly_set_length(rop, op->length);
_fmpq_poly_scalar_div_fmpq(rop->coeffs, rop->den,
op->coeffs, op->den, op->length,
fmpq_numref(c), fmpq_denref(c));
}
}
void fmpq_poly_randtest_unsigned(fmpq_poly_t poly, flint_rand_t state,
long len, mp_bitcnt_t bits)
{
ulong m;
m = n_randlimb(NULL);
fmpq_poly_fit_length(poly, len);
_fmpq_poly_set_length(poly, len);
if (m & 1UL)
{
_fmpz_vec_randtest_unsigned(poly->coeffs, state, len, bits);
}
else
{
fmpz_t x;
fmpz_init(x);
fmpz_randtest_unsigned(x, state, bits / 2);
_fmpz_vec_randtest_unsigned(poly->coeffs, state, len, (bits + 1) / 2);
_fmpz_vec_scalar_mul_fmpz(poly->coeffs, poly->coeffs, len, x);
fmpz_clear(x);
}
if (m & 2UL)
{
fmpz_randtest_not_zero(poly->den, state, FLINT_MAX(bits, 1));
fmpz_abs(poly->den, poly->den);
fmpq_poly_canonicalise(poly);
}
else
{
fmpz_set_ui(poly->den, 1);
_fmpq_poly_normalise(poly);
}
}
void fmpq_poly_zero(fmpq_poly_t poly)
{
_fmpq_poly_set_length(poly, 0);
fmpz_set_ui(poly->den, 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);
}
}
void fmpq_poly_divrem(fmpq_poly_t Q, fmpq_poly_t R,
const fmpq_poly_t poly1, const fmpq_poly_t poly2)
{
slong lenA, lenB, lenQ, lenR;
if (fmpq_poly_is_zero(poly2))
{
flint_printf("Exception (fmpq_poly_divrem). Division by zero.\n");
abort();
}
if (Q == R)
{
flint_printf("Exception (fmpq_poly_divrem). Output arguments aliased.\n");
abort();
}
/* Deal with the various other cases of aliasing. */
if (R == poly1 || R == poly2)
{
if (Q == poly1 || Q == poly2)
{
fmpq_poly_t tempQ, tempR;
fmpq_poly_init(tempQ);
fmpq_poly_init(tempR);
fmpq_poly_divrem(tempQ, tempR, poly1, poly2);
fmpq_poly_swap(Q, tempQ);
fmpq_poly_swap(R, tempR);
fmpq_poly_clear(tempQ);
fmpq_poly_clear(tempR);
return;
}
else
{
fmpq_poly_t tempR;
fmpq_poly_init(tempR);
fmpq_poly_divrem(Q, tempR, poly1, poly2);
fmpq_poly_swap(R, tempR);
fmpq_poly_clear(tempR);
return;
}
}
else
{
if (Q == poly1 || Q == poly2)
{
fmpq_poly_t tempQ;
fmpq_poly_init(tempQ);
fmpq_poly_divrem(tempQ, R, poly1, poly2);
fmpq_poly_swap(Q, tempQ);
fmpq_poly_clear(tempQ);
return;
}
}
if (poly1->length < poly2->length)
{
fmpq_poly_set(R, poly1);
fmpq_poly_zero(Q);
return;
}
lenA = poly1->length;
lenB = poly2->length;
lenQ = lenA - lenB + 1;
lenR = lenB - 1;
fmpq_poly_fit_length(Q, lenQ);
fmpq_poly_fit_length(R, lenA); /* XXX: Need at least that much space */
_fmpq_poly_divrem(Q->coeffs, Q->den, R->coeffs, R->den,
poly1->coeffs, poly1->den, poly1->length,
poly2->coeffs, poly2->den, poly2->length, NULL);
_fmpq_poly_set_length(Q, lenQ);
_fmpq_poly_set_length(R, lenR);
_fmpq_poly_normalise(R);
}