void nf_elem_scalar_div_fmpq(nf_elem_t a, const nf_elem_t b,
const fmpq_t c, const nf_t nf)
{
if (nf->flag & NF_LINEAR)
{
fmpz * den = LNF_ELEM_DENREF(a);
fmpz * num = LNF_ELEM_NUMREF(a);
const fmpz * const den2 = LNF_ELEM_DENREF(b);
const fmpz * const num2 = LNF_ELEM_NUMREF(b);
_fmpq_mul(num, den, num2, den2, fmpq_denref(c), fmpq_numref(c));
}
else if (nf->flag & NF_QUADRATIC)
{
fmpz * den = QNF_ELEM_DENREF(a);
fmpz * num = QNF_ELEM_NUMREF(a);
const fmpz * const den2 = QNF_ELEM_DENREF(b);
const fmpz * const num2 = QNF_ELEM_NUMREF(b);
_fmpq_poly_scalar_div_fmpq(num, den,
num2, den2, 2, fmpq_numref(c), fmpq_denref(c));
} else
{
fmpq_poly_scalar_div_fmpq(NF_ELEM(a),
NF_ELEM(b), c);
}
}
void _fmpq_poly_div(fmpz * Q, fmpz_t q,
const fmpz * A, const fmpz_t a, long lenA,
const fmpz * B, const fmpz_t b, long lenB)
{
long lenQ = lenA - lenB + 1;
ulong d;
const fmpz * lead = B + (lenB - 1);
if (lenB == 1)
{
_fmpq_poly_scalar_div_fmpq(Q, q, A, a, lenA, B, b);
return;
}
/*
From pseudo division over Z we have
lead^d * A = Q * B + R
and thus
{A, a} = {b * Q, a * lead^d} * {B, b} + {R, a * lead^d}.
*/
_fmpz_poly_pseudo_div(Q, &d, A, lenA, B, lenB);
/* 1. lead^d == +-1. {Q, q} = {b Q, a} up to sign */
if (d == 0UL || *lead == 1L || *lead == -1L)
{
fmpz_one(q);
_fmpq_poly_scalar_mul_fmpz(Q, q, Q, q, lenQ, b);
_fmpq_poly_scalar_div_fmpz(Q, q, Q, q, lenQ, a);
if (*lead == -1L && d % 2UL)
_fmpz_vec_neg(Q, Q, lenQ);
}
/* 2. lead^d != +-1. {Q, q} = {b Q, a lead^d} */
else
{
/*
TODO: Improve this. Clearly we do not need to compute
den = a lead^d in many cases, but can determine the GCD from
lead alone already.
*/
fmpz_t den;
fmpz_init(den);
fmpz_pow_ui(den, lead, d);
fmpz_mul(den, a, den);
fmpz_one(q);
_fmpq_poly_scalar_mul_fmpz(Q, q, Q, q, lenQ, b);
_fmpq_poly_scalar_div_fmpz(Q, q, Q, q, lenQ, den);
fmpz_clear(den);
}
}
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_divrem(fmpz * Q, fmpz_t q, fmpz * R, fmpz_t r,
const fmpz * A, const fmpz_t a, slong lenA,
const fmpz * B, const fmpz_t b, slong lenB, const fmpz_preinvn_t inv)
{
slong lenQ = lenA - lenB + 1;
slong lenR = lenB - 1;
ulong d;
const fmpz * lead = B + (lenB - 1);
if (lenB == 1)
{
_fmpq_poly_scalar_div_fmpq(Q, q, A, a, lenA, B, b);
fmpz_one(r);
return;
}
/*
From pseudo division over Z we have
lead^d * A = Q * B + R
and thus
{A, a} = {b * Q, a * lead^d} * {B, b} + {R, a * lead^d}.
*/
_fmpz_poly_pseudo_divrem(Q, R, &d, A, lenA, B, lenB, inv);
/* Determine the actual length of R */
for ( ; lenR != 0 && fmpz_is_zero(R + (lenR - 1)); lenR--) ;
/* 1. lead^d == +-1. {Q, q} = {b Q, a}, {R, r} = {R, a} up to sign */
if (d == UWORD(0) || *lead == WORD(1) || *lead == WORD(-1))
{
fmpz_one(q);
_fmpq_poly_scalar_mul_fmpz(Q, q, Q, q, lenQ, b);
_fmpq_poly_scalar_div_fmpz(Q, q, Q, q, lenQ, a);
fmpz_one(r);
if (lenR > 0)
_fmpq_poly_scalar_div_fmpz(R, r, R, r, lenR, a);
if (*lead == WORD(-1) && d % UWORD(2))
{
_fmpz_vec_neg(Q, Q, lenQ);
_fmpz_vec_neg(R, R, lenR);
}
}
/* 2. lead^d != +-1. {Q, q} = {b Q, a lead^d}, {R, r} = {R, a lead^d} */
else
{
/*
TODO: Improve this. Clearly we do not need to compute
den = a lead^d in many cases, but can determine the GCD from
lead alone already.
*/
fmpz_t den;
fmpz_init(den);
fmpz_pow_ui(den, lead, d);
fmpz_mul(den, a, den);
fmpz_one(q);
_fmpq_poly_scalar_mul_fmpz(Q, q, Q, q, lenQ, b);
_fmpq_poly_scalar_div_fmpz(Q, q, Q, q, lenQ, den);
fmpz_one(r);
if (lenR > 0)
_fmpq_poly_scalar_div_fmpz(R, r, R, r, lenR, den);
fmpz_clear(den);
}
}
