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 _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);
}
}
void ARingZZ::syzygy(const ElementType& a, const ElementType& b,
ElementType& x, ElementType& y) const
{
M2_ASSERT(!is_zero(b));
// First check the special cases a = 0, b = 1, -1. Other cases: use gcd.
if (is_zero(a))
{
set_from_long(x, 1);
set_zero(y);
return;
}
if (fmpz_cmp_ui(&b,1) == 0)
{
set_from_long(x, 1);
negate(y, a);
return;
}
if (fmpz_cmp_si(&b,-1) == 0)
{
set_from_long(x, 1);
set(y, a);
return;
}
ElementType g;
init(g);
fmpz_gcd(&g,&a,&b);
divide(y,a,g);
divide(x,b,g);
if (fmpz_sgn(&x) > 0)
negate(y,y);
else
negate(x,x);
clear(g);
}
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_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
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 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_poly_scalar_div_si(fmpz * rpoly, fmpz_t rden, const fmpz * poly,
const fmpz_t den, long len, long c)
{
if (c == 1)
{
if (rpoly != poly)
{
_fmpz_vec_set(rpoly, poly, len);
fmpz_set(rden, den);
}
}
else if (c == -1)
{
_fmpz_vec_neg(rpoly, poly, len);
fmpz_set(rden, den);
}
else
{
fmpz_t d, f;
fmpz_init(d);
fmpz_init(f);
fmpz_set_si(f, c);
_fmpz_vec_content(d, poly, len);
fmpz_gcd(d, d, f);
if (c > 0)
{
_fmpz_vec_scalar_divexact_fmpz(rpoly, poly, len, d);
fmpz_mul_si(rden, den, c / fmpz_get_si(d));
}
else
{
ulong q = (- (ulong) c) / fmpz_get_ui(d);
fmpz_neg(d, d);
_fmpz_vec_scalar_divexact_fmpz(rpoly, poly, len, d);
fmpz_mul_ui(rden, den, q);
}
fmpz_clear(d);
fmpz_clear(f);
}
}
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_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);
}
}
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;
}
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 _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
_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;
}
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);
}
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);
}
}
/* Assumes len1 != 0 != len2 */
int
_fmpz_poly_gcd_heuristic(fmpz * res, const fmpz * poly1, long len1,
const fmpz * poly2, long len2)
{
ulong bits1, bits2, max_bits, pack_bits, bound_bits, bits_G, bits_Q;
ulong limbs1, limbs2, limbsg, pack_limbs, qlimbs;
ulong log_glen, log_length;
long sign1, sign2, glen, qlen;
fmpz_t ac, bc, d, gc;
fmpz * A, * B, * G, * Q, * t;
mp_ptr array1, array2, arrayg, q, temp;
int divides;
fmpz_init(ac);
fmpz_init(bc);
fmpz_init(d);
/* compute gcd of content of poly1 and poly2 */
_fmpz_poly_content(ac, poly1, len1);
_fmpz_poly_content(bc, poly2, len2);
fmpz_gcd(d, ac, bc);
/* special case, one of the polys is a constant */
if (len2 == 1) /* if len1 == 1 then so does len2 */
{
fmpz_set(res, d);
fmpz_clear(ac);
fmpz_clear(bc);
fmpz_clear(d);
return 1;
}
/* divide poly1 and poly2 by their content */
A = _fmpz_vec_init(len1);
B = _fmpz_vec_init(len2);
_fmpz_vec_scalar_divexact_fmpz(A, poly1, len1, ac);
_fmpz_vec_scalar_divexact_fmpz(B, poly2, len2, bc);
fmpz_clear(ac);
fmpz_clear(bc);
/* special case, one of the polys is length 2 */
if (len2 == 2) /* if len1 == 2 then so does len2 */
{
Q = _fmpz_vec_init(len1 - len2 + 1);
if (_fmpz_poly_divides(Q, A, len1, B, 2))
{
_fmpz_vec_scalar_mul_fmpz(res, B, 2, d);
if (fmpz_sgn(res + 1) < 0)
_fmpz_vec_neg(res, res, 2);
}
else
{
fmpz_set(res, d);
fmpz_zero(res + 1);
}
fmpz_clear(d);
_fmpz_vec_clear(A, len1);
_fmpz_vec_clear(B, len2);
_fmpz_vec_clear(Q, len1 - len2 + 1);
return 1;
}
/*
Determine how many bits (pack_bits) to pack into. The bound
bound_bits ensures that if G | A and G | B with G primitive
then G is the gcd of A and B. The bound is taken from
http://arxiv.org/abs/cs/0206032v1
*/
bits1 = FLINT_ABS(_fmpz_vec_max_bits(A, len1));
bits2 = FLINT_ABS(_fmpz_vec_max_bits(B, len2));
max_bits = FLINT_MAX(bits1, bits2);
bound_bits = FLINT_MIN(bits1, bits2) + 6;
pack_bits = FLINT_MAX(bound_bits, max_bits); /* need to pack original polys */
pack_limbs = (pack_bits - 1)/FLINT_BITS + 1;
if (pack_bits >= 32) /* pack into multiples of limbs if >= 32 bits */
pack_bits = FLINT_BITS*pack_limbs;
/* allocate space to pack into */
limbs1 = (pack_bits*len1 - 1)/FLINT_BITS + 1;
limbs2 = (pack_bits*len2 - 1)/FLINT_BITS + 1;
array1 = flint_calloc(limbs1, sizeof(mp_limb_t));
array2 = flint_calloc(limbs2, sizeof(mp_limb_t));
arrayg = flint_calloc(limbs2, sizeof(mp_limb_t));
/* pack first poly and normalise */
sign1 = (long) fmpz_sgn(A + len1 - 1);
_fmpz_poly_bit_pack(array1, A, len1, pack_bits, sign1);
while (array1[limbs1 - 1] == 0) limbs1--;
/* pack second poly and normalise */
sign2 = (long) fmpz_sgn(B + len2 - 1);
_fmpz_poly_bit_pack(array2, B, len2, pack_bits, sign2);
while (array2[limbs2 - 1] == 0) limbs2--;
/* compute integer GCD */
limbsg = mpn_gcd_full(arrayg, array1, limbs1, array2, limbs2);
/*
Make space for unpacked gcd. May have one extra coeff due to
1 0 -x being packed as 0 -1 -x.
*/
glen = FLINT_MIN((limbsg*FLINT_BITS)/pack_bits + 1, len2);
G = _fmpz_vec_init(glen);
/* unpack gcd */
_fmpz_poly_bit_unpack(G, glen, arrayg, pack_bits, 0);
while (G[glen - 1] == 0) glen--;
/* divide by any content */
fmpz_init(gc);
_fmpz_poly_content(gc, G, glen);
if (!fmpz_is_one(gc))
limbsg = mpn_tdiv_q_fmpz_inplace(arrayg, limbsg, gc);
/* make space for quotient and remainder of first poly by gcd */
qlimbs = limbs1 - limbsg + 1;
qlen = FLINT_MIN(len1, (qlimbs*FLINT_BITS)/pack_bits + 1);
qlimbs = (qlen*pack_bits - 1)/FLINT_BITS + 1;
q = flint_calloc(qlimbs, sizeof(mp_limb_t));
temp = flint_malloc(limbsg*sizeof(mp_limb_t));
divides = 0;
if (mpn_divides(q, array1, limbs1, arrayg, limbsg, temp))
{
/* unpack quotient of first poly by gcd */
Q = _fmpz_vec_init(len1);
t = _fmpz_vec_init(len1 + glen);
_fmpz_poly_bit_unpack(Q, qlen, q, pack_bits, 0);
while (Q[qlen - 1] == 0) qlen--;
/* divide by content */
_fmpz_vec_scalar_divexact_fmpz(G, G, glen, gc);
/* check if we really need to multiply out to check for exact quotient */
bits_G = FLINT_ABS(_fmpz_vec_max_bits(G, glen));
bits_Q = FLINT_ABS(_fmpz_vec_max_bits(Q, qlen));
log_glen = FLINT_BIT_COUNT(glen);
log_length = FLINT_MIN(log_glen, FLINT_BIT_COUNT(qlen));
divides = (bits_G + bits_Q + log_length < pack_bits);
if (!divides) /* need to multiply out to check exact quotient */
divides = multiplies_out(A, len1, Q, qlen, G, glen, sign1, t);
if (divides) /* quotient really was exact */
{
mpn_zero(q, qlimbs);
if (mpn_divides(q, array2, limbs2, arrayg, limbsg, temp))
{
/* unpack quotient of second poly by gcd */
qlimbs = limbs2 - limbsg + 1;
qlen = FLINT_MIN(len2, (qlimbs*FLINT_BITS - 1)/pack_bits + 1);
_fmpz_poly_bit_unpack(Q, qlen, q, pack_bits, 0);
while (Q[qlen - 1] == 0) qlen--;
/* check if we really need to multiply out to check for exact quotient */
bits_Q = FLINT_ABS(_fmpz_vec_max_bits(Q, qlen));
log_length = FLINT_MIN(log_glen, FLINT_BIT_COUNT(qlen));
divides = (bits_G + bits_Q + log_length < pack_bits);
if (!divides) /* we need to multiply out */
divides = multiplies_out(B, len2, Q, qlen, G, glen, sign1, t);
}
}
_fmpz_vec_clear(t, len1 + glen);
_fmpz_vec_clear(Q, len1);
}
flint_free(q);
flint_free(temp);
flint_free(arrayg);
flint_free(array1);
flint_free(array2);
fmpz_clear(gc);
_fmpz_vec_clear(A, len1);
_fmpz_vec_clear(B, len2);
/* we found the gcd, so multiply by content */
if (divides)
{
_fmpz_vec_zero(res + glen, len2 - glen);
_fmpz_vec_scalar_mul_fmpz(res, G, glen, d);
}
fmpz_clear(d);
_fmpz_vec_clear(G, glen);
return divides;
}
