int
main(void)
{
int cflags = 0, i, result;
flint_rand_t state;
printf("lcm....");
fflush(stdout);
flint_randinit(state);
/* Check aliasing of a and c */
for (i = 0; i < 1000; i++)
{
fmpq_poly_t a, b, c;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_randtest(a, state, n_randint(state, 100), 100);
fmpq_poly_randtest(b, state, n_randint(state, 100), 100);
fmpq_poly_lcm(c, a, b);
fmpq_poly_lcm(a, a, b);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(c) ? 0 : 2;
result = (fmpq_poly_equal(a, c) && !cflags);
if (!result)
{
printf("FAIL:\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(c), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
}
/* Check aliasing of b and c */
for (i = 0; i < 1000; i++)
{
fmpq_poly_t a, b, c;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_randtest(a, state, n_randint(state, 100), 100);
fmpq_poly_randtest(b, state, n_randint(state, 100), 100);
fmpq_poly_lcm(c, a, b);
fmpq_poly_lcm(b, a, b);
cflags |= fmpq_poly_is_canonical(b) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(c) ? 0 : 2;
result = (fmpq_poly_equal(b, c) && !cflags);
if (!result)
{
printf("FAIL:\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(c), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
}
/* Generic case when a, b are most likely co-prime ***********************/
/* Verify commutativity and that c is monic */
for (i = 0; i < 1000; i++)
{
fmpq_poly_t a, b, c;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_randtest(a, state, n_randint(state, 100), 100);
fmpq_poly_randtest(b, state, n_randint(state, 100), 100);
fmpq_poly_lcm(c, a, b);
fmpq_poly_lcm(a, b, a);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(c) ? 0 : 2;
result = (fmpq_poly_equal(a, c) && !cflags
&& (fmpq_poly_is_zero(c) || fmpq_poly_is_monic(c)));
if (!result)
{
printf("FAIL:\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(c), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
}
/* Verify that LCM(a, b) GCD(a, b) == a b */
for (i = 0; i < 1000; i++)
{
fmpq_poly_t a, b, lcm, gcd;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(lcm);
fmpq_poly_init(gcd);
fmpq_poly_randtest(a, state, n_randint(state, 100), 100);
fmpq_poly_randtest(b, state, n_randint(state, 100), 100);
fmpq_poly_lcm(lcm, a, b);
fmpq_poly_gcd(gcd, a, b);
fmpq_poly_mul(lcm, lcm, gcd);
fmpq_poly_mul(a, a, b);
fmpq_poly_make_monic(a, a);
result = fmpq_poly_equal(lcm, a);
if (!result)
{
printf("FAIL:\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(lcm), printf("\n\n");
fmpq_poly_debug(gcd), printf("\n\n");
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(lcm);
fmpq_poly_clear(gcd);
}
/* Case when a, b are not co-prime ***************************************/
/* Verify commutativity and that c is monic */
for (i = 0; i < 1000; i++)
{
fmpq_poly_t a, b, c, t;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_init(t);
fmpq_poly_randtest(a, state, n_randint(state, 100), 100);
fmpq_poly_randtest(b, state, n_randint(state, 100), 100);
fmpq_poly_randtest(t, state, n_randint(state, 50), 20);
fmpq_poly_mul(a, a, t);
fmpq_poly_mul(b, b, t);
fmpq_poly_lcm(c, a, b);
fmpq_poly_lcm(a, b, a);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(c) ? 0 : 2;
result = (fmpq_poly_equal(a, c) && !cflags
&& (fmpq_poly_is_zero(c) || fmpq_poly_is_monic(c)));
if (!result)
{
printf("FAIL:\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(c), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
fmpq_poly_clear(t);
}
/* Verify that LCM(a, b) GCD(a, b) == a b */
for (i = 0; i < 1000; i++)
{
fmpq_poly_t a, b, lcm, gcd, t;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(lcm);
fmpq_poly_init(gcd);
fmpq_poly_init(t);
fmpq_poly_randtest(a, state, n_randint(state, 100), 100);
fmpq_poly_randtest(b, state, n_randint(state, 100), 100);
fmpq_poly_randtest(t, state, n_randint(state, 50), 20);
fmpq_poly_mul(a, a, t);
fmpq_poly_mul(b, b, t);
fmpq_poly_lcm(lcm, a, b);
fmpq_poly_gcd(gcd, a, b);
fmpq_poly_mul(lcm, lcm, gcd);
fmpq_poly_mul(a, a, b);
fmpq_poly_make_monic(a, a);
result = fmpq_poly_equal(lcm, a);
if (!result)
{
printf("FAIL:\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(lcm), printf("\n\n");
fmpq_poly_debug(gcd), printf("\n\n");
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(lcm);
fmpq_poly_clear(gcd);
fmpq_poly_clear(t);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("evaluate_fmpz....");
fflush(stdout);
/* Check that (f+g)(a) = f(a) + g(a) */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_t a;
fmpq_poly_t f, g, h;
fmpq_t x, y;
fmpq_init(x);
fmpq_init(y);
fmpz_init(a);
fmpq_poly_init(f);
fmpq_poly_init(g);
fmpq_poly_init(h);
fmpq_poly_randtest(f, state, n_randint(state, 100), 200);
fmpq_poly_randtest(g, state, n_randint(state, 100), 200);
fmpz_randtest(a, state, n_randint(state, 100));
fmpq_poly_evaluate_fmpz(x, f, a);
fmpq_poly_evaluate_fmpz(y, g, a);
fmpq_add(x, x, y);
fmpq_poly_add(h, f, g);
fmpq_poly_evaluate_fmpz(y, h, a);
result = (fmpq_equal(x, y));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("f = "), fmpq_poly_debug(f), flint_printf("\n");
flint_printf("g = "), fmpq_poly_debug(g), flint_printf("\n");
flint_printf("a = "), fmpz_print(a), flint_printf("\n");
flint_printf("f(a) + g(a) = "), fmpq_print(x), flint_printf("\n\n");
flint_printf("(f + g)(a) = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_clear(x);
fmpq_clear(y);
fmpz_clear(a);
fmpq_poly_clear(f);
fmpq_poly_clear(g);
fmpq_poly_clear(h);
}
/* Check that (f*g)(a) = f(a) * g(a) */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_t a;
fmpq_poly_t f, g;
fmpq_t x, y;
fmpq_init(x);
fmpq_init(y);
fmpz_init(a);
fmpq_poly_init(f);
fmpq_poly_init(g);
fmpq_poly_randtest(f, state, n_randint(state, 100), 200);
fmpq_poly_randtest(g, state, n_randint(state, 100), 200);
fmpz_randtest(a, state, n_randint(state, 100));
fmpq_poly_evaluate_fmpz(x, f, a);
fmpq_poly_evaluate_fmpz(y, g, a);
fmpq_mul(x, x, y);
fmpq_poly_mul(f, f, g);
fmpq_poly_evaluate_fmpz(y, f, a);
result = (fmpq_equal(x, y));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_print(a), flint_printf("\n\n");
abort();
}
fmpq_clear(x);
fmpq_clear(y);
fmpz_clear(a);
fmpq_poly_clear(f);
fmpq_poly_clear(g);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
ulong cflags = UWORD(0);
FLINT_TEST_INIT(state);
flint_printf("derivative....");
fflush(stdout);
/* Check aliasing */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpq_poly_t a, b;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_randtest(a, state, n_randint(state, 100), 200);
fmpq_poly_derivative(b, a);
fmpq_poly_derivative(a, a);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(b) ? 0 : 2;
result = (fmpq_poly_equal(a, b) && !cflags);
if (!result)
{
flint_printf("FAIL:\n");
fmpq_poly_debug(a), flint_printf("\n\n");
fmpq_poly_debug(b), flint_printf("\n\n");
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
}
/* Check constants have derivative zero */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpq_poly_t a, b;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_randtest(a, state, n_randint(state, 2), 200);
fmpq_poly_derivative(b, a);
cflags |= fmpq_poly_is_canonical(b) ? 0 : 1;
result = fmpq_poly_is_zero(b) && !cflags;
if (!result)
{
flint_printf("FAIL:\n");
fmpq_poly_debug(a), flint_printf("\n\n");
fmpq_poly_debug(b), flint_printf("\n\n");
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
}
/* Check (f g)' = f' g + f g' */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpq_poly_t a, b, c, d, lhs, rhs;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_init(d);
fmpq_poly_init(lhs);
fmpq_poly_init(rhs);
fmpq_poly_randtest(a, state, n_randint(state, 100), 200);
fmpq_poly_randtest(b, state, n_randint(state, 100), 200);
fmpq_poly_mul(lhs, a, b);
fmpq_poly_derivative(lhs, lhs);
fmpq_poly_derivative(c, a);
fmpq_poly_derivative(d, b);
fmpq_poly_mul(c, c, b);
fmpq_poly_mul(d, a, d);
fmpq_poly_add(rhs, c, d);
cflags |= fmpq_poly_is_canonical(lhs) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(rhs) ? 0 : 2;
result = fmpq_poly_equal(lhs, rhs) && !cflags;
if (!result)
{
flint_printf("FAIL:\n");
fmpq_poly_debug(a), flint_printf("\n\n");
fmpq_poly_debug(b), flint_printf("\n\n");
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
fmpq_poly_clear(d);
fmpq_poly_clear(lhs);
fmpq_poly_clear(rhs);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("mul....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
slong qbits1, qbits2, rbits1, rbits2, rbits3;
fmpq_poly_t A, B, C;
arb_poly_t a, b, c, d;
qbits1 = 2 + n_randint(state, 200);
qbits2 = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
rbits3 = 2 + n_randint(state, 200);
fmpq_poly_init(A);
fmpq_poly_init(B);
fmpq_poly_init(C);
arb_poly_init(a);
arb_poly_init(b);
arb_poly_init(c);
arb_poly_init(d);
fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1);
fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2);
fmpq_poly_mul(C, A, B);
arb_poly_set_fmpq_poly(a, A, rbits1);
arb_poly_set_fmpq_poly(b, B, rbits2);
arb_poly_mul(c, a, b, rbits3);
if (!arb_poly_contains_fmpq_poly(c, C))
{
flint_printf("FAIL\n\n");
flint_printf("bits3 = %wd\n", rbits3);
flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n");
flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n");
flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n");
flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n");
abort();
}
arb_poly_set(d, a);
arb_poly_mul(d, d, b, rbits3);
if (!arb_poly_equal(d, c))
{
flint_printf("FAIL (aliasing 1)\n\n");
abort();
}
arb_poly_set(d, b);
arb_poly_mul(d, a, d, rbits3);
if (!arb_poly_equal(d, c))
{
flint_printf("FAIL (aliasing 2)\n\n");
abort();
}
/* test squaring */
arb_poly_set(b, a);
arb_poly_mul(c, a, b, rbits3);
arb_poly_mul(d, a, a, rbits3);
if (!arb_poly_overlaps(c, d)) /* not guaranteed to be identical */
{
flint_printf("FAIL (squaring)\n\n");
flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n");
abort();
}
arb_poly_mul(a, a, a, rbits3);
if (!arb_poly_equal(d, a))
{
flint_printf("FAIL (aliasing, squaring)\n\n");
flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n");
flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n");
abort();
}
fmpq_poly_clear(A);
fmpq_poly_clear(B);
fmpq_poly_clear(C);
arb_poly_clear(a);
arb_poly_clear(b);
arb_poly_clear(c);
arb_poly_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("resultant_div....");
fflush(stdout);
for (i = 0; i < 50; i++)
{
fmpq_poly_t f, g, h, p;
fmpq_t x, y, z, zz;
fmpz_t den;
slong nbits;
fmpq_poly_init(f);
fmpq_poly_init(g);
fmpq_poly_init(p);
fmpq_poly_init(h);
fmpq_init(x);
fmpq_init(y);
fmpq_init(z);
fmpq_init(zz);
fmpz_init(den);
fmpq_poly_randtest(f, state, n_randint(state, 50), 100);
fmpq_poly_randtest(g, state, n_randint(state, 50), 100);
fmpq_poly_randtest(h, state, n_randint(state, 50), 100);
fmpz_set(den, fmpq_poly_denref(f));
fmpq_poly_scalar_mul_fmpz(f, f, den);
fmpz_set(den, fmpq_poly_denref(g));
fmpq_poly_scalar_mul_fmpz(g, g, den);
fmpz_set(den, fmpq_poly_denref(h));
fmpq_poly_scalar_mul_fmpz(h, h, den);
fmpq_poly_mul(p, f, g);
fmpq_poly_resultant(x, f, h);
if (!fmpz_is_one(fmpq_denref(x)))
{
flint_printf("FAIL resultant not integral\n");
flint_printf("f = "), fmpq_poly_print(f), flint_printf("\n\n");
flint_printf("g = "), fmpq_poly_print(g), flint_printf("\n\n");
flint_printf("y = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_poly_resultant(y, g, h);
if (!fmpz_is_one(fmpq_denref(y)))
{
flint_printf("FAIL resultant not integral\n");
flint_printf("h = "), fmpq_poly_print(f), flint_printf("\n\n");
flint_printf("g = "), fmpq_poly_print(g), flint_printf("\n\n");
flint_printf("z = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_poly_resultant(z, p, h);
if (!fmpz_is_one(fmpq_denref(z)))
{
flint_printf("FAIL resultant not integral\n");
flint_printf("p = "), fmpq_poly_print(f), flint_printf("\n\n");
flint_printf("g = "), fmpq_poly_print(g), flint_printf("\n\n");
flint_printf("y = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
if (fmpq_is_zero(z))
{
fmpq_poly_clear(f);
fmpq_poly_clear(g);
fmpq_poly_clear(h);
fmpq_poly_clear(p);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
fmpq_clear(zz);
fmpz_clear(den);
continue;
}
nbits = (slong)fmpz_bits(fmpq_numref(y)) + 1;
fmpq_poly_resultant_div(z, p, h, fmpq_numref(x), nbits);
fmpq_poly_resultant(zz, p, h);
result = fmpq_equal(z, y);
if (!result)
{
flint_printf("FAIL (res(p, g)/div == res(p, g)/div:\n");
flint_printf("p = "), fmpq_poly_print_pretty(p, "x"), flint_printf("\n\n");
flint_printf("h = "), fmpq_poly_print_pretty(h, "x"), flint_printf("\n\n");
flint_printf("res(p, h) = "), fmpq_print(zz), flint_printf("\n\n");
flint_printf("res(p, h) = "), fmpq_print(x), flint_printf(" * "), fmpq_print(y), flint_printf("\n\n");
flint_printf("supplied divisor = "), fmpq_print(x), flint_printf("\n\n");
flint_printf("nbits = %wu\n\n", nbits);
flint_printf("divisor found = "), fmpq_print(z), flint_printf("\n\n");
flint_printf("correct result = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_poly_clear(f);
fmpq_poly_clear(g);
fmpq_poly_clear(h);
fmpq_poly_clear(p);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
fmpq_clear(zz);
fmpz_clear(den);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
padic_ctx_t ctx;
fmpz_t p;
slong N;
FLINT_TEST_INIT(state);
flint_printf("mul... ");
fflush(stdout);
/* Check aliasing of a and b */
for (i = 0; i < 1000; i++)
{
padic_poly_t a, b, c;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = n_randint(state, PADIC_TEST_PREC_MAX - PADIC_TEST_PREC_MIN)
+ PADIC_TEST_PREC_MIN;
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_poly_init2(a, 0, N);
padic_poly_init2(b, 0, N);
padic_poly_init2(c, 0, N);
padic_poly_randtest(b, state, n_randint(state, 50), ctx);
padic_poly_randtest(c, state, n_randint(state, 50), ctx);
padic_poly_mul(a, b, c, ctx);
padic_poly_mul(b, b, c, ctx);
result = (padic_poly_equal(a, b) && padic_poly_is_reduced(a, ctx));
if (!result)
{
flint_printf("FAIL (aliasing a and b):\n");
padic_poly_print(a, ctx), flint_printf("\n\n");
padic_poly_print(b, ctx), flint_printf("\n\n");
abort();
}
padic_poly_clear(a);
padic_poly_clear(b);
padic_poly_clear(c);
padic_ctx_clear(ctx);
fmpz_clear(p);
}
/* Check aliasing of a and c */
for (i = 0; i < 1000; i++)
{
padic_poly_t a, b, c;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = n_randint(state, PADIC_TEST_PREC_MAX - PADIC_TEST_PREC_MIN)
+ PADIC_TEST_PREC_MIN;
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_poly_init2(a, 0, N);
padic_poly_init2(b, 0, N);
padic_poly_init2(c, 0, N);
padic_poly_randtest(b, state, n_randint(state, 50), ctx);
padic_poly_randtest(c, state, n_randint(state, 50), ctx);
padic_poly_mul(a, b, c, ctx);
padic_poly_mul(c, b, c, ctx);
result = (padic_poly_equal(a, c) && padic_poly_is_reduced(a, ctx));
if (!result)
{
flint_printf("FAIL (aliasing a and c):\n");
padic_poly_print(a, ctx), flint_printf("\n\n");
padic_poly_print(c, ctx), flint_printf("\n\n");
abort();
}
padic_poly_clear(a);
padic_poly_clear(b);
padic_poly_clear(c);
padic_ctx_clear(ctx);
fmpz_clear(p);
}
/* Check (b * c) + (b * d) = b * (c + d) */
for (i = 0; i < 1000; i++)
{
padic_poly_t a1, a2, b, c, d, t;
slong v;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = n_randint(state, PADIC_TEST_PREC_MAX - PADIC_TEST_PREC_MIN)
+ PADIC_TEST_PREC_MIN;
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_poly_init2(b, 0, N);
padic_poly_init2(c, 0, N);
padic_poly_init2(d, 0, N);
padic_poly_init2(t, 0, N);
padic_poly_randtest(b, state, n_randint(state, 100), ctx);
padic_poly_randtest(c, state, n_randint(state, 100), ctx);
padic_poly_randtest(d, state, n_randint(state, 100), ctx);
v = FLINT_MIN(b->val, c->val);
v = FLINT_MIN(v, d->val);
v = FLINT_MIN(v, 0);
if (v >= 0 || -v < N) /* Otherwise, no precision left */
{
slong N2 = (v >= 0) ? N : N + v;
padic_poly_init2(a1, 0, N2);
padic_poly_init2(a2, 0, N2);
padic_poly_mul(a1, b, c, ctx);
padic_poly_mul(t, b, d, ctx);
padic_poly_add(a1, a1, t, ctx); /* Lower precision */
padic_poly_add(t, c, d, ctx);
padic_poly_mul(a2, b, t, ctx); /* Lower precision */
result = (padic_poly_equal(a1, a2) && padic_poly_is_reduced(a1, ctx));
if (!result)
{
flint_printf("FAIL (distributivity):\n");
flint_printf("p = "), fmpz_print(ctx->p), flint_printf("\n\n");
flint_printf("N = %wd\n\n", N);
flint_printf("b = "), padic_poly_print(b, ctx), flint_printf("\n\n");
flint_printf("c = "), padic_poly_print(c, ctx), flint_printf("\n\n");
flint_printf("d = "), padic_poly_print(d, ctx), flint_printf("\n\n");
flint_printf("a1 = "), padic_poly_print(a1, ctx), flint_printf("\n\n");
flint_printf("a2 = "), padic_poly_print(a2, ctx), flint_printf("\n\n");
abort();
}
padic_poly_clear(a1);
padic_poly_clear(a2);
}
padic_poly_clear(b);
padic_poly_clear(c);
padic_poly_clear(d);
padic_ctx_clear(ctx);
fmpz_clear(p);
}
/* Compare with Q */
for (i = 0; i < 10000; i++)
{
padic_poly_t a, b, c, d;
fmpq_poly_t x, y, z;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = n_randint(state, PADIC_TEST_PREC_MAX - PADIC_TEST_PREC_MIN)
+ PADIC_TEST_PREC_MIN;
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_poly_init2(a, 0, N);
padic_poly_init2(b, 0, N);
padic_poly_init2(c, 0, N);
padic_poly_init2(d, 0, N);
fmpq_poly_init(x);
fmpq_poly_init(y);
fmpq_poly_init(z);
padic_poly_randtest(b, state, n_randint(state, 50), ctx);
padic_poly_randtest(c, state, n_randint(state, 50), ctx);
padic_poly_mul(a, b, c, ctx);
padic_poly_get_fmpq_poly(y, b, ctx);
padic_poly_get_fmpq_poly(z, c, ctx);
fmpq_poly_mul(x, y, z);
padic_poly_set_fmpq_poly(d, x, ctx);
result = (padic_poly_equal(a, d) && padic_poly_is_reduced(a, ctx));
if (!result)
{
flint_printf("FAIL (cmp with Q):\n");
flint_printf("N = %wd, val(b) = %wd, val(c) = %wd\n", N, b->val, c->val);
padic_poly_print(c, ctx), flint_printf("\n\n");
padic_poly_print(d, ctx), flint_printf("\n\n");
abort();
}
padic_poly_clear(a);
padic_poly_clear(b);
padic_poly_clear(c);
padic_poly_clear(d);
fmpq_poly_clear(x);
fmpq_poly_clear(y);
fmpq_poly_clear(z);
padic_ctx_clear(ctx);
fmpz_clear(p);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(void)
{
int i, result;
ulong cflags = UWORD(0);
FLINT_TEST_INIT(state);
flint_printf("compose....");
fflush(stdout);
/* Check aliasing of the first argument */
for (i = 0; i < 10 * flint_test_multiplier(); i++)
{
fmpq_poly_t f, g, h;
fmpq_poly_init(f);
fmpq_poly_init(g);
fmpq_poly_init(h);
fmpq_poly_randtest(g, state, n_randint(state, 50), 100);
fmpq_poly_randtest(h, state, n_randint(state, 20), 50);
fmpq_poly_compose(f, g, h);
fmpq_poly_compose(g, g, h);
cflags |= fmpq_poly_is_canonical(f) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(g) ? 0 : 2;
result = (fmpq_poly_equal(f, g) && !cflags);
if (!result)
{
flint_printf("FAIL (aliasing 1):\n");
fmpq_poly_debug(f), flint_printf("\n\n");
fmpq_poly_debug(g), flint_printf("\n\n");
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_poly_clear(f);
fmpq_poly_clear(g);
fmpq_poly_clear(h);
}
/* Check aliasing of the second argument */
for (i = 0; i < 10 * flint_test_multiplier(); i++)
{
fmpq_poly_t f, g, h;
fmpq_poly_init(f);
fmpq_poly_init(g);
fmpq_poly_init(h);
fmpq_poly_randtest(g, state, n_randint(state, 50), 100);
fmpq_poly_randtest(h, state, n_randint(state, 20), 50);
fmpq_poly_compose(f, g, h);
fmpq_poly_compose(h, g, h);
cflags |= fmpq_poly_is_canonical(f) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(h) ? 0 : 2;
result = (fmpq_poly_equal(f, h) && !cflags);
if (!result)
{
flint_printf("FAIL (aliasing 2):\n");
fmpq_poly_debug(f), flint_printf("\n\n");
fmpq_poly_debug(h), flint_printf("\n\n");
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_poly_clear(f);
fmpq_poly_clear(g);
fmpq_poly_clear(h);
}
/* Compare with the naive method for g(h(t)) */
for (i = 0; i < 10 * flint_test_multiplier(); i++)
{
fmpq_poly_t f, g, h, s, t, u;
mpq_t c;
slong k;
fmpq_poly_init(f);
fmpq_poly_init(g);
fmpq_poly_init(h);
fmpq_poly_init(s);
fmpq_poly_init(t);
fmpq_poly_init(u);
mpq_init(c);
fmpq_poly_randtest(g, state, n_randint(state, 20), 65);
fmpq_poly_randtest(h, state, n_randint(state, 20), 65);
fmpq_poly_zero(s);
fmpq_poly_set_ui(t, UWORD(1));
for (k = WORD(0); k < g->length; k++)
{
fmpq_poly_get_coeff_mpq(c, g, k);
fmpq_poly_scalar_mul_mpq(u, t, c);
fmpq_poly_add(s, s, u);
fmpq_poly_mul(t, t, h);
}
fmpq_poly_compose(f, g, h);
result = (fmpq_poly_equal(f, s));
if (!result)
{
flint_printf("FAIL (compare with naive):\n");
flint_printf("g = "), fmpq_poly_debug(g), flint_printf("\n\n");
flint_printf("h = "), fmpq_poly_debug(h), flint_printf("\n\n");
flint_printf("f = "), fmpq_poly_debug(f), flint_printf("\n\n");
flint_printf("s = "), fmpq_poly_debug(s), flint_printf("\n\n");
abort();
}
fmpq_poly_clear(f);
fmpq_poly_clear(g);
fmpq_poly_clear(h);
fmpq_poly_clear(s);
fmpq_poly_clear(t);
fmpq_poly_clear(u);
mpq_clear(c);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int cflags = 0, i, result;
flint_rand_t state;
printf("xgcd....");
fflush(stdout);
flint_randinit(state);
/* Generic case, where a and b are coprime *******************************/
/* Verify d == s a + t b */
for (i = 0; i < 100; i++)
{
fmpq_poly_t a, b, d, e, f, s, t;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(d);
fmpq_poly_init(e);
fmpq_poly_init(f);
fmpq_poly_init(s);
fmpq_poly_init(t);
fmpq_poly_randtest(a, state, n_randint(state, 60), 80);
fmpq_poly_randtest(b, state, n_randint(state, 60), 80);
fmpq_poly_xgcd(d, s, t, a, b);
fmpq_poly_mul(e, s, a);
fmpq_poly_mul(f, t, b);
fmpq_poly_add(e, e, f);
cflags |= fmpq_poly_is_canonical(d) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(s) ? 0 : 2;
cflags |= fmpq_poly_is_canonical(t) ? 0 : 4;
result = (fmpq_poly_equal(d, e) && !cflags);
if (!result)
{
printf("FAIL (correctness #1):\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(d), printf("\n\n");
fmpq_poly_debug(s), printf("\n\n");
fmpq_poly_debug(t), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(d);
fmpq_poly_clear(e);
fmpq_poly_clear(f);
fmpq_poly_clear(s);
fmpq_poly_clear(t);
}
/* Verify consistency with GCD */
for (i = 0; i < 100; i++)
{
fmpq_poly_t a, b, d, s, t;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(d);
fmpq_poly_init(s);
fmpq_poly_init(t);
fmpq_poly_randtest(a, state, n_randint(state, 60), 80);
fmpq_poly_randtest(b, state, n_randint(state, 60), 80);
fmpq_poly_xgcd(d, s, t, a, b);
fmpq_poly_gcd(a, a, b);
cflags |= fmpq_poly_is_canonical(d) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(s) ? 0 : 2;
cflags |= fmpq_poly_is_canonical(t) ? 0 : 4;
result = (fmpq_poly_equal(d, a) && !cflags);
if (!result)
{
printf("FAIL (GCD #1):\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(d), printf("\n\n");
fmpq_poly_debug(s), printf("\n\n");
fmpq_poly_debug(t), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(d);
fmpq_poly_clear(s);
fmpq_poly_clear(t);
}
/* Generic case when a, b are most likely co-prime ***********************/
/* Verify d == s a + t b */
for (i = 0; i < 100; i++)
{
fmpq_poly_t a, b, d, s, t, z;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(d);
fmpq_poly_init(s);
fmpq_poly_init(t);
fmpq_poly_init(z);
fmpq_poly_randtest(a, state, n_randint(state, 60), 80);
fmpq_poly_randtest(b, state, n_randint(state, 60), 80);
fmpq_poly_randtest(z, state, n_randint(state, 20), 20);
fmpq_poly_mul(a, a, z);
fmpq_poly_mul(b, b, z);
fmpq_poly_xgcd(d, s, t, a, b);
fmpq_poly_mul(a, s, a);
fmpq_poly_mul(b, t, b);
fmpq_poly_add(a, a, b);
cflags |= fmpq_poly_is_canonical(d) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(s) ? 0 : 2;
cflags |= fmpq_poly_is_canonical(t) ? 0 : 4;
result = (fmpq_poly_equal(d, a) && !cflags);
if (!result)
{
printf("FAIL (correctness #2):\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(d), printf("\n\n");
fmpq_poly_debug(s), printf("\n\n");
fmpq_poly_debug(t), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(d);
fmpq_poly_clear(s);
fmpq_poly_clear(t);
fmpq_poly_clear(z);
}
/* Verify consistency with GCD */
for (i = 0; i < 100; i++)
{
fmpq_poly_t a, b, d, s, t, z;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(d);
fmpq_poly_init(s);
fmpq_poly_init(t);
fmpq_poly_init(z);
fmpq_poly_randtest(a, state, n_randint(state, 60), 80);
fmpq_poly_randtest(b, state, n_randint(state, 60), 80);
fmpq_poly_randtest(z, state, n_randint(state, 20), 20);
fmpq_poly_mul(a, a, z);
fmpq_poly_mul(b, b, z);
fmpq_poly_xgcd(d, s, t, a, b);
fmpq_poly_gcd(a, a, b);
cflags |= fmpq_poly_is_canonical(d) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(s) ? 0 : 2;
cflags |= fmpq_poly_is_canonical(t) ? 0 : 4;
result = (fmpq_poly_equal(d, a) && !cflags);
if (!result)
{
printf("FAIL (GCD #2):\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(d), printf("\n\n");
fmpq_poly_debug(s), printf("\n\n");
fmpq_poly_debug(t), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(d);
fmpq_poly_clear(s);
fmpq_poly_clear(t);
fmpq_poly_clear(z);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("evaluate_fmpq....");
fflush(stdout);
flint_randinit(state);
/* Check aliasing */
for (i = 0; i < 1000; i++)
{
fmpz_t a, b;
fmpq_t x, y;
fmpq_poly_t f;
fmpz_init(a);
fmpz_init(b);
fmpq_init(x);
fmpq_init(y);
fmpq_poly_init(f);
fmpq_poly_randtest(f, state, n_randint(state, 80), 100);
fmpz_randtest(a, state, 80);
fmpz_randtest_not_zero(b, state, 80);
fmpz_set(fmpq_numref(x), a);
fmpz_set(fmpq_denref(x), a);
fmpq_canonicalise(x);
fmpq_poly_evaluate_fmpq(y, f, x);
fmpq_poly_evaluate_fmpq(x, f, x);
result = (fmpq_equal(x, y));
if (!result)
{
printf("FAIL:\n");
fmpz_print(a), printf("\n\n");
fmpz_print(b), printf("\n\n");
fmpq_poly_debug(f), printf("\n\n");
abort();
}
fmpz_clear(a);
fmpz_clear(b);
fmpq_clear(x);
fmpq_clear(y);
fmpq_poly_clear(f);
}
/* Check that (f+g)(a) = f(a) + g(a) */
for (i = 0; i < 1000; i++)
{
fmpz_t a, b;
fmpq_t x, y, z;
fmpq_poly_t f, g;
fmpz_init(a);
fmpz_init(b);
fmpq_init(x);
fmpq_init(y);
fmpq_init(z);
fmpq_poly_init(f);
fmpq_poly_init(g);
fmpq_poly_randtest(f, state, n_randint(state, 80), 100);
fmpq_poly_randtest(g, state, n_randint(state, 80), 100);
fmpz_randtest(a, state, 80);
fmpz_randtest_not_zero(b, state, 80);
fmpz_set(fmpq_numref(x), a);
fmpz_set(fmpq_denref(x), a);
fmpq_canonicalise(x);
fmpq_poly_evaluate_fmpq(y, f, x);
fmpq_poly_evaluate_fmpq(z, g, x);
fmpq_add(y, y, z);
fmpq_poly_add(f, f, g);
fmpq_poly_evaluate_fmpq(z, f, x);
result = (fmpq_equal(y, z));
if (!result)
{
printf("FAIL:\n");
fmpz_print(a), printf("\n\n");
fmpz_print(b), printf("\n\n");
abort();
}
fmpz_clear(a);
fmpz_clear(b);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
fmpq_poly_clear(f);
fmpq_poly_clear(g);
}
/* Check that (f*g)(a) = f(a) * g(a) */
for (i = 0; i < 1000; i++)
{
fmpz_t a, b;
fmpq_t x, y, z;
fmpq_poly_t f, g;
fmpz_init(a);
fmpz_init(b);
fmpq_init(x);
fmpq_init(y);
fmpq_init(z);
fmpq_poly_init(f);
fmpq_poly_init(g);
fmpq_poly_randtest(f, state, n_randint(state, 50), 80);
fmpq_poly_randtest(g, state, n_randint(state, 50), 80);
fmpz_randtest(a, state, 80);
fmpz_randtest_not_zero(b, state, 80);
fmpz_set(fmpq_numref(x), a);
fmpz_set(fmpq_denref(x), a);
fmpq_canonicalise(x);
fmpq_poly_evaluate_fmpq(y, f, x);
fmpq_poly_evaluate_fmpq(z, g, x);
fmpq_mul(y, y, z);
fmpq_poly_mul(f, f, g);
fmpq_poly_evaluate_fmpq(z, f, x);
result = (fmpq_equal(y, z));
if (!result)
{
printf("FAIL:\n");
fmpz_print(a), printf("\n\n");
fmpz_print(b), printf("\n\n");
abort();
}
fmpz_clear(a);
fmpz_clear(b);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
fmpq_poly_clear(f);
fmpq_poly_clear(g);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int main(int argc, char* argv[]) {
int i, j, k;
int levels[argc-1];
fmpq_poly_t Pn, Ep;
long deg;
char *strf;
acb_ptr nodes;
acb_ptr weights;
int solvable;
int validate_extension, validate_weights;
int valid;
int comp_nodes, comp_weights;
int target_prec;
int nrprintdigits;
int loglevel;
if(argc <= 1) {
printf("Compute a nested generalized Kronrod extension of a Gauss rule\n");
printf("Syntax: kes [-ve] [-vw] [-cn] [-cw] [-dc D] [-dp D] [-l L] n p1 p2 ... pk\n");
printf("Options:\n");
printf(" -ve Validate the polynomial extension by nodes\n");
printf(" -vw Validate the polynomial extension by weights\n");
printf(" -cn Compute the nodes\n");
printf(" -cw Compute the weights\n");
printf(" -dc Compute nodes and weights up to this number of decimal digits\n");
printf(" -dp Print this number of decimal digits\n");
printf(" -l Set the log level\n");
return EXIT_FAILURE;
}
target_prec = 53;
nrprintdigits = 20;
loglevel = 8;
comp_nodes = 0;
comp_weights = 0;
validate_extension = 0;
validate_weights = 0;
k = 0;
for(i = 1; i < argc; i++) {
if (!strcmp(argv[i], "-ve")) {
validate_extension = 1;
} else if (!strcmp(argv[i], "-vw")) {
validate_weights = 1;
} else if (!strcmp(argv[i], "-cn")) {
comp_nodes = 1;
} else if (!strcmp(argv[i], "-cw")) {
comp_weights = 1;
} else if (!strcmp(argv[i], "-dc")) {
/* 'digits' is in base 10 and log(10)/log(2) = 3.32193 */
target_prec = 3.32193 * atoi(argv[i+1]);
i++;
} else if (!strcmp(argv[i], "-dp")) {
nrprintdigits = atoi(argv[i+1]);
i++;
} else if (!strcmp(argv[i], "-l")) {
loglevel = atoi(argv[i+1]);
i++;
} else {
levels[k] = atoi(argv[i]);
k++;
}
}
/* Compute extension */
fmpq_poly_init(Pn);
polynomial(Pn, levels[0]);
printf("Starting with polynomial:\n");
strf = fmpq_poly_get_str_pretty(Pn, "t");
flint_printf("P : %s\n", strf);
printf("Extension levels are:");
for(i = 0; i < k; i++) {
printf(" %i", levels[i]);
}
printf("\n");
fmpq_poly_init(Ep);
solvable = find_multi_extension(Ep, Pn, k, levels, validate_extension, loglevel);
fmpq_poly_mul(Pn, Pn, Ep);
fmpq_poly_canonicalise(Pn);
if(solvable) {
if(! fmpq_poly_is_squarefree(Pn)) {
printf("=====> FINAL POLYNOMIAL NOT SQF <=====");
}
if(loglevel >= 2) {
printf("-------------------------------------------------\n");
printf("Ending with final polynomial:\n");
strf = fmpq_poly_get_str_pretty(Pn, "t");
flint_printf("P : %s\n", strf);
}
deg = fmpq_poly_degree(Pn);
nodes = _acb_vec_init(deg);
weights = _acb_vec_init(deg);
if(comp_weights || validate_weights) {
compute_nodes_and_weights(nodes, weights, Pn, target_prec, loglevel);
} else if(comp_nodes) {
compute_nodes(nodes, Pn, target_prec, loglevel);
}
valid = 1;
if(validate_weights) {
valid = validate_extension_by_weights(weights, deg, target_prec, loglevel);
}
if(! valid) {
printf("**************************************\n");
printf("*** EXTENSION WITH INVALID WEIGHTS ***\n");
printf("**************************************\n");
}
/* Print roots and weights */
if((validate_weights && valid) || ! validate_weights) {
if(comp_nodes) {
printf("-------------------------------------------------\n");
printf("The nodes are:\n");
for(j = 0; j < deg; j++) {
printf("| ");
acb_printd(nodes + j, nrprintdigits);
printf("\n");
}
}
if(comp_weights) {
printf("-------------------------------------------------\n");
printf("The weights are:\n");
for(j = 0; j < deg; j++) {
printf("| ");
acb_printd(weights + j, nrprintdigits);
printf("\n");
}
}
}
_acb_vec_clear(nodes, deg);
_acb_vec_clear(weights, deg);
}
flint_free(strf);
fmpq_poly_clear(Pn);
fmpq_poly_clear(Ep);
return EXIT_SUCCESS;
}
int
main(void)
{
int cflags = 0, i, result;
flint_rand_t state;
printf("gcd....");
fflush(stdout);
flint_randinit(state);
/* Check aliasing of a and c */
for (i = 0; i < 1000; i++)
{
fmpq_poly_t a, b, c;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_randtest(a, state, n_randint(state, 100), 100);
fmpq_poly_randtest(b, state, n_randint(state, 100), 100);
fmpq_poly_gcd(c, a, b);
fmpq_poly_gcd(a, a, b);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(c) ? 0 : 2;
result = (fmpq_poly_equal(a, c) && !cflags);
if (!result)
{
printf("FAIL (aliasing a, c):\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(c), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
}
/* Check aliasing of b and c */
for (i = 0; i < 1000; i++)
{
fmpq_poly_t a, b, c;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_randtest(a, state, n_randint(state, 100), 100);
fmpq_poly_randtest(b, state, n_randint(state, 100), 100);
fmpq_poly_gcd(c, a, b);
fmpq_poly_gcd(b, a, b);
cflags |= fmpq_poly_is_canonical(b) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(c) ? 0 : 2;
result = (fmpq_poly_equal(b, c) && !cflags);
if (!result)
{
printf("FAIL (aliasing b, c):\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(c), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
}
/* Generic case when a, b are most likely co-prime ***********************/
/* Verify commutativity and that c is monic */
for (i = 0; i < 1000; i++)
{
fmpq_poly_t a, b, c;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_randtest(a, state, n_randint(state, 100), 100);
fmpq_poly_randtest(b, state, n_randint(state, 100), 100);
fmpq_poly_gcd(c, a, b);
fmpq_poly_gcd(a, b, a);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(c) ? 0 : 2;
result = (fmpq_poly_equal(a, c) && !cflags
&& (fmpq_poly_is_zero(c) || fmpq_poly_is_monic(c)));
if (!result)
{
printf("FAIL (commutativity #1):\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(c), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
}
/* Verify that GCD(a, b) divides a, b */
for (i = 0; i < 1000; i++)
{
fmpq_poly_t a, b, c, r1, r2;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_init(r1);
fmpq_poly_init(r2);
fmpq_poly_randtest(a, state, n_randint(state, 100), 100);
fmpq_poly_randtest(b, state, n_randint(state, 100), 100);
fmpq_poly_gcd(c, a, b);
if (!fmpq_poly_is_zero(c))
{
fmpq_poly_rem(r1, a, c);
fmpq_poly_rem(r2, b, c);
}
result = fmpq_poly_is_zero(r1) && fmpq_poly_is_zero(r2);
if (!result)
{
printf("FAIL (division #1):\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(c), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
fmpq_poly_clear(r1);
fmpq_poly_clear(r2);
}
/* Case when a, b are not co-prime ***************************************/
/* Verify commutativity and that c is monic */
for (i = 0; i < 1000; i++)
{
fmpq_poly_t a, b, c, t;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_init(t);
fmpq_poly_randtest(a, state, n_randint(state, 100), 100);
fmpq_poly_randtest(b, state, n_randint(state, 100), 100);
fmpq_poly_randtest(t, state, n_randint(state, 50), 20);
fmpq_poly_mul(a, a, t);
fmpq_poly_mul(b, b, t);
fmpq_poly_gcd(c, a, b);
fmpq_poly_gcd(a, b, a);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(c) ? 0 : 2;
result = (fmpq_poly_equal(a, c) && !cflags
&& (fmpq_poly_is_zero(c) || fmpq_poly_is_monic(c)));
if (!result)
{
printf("FAIL (commutativity #2):\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(c), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
fmpq_poly_clear(t);
}
/* Verify that GCD(a, b) divides a, b */
for (i = 0; i < 1000; i++)
{
fmpq_poly_t a, b, c, r1, r2, t;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_init(r1);
fmpq_poly_init(r2);
fmpq_poly_init(t);
fmpq_poly_randtest(a, state, n_randint(state, 100), 100);
fmpq_poly_randtest(b, state, n_randint(state, 100), 100);
fmpq_poly_randtest(t, state, n_randint(state, 50), 20);
fmpq_poly_mul(a, a, t);
fmpq_poly_mul(b, b, t);
fmpq_poly_gcd(c, a, b);
if (!fmpq_poly_is_zero(c))
{
fmpq_poly_rem(r1, a, c);
fmpq_poly_rem(r2, b, c);
}
result = fmpq_poly_is_zero(r1) && fmpq_poly_is_zero(r2);
if (!result)
{
printf("FAIL (division #2):\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
fmpq_poly_debug(c), printf("\n\n");
printf("cflags = %d\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
fmpq_poly_clear(r1);
fmpq_poly_clear(r2);
fmpq_poly_clear(t);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
var MulPolyQ(const Tuple& x,const Tuple& y){
fmpq_poly_t res;
fmpq_poly_init(res);
fmpq_poly_mul(res,to_fmpq_poly(x),to_fmpq_poly(y));
return from_fmpq_poly(res);
}
