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// Test polynomials.
#include "pbc.h"
#include "pbc_fp.h"
#include "pbc_poly.h"
#include "pbc_test.h"
#include "misc/darray.h"
static void elfree(void *data) {
element_clear(data);
pbc_free(data);
}
static void inner(void *data2, element_ptr f, field_t fx, darray_t prodlist) {
element_ptr g = data2;
if (!poly_degree(f) || !poly_degree(g)) return;
if (poly_degree(f) + poly_degree(g) > 3) return;
element_ptr h = pbc_malloc(sizeof(*h));
element_init(h, fx);
element_mul(h, f, g);
darray_append(prodlist, h);
EXPECT(!poly_is_irred(h));
}
static void outer(void *data, darray_t list, field_t fx, darray_t prodlist) {
element_ptr f = data;
darray_forall4(list, (void(*)(void*,void*,void*,void*))inner, f, fx, prodlist);
}
int isf(void *data, element_ptr f) {
element_ptr f1 = data;
return !element_cmp(f, f1);
}
int main(void) {
field_t fp, fx;
mpz_t prime;
darray_t list;
int p = 7;
// Exercise poly_is_irred() with a sieve of Erastosthenes for polynomials.
darray_init(list);
mpz_init(prime);
mpz_set_ui(prime, p);
field_init_fp(fp, prime);
field_init_poly(fx, fp);
element_t e;
element_init(e, fp);
// Enumerate polynomials in F_p[x] up to degree 2.
int a[3], d;
a[0] = a[1] = a[2] = 0;
for(;;) {
element_ptr f = pbc_malloc(sizeof(*f));
element_init(f, fx);
int j;
for(j = 0; j < 3; j++) {
element_set_si(e, a[j]);
poly_set_coeff(f, e, j);
}
// Test poly_degree().
for(j = 2; j >= 0 && !a[j]; j--);
EXPECT(poly_degree(f) == j);
// Add monic polynomials to the list.
if (j >= 0 && a[j] == 1) darray_append(list, f);
else {
element_clear(f);
pbc_free(f);
}
// Next!
d = 0;
for(;;) {
a[d]++;
if (a[d] >= p) {
a[d] = 0;
d++;
if (d > 2) goto break2;
} else break;
}
}
break2: ;
// Find all composite monic polynomials of degree 3 or less.
darray_t prodlist;
darray_init(prodlist);
darray_forall4(list, (void(*)(void*,void*,void*,void*))outer, list, fx, prodlist);
// Enumerate all monic polynomials in F_p[x] up to degree 3.
a[0] = a[1] = a[2] = 0;
for(;;) {
element_t f;
element_init(f, fx);
int j;
for(j = 0; j < 3; j++) {
element_set_si(e, a[j]);
poly_set_coeff(f, e, j);
}
for(j = 2; j >= 0 && !a[j]; j--);
element_set1(e);
poly_set_coeff(f, e, j + 1);
// Check f is a unit or appears on the list of composites if and only if
// poly_is_irred() returns 0.
if (poly_is_irred(f)) {
EXPECT(!darray_at_test(prodlist, (int(*)(void*,void*))isf, f));
} else if (poly_degree(f)) {
EXPECT(darray_at_test(prodlist, (int(*)(void*,void*))isf, f));
}
element_clear(f);
// Next!
d = 0;
for(;;) {
a[d]++;
if (a[d] >= p) {
a[d] = 0;
d++;
if (d > 2) goto break3;
} else break;
}
}
break3: ;
darray_forall(list, elfree);
darray_forall(prodlist, elfree);
darray_clear(prodlist);
darray_clear(list);
mpz_clear(prime);
field_clear(fx);
field_clear(fp);
element_clear(e);
return pbc_err_count;
}
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