// BenOr algorithm
// Why not return true or false? - of course C was written by the dinosours and booleans did not exist
// during that era. :/
int getReducibilty(unsigned long val) {
bits temp = bits_initlong(val);
int degree = poly_degree(temp);
bits one = bits_initlong(1l);
int i = 1;
for(; i <= degree/2; i++) {
bits b = poly_reduceExp(temp, i);
bits g = poly_gcd(temp, b);
if (!eq(one, g))
return 1;
}
return 0;
}
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; !a[j] && j >= 0; 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);
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);
void outer(void *data) {
element_ptr f = data;
void inner(void *data2) {
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));
}
