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// Test quadratic field extensions.
#include "pbc.h"
#include "pbc_fp.h"
#include "pbc_fieldquadratic.h"
#include "pbc_test.h"
int main(void) {
field_t fp, fp2;
mpz_t prime;
element_t a, b, c;
mpz_init(prime);
// Prime is 3 mod 4 so that -1 is a quadratic nonresidue.
// For smaller tests, try the prime 83.
mpz_setbit(prime, 256);
do {
mpz_nextprime(prime, prime);
} while (mpz_fdiv_ui(prime, 4) != 3);
field_init_fp(fp, prime);
field_init_fi(fp2, fp);
element_init(a, fp2);
element_init(b, fp2);
element_init(c, fp2);
element_printf("field: %Z^2\n", prime);
element_random(a);
element_random(b);
element_printf("a = %B, b = %B\n", a, b);
element_add(c, a, b);
element_printf("a + b = %B\n", c);
element_mul(c, a, b);
element_printf("a * b = %B\n", c);
for (;;) {
element_random(a);
element_printf("new a = %B\n", a);
if (element_is_sqr(a)) break;
printf(" is not a square\n");
}
element_sqrt(c, a);
element_printf("sqrt(a) = %B\n", c);
element_mul(c, c, c);
element_printf("sqrt(a) * sqrt(a) = %B\n", c);
element_invert(c, a);
element_printf("1/a = %B\n", c);
element_mul(c, c, a);
element_printf("1/a * a = %B\n", c);
element_clear(a);
element_clear(b);
element_clear(c);
field_clear(fp);
field_clear(fp2);
mpz_clear(prime);
return 0;
}
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