Example #1
0
/**
 * Compute the primitive part and the content of a modular multivariate
 * polynomial e \in Z_p[x_n][x_0, \ldots, x_{n-1}], i.e. e is considered
 * a polynomial in variables x_0, \ldots, x_{n-1} with coefficients being
 * modular polynomials Z_p[x_n]
 * @param e polynomial to operate on
 * @param pp primitive part of @a e, will be computed by this function
 * @param c content (in the sense described above) of @a e, will be
 *        computed by this function
 * @param vars variables x_0, \ldots, x_{n-1}, x_n
 * @param p modulus
 */
void primpart_content(ex& pp, ex& c, ex e, const exvector& vars,
		      const long p)
{
	static const ex ex1(1);
	static const ex ex0(0);
	e = e.expand();
	if (e.is_zero()) {
		pp = ex0;
		c = ex1;
		return;
	}
	exvector rest_vars = vars;
	rest_vars.pop_back();
	ex_collect_t ec;
	collect_vargs(ec, e, rest_vars);

	if (ec.size() == 1) {
		// the input polynomial factorizes into 
		// p_1(x_n) p_2(x_0, \ldots, x_{n-1})
		c = ec.rbegin()->second;
		ec.rbegin()->second = ex1;
		pp = ex_collect_to_ex(ec, rest_vars).expand().smod(numeric(p));
		return;
	}

	// Start from the leading coefficient (which is stored as a last
	// element of the terms array)
	auto i = ec.rbegin();
	ex g = i->second;
	// there are at least two terms, so it's safe to...
	++i;
	while (i != ec.rend() && !g.is_equal(ex1)) {
		g = euclid_gcd(i->second, g, vars.back(), p);
		++i;
	}
	if (g.is_equal(ex1)) {
		pp = e;
		c = ex1;
		return;
	}
	exvector mainvar;
	mainvar.push_back(vars.back());
	for (i = ec.rbegin(); i != ec.rend(); ++i) {
		ex tmp(0);
		if (!divide_in_z_p(i->second, g, tmp, mainvar, p))
			throw std::logic_error(std::string(__func__) +
					": bogus division failure");
		i->second = tmp;
	}

	pp = ex_collect_to_ex(ec, rest_vars).expand().smod(numeric(p));
	c = g;
}
Example #2
0
int main(int argc, char *argv[])
{
    int primes[168] = {
        2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
        73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
        157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
        239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
        331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
        421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
        509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
        613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
        709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811,
        821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
        919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
    };
    int t = gint();
    int i, a, b, gcd, ans, tmp;
    while(t--){
        a = gint();
        b = gint();
        gcd = euclid_gcd(a, b);
        ans = 1;
        for (i = 0; i < 168; ++i)
        {
            if (gcd <= 1)
                break;
            tmp = 0;
            while(!(gcd % primes[i])){
                gcd /= primes[i];
                tmp++;
            }
            ans *= tmp + 1;
        }
        if(gcd > 1)
            ans *= 2;
        pint(ans);
        putchar_unlocked('\n');
    }
    return 0;
}