divisor& divisor::random(divdeg_t dgr){ // Underlying curve is not touched
assert(s_hcurve.is_valid_curve());
// A random valid divisor is generated by the following algorithm:
// generate a degree 1 divisor [x - a1, b1] by choosing a1 by random
// then trying to solve quadratic equation
// x^2 + h(a1)*x - f(a1) for b1.
// Note that finding a root of an equation by calling routine
// FindRoot(root, poly) may go into an infinite loop if poly does
// not split completely. We avoid this by calling irreducibility
// test routine DetIrredTest(poly). After a degree 1 divisor is
// found, this divisor is doubled by calling add_cantor() to return
// a degree 2 polynomial.
field_t a1, b1, f_of_a1, h_of_a1;
poly_t poly; // polynomial x^2 + h(a1)*x - f(a1)
SetCoeff(poly, 2); // set degree 2 leading term to 1
do {
do{
NTL_NNS random(a1);
eval(f_of_a1, s_hcurve.get_f(), a1);
eval(h_of_a1, s_hcurve.get_h(), a1);
SetCoeff(poly, 1, h_of_a1);
SetCoeff(poly, 0, - f_of_a1);
} while ( DetIrredTest(poly) );
FindRoot(b1, poly);
// Set upoly = x - a1
SetX(upoly);
SetCoeff(upoly, 0, -a1);
// Set vpoly = b1
vpoly = b1;
update();
} while (*this == -*this); // Avoid getting unit after doubling
// return a degree one divisor if dgr = 1
if (dgr == DEGREE_1)
return *this;
// Double the degree 1 divisor to get a degree 2 divisor, otherwise
add_cantor(*this, *this, *this);
if (is_valid_divisor())
return *this;
cerr << "Random divisor failed to generate" << endl;
abort();
}
NTL_CLIENT
int main()
{
zz_p::init(17);
zz_pX P;
BuildIrred(P, 10);
zz_pE::init(P);
zz_pEX f, g, h;
random(f, 20);
SetCoeff(f, 20);
random(h, 20);
g = MinPolyMod(h, f);
if (deg(g) < 0) Error("bad zz_pEXTest (1)");
if (CompMod(g, h, f) != 0)
Error("bad zz_pEXTest (2)");
vec_pair_zz_pEX_long v;
long i;
for (i = 0; i < 5; i++) {
long n = RandomBnd(20)+1;
cerr << n << " ";
random(f, n);
SetCoeff(f, n);
v = CanZass(f);
g = mul(v);
if (f != g) cerr << "oops1\n";
long i;
for (i = 0; i < v.length(); i++)
if (!DetIrredTest(v[i].a))
Error("bad zz_pEXTest (3)");
}
cerr << "\n";
cerr << "zz_pEXTest OK\n";
}