private void MultTest()
{
IntegerPolynomial i1 = new IntegerPolynomial(new int[] { 1368, 2047, 672, 871, 1662, 1352, 1099, 1608 });
IntegerPolynomial i2 = new IntegerPolynomial(new int[] { 1729, 1924, 806, 179, 1530, 1381, 1695, 60 });
LongPolynomial2 a = new LongPolynomial2(i1);
LongPolynomial2 b = new LongPolynomial2(i2);
IntegerPolynomial c1 = i1.Multiply(i2, 2048);
IntegerPolynomial c2 = a.Multiply(b).ToIntegerPolynomial();
if (!Compare.AreEqual(c1.Coeffs, c2.Coeffs))
throw new Exception("LongPolynomial2 multiply test failed!");
// test 10 random polynomials
Random rng = new Random();
for (int i = 0; i < 10; i++)
{
int N = 2 + rng.Next(2000);
i1 = (IntegerPolynomial)PolynomialGeneratorForTesting.GenerateRandom(N, 2048);
i2 = (IntegerPolynomial)PolynomialGeneratorForTesting.GenerateRandom(N, 2048);
a = new LongPolynomial2(i1);
b = new LongPolynomial2(i2);
c1 = i1.Multiply(i2);
c1.ModPositive(2048);
c2 = a.Multiply(b).ToIntegerPolynomial();
if (!Compare.AreEqual(c1.Coeffs, c2.Coeffs))
throw new Exception("LongPolynomial2 multiply test failed!");
}
}
/// <summary>
/// Resultant of this polynomial with <c>x^n-1 mod p</c>.
/// </summary>
///
/// <param name="P">P value</param>
///
/// <returns>Returns <c>(rho, res)</c> satisfying <c>res = rho*this + t*(x^n-1) mod p</c> for some integer <c>t</c>.</returns>
public ModularResultant Resultant(int P)
{
// Add a coefficient as the following operations involve polynomials of degree deg(f)+1
int[] fcoeffs = Coeffs.CopyOf(Coeffs.Length + 1);
IntegerPolynomial f = new IntegerPolynomial(fcoeffs);
int N = fcoeffs.Length;
IntegerPolynomial a = new IntegerPolynomial(N);
a.Coeffs[0] = -1;
a.Coeffs[N - 1] = 1;
IntegerPolynomial b = new IntegerPolynomial(f.Coeffs);
IntegerPolynomial v1 = new IntegerPolynomial(N);
IntegerPolynomial v2 = new IntegerPolynomial(N);
v2.Coeffs[0] = 1;
int da = N - 1;
int db = b.Degree();
int ta = da;
int c = 0;
int r = 1;
while (db > 0)
{
c = Invert(b.Coeffs[db], P);
c = (c * a.Coeffs[da]) % P;
a.MultShiftSub(b, c, da - db, P);
v1.MultShiftSub(v2, c, da - db, P);
da = a.Degree();
if (da < db)
{
r *= Pow(b.Coeffs[db], ta - da, P);
r %= P;
if (ta % 2 == 1 && db % 2 == 1)
r = (-r) % P;
IntegerPolynomial temp = a;
a = b;
b = temp;
int tempdeg = da;
da = db;
temp = v1;
v1 = v2;
v2 = temp;
ta = db;
db = tempdeg;
}
}
r *= Pow(b.Coeffs[0], da, P);
r %= P;
c = Invert(b.Coeffs[0], P);
v2.Multiply(c);
v2.Mod(P);
v2.Multiply(r);
v2.Mod(P);
// drop the highest coefficient so #coeffs matches the original input
v2.Coeffs = v2.Coeffs.CopyOf(v2.Coeffs.Length - 1);
return new ModularResultant(new BigIntPolynomial(v2), BigInteger.ValueOf(r), BigInteger.ValueOf(P));
}
private void MultTest(int[] coeffs1, int[] coeffs2)
{
IntegerPolynomial i1 = new IntegerPolynomial(coeffs1);
IntegerPolynomial i2 = new IntegerPolynomial(coeffs2);
LongPolynomial5 a = new LongPolynomial5(i1);
DenseTernaryPolynomial b = new DenseTernaryPolynomial(i2);
IntegerPolynomial c1 = i1.Multiply(i2, 2048);
IntegerPolynomial c2 = a.Multiply(b).ToIntegerPolynomial();
if (!EqualsMod(c1.Coeffs, c2.Coeffs, 2048))
throw new Exception("LongPolynomial5 multiply test failed!");
}
private void Mult2AndTest()
{
IntegerPolynomial i1 = new IntegerPolynomial(new int[] { 1368, 2047, 672, 871, 1662, 1352, 1099, 1608 });
LongPolynomial2 i2 = new LongPolynomial2(i1);
i2.Mult2And(2047);
i1.Multiply(2);
i1.ModPositive(2048);
if (!Compare.AreEqual(i1.Coeffs, i2.ToIntegerPolynomial().Coeffs))
throw new Exception("LongPolynomial2 Mult2And test failed!");
}
private void MultTest()
{
// multiplication modulo q
IntegerPolynomial a = new IntegerPolynomial(new int[] { -1, 1, 1, 0, -1, 0, 1, 0, 0, 1, -1 });
IntegerPolynomial b = new IntegerPolynomial(new int[] { 14, 11, 26, 24, 14, 16, 30, 7, 25, 6, 19 });
IntegerPolynomial c = a.Multiply(b, 32);
AssertEqualsMod(new int[] { 3, -7, -10, -11, 10, 7, 6, 7, 5, -3, -7 }, c.Coeffs, 32);
a = new IntegerPolynomial(new int[] { 15, 27, 18, 16, 12, 13, 16, 2, 28, 22, 26 });
b = new IntegerPolynomial(new int[] { -1, 0, 1, 1, 0, 1, 0, 0, -1, 0, -1 });
c = a.Multiply(b, 32);
AssertEqualsMod(new int[] { 8, 25, 22, 20, 12, 24, 15, 19, 12, 19, 16 }, c.Coeffs, 32);
// multiplication without a modulus
a = new IntegerPolynomial(new int[] { 1, 1, 0, 0, -1, -1, 0, 0, -1, 0, 1 });
b = new IntegerPolynomial(new int[] { 2, 14, -10, 10, -4, -10, 2, 12, 11, -2, 8 });
c = a.Multiply(b);
if (!Compare.AreEqual(new int[] { 0, -13, 15, -12, -26, -39, 2, 17, 13, 17, 26 }, c.Coeffs))
throw new Exception("IntegerPolynomial multiplication test failed!");
// mult(p, modulus) should give the same result as mult(p) followed by modulus
a = new IntegerPolynomial(new int[] { 1, 0, -1, 1, 0, 1, 1, 1, -1, 1, -1 });
b = new IntegerPolynomial(new int[] { 0, 1, 1, 0, 0, -1, -1, 1, 1, -1, 1 });
c = a.Multiply(b);
c.ModPositive(20);
IntegerPolynomial d = a.Multiply(b, 20);
d.ModPositive(20);
if (!Compare.AreEqual(c.Coeffs, d.Coeffs))
throw new Exception("IntegerPolynomial multiplication test failed!");
}
// tests if a*b=1 (mod modulus)
private void VerifyInverse(IntegerPolynomial a, IntegerPolynomial b, int modulus)
{
IntegerPolynomial c = a.Multiply(b, modulus);
for (int i = 1; i < c.Coeffs.Length; i++)
c.Coeffs[i] %= modulus;
c.EnsurePositive(modulus);
if (!c.EqualsOne())
throw new Exception("IntegerPolynomialTest Modulus inverse test failed!");
}