public static RationalMatrix operator *(RationalMatrix left, RationalMatrix right)
{
if (left._columns != right._rows)
{
throw new Exception("Incompatible matrices");
}
RationalMatrix result = new RationalMatrix(left._rows, right._columns);
for (int i = 0; i < left._rows; i++)
{
for (int j = 0; j < right._columns; j++)
{
for (int k = 0; k < left._columns; k++)
{
result._values[i, j] += left[i, k] * right[k, j];
}
}
}
return(result);
}
public static RationalMatrix GaussianElimination(RationalMatrix a, RationalMatrix b)
{
RationalNumber[,] ap = (RationalNumber[, ])a._values.Clone();
RationalNumber[,] bp = (RationalNumber[, ])b._values.Clone();
int n = b._rows;
for (int k = 1; k <= n; k++)
{
for (int i = k + 1; i <= n; i++)
{
RationalNumber m = ap[i - 1, k - 1] / ap[k - 1, k - 1];
ap[i - 1, k - 1] = RationalNumber.Zero;
for (int j = k + 1; j <= n; j++)
{
ap[i - 1, j - 1] -= m * ap[k - 1, j - 1];
}
bp[i - 1, 0] -= m * bp[k - 1, 0];
}
}
RationalMatrix x = new RationalMatrix(n, 1);
for (int i = n; i >= 1; i--)
{
for (int j = i + 1; j <= n; j++)
{
bp[i - 1, 0] -= ap[i - 1, j - 1] * x[j - 1, 0];
}
x[i - 1, 0] = bp[i - 1, 0] / ap[i - 1, i - 1];
}
return(x);
}
public static ModulusNumber F(int w, BigInteger h)
{
if (w == 0 || h == 0)
{
return(ModulusNumber.One);
}
EvenOdd[] previous = new EvenOdd[w];
EvenOdd[] current = new EvenOdd[w];
for (int i = 0; i < w; i++)
{
current[i] = EvenOdd.OneEven;
}
RationalMatrix aEven = new RationalMatrix(w + 1, w + 1);
RationalMatrix bEven = new RationalMatrix(w + 1, 1);
RationalMatrix aOdd = new RationalMatrix(w + 1, w + 1);
RationalMatrix bOdd = new RationalMatrix(w + 1, 1);
for (int i = 1; i <= (w + 1) * 2; i++)
{
EvenOdd[] temp = previous;
previous = current;
current = temp;
for (int j = 1; j <= w; j++)
{
EvenOdd result = Get(current, j - 1) + Get(previous, j).Swap;
for (int k = 1; k < j; k++)
{
EvenOdd subResult0 = Get(previous, k).Swap;
EvenOdd subResult1 = Get(current, j - k - 1);
EvenOdd total = subResult0 * subResult1;
result += total;
}
Set(current, j, result);
}
if (i % 2 == 0)
{
long x = i;
BigInteger y = previous[w - 1].Odd;
BigInteger xe = 1;
for (int j = 0; j < w + 1; j++)
{
aEven[(i - 1) / 2, j] = new RationalNumber(xe, 1);
xe *= x;
}
bEven[(i - 1) / 2, 0] = new RationalNumber(y, 1);
}
else
{
long x = i;
BigInteger y = previous[w - 1].Odd;
BigInteger xe = 1;
for (int j = 0; j < w + 1; j++)
{
aOdd[(i - 1) / 2, j] = new RationalNumber(xe, 1);
xe *= x;
}
bOdd[(i - 1) / 2, 0] = new RationalNumber(y, 1);
}
}
RationalMatrix cEven = RationalMatrix.GaussianElimination(aEven, bEven);
RationalNumber[] coefficientsEven = cEven.GetColumn(0);
RationalMatrix cOdd = RationalMatrix.GaussianElimination(aOdd, bOdd);
RationalNumber[] coefficientsOdd = cOdd.GetColumn(0);
RationalNumber[] highCoefficients;
RationalNumber[] lowCoefficients;
if (h % 2 == 0)
{
highCoefficients = coefficientsEven;
lowCoefficients = coefficientsOdd;
}
else
{
highCoefficients = coefficientsOdd;
lowCoefficients = coefficientsEven;
}
RationalNumber sum = RationalNumber.Zero;
RationalNumber power = RationalNumber.One;
for (int i = 0; i < w + 1; i++)
{
RationalNumber rationalValue = highCoefficients[i] * power;
sum += rationalValue;
power *= new RationalNumber(h, 1);
}
if (sum.Denominator != 1)
{
throw new Exception();
}
if (h > 2)
{
power = RationalNumber.One;
for (int i = 0; i < w + 1; i++)
{
RationalNumber rationalValue = lowCoefficients[i] * power;
sum -= rationalValue;
power *= new RationalNumber(h - 1, 1);
}
}
return(new ModulusNumber((uint)(sum.Numerator % ModulusNumber.Mod)));
}