public Normalizer(int[] height)
{
var m = height.Max();
FactoredDifference = new FactoredRational[m + 1, m + 1];
for (int i = 0; i <= m; i++)
{
for (int j = 0; j <= m; j++)
{
FactoredDifference[i, j] = new FactoredRational(i - j);
}
}
InsideProduct = new FactoredRational[height.Length, m + 1];
for (int i = 0; i < height.Length; i++)
{
for (int j = 0; j <= height[i]; j++)
{
InsideProduct[i, j] = new FactoredRational()
{
K = new List <int>(), Sign = 1
};
for (int k = 0; k <= height[i]; k++)
{
if (k == j)
{
continue;
}
InsideProduct[i, j] *= FactoredDifference[j, k];
}
}
}
}
public FactoredRational Get(int[] a)
{
var normalizer = new FactoredRational()
{
K = new List <int>(), Sign = 1
};
for (int i = 0; i < a.Length; i++)
{
normalizer *= InsideProduct[i, a[i]];
}
return(normalizer);
}
public int GetCoefficient(int[] power)
{
_normalizer = new Normalizer(power);
var a = new int[power.Length];
long top = 0L;
long bottom = 1L;
var partialProduct = new FactoredRational()
{
K = new List <int>(), Sign = 1
};
SumTerms(0, a, power, ref partialProduct, ref top, ref bottom);
return((int)(top / bottom));
}
void SumTerms(int w, int[] a, int[] power, ref FactoredRational partialProduct, ref long top, ref long bottom)
{
if (w == power.Length)
{
var r = partialProduct / _normalizer.Get(a);
int top2;
int bottom2;
r.ToRational(out top2, out bottom2);
top = top * bottom2 + bottom * top2;
bottom = bottom * bottom2;
var gcd = GCD(top, bottom);
top /= gcd;
bottom /= gcd;
}
else
{
for (int j = 0; j <= power[w]; j++)
{
a[w] = j;
var current = new FactoredRational()
{
K = new List <int>(), Sign = 1
};
foreach (var v in _priorNeighbors[w])
{
current *= _normalizer.FactoredDifference[a[v], a[w]];
}
if (current.Sign == 0)
{
continue;
}
partialProduct *= current;
SumTerms(w + 1, a, power, ref partialProduct, ref top, ref bottom);
partialProduct /= current;
}
}
}
