public static Zp EvalutePolynomialAtPoint(IList <Zp> polynomial, Zp point)
{
long evaluation = 0;
for (int i = 0; i < polynomial.Count; i++)
{
evaluation += polynomial[i].Value * NumTheoryUtils.ModPow(point.Value, i, point.Prime);
}
return(new Zp(point.Prime, evaluation));
}
public static ZpMatrix GetPrimitiveVandermondeMatrix(int rowNum, int colNum, long prime)
{
int primitive = NumTheoryUtils.GetFieldMinimumPrimitive(prime);
if (primitive == 0)
{
throw new ArgumentException("Cannot create a primitive Vandermonde matrix from a non-prime number. ");
}
var A = new ZpMatrix(rowNum, colNum, prime);
for (int j = 0; j < colNum; j++)
{
A.data[0][j] = 1;
}
if (rowNum == 1)
{
return(A);
}
/* This variable represents primitive^j for the j-th player*/
long primitive_j = 1;
for (int j = 0; j < colNum; j++)
{
A.data[1][j] = primitive_j;
primitive_j = Zp.Modulo(primitive_j * primitive, prime);
}
for (int j = 0; j < colNum; j++)
{
for (int i = 2; i < rowNum; i++)
{
A.data[i][j] = Zp.Modulo(A.data[i - 1][j] * A.data[1][j], prime);
}
}
return(A);
}