public static FiniteField operator *(FiniteField a, FiniteField b)
{
if (a.Prime != b.Prime)
{
throw new ArgumentException("The prime number must be the same");
}
var value = ModuloOperation.Run(a.Value * b.Value, a.Prime);
return(new FiniteField(value, a.Prime));
}
public static FiniteField operator /(FiniteField a, FiniteField b)
{
if (a.Prime != b.Prime)
{
throw new ArgumentException("The prime number must be the same");
}
//Converts the division into multiplication using Fermat's little theorem
//prime = 19 ===> 2/7 = 2*7 pow (19 – 2)
var expNumber = a.Prime - 2;
long expResult = a.Value;
for (long i = 0; i < expNumber; i++)
{
expResult = ModuloOperation.Run(expResult * b.Value, a.Prime);
}
return(new FiniteField(expResult, a.Prime));
}
public static FiniteField Pow(FiniteField a, long pow)
{
long value = a.Value;
long adaptedPow = pow;
//Convert negative pow into positive using Fermat's little theorem
if (pow < 0)
{
while (adaptedPow < 0)
{
adaptedPow += a.Prime - 1;
}
adaptedPow -= 1;
}
for (long i = 0; i < adaptedPow; i++)
{
value = ModuloOperation.Run(value * a.Value, a.Prime);
}
return(new FiniteField(value, a.Prime));
}