public static Rational EvaluateRationalPower(Rational a, Rational power,int precision)
{
if (a < 0)
{
throw new NotImplementedException("exponentation of negative numbers not yet supported");
}
SignedBigInteger normalexponentiations = power.Numerator / power.Denominator;
SignedBigInteger funkyexponentiation = power.Numerator % power.Denominator;
Rational result;
if (normalexponentiations > 0)
{
result = a.Clone();
for (int i = 1; i < normalexponentiations; i++)
{
result *= a;
}
}
else
{
result = 1;
}
Rational upperbound;
if (a > 1)
{
upperbound = a.Clone();
}
else
{
upperbound = new Rational(a.Denominator, a.Numerator);
}
SignedBigInteger flippedtarget = power.Denominator;
Rational lowerbound = 0;
Rational target = upperbound.Clone();
for (long i = 0; i < precision * 5; i++)
{
Rational error = (upperbound - lowerbound) / 2;
Rational guess = lowerbound + error;
Rational bound = guess.Clone();
for (int j = 1; j < flippedtarget; j++)
{
guess *= bound;
}
if (guess > target)
{
upperbound = bound;
}
if (guess < target)
{
lowerbound = bound;
}
}
for (int i = 0; i < funkyexponentiation; i++)
{
result *= lowerbound;
}
return result;
}
private IEnumerable <Rational> Expansions()
{
// first expansion
yield return(new Rational(3, 2));
var r = new Rational(5, 2);
var count = 0;
do
{
// equivalent to adding 1
var r_ = r.Clone();
r_.SetToReciprocal();
r_.Numerator += r_.Denominator;
yield return(r_);
count++;
// equivalent to 2 + 1/r
r.SetToReciprocal();
r.Numerator += r.Denominator * 2;
} while (true);
}
public Complex(Rational real, Rational imaginary)
{
Real = real.Clone();
Imaginary = imaginary.Clone();
}
