public static MyFraction FractionIdentities(MyFraction fraction)
{
double a = fraction.Numerator; //double.Parse(fraction.Numerator.ToString());
double b = fraction.Denominator; //decimal.Parse(fraction.Denominator.ToString());
MyFraction identity;
identity = new MyFraction(1, (b * (a * b + 1)));
return(identity);
}
public static MyFraction FractionSplitter(MyFraction fraction, out MyFraction outFraction)
{
// use Natural Numbers to split fraction into two sub-fractions a, and b
int[] natNums = new int[] { 100, 60, 24, 20, 12, 8, 6 };
int a = 0;
int b = 0;
foreach (int item in natNums) //NaturalNumbers)
{
// pick the highest NaturalNumber that is less than numerator and subtract from numerator creating n1 and n2
if (MyEgyptianFractions.CompareThese((int)fraction.Numerator, item) == 1)
{
a = (int)fraction.Numerator - item;
b = item;
MyFraction fraction1 = new MyFraction(a, (int)fraction.Denominator);
outFraction = new MyFraction(b, (int)fraction.Denominator);
return(fraction1);
}
}
outFraction = new MyFraction(0, 0); // returns a detectible done message as a 0 value fraction
return(fraction); // return the orginal fraction because it is the smallest it can be
}
public static List <MyFraction> IdentitiesDriver(MyFraction fraction)
{
List <MyFraction> fractionsList = new List <MyFraction>(); // start the tracking list using 1 / n where n is existing denominator
if (fraction.Numerator == 1)
{
fractionsList.Add(fraction);
//return fractionsList;
}
MyFraction temp = new MyFraction(1, fraction.Denominator);
fractionsList.Add(temp); // store the 1/n fraction to the list
decimal sumTotal = fraction.DecimalEquivalent(); // use sumTotal to discover remaining work to be done?
sumTotal -= temp.DecimalEquivalent(); // decrement 1/n from sumTotal
while (sumTotal > 0)
{
MyFraction differenceRemaining = fraction.Difference(temp);
temp = FractionIdentities(differenceRemaining);
fractionsList.Add(temp);
sumTotal -= temp.DecimalEquivalent(); // remove 1/n from the total
}
return(fractionsList); // no more work to do since fraction is 1/n already
}
public MyFraction Difference(MyFraction other)
{
// take two fractions e.g 2/3 and 4/5 and find the difference
// Difference( 10/15, 12/15) => 2/15
double productDenominator = this.Denominator * other.Denominator;
double newFirstNumerator = this.Numerator * other.Denominator;
double newSecondNumerator = other.Numerator * this.Denominator;
double differenceNumerator;
if (this.Numerator > other.Numerator)
{
differenceNumerator = newFirstNumerator - newSecondNumerator;
}
else
{
differenceNumerator = newSecondNumerator - newFirstNumerator;
}
if (productDenominator % differenceNumerator == 0)
{
productDenominator /= differenceNumerator;
differenceNumerator = 1;
}
return(new MyFraction(differenceNumerator, productDenominator));
}