PrimesAndFractions: A C# repository from CSF Software Limited

This library deals with prime numbers (generating collections of them), getting the prime factors for arbitrary positive integers and also provides fraction data type which may be used to represent, format and calculate with rational numbers.

All types described below are in the namespace CSF.

Getting prime numbers

To get a collection of prime numbers, use the service PrimeNumberGenerator, which implements the interface CSF.IGetsPrimeNumbers. The method GetPrimeNumbers will return a collection of prime numbers up to a specified upper limit. If you instead wish to get the first X amount of prime numbers, use an arbitrarily high upper limit combined with Linq .Take. For example:

var firstTwentyPrimes = new PrimeNumberGenerator().GetPrimeNumbers(10000).Take(20);

This mechanism will not result in extra work, calculating primes beyond the 20th.

Getting prime factors

To calculate the prime factors for an arbitrary positive integer, use the service PrimeFactorProvider, which implements the interface IGetsPrimeFactors. The method GetPrimeFactors will return a collection of all of the prime factors for the specified number. It will return duplicates if the same prime factor goes more than once into the number. For example:

var primeFactors = new PrimeFactorProvider().GetPrimeFactors(18);
// primeFactors will be equivalent to new [] { 2, 3, 3, 3 }

Getting common prime factors

To get the prime factors which are common to two specified positive integers, use the service CommonPrimeFactorProvider, which implements IGetsCommonPrimeFactors. The GetPrimeFactors method will return a collection of prime factors which are common to both specified inputs. For example:

var commonFactors = new CommonPrimeFactorProvider().GetPrimeFactors(18, 6);
// commonFactors will be equivalent to new [] { 2, 3 }

Fractions

The Fraction struct is a powerful representation of rational numbers, both positive and negative. It may represent both a whole-number/integer component as well as a fractional (numerator/denominator) component. The fractional component may be a vulgar fraction, whereby the numerator is greater than the denominator.

Creating a fraction

// Via a constructor
var fraction = new Fraction(3, 4);              // Three-quarters

// Via a constructor with a whole-number part
var fraction = new Fraction(2, 3, 4);           // Two and three-quarters

// Via a constructor with a negative amount
var fraction = new Fraction(-2, 3, 4);          // Negative two and three-quarters

// Via a constructor with a negative fraction-only
var fraction = new Fraction(-3, 4);             // Negative three-quarters

// Parsing a fraction from string
var fraction = Fraction.Parse("3/4");           // Three-quarters

// Parsing a fraction from string with a whole-number part
var fraction = Fraction.Parse("2 3/4");         // Two and three-quarters

// Parsing a negative fraction from string
var fraction = Fraction.Parse("-3/4");          // Negative three-quarters

// Parsing a fraction using a service; any parsing
// example above may be performed this way.  The FractionParser
// implements the interface IParsesFraction.
new FractionParser().Parse("3/4")               // Three-quarters

// Whole numbers may also be implicitly cast as fractions
Fraction fraction = 5;                          // Five

Math with fractions

Fractions may be added, subtracted, multiplied and divided:

Fraction.Parse("3/4") * 2;                      // One and one-half

Comparing fractions

Fractions implement IComparable<Fraction>, IComparable and provide the operators <, >, <= and >=:

Fraction.Parse("3/4") > Fraction.Parse("3/5")   // True

Fractions may also be tested for equality with one another; the operators == and != are also implemented. When performing any kind of comparison, fractions are simplified (see below) before the comparison is made. This means that (for example), one-quarter is correctly treated as equal to two-eights.

Simplifying fractions

Fractions may be simplified to their smallest form. An optional parameter specifies whether or not prefer simplification to a vulgar fraction (if applicable) or not. By default vulgar fractions are not preferred.

// Simplify a fraction
Fraction.Parse("50/100").Simplify()             // One-half

// Simplify a vulgar fraction to become mixed-whole-number-and-fraction
Fraction.Parse("125/50").Simplify()             // Two and one-half

// Simplify a fraction and prefer vulgar fractions
Fraction.Parse("125/50").Simplify(true)         // Five-halves

Formatting fractions

Fractions may be formatted as strings. The Fraction.ToString() method internally uses the standard mechanism described below, without simplification (the first example). For more functionality use the service FractionFormatter, which implements IFormatsFraction.

// Standard mechanism, without simplification
var result = new FractionFormatter().Format(Fraction.Parse("125/100"), "S");
// result is "125/100"

// Standard mechanism, with simplification; this is also the
// default if the format specifier is omitted
var result = new FractionFormatter().Format(Fraction.Parse("125/100"), "s");
// result is "1 1/4"

// Force a leading zero, without simplification
var result = new FractionFormatter().Format(Fraction.Parse("25/100"), "Z");
// result is "0 25/100"

// Force a leading zero, with simplification
var result = new FractionFormatter().Format(Fraction.Parse("25/100"), "z");
// result is "0 1/4"

// Prefer vulgar fraction (implies simplification)
var result = new FractionFormatter().Format(Fraction.Parse("125/100"), "v");
// result is "5/4"

Converting to plain numbers

Fractions may be cast/converted to numeric types. Because of the risk of data-loss, casts must be explicit.

decimal number = (decimal) Fraction.Parse("3/4");
// number is 0.75m

The same principle applies to double and float. Fractions may also be cast to integer types: sbyte, short, int, long, byte, ushort, uint or ulong, but when doing so only the whole-number portion of the fraction will be used.

csf-dev/PrimesAndFractions