Module: Math

Defined in:
lib/combinatorics/extensions/math.rb

Overview

Author:

Class Method Summary collapse

Class Method Details

.factorial(x = 1) ⇒ Integer

Note:

The factorial of zero equals one!

Apply the well-known factorial function to the given Integer.

Examples:

factorial(4)
# => 24

Parameters:

  • x (Fixnum) (defaults to: 1) —

    Positive integer to apply algebraic factorial function to.

Returns:

  • (Integer) —

    Solution to factorial function as a whole number.

Raises:

  • (RangeError) —

    The given number must be non-negative.

See Also:

Since:

  • 0.4.0



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# File 'lib/combinatorics/extensions/math.rb', line 171

def Math.factorial(x=1)
  if    x >= 1  then pi(1..x)
  elsif x == 0  then 1
  else
    raise(RangeError,"x must be non-negative")
  end
end

.pi(r) {|i| ... } ⇒ Integer

Pi notation for iterative product computations.

Examples:

Math.pi(1..4)
# => 24

Parameters:

  • r (Range<Integer>) —

    Inclusive range of Integers.

Yields:

  • (i) —

    The given block will be passed elements of r. The return value from the block will be combined with the product.

  • (Integer) —

    i An element from r.

Returns:

  • (Integer) —

    The total product after iterating over each element in r.

Raises:

  • (TypeError) —

    r must be a Range.

See Also:

Since:

  • 0.4.0



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# File 'lib/combinatorics/extensions/math.rb', line 91

def Math.pi(r)
  unless r.kind_of?(Range)
    raise(TypeError,"r must be a Range")
  end

  k = 1

  if block_given?
    r.each { |n| k *= yield n }
  else
    r.each { |n| k *= n }
  end

  k
end

.Pi(r) ⇒ Object

CamelCase alias for pi (defined above)

See Also:

Since:

  • 0.4.0



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# File 'lib/combinatorics/extensions/math.rb', line 114

def Math.Pi(r)
  Math.pi(r)
end

.Sigma(r) ⇒ Object

CamelCase alias for sigma (defined above)

See Also:

Since:

  • 0.4.0



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# File 'lib/combinatorics/extensions/math.rb', line 60

def Math.Sigma(r)
  Math.sigma(r)
end

.sigma(r) {|i| ... } ⇒ Integer

Note:

"chalkboard" notation for summation is the capital Greek letter Sigma.

Mathematical summation (invokes a block for k = 1 until ++k = n).

Examples:

sigma(1..4) { |i| i }
# => 10

Parameters:

  • r (Range) —

    Range containing the number of times to yield.

Yields:

  • (i) —

    The given block is expected to return an Integer, which is added to the total sum.

Yield Parameters:

  • i (Integer) —

    An element from r.

Returns:

  • (Integer) —

    Total sum after yielding for each element in r.

Raises:

  • (TypeError) —

    r must be a Range.

See Also:

Since:

  • 0.4.0



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# File 'lib/combinatorics/extensions/math.rb', line 37

def Math.sigma(r)
  unless r.kind_of?(Range)
    raise(TypeError,"r must be a Range")
  end

  k = 0

  if block_given?
    r.each { |n| k += yield n }
  else
    r.each { |n| k += n }
  end

  k
end

.subfactorial(n) ⇒ Integer

Note:

The notation used in academia for subfactorial notation is "!n"

Subfactorial function for calculation of derangement cardinalities.

Examples:

subfactorial([1, 2, 3].size)
# => 2

Parameters:

  • n (Fixnum) —

    The length of sequence.

Returns:

  • (Integer) —

    Cardinality of derangements set.

Raises:

  • (RangeError) —

    n must be non-negative.

See Also:

Since:

  • 0.4.0



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# File 'lib/combinatorics/extensions/math.rb', line 141

def Math.subfactorial(n)
  if    n >= 1 then ((Math.factorial(n) + 1) / Math::E).floor
  elsif n == 0 then 1
  else
    raise(RangeError,"n must be non-negative")
  end
end