Class: Keisan::AST::Exponent

Inherits:
ArithmeticOperator show all
Defined in:
lib/keisan/ast/exponent.rb

Constant Summary

Constants inherited from Operator

Operator::ARITIES, Operator::ARITY_PRIORITY_ASSOCIATIVITY, Operator::ASSOCIATIVITIES, Operator::ASSOCIATIVITY_OF_PRIORITY, Operator::PRIORITIES

Instance Attribute Summary

Attributes inherited from Parent

#children

Class Method Summary collapse

Instance Method Summary collapse

Methods inherited from Operator

#arity, arity, #associativity, associativity, associativity_of_priority, #evaluate_assignments, #initialize, priority, #priority, #symbol, #to_s, #value

Methods inherited from Parent

#==, #deep_dup, #freeze, #initialize, #is_constant?, #replace, #traverse, #unbound_functions, #unbound_variables

Methods inherited from Node

#!, #%, #&, #*, #**, #+, #+@, #-, #-@, #/, #<, #<<, #<=, #>, #>=, #>>, #^, #and, #coerce, #contains_a?, #deep_dup, #differentiated, #equal, #evaluate_assignments, #evaluated, #false?, #is_constant?, #not_equal, #or, #replace, #replaced, #simplified, #to_cell, #to_node, #traverse, #true?, #unbound_functions, #unbound_variables, #value, #well_defined?, #|, #~

Constructor Details

This class inherits a constructor from Keisan::AST::Operator

Class Method Details

.symbol ⇒ Object 



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# File 'lib/keisan/ast/exponent.rb', line 4

def self.symbol
  :**
end

Instance Method Details

#blank_value ⇒ Object 



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# File 'lib/keisan/ast/exponent.rb', line 8

def blank_value
  1
end

#differentiate(variable, context = nil) ⇒ Object

d ( a^b ) = d ( exp(b log(a)) ) = a^b * d (b log(a))

a^b * [ db * log(a) + da * b/a] = da b a^(b-1) + db log(a) a^b



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# File 'lib/keisan/ast/exponent.rb', line 48

def differentiate(variable, context = nil)
  context ||= Context.new

  # Reduce to binary form
  unless children.count == 2
    return simplify(context).differentiate(variable, context)
  end

  base     = children[0].simplified(context)
  exponent = children[1].simplified(context)

  # Special simple case where exponent is a pure number
  if exponent.is_a?(Number)
    return (exponent * base.differentiate(variable, context) * base ** (exponent -1)).simplify(context)
  end

  base_diff     = base.differentiate(variable, context)
  exponent_diff = exponent.differentiate(variable, context)

  res = base ** exponent * (
    exponent_diff * Function.new([base], "log") +
    base_diff * exponent / base
  )
  res.simplify(context)
end

#evaluate(context = nil) ⇒ Object 



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# File 'lib/keisan/ast/exponent.rb', line 42

def evaluate(context = nil)
  children.reverse[1..-1].inject(children.last.evaluate(context)) {|total, child| child.evaluate(context) ** total}
end

#simplify(context = nil) ⇒ Object 



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# File 'lib/keisan/ast/exponent.rb', line 12

def simplify(context = nil)
  context ||= Context.new

  super(context)

  # Reduce to basic binary exponents
  reduced = children.reverse[1..-1].inject(children.last) do |total, child|
    child ** total
  end

  unless reduced.is_a?(Exponent)
    return reduced.simplify(context)
  end

  if reduced.children.count != 2
    raise Exceptions::InternalError.new("Exponent should be binary")
  end
  @children = reduced.children

  if children[1].is_a?(Number) && children[1].value(context) == 1
    return children[0]
  end

  if children.all? {|child| child.is_a?(Number)}
    (children[0] ** children[1]).simplify(context)
  else
    self
  end
end