Class: Equation

Inherits:
Object
  • Object
show all
Defined in:
lib/symcalc.rb

Instance Method Summary collapse

Instance Method Details

#*(eq) ⇒ Object 



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# File 'lib/symcalc.rb', line 34

def *(eq)
  return Multiplication.new(self, to_equation(eq))
end

#**(eq) ⇒ Object 



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# File 'lib/symcalc.rb', line 50

def **(eq)
  return Power.new(self, to_equation(eq))
end

#+(eq) ⇒ Object 



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# File 'lib/symcalc.rb', line 42

def +(eq)
  return Sum.new(self, to_equation(eq))
end

#-(eq) ⇒ Object 



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# File 'lib/symcalc.rb', line 46

def -(eq)
  return Subtraction.new(self, to_equation(eq))
end

#/(eq) ⇒ Object 



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# File 'lib/symcalc.rb', line 38

def /(eq)
  return Division.new(self, to_equation(eq))
end

#__simplify__ ⇒ Object 



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# File 'lib/symcalc.rb', line 85

def __simplify__
  return self
end

#__sub__(original, replacement) ⇒ Object 



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# File 'lib/symcalc.rb', line 211

def __sub__ original, replacement
  return to_equation(replacement) if self == to_equation(original)
  return self
end

#coerce(other) ⇒ Object 



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# File 'lib/symcalc.rb', line 30

def coerce(other)
  [to_equation(other), self]
end

#derivative(order: 1, variable: nil) ⇒ Object

Calculate the derivative of the given function Accepts parameters order and variable. If the function has more than one dimensional, the variable needs to be provided

Example: x = SymCalc.var(“x”) y = SymCalc.var(“y”) fx = x ** 2 fx.derivative order: 2

fxy = x ** 2 + 3 * y fxy.derivative variable: x



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# File 'lib/symcalc.rb', line 67

def derivative(order: 1, variable: nil)
  if variable == nil && self.all_variables.size < 2
    fx = self
    order.times do
      fx = fx.simplify.__derivative__.simplify
    end
    return fx
  elsif variable == nil && self.all_variables.size > 1
    raise "Expected a variable as input for a #{self.all_variables.size}-dimensional function"
  else
    fx = self
    order.times do 
      fx = fx.simplify.__derivative__(variable: variable).simplify
    end
    return fx
  end
end

#eval(var_hash) ⇒ Object

Evaluates the function at given variable values Accepts the hash of variables and their values to evalualte the function

Example: x = SymCalc.var(“x”) fx = x ** 2 puts fx.eval(x: 3)



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# File 'lib/symcalc.rb', line 194

def eval(var_hash)
  if var_hash.values.size == 0
    result = self.__eval__(Hash.new)
  elsif !var_hash.values[0].is_a?(Array)
    result = self.__eval__ var_hash
  elsif var_hash.values[0].is_a? Array
    result = []
    var_hash.values[0].size.times do |i|
      hash = var_hash.map {|k, v| [k, v[i]]}.to_h
      result << self.__eval__(hash)
    end
  end
  result
end

#inspect ⇒ Object 



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# File 'lib/symcalc.rb', line 26

def inspect
  self.display()
end

#simplify ⇒ Object

Simplifies the given function Accepts no arguments



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# File 'lib/symcalc.rb', line 92

def simplify
  
  simplified = self.__simplify__
  
  if [Multiplication, Division].include? simplified.class
    m_els = simplified.__get_m_elements__(Hash.new)
    
    if m_els.keys.size == 0
      return EquationValue.new(0)
    elsif m_els.keys.size == 1
      part = m_els.keys[0]
      power = to_equation(m_els.values[0])
      if part == "exp"
        part = (power == to_equation(1)) ? BasicVars::E : Exp.new(power)
      else
        part = part ** power if power != to_equation(1)
      end
      return part
    else      
      els_index = 0
      eq = nil
      
      coeff = to_equation(1)
        
      m_els.size.times do |els_index|
        base = m_els.keys[els_index]
        power = m_els[base]
        
        base = base.simplify if base.is_a? Equation
        power = power.simplify if power.is_a? Equation
        
        base = to_equation base if base != "exp"
        power = to_equation power
        
        if power == to_equation(0)
          next
        end
        
        if base.is_a?(EquationValue) && power.is_a?(EquationValue)
          case power
          when EquationValue.new(1)
            coeff *= base
          else
            coeff *= base ** power
          end
          next
        end
        
        if base == "exp"
          case power
          when to_equation(1)
            part = BasicVars::E
          else
            part = Exp.new(power)
          end
        else
          case power
          when to_equation(1)
            part = base
          else
            part = base ** power
          end
        end
        
        if eq == nil
          eq = part
        else
          eq *= part
        end
        
      end
      
      coeff = coeff.__simplify__
      
      if coeff == to_equation(1)
        eq = eq
      elsif coeff == to_equation(0)
        eq = to_equation(0)
      elsif eq == nil
        eq = coeff
      else
        eq = coeff * eq
      end
      
      return eq
    end
    
  else
    return simplified
  end
  
end

#sub(original, replacement) ⇒ Object

Returns an equation with an expression substituted for the replacement

Example: a = SymCalc.var(“a”) f = a ** 2 x = SymCalc.var(“x”) puts f.sub(a, 3 * x) # => (3 * x) ** 2



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# File 'lib/symcalc.rb', line 224

def sub original, replacement
  self.__sub__(original, replacement).simplify
end

#to_s ⇒ Object 



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# File 'lib/symcalc.rb', line 22

def to_s
  self.display()
end