Class: SyMath::Definition::Exp

Inherits:
Function show all
Defined in:
lib/symath/definition/exp.rb

Instance Attribute Summary

Attributes inherited from Operator

#args, #exp

Attributes inherited from SyMath::Definition

#name

Instance Method Summary collapse

Methods inherited from Function

#check_pi_fraction, functions, init_builtin, #is_function?, #latex_format

Methods inherited from Operator

#<=>, #==, #arity, #call, #compose_with_simplify, #dump, #evaluate_call, init_builtin, #is_operator?, #latex_format, operators, #replace, #to_latex, #to_s, #validate_args

Methods inherited from SyMath::Definition

#<=>, #==, #arity, define, defined?, definitions, get, #hash, init_builtin, #inspect, #is_constant?, #is_function?, #is_operator?, #replace, #to_latex, #to_s, undefine, #variables

Methods inherited from Value

#*, #**, #+, #-, #-@, #/, #<, #<=, #<=>, #>, #>=, #^, #add, #base, compose_with_simplify, create, #deep_clone, #div, #dump, #evaluate, #exponent, #factors, #inspect, #inv, #is_divisor_factor?, #is_finite?, #is_nan?, #is_negative?, #is_negative_number?, #is_number?, #is_positive?, #is_prod_exp?, #is_sum_exp?, #is_unit_quaternion?, #is_zero?, #mul, #neg, #power, #reduce, #reduce_modulo_sign, #sign, #sub, #terms, #to_m, #type, #wedge

Methods included from Operation::Exterior

#flat, #hodge, #sharp

Methods included from Operation::Integration

#anti_derivative, #get_linear_constants, initialize, #int_constant, #int_failure, #int_function, #int_inv, #int_pattern, #int_power, #int_product, #int_sum, #integral_bounds

Methods included from Operation::Differential

#_d_wedge, #d, #d_failure, #d_fraction, #d_function, #d_function_def, #d_power, #d_product, initialize

Methods included from Operation

#iterate, #recurse

Methods included from Operation::DistributiveLaw

#combfrac_add_term, #combfrac_sum, #combine_fractions, #expand, #expand_product, #expand_single_pass, #factorize, #factorize_integer_poly, #factorize_simple, #has_fractional_terms?

Methods included from Operation::Normalization

#combine_factors, #compare_factors_and_swap, #normalize, #normalize_matrix, #normalize_power, #normalize_product, #normalize_single_pass, #normalize_sum, #order_product, #product_on_fraction_form, #reduce_constant_factors, #replace_combined_factors, #swap_factors

Methods included from Operation::Match

#build_assoc_op, #match, #match_assoc, #match_replace

Constructor Details

#initialize ⇒ Exp

Returns a new instance of Exp.



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# File 'lib/symath/definition/exp.rb', line 5

def initialize()
  super(:exp)
end

Instance Method Details

#description ⇒ Object 



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# File 'lib/symath/definition/exp.rb', line 9

def description()
  return 'exp(x) - exponential function (e**x)'
end

#reduce_call(call) ⇒ Object 



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# File 'lib/symath/definition/exp.rb', line 13

def reduce_call(call)
  arg = call.args[0]
  
  if arg.is_nan?
    return :nan.to_m
  end

  if arg == 0
    return 1.to_m
 elsif arg == 1
    return :e.to_m
  end

  if arg.is_finite? == false
    if SyMath.setting(:complex_arithmetic)
      return :nan.to_m
    else
      if arg.is_positive? == true
        return :oo.to_m
      else
        return 0.to_m
      end
    end
  end

  if SyMath.setting(:complex_arithmetic)
    ret = 1.to_m
  
    arg.terms.each do |t|
      if t.is_a?(SyMath::Minus)
        t = t.args[0]
        minus = true
      else
        minus = false
      end

      if t.class.method_defined?('definition') and
        t.definition.is_a?(SyMath::Definition::Ln)
        # exp(ln(c)) = c
        t2 = t.args[0]
      else
        # Euler's formula
        c, dc = check_pi_fraction(t, true)
        if !c.nil?
          if dc == 1
            c *= 2
          elsif dc != 2
            # Not reducible
            return call
          end

          case c % 4
          when 0
            t2 = 1
          when 1
            t2 = :i
          when 2
            t2 = -1
          when 3
            t2 = -:i
          end
        else
          # Cannot reduce
          return call
        end
      end

      ret = minus ? ret/t2 : ret*t2
    end

    return ret
  else
    ret = 1.to_m

    call.args[0].terms.each do |t|
      if t.is_a?(SyMath::Minus)
        t = t.args[0]
        minus = true
      else
        minus = false
      end

      # exp(ln(c)) = c for positive c
      if t.class.method_defined?('definition') and
        t.definition.is_a?(SyMath::Definition::Ln)
        if t.args[0].is_number?
          ret = minus ? ret/t.args[0] : ret*t.args[0]
          next
        end
      end

      # Cannot reduce
      return call
    end

    return ret
  end
end