Class: SyMath::Fraction

Inherits:
Operator show all
Defined in:
lib/symath/fraction.rb

Instance Attribute Summary

Attributes inherited from Operator

#args, #definition

Class Method Summary collapse

Instance Method Summary collapse

Methods inherited from Operator

#<=>, #==, #args_assoc, #arity, #dump, #hash, #is_associative?, #is_commutative?, #is_constant?, #name, #reduce, #replace, #variables

Methods inherited from Value

#*, #**, #+, #-, #-@, #/, #<, #<=, #<=>, #>, #>=, #^, #add, #base, create, #deep_clone, #div, #dump, #exponent, #inspect, #inv, #is_divisor_factor?, #is_finite?, #is_nan?, #is_negative?, #is_negative_number?, #is_number?, #is_positive?, #is_sum_exp?, #is_unit_quaternion?, #is_zero?, #mul, #neg, #power, #reduce, #reduce_modulo_sign, #sign, #sub, #terms, #to_m, #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(dividend, divisor) ⇒ Fraction

Returns a new instance of Fraction.



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# File 'lib/symath/fraction.rb', line 90

def initialize(dividend, divisor)
  super('/', [dividend, divisor])
end

Class Method Details

.compose_with_simplify(a, b) ⇒ Object 



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# File 'lib/symath/fraction.rb', line 5

def self.compose_with_simplify(a, b)
  a = a.to_m
  b = b.to_m

  return a if b == 1

  if a.is_finite?() == false or b.is_finite?() == false
    return self.simplify_inf(a, b)
  end
  
  # Divide by zero
  if b.is_zero?
    if SyMath.setting(:complex_arithmetic)
      if a.is_zero?
        return :nan.to_m
      else
        return :oo.to_m
      end
    else
      return :nan.to_m
    end
  end

  if a.is_a?(SyMath::Fraction)
    if b.is_a?(SyMath::Fraction)
      return self.new(a.dividend*b.divisor, a.divisor*b.dividend)
    else
      return self.new(a.dividend, a.divisor*b)
    end
  elsif b.is_a?(SyMath::Fraction)
    return self.new(a*b.divisor, b.dividend)
  end

  return self.new(a, b)
end

.simplify_inf(a, b) ⇒ Object

Divide infinite values



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# File 'lib/symath/fraction.rb', line 42

def self.simplify_inf(a, b)
  # Indefinite factors
  if a.is_finite?.nil? or b.is_finite?.nil?
    return self.new(a, b)
  end

  # NaN/* = */NaN = NaN
  if a.is_nan? or b.is_nan?
    return :nan.to_m
  end
  
  # oo/oo = oo/-oo = -oo/oo = NaN
  if a.is_finite? == false and b.is_finite? == false
    return :nan.to_m
  end

  # */0 = NaN
  if b.is_zero?
    if SyMath.setting(:complex_arithmetic)
      return :oo.to_m
    else
      return :nan.to_m
    end
  end

  # n/oo = n/-oo = 0
  if a.is_finite?
    return 0.to_m
  end

  # oo/n = -oo/-n = oo, -oo/n = oo/-n = -oo
  if b.is_finite?
    if SyMath.setting(:complex_arithmetic)
      return :oo.to_m
    else
      if a.sign == b.sign
        return :oo.to_m
      else
        return -:oo.to_m
      end
    end
  end

  # :nocov:
  raise 'Internal error'
  # :nocov:
end

Instance Method Details

#dividend ⇒ Object 



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# File 'lib/symath/fraction.rb', line 94

def dividend()
  return @args[0]
end

#divisor ⇒ Object 



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# File 'lib/symath/fraction.rb', line 98

def divisor()
  return @args[1]
end

#evaluate ⇒ Object 



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# File 'lib/symath/fraction.rb', line 117

def evaluate()
  # Evaluate matrix division by divding elements
  if dividend.is_a?(SyMath::Matrix)
    return dividend.matrix_div(divisor)
  end

  # Evaluate df/dx expression.
  if dividend.is_a?(SyMath::Operator) and
    dividend.definition.is_a?(SyMath::Definition::D)
    # Evaluate if the divisor is a simple dform. The composed form
    # d(x) is accepted as well as the simple dx variable.
    if divisor.is_a?(SyMath::Definition::Variable) and divisor.is_d?
      v = divisor.undiff
    elsif divisor.is_a?(SyMath::Definition::D) and
         divisor.args[0].is_a?(SyMath::Definition::Variable) and
         divisor.args[0].type.is_scalar?
      v = divisor.args[0]
    else
      return super
    end

    diff = dividend.args[0].evaluate.d([v]).normalize
    # Hack: We must divide all terms by dv since the simplification does
    # not recognize factors common to each term
    ret = 0
    dv = v.to_d
    diff.terms.each do |t|
      ret += (t/dv).normalize
    end

    return ret
  end

  return super
end

#factors ⇒ Object 



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# File 'lib/symath/fraction.rb', line 106

def factors()
  return Enumerator.new do |f|
    dividend.factors.each { |d1| f << d1 }
    divisor.factors.each { |d2|
      if d2 != 1
        f << d2**-1
      end
    }
  end
end

#is_prod_exp? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/symath/fraction.rb', line 102

def is_prod_exp?()
  return true
end

#to_latex ⇒ Object 



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# File 'lib/symath/fraction.rb', line 173

def to_latex()
  return '\frac{' + dividend.to_latex + '}{' + divisor.to_latex + '}'
end

#to_s ⇒ Object 



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# File 'lib/symath/fraction.rb', line 161

def to_s()
  dividend_str = dividend.is_sum_exp? ? '(' + dividend.to_s + ')' : dividend.to_s
  divisor_str = (divisor.is_sum_exp? or divisor.is_prod_exp?) ?
                  '(' + divisor.to_s + ')' :
                  divisor.to_s
  if SyMath.setting(:expl_parentheses)
    return '('.to_s + dividend_str + '/' + divisor_str + ')'.to_s
  else
    return dividend_str + '/' + divisor_str
  end
end

#type ⇒ Object 



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# File 'lib/symath/fraction.rb', line 153

def type()
  if dividend.type.is_subtype?('rational')
    return 'rational'.to_t
  else
    return dividend.type
  end
end