Class: SyMath::Sum

Inherits:
Operator show all
Defined in:
lib/symath/sum.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_constant?, #name, #reduce, #replace, #variables

Methods inherited from Value

#*, #**, #+, #-, #-@, #/, #<, #<=, #<=>, #>, #>=, #^, #add, #base, create, #deep_clone, #div, #dump, #exponent, #factors, #inspect, #inv, #is_divisor_factor?, #is_finite?, #is_nan?, #is_negative?, #is_negative_number?, #is_number?, #is_positive?, #is_prod_exp?, #is_unit_quaternion?, #is_zero?, #mul, #neg, #power, #reduce, #reduce_modulo_sign, #sign, #sub, #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(arg1, arg2) ⇒ Sum

Returns a new instance of Sum.



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# File 'lib/symath/sum.rb', line 110

def initialize(arg1, arg2)
  super('+', [arg1, arg2])
end

Class Method Details

.compose_with_simplify(a, b) ⇒ Object 



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

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

  # Adding a value to an equation adds it to both sides, preserving
  # the balance of the equation
  if b.is_a?(SyMath::Equation)
    return eq(a + b.args[0], a + b.args[1])
  end

  if a.is_finite?() == false or b.is_finite?() == false
    return self.simplify_inf(a, b)
  end

  return a if b == 0
  return b if a == 0

  sc = 1
  sf = []
  oc = 1
  of = []

  a.factors.each do |f|
    if f == -1
      sc *= -1
    elsif f.is_number?
      sc *= f.value
    else
      sf.push f
    end
  end

  b.factors.each do |f|
    if f == -1
      oc *= -1
    elsif f.is_number?
      oc *= f.value
    else
      of.push f
    end
  end
  
  sc += oc

  if sf == of
    if sc == 0
      return 0.to_m
    end

    if sc != 1
      sf.unshift sc.to_m
    end

    return sf.empty? ? 1.to_m : sf.inject(:*)
  end

  return self.new(a, b)
end

.simplify_inf(a, b) ⇒ Object 



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# File 'lib/symath/sum.rb', line 64

def self.simplify_inf(a, b)
  # Indefinite terms
  if a.is_finite?.nil? or b.is_finite?.nil?
    return a.add(b)
  end
  
  # NaN add to NaN
  if a.is_nan? or b.is_nan?
    return :nan.to_m
  end

  if SyMath.setting(:complex_arithmetic)
    # +- oo +- oo = NaN
    if (a.is_finite? == false and b.is_finite? == false)
      return :nan.to_m
    end

    # oo + n = n + oo = NaN
    if (a.is_finite? == false or b.is_finite? == false)
      return :oo.to_m
    end
  else
    # oo - oo = -oo + oo = NaN
    if (a.is_finite? == false and b.is_finite? == false)
      if (a.is_positive? and b.is_negative?) or
        (a.is_negative? and b.is_positive?)
        return :nan.to_m
      end
    end

    # oo + n = n + oo = oo + oo = oo
    if a.is_finite? == false
      return a
    end

    # n - oo = - oo + n = -oo - oo = -oo
    if b.is_finite? == false
      return b
    end
  end

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

Instance Method Details

#evaluate ⇒ Object 



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# File 'lib/symath/sum.rb', line 142

def evaluate
  if term1.type.is_matrix?
    return term1.matrix_add(term2)
  end

  return super
end

#is_associative? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/symath/sum.rb', line 126

def is_associative?()
  return true
end

#is_commutative? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/symath/sum.rb', line 122

def is_commutative?()
  return true
end

#is_sum_exp? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/symath/sum.rb', line 130

def is_sum_exp?()
  return true
end

#term1 ⇒ Object 



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# File 'lib/symath/sum.rb', line 114

def term1()
  return @args[0]
end

#term2 ⇒ Object 



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# File 'lib/symath/sum.rb', line 118

def term2()
  return @args[1]
end

#terms ⇒ Object

Return all terms in the sum



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# File 'lib/symath/sum.rb', line 135

def terms()
  return Enumerator.new do |s|
    term1.terms.each { |s1| s << s1 }
    term2.terms.each { |s2| s << s2 }
  end
end

#to_latex ⇒ Object 



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# File 'lib/symath/sum.rb', line 166

def to_latex()
  if term2.is_a?(SyMath::Minus)
    return term1.to_latex + ' ' + term2.to_latex
  else
    return term1.to_latex + ' + ' + term2.to_latex
  end
end

#to_s ⇒ Object 



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# File 'lib/symath/sum.rb', line 154

def to_s()
  if SyMath.setting(:expl_parentheses)
    return '('.to_s + term1.to_s + ' + ' + term2.to_s + ')'.to_s
  else
    if term2.is_a?(SyMath::Minus)
      return term1.to_s + " " + term2.to_s
    else
      return term1.to_s + " + " + term2.to_s
    end
  end
end

#type ⇒ Object 



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# File 'lib/symath/sum.rb', line 150

def type()
  return term1.type.sum(term2.type)
end