Class: SyMath::Power

Inherits:
Operator show all
Defined in:
lib/symath/power.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, #evaluate, #hash, #is_associative?, #is_commutative?, #is_constant?, #name, #reduce, #replace, #variables

Methods inherited from Value

#*, #**, #+, #-, #-@, #/, #<, #<=, #<=>, #>, #>=, #^, #add, create, #deep_clone, #div, #dump, #evaluate, #factors, #inspect, #inv, #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, #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(base, exponent) ⇒ Power

Returns a new instance of Power.



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# File 'lib/symath/power.rb', line 83

def initialize(base, exponent)
  super('**', [base, exponent])
end

Class Method Details

.compose_with_simplify(a, b) ⇒ Object 



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

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

  if a.is_finite?() == false or b.is_finite?() == false
    return self.simplify_inf(a, b)
  end
        
  # 0**0 = NaN
  if a.is_zero? and b.is_zero?
    return :nan.to_m
  end

  # n**1 = n
  if b == 1
    return a
  end
  
  if a.is_a?(SyMath::Power)
    return a.base**(a.exponent*b)
  end

  return self.new(a, b)
end

.simplify_inf(a, b) ⇒ Object 



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# File 'lib/symath/power.rb', line 30

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 = NaN
  if a.is_nan? or b.is_nan?
    return :nan.to_m
  end

  # 1**oo = 1**-oo = oo**0 = -oo**0 = NaN
  if a == 1 or b.is_zero?
    return :nan.to_m
  end

  if SyMath.setting(:complex_arithmetic)
    if b.is_finite? == false
      return :nan.to_m
    else
      return :oo.to_m
    end
  else
    if a.is_zero? and b.is_finite? == false
      return :nan.to_m
    end

    # n**-oo = oo**-oo = -oo**-oo = 0
    if b.is_finite? == false and b.is_negative?
      return 0.to_m
    end
    
    if a.is_finite? == false and a.is_negative?
      if b.is_finite? == true
        # -oo*n = oo*(-1**n)
        return :oo.to_m.mul(a.sign**b)
      else
        # -oo**oo = NaN
        return :nan.to_m
      end
    end

    # -n**oo => NaN
    if a.is_finite? and a.is_negative?
      return :nan.to_m
    end
    
    # The only remaining possibilities:
    # oo**n = n*oo = oo*oo = oo
    return :oo.to_m
  end
end

Instance Method Details

#base ⇒ Object 



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# File 'lib/symath/power.rb', line 87

def base()
  return @args[0]
end

#exponent ⇒ Object 



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# File 'lib/symath/power.rb', line 91

def exponent()
  return @args[1]
end

#is_divisor_factor? ⇒ Boolean

Expression is on the form a**-n, n is a positive number

Returns:

  • (Boolean) 


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# File 'lib/symath/power.rb', line 96

def is_divisor_factor?()
  return exponent.is_negative_number?
end

#reduce_modulo_sign ⇒ Object

Simple reduction rules, allows sign to change. Returns (reduced exp, sign, changed).



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

def reduce_modulo_sign
  # a to the power of 1 reduces to a
  if exponent == 1
    return base, 1, true
  end
  
  # Powers of 1 reduces to 1
  if base == 1 and exponent.is_finite?
    return base, 1, true
  end

  # Power of 0 reduces to 0
  if base == 0 and exponent.is_finite? and exponent != 0
    return 0.to_m, 1, true
  end
  
  if base != 0 and exponent == 0
    return 1.to_m, 1, true
  end

  if base == :e
    fn = fn(:exp, exponent)
    # FIXME: Merge functions reduce and reduce_modulo_sign
    red = fn.reduce
    if red != fn
      return red, 1, true
    end
  end

  # Reduce negative number
  if base.is_a?(SyMath::Minus)
    if exponent.is_number?
      exp = exponent
    elsif exponent.is_negative_number?
      exp = exponent.argument
    else
      exp = nil
    end

    if !exp.nil?
      e, sign, changed = (base.argument**exp).reduce_modulo_sign
      if exp.value.odd?
        sign *= -1
      end
      return e, sign, true
    end
  end

  # Number power of number reduces to number
  if base.is_number?
    if exponent.is_number?
      return (base.value ** exponent.value).to_m, 1, true
    end

    if exponent.is_negative_number? and exponent.argument.value > 1
      return (base.value ** exponent.argument.value).to_m.power(-1), 1, true
    end
  end

  # p**q**r reduces to p**(q*r)
  if base.is_a?(SyMath::Power)
    return base.base.power(base.exponent.mul(exponent)), 1, true
  end

  # Reduce positive integer power of vectors and dforms to zero
  if (base.type.is_dform? or base.type.is_vector?) and
    exponent.is_number?
    return 0.to_m, 1, true
  end
  
  # Remaining code reduces only quaternions
  if !base.is_unit_quaternion?
    return self, 1, false
  end
  
  # q**n for some unit quaternion
  # Exponent is 1 or not a number
  if !exponent.is_number? or exponent == 1
    return self, 1, false
  end

  # e is on the form q**n for some integer n >= 2
  x = exponent.value
  
  if x.odd?
    ret = base
    x -= 1
  else
    ret = 1.to_m
  end

  if (x/2).odd?
    return ret, -1, true
  else
    return ret, 1, true
  end
end

#to_latex ⇒ Object 



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# File 'lib/symath/power.rb', line 214

def to_latex()
  if base.is_sum_exp? or base.is_prod_exp? or base.is_a?(SyMath::Power)
    base_str = '\left(' + base.to_latex + '\right)'
  else
    base_str = base.to_latex
  end

  return base_str + '^' + '{' + exponent.to_latex + '}'
end

#to_s ⇒ Object 



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# File 'lib/symath/power.rb', line 200

def to_s()
  if base.is_sum_exp? or base.is_prod_exp? or base.is_a?(SyMath::Power)
    base_str = '(' + base.to_s + ')'
  else
    base_str = base.to_s
  end

  expo_str = (exponent.is_sum_exp? or exponent.is_prod_exp?) ?
             '(' + exponent.to_s + ')' :
             exponent.to_s
  
  return base_str + '**' + expo_str
end