Class: SyMath::Definition::Constant

Inherits:
SyMath::Definition show all
Defined in:
lib/symath/definition/constant.rb

Constant Summary collapse

@@ltx_symbol = 
{
  :pi  => '\pi',
  :e   => '\mathrm{e}',
  :phi => '\varphi',
  :nan => '\mathrm{NaN}',
  :oo  => '\infty',
}
@@descriptions = 
{
  :pi  => 'ratio of cirle cirumference/diameter (3.14159265...)',
  :e   => 'eulers number (2.71828182...)',
  :phi => 'golden ratio (1.61803398...)',
  :nan => "'not a number', i.e. an invalid value",
  :oo  => 'positive infinity',
  :i   => 'imaginary unit, first basic quaternion',
  :j   => 'second basic quaternion',
  :k   => 'third basic quaternion',
}
@@unit_quaternions = 
[:i, :j, :k].to_set

Instance Attribute Summary

Attributes inherited from SyMath::Definition

#name

Class Method Summary collapse

Instance Method Summary collapse

Methods inherited from SyMath::Definition

#<=>, #==, #arity, define, defined?, definitions, get, #hash, #initialize, #inspect, #is_constant?, #is_function?, #is_operator?, #reduce_call, #replace, #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_negative?, #is_negative_number?, #is_number?, #is_prod_exp?, #is_sum_exp?, #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

This class inherits a constructor from SyMath::Definition

Class Method Details

.constants ⇒ Object 



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# File 'lib/symath/definition/constant.rb', line 39

def self.constants()
  return self.definitions.grep(SyMath::Definition::Constant)
end

.init_builtin ⇒ Object 



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# File 'lib/symath/definition/constant.rb', line 27

def self.init_builtin()
  # Define the builtin constants
  self.new(:pi)
  self.new(:e)
  self.new(:phi)
  self.new(:nan)
  self.new(:oo)
  self.new(:i)
  self.new(:j)
  self.new(:k)
end

Instance Method Details

#calc_unit_quaternions(q) ⇒ Object 



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# File 'lib/symath/definition/constant.rb', line 67

def calc_unit_quaternions(q)
  # Calculation map for unit quaternions
  qmap = {
    :i => {
      :i => -1.to_m,
      :j => :k.to_m,
      :k => -:j.to_m,
    },
    :j => {
      :i => -:k.to_m,
      :j => -1.to_m,
      :k => :i.to_m,
    },
    :k => {
      :i => :j.to_m,
      :j => -:i.to_m,
      :k => -1.to_m,
    },
  }

  return qmap[@name][q.name]
end

#description ⇒ Object 



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# File 'lib/symath/definition/constant.rb', line 43

def description()
  return "#{@name} - #{@@descriptions[@name]}"
end

#is_finite? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/symath/definition/constant.rb', line 51

def is_finite?()
  return (@name != :oo and @name != :nan)
end

#is_nan? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/symath/definition/constant.rb', line 47

def is_nan?()
  return @name == :nan
end

#is_positive? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/symath/definition/constant.rb', line 55

def is_positive?()
  return (!is_zero? and !is_nan?)
end

#is_unit_quaternion? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/symath/definition/constant.rb', line 63

def is_unit_quaternion?()
  return @@unit_quaternions.member?(@name)
end

#is_zero? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/symath/definition/constant.rb', line 59

def is_zero?()
  return false
end

#to_latex ⇒ Object 



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# File 'lib/symath/definition/constant.rb', line 103

def to_latex()
  if @@ltx_symbol.key?(@name)
    return @@ltx_symbol[@name]
  else
    return @name.to_s
  end
end

#type ⇒ Object 



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# File 'lib/symath/definition/constant.rb', line 90

def type()
  n = @name
  if n == :e or n == :pi or n == :phi
    return 'real'.to_t
  elsif n == :i
    return 'imaginary'.to_t
  elsif is_unit_quaternion?
    return 'quaternion'.to_t
  else
    return 'nonfinite'.to_t
  end
end