Module: SyMath::Operation::Exterior

Included in:
Value
Defined in:
lib/symath/operation/exterior.rb

Instance Method Summary collapse

Instance Method Details

#flat ⇒ Object

Lower indices, transforming vectors to differential forms



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# File 'lib/symath/operation/exterior.rb', line 9

def flat()
  res = recurse('flat', nil)

  if res.is_a?(SyMath::Definition::Variable)
    if res.type.is_subtype?('vector')
      return res.lower_vector
    end
  end
  
  return res
end

#hodge ⇒ Object

Calculate hodge star duality



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# File 'lib/symath/operation/exterior.rb', line 35

def hodge()
  # Recurse down sums and subtractions
  if is_sum_exp?
    return terms.map do |t|
      if t.is_a?(SyMath::Minus)
        - t.argument.hodge
      else
        t.hodge
      end
    end.inject(:+)
  else
    # FIXME: If expression is a product of sums, expand the product first
    # (distributive law), then hodge op on the new sum.
    
    # Replace nvectors and nforms with their hodge dual
    s = []
    v = []
    factors.each do |f|
      if f.type.is_vector? or f.type.is_dform?
        v.push f
      else
        s.push f
      end
    end
    
    h = SyMath::Definition::Variable.hodge_dual(v.inject(1.to_m, :*))
    return s.inject(1.to_m, :*)*h
  end
end

#sharp ⇒ Object

Raise indices, transforming differential forms to vectors



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# File 'lib/symath/operation/exterior.rb', line 22

def sharp()
  res = recurse('sharp', nil)

  if res.is_a?(SyMath::Definition::Variable)
    if res.type.is_subtype?('dform')
      return res.raise_dform
    end
  end

  return res
end