class_docstr: A Dyadic object.
  
  See:
  https://en.wikipedia.org/wiki/Dyadic_tensor
  Kane, T., Levinson, D. Dynamics Theory and Applications. 1985 McGraw-Hill
  
  A more powerful way to represent a rigid body's inertia. While it is more
  complex, by choosing Dyadic components to be in body fixed basis vectors,
  the resulting matrix is equivalent to the inertia tensor.
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docstr: Replace occurrences of objects within the measure numbers of the
  Dyadic.
  
  Parameters
  ==========
  
  rule : dict-like
      Expresses a replacement rule.
  
  Returns
  =======
  
  Dyadic
      Result of the replacement.
  
  Examples
  ========
  
  >>> from sympy import symbols, pi
  >>> from sympy.physics.vector import ReferenceFrame, outer
  >>> N = ReferenceFrame('N')
  >>> D = outer(N.x, N.x)
  >>> x, y, z = symbols('x y z')
  >>> ((1 + x*y) * D).xreplace({x: pi})
  (pi*y + 1)*(N.x|N.x)
  >>> ((1 + x*y) * D).xreplace({x: pi, y: 2})
  (1 + 2*pi)*(N.x|N.x)
  
  Replacements occur only if an entire node in the expression tree is
  matched:
  
  >>> ((x*y + z) * D).xreplace({x*y: pi})
  (z + pi)*(N.x|N.x)
  >>> ((x*y*z) * D).xreplace({x*y: pi})
  x*y*z*(N.x|N.x)
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code: def xreplace(self, rule):
      """
      Replace occurrences of objects within the measure numbers of the
      Dyadic.
  
      Parameters
      ==========
  
      rule : dict-like
          Expresses a replacement rule.
  
      Returns
      =======
  
      Dyadic
          Result of the replacement.
  
      Examples
      ========
  
      >>> from sympy import symbols, pi
      >>> from sympy.physics.vector import ReferenceFrame, outer
      >>> N = ReferenceFrame('N')
      >>> D = outer(N.x, N.x)
      >>> x, y, z = symbols('x y z')
      >>> ((1 + x*y) * D).xreplace({x: pi})
      (pi*y + 1)*(N.x|N.x)
      >>> ((1 + x*y) * D).xreplace({x: pi, y: 2})
      (1 + 2*pi)*(N.x|N.x)
  
      Replacements occur only if an entire node in the expression tree is
      matched:
  
      >>> ((x*y + z) * D).xreplace({x*y: pi})
      (z + pi)*(N.x|N.x)
      >>> ((x*y*z) * D).xreplace({x*y: pi})
      x*y*z*(N.x|N.x)
  
      """
  
      new_args = []
      for inlist in self.args:
          new_inlist = list(inlist)
          new_inlist[0] = new_inlist[0].xreplace(rule)
          new_args.append(tuple(new_inlist))
      return Dyadic(new_args)
  
imports: from sympy import sympify, Add, ImmutableMatrix
  from sympy.core.evalf import EvalfMixin
  from sympy.printing.defaults import Printable
  from mpmath.libmp.libmpf import prec_to_dps
label_desc: Use image node_id 26 for calling the Dyadic obj's underlying member method code with example usage: obj.xreplace(rule) and returns: Dyadic