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Orderless

Orderless
is an attribute that can be assigned to a symbol f to indicate that the elements ei in expressions of the form f[e1, e2, ...] should automatically be sorted into canonical order. This property is accounted for in pattern matching.
  • The Orderless attribute for a function corresponds to the mathematical property of commutativity.
  • Functions with the Orderless attribute use canonical order as described in the notes for Sort.
  • For an object that represents a matrix or a tensor, the Orderless attribute represents symmetry among indices.
  • In matching patterns with Orderless functions, all possible orders of arguments are tried.
  • The Orderless attribute must be assigned before defining any values for an Orderless function.
All possible argument orderings are tried to match a definition for an orderless function:
Elements of an expression whose head is orderless are sorted into standard order:
Pattern matching with orderless functions can lead to a large number of possible cases:
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