This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)
 Documentation / Mathematica / Built-in Functions / Programming / Attributes  /
Orderless

  • Orderless is an attribute that can be assigned to a symbol f to indicate that the elements in expressions of the form f [ , , ... ] 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.
  • Functions like Plus and Times are Orderless.
  • 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.
  • See the Mathematica book: Section 2.3.7Section 2.5.3.
  • See also: Sort, Flat, OneIdentity.

    Further Examples

    Functions without the Orderless attribute are not rearranged into a canonical order; with it, they are.

    In[1]:=

    Out[1]=

    In[2]:=

    In[3]:=

    Out[3]=

    In[4]:=