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.

Details

  • 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.

Examples

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Basic Examples  (3)

Plus sorts its arguments because it has attribute Orderless:

Any orderless function will sort its arguments:

The pattern matcher reorders arguments of Orderless functions to obtain matches:

Note that Plus itself does not reorder these particular arguments:

Properties & Relations  (2)

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:

This sorting occurs as part of the standard evaluation process:

Possible Issues  (1)

Pattern matching with orderless functions can lead to a large number of possible cases:

Introduced in 1988
 (1.0)