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A.3.9 Ordering of Expressions

The canonical ordering of expressions used automatically with the attribute Orderless and in functions such as Sort satisfies the following rules:

  • Integers, rational and approximate real numbers are ordered by their numerical values.
  • Complex numbers are ordered by their real parts, and in the event of a tie, by the absolute values of their imaginary parts.
  • Symbols are ordered according to their names, and in the event of a tie, by their contexts.
  • Expressions are usually ordered by comparing their parts in a depth-first manner. Shorter expressions come first.
  • Powers and products are treated specially, and are ordered to correspond to terms in a polynomial.
  • Strings are ordered as they would be in a dictionary, with the upper-case versions of letters coming after lower-case ones. Ordinary letters appear first, followed in order by script, Gothic, double-struck, Greek and Hebrew. Mathematical operators appear in order of decreasing precedence.