the calculator home page  What is Reverse Polish Notation?  RPN
calculator buttons When you are at school you learn that
different arithmetic operators have different precedence,
although that may not be the exact phrase the teacher uses. You
are probably given a mnemonic such as "Please Excuse My Dear
Aunt Sally" (meaning Parentheses, Exponentiation (roots and
powers), Multiplication, Division, Addition, Subtraction) to
tell you the order in which to do sums. For example, if you are
given:  1 + 2 x 3 = ?  you know to multiply 2 by 3 before adding
the 1. Early pocket calculators were not acquainted with Aunt
Sally, and would evaluate this expression as 9.  Another school-
days mnemonic, BODMAS, tells us to attend to the bracketed
expressions first, followed by the usual algebraic operator
precedence. Brackets (or more properly parentheses) remove any
ambiguity about the order of evaluation of expressions. Most
complex expressions could not be expressed in conventional
arithmetic notation without brackets, and