postfix notation

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postfix notation

A student writes a mathematical expression in postfix notation on a whiteboard.

Definition
  1. Noun:
    • A method of writing mathematical expressions without parentheses: "postfix notation" is a specific way to write mathematical or logical expressions where every operator (like +, -, ×) is placed after its operands (the numbers or variables it acts upon). This structure eliminates the need for parentheses to indicate the order of operations.
Usage
  • Noun:
    • The expression "3 4 +" in postfix notation is equivalent to "3 + 4" in standard notation.
    • Many calculators use postfix notation because it is efficient for computer processing.
    • To evaluate an expression in postfix notation, you read from left to right and apply operators to the most recent operands.
Advanced Usage
  • "Reverse Polish Notation (RPN)": This is the most common synonym for . It is named after the Polish logician Jan Łukasiewicz.
    • The Hewlett-Packard series of scientific calculators popularized the use of Reverse Polish Notation.
  • Contrast with other notations: is one of three primary forms. It contrasts with:
    • Infix notation: The standard form (e.g., A + B), where operators are placed between operands.
    • Prefix notation (or Polish notation): Where operators are placed before their operands (e.g., + A B).
Variants and Related Words
  • Postfix (adj/n): Pertaining to or being in . Sometimes used as a shorter form.
    • A postfix expression is parsed unambiguously.
  • RPN (n): A common abbreviation for Reverse Polish Notation, synonymous with .
    • Enable RPN mode on your calculator for this calculation.
Synonyms
  • Reverse Polish Notation (RPN): The full, most widely used synonym.
  • Suffix notation: A less common technical synonym.
Related Concepts (Not Phrasal Verbs or Idioms)
  • Stack (data structure): The primary data structure used to evaluate expressions in . Operands are pushed onto a stack, and operators pop operands from the stack, compute a result, and push it back.
    • Evaluation of postfix notation relies heavily on a stack.
  • Unambiguous parsing: A key property of ; the order of operations is inherently clear without parentheses or complex precedence rules.
    • The advantage of postfix notation is its unambiguous parsing.
postfix notation

A student writes a mathematical expression in postfix notation on a whiteboard.

Noun
  1. a parenthesis-free notation for forming mathematical expressions in which each operator follows its operands

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