more examples of reverse Polish notation

The following examples, presented first in standard infix notation, converted to reverse Polish notation by using the shunting yard algorithm, all use the same four operands but combined with different operators and parentheses. Operators are assumed to be binary.

$(1+2)\times (3+4)$ in standard infix notation becomes $1\mathit{\hspace{1em}}2+3\mathit{\hspace{1em}}4+\mathit{\hspace{1em}}\times$ in reverse Polish notation. Both expressions should evaluate to 21, each in the appropriate calculator.

$1+2\times 3+4$ standard becomes $1\mathit{\hspace{1em}}2\mathit{\hspace{1em}}3\times 4+$ RPN. Both evaluate to 11.

$1+2\times (3+4)$ turns to $1\mathit{\hspace{1em}}2\mathit{\hspace{1em}}3\mathit{\hspace{1em}}4+\mathit{\hspace{1em}}\times \mathit{\hspace{1em}}+$. Evaluate to 15.

$(1+2)\times 3+4$ is $1\mathit{\hspace{1em}}2+3\times 4+$. Evaluate to 13.

Title	more examples of reverse Polish notation
Canonical name	MoreExamplesOfReversePolishNotation
Date of creation	2013-03-22 16:10:19
Last modified on	2013-03-22 16:10:19
Owner	Mravinci (12996)
Last modified by	Mravinci (12996)
Numerical id	5
Author	Mravinci (12996)
Entry type	Example
Classification	msc 03B70
Classification	msc 68N17