Parallel (operator): Difference between revisions

Revision as of 14:58, 3 June 2025

Latest revision as of 02:52, 11 June 2025

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{{use dmy dates|date=July 2019|cs1-dates=y}}

{{use list-defined references|date=December 2021}}

[[File:Parallelitätsoperator.svg|thumb|Graphical interpretation of the parallel operator with <math>a \parallel b = c</math>.]]

The '''parallel operator''' <math>\|</math> (pronounced "parallel",<ref name="Duffin_1971"/> following the [[parallel (geometry)#Symbol|parallel lines notation from geometry]];<ref name="Kersey_1673"/><ref name="Cajori_1928"/> also known as '''reduced sum''', '''parallel sum''' or '''parallel addition''') is a [[binary operation]] which is used as a shorthand in [[electrical engineering]],<ref name="TI_2004"/><ref name="Bober_2016"/><ref name="EECS_2018"/><ref group="nb" name="NB_Origin"/> but is also used in [[kinetics (physics)|kinetics]], [[fluid mechanics]] and [[financial mathematics]].<ref name="Ellerman_1995"/><ref name="Ellerman_2004"/> The name ''parallel'' comes from the use of the operator computing the combined resistance of [[Resistor#Series and parallel resistors|resistors in parallel]].

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==Implementation==

[[File:Hp30bwp34s.jpg|thumb|150px|[[WP&nbsp;34S]] with parallel operator (<kbd>∥</kbd>) on the {{keypress|g|÷}} key.]]

Suggested already by Kent E. Erickson as a subroutine in digital computers in 1959,<ref name="Erickson_1959"/> the parallel operator is implemented as a keyboard operator on the [[Reverse Polish Notation]] (RPN) scientific calculators [[WP&nbsp;34S]] since 2008<ref name="Bonin_2012"/><ref name="Bonin_2015"/><ref name="Bonin_2016"/> as well as on the [[WP&nbsp;34C]]<ref name="Dowrick_2015"/> and [[WP&nbsp;43S]] since 2015,<ref name="Bonin_2019_OG"/><ref name="Bonin_2019_RG"/> allowing to solve even cascaded problems with few keystrokes like {{keypress|270}}{{keypress|ENTER}}{{keypress|180}}{{keypress|∥}}{{keypress|120}}{{keypress|∥}}.

==Projective view==