Talk:PlanetPhysics/Multigrade Operator

Original TeX Content from PlanetPhysics Archive

%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: multigrade operator %%% Primary Category Code: 02. %%% Filename: MultigradeOperator.tex %%% Version: 1 %%% Owner: Jon Awbrey %%% Author(s): Jon Awbrey %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

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A \textbf{multigrade operator} $\Omega$ is a \htmladdnormallink{parametric operator}{http://planetphysics.us/encyclopedia/ParametricOperator.html} with \htmladdnormallink{parameter}{http://planetphysics.us/encyclopedia/Parameter.html} $k$ in the set $\mathbb{N}$ of non-negative integers.

The application of a multigrade operator $\Omega$ to a finite sequence of operands $(x_1, \ldots, x_k)$ is typically denoted with the parameter $k$ left tacit, as the appropriate application is implicit in the number of operands listed. Thus $\Omega(x_1, \ldots, x_k)$ may be taken for $\Omega_k(x_1, \ldots, x_k).$

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