Vector Field

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{math}
\usepackage{ifthen}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1pt}
%
% File name: directional-angles.tex
% Description: 
% The directional angles of a vector are geometrically represented.
% 
% Date of creation: August, 29th, 2021.
% Date of last modification: October, 9th, 2022.
% Author: Efraín Soto Apolinar.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% Source: page 36 of the 
% Glosario Ilustrado de Matem\'aticas Escolares.
% https://tinyurl.com/5udm2ufy
%
% Terms of use:
% According to TikZ.net
% https://creativecommons.org/licenses/by-nc-sa/4.0/
% Your commitment to the terms of use is greatly appreciated.
%
\begin{document}
%
\begin{tikzpicture}
    % Components of the vector field
    \tikzmath{function equis(\x,\y) {return (\y*\y-0.25*\x);};}
    \tikzmath{function ye(\x,\y) {return \x*\x-\y;};}
    \tikzmath{function zeta(\x,\y) {return \x+\y;};}    
    \tikzmath{function magnitud(\x,\y) {return sqrt(\x*\x+\y*\y);};} % magnitude of the vector at (x, y, z) 
    %   
    \pgfmathsetmacro{\dominio}{3.0} % domain for computation 
    \pgfmathsetmacro{\step}{\dominio/10.0} % step size
    \pgfmathsetmacro{\max}{\dominio}
    \pgfmathsetmacro{\xi}{-\dominio}
    \pgfmathsetmacro{\xf}{\dominio}
    \pgfmathsetmacro{\xs}{\xi+\step}
    \pgfmathsetmacro{\yi}{-\dominio}
 
 
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