[Tex/LaTex] How to define a mathematical function as a LaTeX macro

calculationspst-plotpstricks

I am attempting to create a usable function within LaTeX such that its inputs are transformed mathematically. However, I cannot find any documentation that can perform such mathematical function definition.

Here is an example of what I am seeking:

Having defined a function entitled \myMathFunction which accepts only one parameter, the follow usage:

\myMathFunction{2}

should output 6 if the function is defined as follows: ({#1} * 5) - {#1}^2

Where {#1} is the parameter, and in the case of my example, is equal to 2.

Additionally, the function should be usable within a PSTricks plot. E.g.

\psplot[
    algebraic,
    linecolor   = red,
    linewidth   = 1pt
]{0}{TwoPi}
{\myMathFunction{x}}

Best Answer

A calculated table and the plotted curve:

\documentclass{article}
\usepackage{pst-plot}
\usepackage{xparse}
\ExplSyntaxOn%% allow _ : as a letter
\newcommand\myMathFunction[1]{% 
  \ifx#1x ((#1) * 5) - (#1)^2  
  \else \fp_to_decimal:n {((#1) * 5) - (#1)^2} \fi}
\ExplSyntaxOff
\begin{document}
\begin{tabular}{ r r }
$x$ & $f(x)$ \\\hline
0 & \myMathFunction{0}\\
1 & \myMathFunction{1}\\
2 & \myMathFunction{2}\\
3.3 & \myMathFunction{3.3}\\
4 & \myMathFunction{4}\\
5 & \myMathFunction{5}\\\hline
\end{tabular}
%
\pspicture[shift=*](-1,0)(6,7)
\psaxes{->}(5.5,6)
\psplot[algebraic,linecolor=red,linewidth=1.5pt]{0}{5}{\myMathFunction{x}}
\endpspicture
\end{document}

enter image description here

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You don't want to “expand” macros, but rather to do computations. Expansion is the process by which a macro is replaced by its “replacement text”. So, when TeX finds \A it replaces it with 1; however TeX will never do computations unless precisely instructed to do so, because it's a language aimed at typesetting and somebody would want to print

2 + 2 = 4

and this shouldn't be replaced by 4=4 under the hood.

You can easily define a \compute macro for doing with integers.

\documentclass{article}

\newcommand* \A {1}
\newcommand* \B {2}
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\newcommand{\compute}[1]{\number\numexpr#1\relax}

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$A = \compute{\A}$, $B = \compute{\B}$, 
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enter image description here

Of course, \compute{\A} isn't really necessary, since \A expands directly to 1.

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pstricks loads the xcolor package. If you want a broader choice, pass the option, say, x11names to xcolor (via \documentclass). This option gives access to nearly 320 predefined colours. See § 4, Colors by Names, pp38–40 of the documentation. You also can use the option svgnames which more or less the same as HTML colour names.

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Best Answer

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