LaTeX software to evaluate expressions

Question

I am looking for a latex package that can evaluate symbolic expressions by substituting the values of symbols declared in some header. For example, in these set of equations, as you can see, I get certain values of p1, p2 by substituting the values of R, L and C.

Here I had to calculate the values of p1,p2 outside of latex software and then manually enter them in (17).

I am looking for a feature where I can declare values of some special variables, R, C and L at the start of the code and then p1, p2 will be automatically evaluated in equation (17) if I use some option telling compiler to substitute the numerical value (I imagine something like : \begin{equation}{evauate = 1}\end{equation}) this will save a lot of time for me as often i make calculation mistakes in these trivial equations and the error propagates in all following equations and lot of unwarranted time wastage happens.

I have heard that in tikz package we can plot functions so I am hoping this has also been possibly implemented.

thanks!

Just a clarification: are you looking for a way to evaluate expressions typeset in LaTeX? Or would you be OK with a solution that simply makes proper calculations inside LaTeX, independently of the typesetting? In the second case, I think that Lua is a better solution that PGF, since it's both more efficient and more precise. — Miyase, Jun 03 '22 at 19:19
The numerica package may be of interest to you. https://www.ctan.org/pkg/numerica — LaTeXereXeTaL, Jun 03 '22 at 19:47
@Miyase presently, I would like to evaluate only expressions typeset in LaTex — Kutsit, Jun 05 '22 at 05:03
@LaTeXereXeTaL numerica looks very useful, but i installed it, as well as l3kernel and l3packages, mathtools and amsmath however it is not compiling, is something additional needed? as soon i include usepackage{numerica} it, it says missing $ inserted in graphics.sty, did you face something like this — Kutsit, Jun 05 '22 at 05:22
I get no errors with numerica. I am using an up to date TeX Live 2022. Without seeing your code I have no way of knowing what to tell you next. — LaTeXereXeTaL, Jun 05 '22 at 17:35
@LaTeXereXeTaL, sorted, I needed to update MikTex, I never opened since i installed it years ago, It is working now — Kutsit, Jun 06 '22 at 07:40

score 5 · Answer 1 · answered Jun 03 '22 at 19:30

Probably overkill here, but another possibility is to use the sagetex package, which requires installation of SageMath. The source below was processed with pdflatex inside TeXShop, so the directive in the first line was included; in other environments, you would need to run the sage command directly from a command line.

 % !TEX TS-program = sage
\documentclass{article}
\usepackage{amsmath,amsfonts}
\usepackage{sagetex}
\begin{document}
\begin{sageblock}
L=1;C=1;R=4;
p1 = -R/(2L) + sqrt(R^2/(L^2) - 4/(LC))/2
p2 = -R/(2L) - sqrt(R^2/(L^2) - 4/(LC))/2
\end{sageblock}
\begin{align}
p_{1} &= \sage{p1} & p_{2} &= \sage{p2},
\
p_{1} &\approx \sage{n(p1)} & p_{2} &\approx \sage{n(p2)},
\end{align}
\end{document}

(see embedding - Using Python within LaTeX and accessing its variables - TeX - LaTeX Stack Exchange for other packages that allow you to use Python within LaTeX.) — user202729, Jun 04 '22 at 05:56

Peter Grill · Answer 2 · 2022-06-03T19:09:23.760

4

You can use pgfmath which is built into tikz:

Code:

\documentclass{article}
\usepackage{pgfmath}% not needed if inckuding `tikz` or `pgfplots`
\newcommand{\ComputeValue}[5][+]{%
    %% #1 = + | -
    %% #2 = macro to contain value
    %% #3 = R
    %% #4 = L
    %% #5 = C
    \pgfmathsetmacro{#2}{%
        -(#3)/(2 * (#4))
        #1 %% Choose + or - (default is + if not specified)
        sqrt(((#3)/(#4))^2 - 4/((#4)*(#5))) / 2
    }%
}%
\newcommand{\ValueR}{4}
\newcommand{\ValueL}{1}
\newcommand{\ValueC}{1}
\begin{document}
\ComputeValue{\ValueP}{\ValueR}{\ValueL}{\ValueC}
\verb|\ValueP| is \ValueP.
\ComputeValue[-]{\ValueQ}{\ValueR}{\ValueL}{\ValueC}
\verb|\ValueQ| is \ValueQ.
\end{document}

edited Jun 03 '22 at 19:09

answered Jun 03 '22 at 17:32

Peter Grill

223,288

Disadvantage is that you have to type the equation twice, once in typesetted LaTeX form and once in pgfmath expression form. I think something like SageTeX (or any proper symbolic engine) will be able to convert the symbolic expression to LaTeX form automatically (although the autogenerated formula might look aesthetically bad at sometimes...) – user202729 Jun 04 '22 at 05:55

LaTeXereXeTaL · Answer 3 · 2022-06-20T17:09:16.950

I felt I should add this as an answer demonstrating the numerica package rather than just a comment, and because I feel it is probably the simplest answer. I note your example contains a complex number and I don't think numerica supports that. I encourage you to contact the developer if necessary. He is active and very open to discussion.

MWE:

% !TEX program = lualatexmk
% !TEX encoding = UTF-8 Unicode
\documentclass{article}
\usepackage{numerica}
\begin{document}
\textsf{numerica} has many options so please do read the documentation carefully. 
Note how \verb|\eval*| suppresses the variable list. Using \verb|xx| forces 
scientific notation to mantissas in the interval ( [1,10) ); the number sets 
the number of displayed figures.
\begin{align}
  p_1 &= \eval{ -\frac{R}{2L} + \frac{\sqrt{R^2/L^2 - 4/LC}}{2} }[R=4,L=1,C=1][10] \
  p_2 &= \eval{ -\frac{R}{2L} - \frac{\sqrt{R^2/L^2 - 4/LC}}{2} }[R=4,L=1,C=1][10]
\end{align}
\begin{align}
  p_1 &= \eval{ -\frac{R}{2L} + \frac{\sqrt{R^2/L^2 - 4/LC}}{2} }[R=4,L=1,C=1][6xx] \
  p_2 &= \eval{ -\frac{R}{2L} - \frac{\sqrt{R^2/L^2 - 4/LC}}{2} }[R=4,L=1,C=1][6xx]
\end{align}
You can define and store variables as macros. See the documentation for details.
\NewDocumentCommand{\myR}{}{4} % or \newcommand{\myR}{4} or \def\myR{4}
\NewDocumentCommand{\myL}{}{1} % or \newcommand{\myL}{1} or \def\myL{1}
\NewDocumentCommand{\myC}{}{1} % or \newcommand{\myC}{1} or \def\myC{1}
\macros{\myR,\myL,\myC}
\begin{align}
  p_1 &= \eval{ -\frac{\myR}{2\myL} + \frac{\sqrt{\myR^2/\myL^2 - 4/\myL\myC}}{2} }[6xx] \
  p_2 &= \eval{ -\frac{\myR}{2\myL} - \frac{\sqrt{\myR^2/\myL^2 - 4/\myL\myC}}{2} }[6xx]
\end{align*}
\end{document}

This is the output.

LaTeX software to evaluate expressions

3 Answers3

Code:

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