Calling a Global Variable using Expl3

Question

I've written a macro for my document that producing a random discontinuous but otherwise smooth curve, given a few randomly assigned points. I then ask what the output is for particular (not random) values of the input, this is using expl3 and TikZ. Now I'm trying to take one of the randomly generated outputs using in the macro and reference it in the document but I can't seem to figure out how to do it, and haven't found anything explicit enough for me to understand. This is what I've written:

\documentclass[12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[margin=0.75in]{geometry}
\usepackage[utf8]{inputenc}
\usepackage{graphicx}
\usepackage{amsmath,amssymb,enumitem}
\usepackage[first=-20, last=20]{lcg}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usepackage{calculator}
\usepackage{calculus}
\usepackage{ifthen}
\usepackage{xfp}
\usepackage{pgfplots}
\pgfplotsset{ every non boxed x axis/.append style={x axis line style=-}, every non boxed y axis/.append style={y axis line style=-}}
\newcommand{\randi}{\rand\arabic{rand}}
\ExplSyntaxOn\newcommand{\intR}[2]{\chgrand[first=#1, last=#2] \randi}\ExplSyntaxOff
\usepackage{pgffor}
\newcommand{\addsub}{\pgfmathrandomitem{\choice}{choices1}\choice}
\pgfmathdeclarerandomlist{choices1}{{+}{-}}
\newcommand{\subnone}{\pgfmathrandomitem{\choice}{choices3}\choice}
\pgfmathdeclarerandomlist{choices3}{{}{-}}
\ExplSyntaxOn
\int_new:N \l_LeftEnd_int
\int_new:N \l_LeftMid_int
\int_new:N \g_hole_int
\int_new:N \l_RightEnd_int
\NewDocumentCommand{\smoothplot}{}
{
\int_set:Nn \l_LeftEnd_int { \int_rand:nn { 1 } { 5 } }
\int_set:Nn \l_LeftMid_int { \int_rand:nn { -2 } { 2 } }
\int_set:Nn \l_RightEnd_int { \int_rand:nn { -4 } { 5 } }
\int_gset:N \g_hole_int { \l_LeftMid_int }
\begin{tikzpicture}
\begin{axis}[
        width=1\textwidth,
        height=0.5\textwidth,
        grid=major,
        xmax=4.5,
        xmin=-4.5,
        ymin=-4.5,
        ymax=5.5,
        xtick={-4,-3,-2,-1,0,1,2,3,4},
        ytick={-4,-3,-2,-1,0,1,2,3,4,5},
        ylabel={$g(x)$},
        xlabel={$x$}
          ]
\addplot [smooth, red, mark=none, thick] coordinates
    {(-4, \l_LeftEnd_int) (-3,2rand-2) (-2,2floor{rand}) (-1,3rand+1) (0,3floor{rand}) (1, \l_LeftMid_int+2) (2,\l_LeftMid_int)};
\addplot [red, only~marks] coordinates {(-4, \l_LeftEnd_int) (2, \l_LeftMid_int) (4, \l_RightEnd_int)};
\addplot [red, mark=o] coordinates {(2, \l_LeftMid_int+2)};
\addplot [smooth, red, mark=none, thick] coordinates {(2, \l_LeftMid_int+2) (2.7, rand+3) (3.3, 2*rand+1.5) (4, \l_RightEnd_int)};
\end{axis}
\end{tikzpicture}
}
\NewDocumentCommand{\hole}{} % This is the part that I'm trying to get to reference the variable
{
\g_hole_int
}
\ExplSyntaxOff
\begin{document}
\section*{Problem 3}
\smoothplot \
Find the values for $x  = -4, -2, 0, 2, 4$.\
Find the domain and range of $g(x)$.\
% \ADD{\hole}{2}{\temp}\sol % This line doesn't work, but I'll revisit this
% \hole
For what value(s) of $x$ does $g(x) =$ \hole + 2
\end{document}

Sorry for the blurriness

please use the expl3 naming convention. Your variables should have a module name part. — Ulrike Fischer, Oct 30 '20 at 17:35
@UlrikeFischer Could you describe this naming convention more, or could you give an example / correction to what you mean? Also, are you saying this will fix this issue or just giving advice about better practice? — David G., Oct 30 '20 at 19:53
see expl3.pdf (open it with texdoc expl3) for the naming scheme, and no it will not solve your problem, that is only about best practice. — Ulrike Fischer, Oct 30 '20 at 19:59

score 1 · Accepted Answer · answered Nov 15 '23 at 08:21

I'd separate the expl3 from the TikZ/pgfplots part.

In the expl3 part the plot building command is passed three random integers already in explicit form.

The \makesmoothplot command also globally defines \hole to expand to the desired value.

\documentclass[12pt]{article}
\usepackage[margin=0.75in]{geometry}
\usepackage{amsmath,amssymb,enumitem}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usepackage{pgfplots}
\pgfplotsset{
  compat=1.18,
  every non boxed x axis/.append style={x axis line style=-},
  every non boxed y axis/.append style={y axis line style=-},
}
\ExplSyntaxOn
\NewDocumentCommand{\smoothplot}{}
 {
  \exp_args:Neee
  \makesmoothplot{ \int_rand:nn {  1 } { 5 } }% LeftEnd
                 { \int_rand:nn { -2 } { 2 } }% LeftMid
                 { \int_rand:nn { -4 } { 5 } }% RightEnd
 }
\NewDocumentCommand{\definehole}{m}
 {
  \tl_gset:Nx \hole { \int_eval:n { #1 + 2 } }
 }
\ExplSyntaxOff
\NewDocumentCommand{\makesmoothplot}{mmm}{%
  \begin{tikzpicture}
  \begin{axis}[
    width=1\textwidth,
    height=0.5\textwidth,
    grid=major,
    xmax=4.5,
    xmin=-4.5,
    ymin=-4.5,
    ymax=5.5,
    xtick={-4,-3,-2,-1,0,1,2,3,4},
    ytick={-4,-3,-2,-1,0,1,2,3,4,5},
    ylabel={$g(x)$},
    xlabel={$x$}
  ]
  \addplot [smooth, red, mark=none, thick] coordinates {
    (-4, #1)
    (-3,2rand-2)
    (-2,2floor{rand})
    (-1,3rand+1)
    (0,3floor{rand})
    (1, #2+2)
    (2,#2)
  };
  \addplot [red, only marks] coordinates {
    (-4, #1)
    (2, #2)
    (4, #3)
  };
  \addplot [red, mark=o] coordinates {(2, #2+2)};
  \addplot [smooth, red, mark=none, thick] coordinates {
    (2, #2+2)
    (2.7, rand+3)
    (3.3, 2*rand+1.5)
    (4, #3)
  };
  \end{axis}
  \end{tikzpicture}
  \definehole{#2}
}
\begin{document}
\section*{Problem 3}
\smoothplot
Find the values for $x  = -4, -2, 0, 2, 4$.
Find the domain and range of $g(x)$.
For what value(s) of $x$ does $g(x) = \hole$?
\end{document}

score 0 · Answer 2 · answered Oct 30 '20 at 20:13

I added \int_use:N infrom of my global variable for the NewDocumentCommand{\hole}, also I changed the variable names:

\ExplSyntaxOn
\int_new:N \l_point_LeftEnd_int
\int_new:N \l_point_LeftMid_int
\int_new:N \g_point_LeftMid_int
\int_new:N \l_point_RightEnd_int
\NewDocumentCommand{\smoothplot}{}
{
\int_set:Nn \l_point_LeftEnd_int { \int_rand:nn { 1 } { 5 } }
\int_set:Nn \l_point_LeftMid_int { \int_rand:nn { -2 } { 2 } }
\int_set:Nn \l_point_RightEnd_int { \int_rand:nn { -4 } { 5 } }
\int_gset:Nn \g_point_LeftMid_int { \l_point_LeftMid_int }
\begin{tikzpicture}
\begin{axis}[
        width=1\textwidth,
        height=0.5\textwidth,
        grid=major,
        xmax=4.5,
        xmin=-4.5,
        ymin=-4.5,
        ymax=5.5,
        xtick={-4,-3,-2,-1,0,1,2,3,4},
        ytick={-4,-3,-2,-1,0,1,2,3,4,5},
        ylabel={$g(x)$},
        xlabel={$x$}
          ]
\addplot [smooth, red, mark=none, thick] coordinates
    {(-4, \l_point_LeftEnd_int) (-3,2rand-2) (-2,2floor{rand}) (-1,3rand+1) (0,3floor{rand}) (1, \l_point_LeftMid_int+2) (2,\l_point_LeftMid_int)};
\addplot [red, only~marks] coordinates {(-4, \l_point_LeftEnd_int) (2, \l_point_LeftMid_int) (4, \l_point_RightEnd_int)};
\addplot [red, mark=o] coordinates {(2, \l_point_LeftMid_int+2)};
\addplot [smooth, red, mark=none, thick] coordinates {(2, \l_point_LeftMid_int+2) (2.7, rand+3) (3.3, 2*rand+1.5) (4, \l_point_RightEnd_int)};
\end{axis}
\end{tikzpicture}
}
\NewDocumentCommand{\hole}{}
{
\ADD{ \int_use:N \g_point_LeftMid_int }{ 2 }\sol~
\sol
}
\ExplSyntaxOff

Could someone comment on why I needed to include \int_use:N for the \hole command but not for when calling the variables in my \smoothplot command?

What’s the reason for using \ADD and not the built-ins of expl3? — egreg, Oct 31 '20 at 09:07
Outside of me not having any familiarity with the expl3 functions, not much. I was using it later in the document so I know how it works. I wish I new expl3 a lot better, but unfortunately I cannot find any good tutorials going over how to code with it. The only resource I have is a rather dense 16 page document that hasn't helped me much — David G., Oct 31 '20 at 19:16
Old comment, but latex3 - Where I can find introduction to programming in expl3? - TeX - LaTeX Stack Exchange has a link to Alan Shawn's blog (basic programming guide only. No token manipulation/input stream manipulation etc., unfortunately.). The API reference is in interface3.pdf which is... yes, dense. — user202729, Jul 23 '22 at 04:41

Calling a Global Variable using Expl3

2 Answers2