[Tex/LaTex] pgfmath and doing some simple calculations using a variable

pgfmath

I'm creating addition worksheets for little oompa loompas.
It works using:

\documentclass{article}  

\usepackage{geometry}  
\geometry{letterpaper, portrait, margin=1.5cm, tmargin=2.5cm }  
\usepackage{tabularx}  
\usepackage{array}  
\usepackage{siunitx}  
\usepackage{tikz}  
\usepackage{pgf}  
\DeclareMathSizes{10.0}{17}{12}{12}  

\begin{document}  
\begin{flushleft}  
    
% fixed width, right justified column  
\newcolumntype{R}[1]{>{\raggedleft\arraybackslash}p{#1}}  



% print 2 numbers
%
%     42
%    + 7
%
\newcommand{\allan}{  
    & \pgfmathparse{random(10,99)}\pgfmathresult \\  
    + & \pgfmathparse{random(0,9)}\pgfmathresult \\  
}  

% create 7x9 grid of addition problems
\foreach \n in {0,...,8}{  
    \foreach \n in {0,...,6}{  
        \begin{tabularx}{1.8cm}{>{$}R{.3cm}<{$} >{$}R{.7cm}<{$}}  
            \allan  
            \hline  
        \end{tabularx}  
        \hspace{.4cm}  
    }  
    \vspace{1.5cm}  
}  


\end{flushleft} 
\end{document}

However, in the \newcommand \allan, what I'd really like is to be
able to eliminate addition problems that have a carry in them.

something like:

random1 = first random # from 10 to 99

random2 = 2nd random # from 0 to (9 – (random1 modulo 10))

Best Answer

The result of the calculation can be directly assigned to a macro using \pgfmathsetmacro.

Table cells are local groups, therefore the following definition of \allan first performs the calculations, defines a macro for the table rows with the expanded calculation results and calls the macro to actually set the rows:

\newcommand{\allan}{
    \pgfmathsetmacro\RandomA{random(10,99)}%
    \pgfmathsetmacro\RandomB{random(0, int(9 - mod(\RandomA,10)))}%
    \edef\next{%
      & \RandomA \noexpand\\%
      + & \RandomB \noexpand\\%
    }%
    \next
}

Full example:

\documentclass{article}

\usepackage{geometry}
\geometry{letterpaper, portrait, margin=1.5cm, tmargin=2.5cm }
\usepackage{tabularx}
\usepackage{array}
\usepackage{siunitx}
\usepackage{tikz}
\usepackage{pgf}
\DeclareMathSizes{10.0}{17}{12}{12}

\begin{document}
\begin{flushleft}

% fixed width, right justified column
\newcolumntype{R}[1]{>{\raggedleft\arraybackslash}p{#1}}



% print 2 numbers
%
%     42
%    + 7
%
\newcommand{\allan}{
    \pgfmathsetmacro\RandomA{random(10,99)}%
    \pgfmathsetmacro\RandomB{random(0, int(9 - mod(\RandomA,10)))}%
    \edef\next{%
      & \RandomA \noexpand\\%
      + & \RandomB \noexpand\\%
    }%
    \next
}

% create 7x9 grid of addition problems
\foreach \n in {0,...,8}{
    \foreach \n in {0,...,6}{
        \begin{tabularx}{1.8cm}{>{$}R{.3cm}<{$} >{$}R{.7cm}<{$}}
            \allan
            \hline
        \end{tabularx}
        \hfill
    }
    \par
    \vspace{1.5cm}
}


\end{flushleft}
\end{document}

Variant without tabularx, which fills the space on the page:

\documentclass{article}

\usepackage{geometry}
\geometry{letterpaper, portrait, margin=1.5cm, tmargin=2.5cm }
\usepackage{tabularx}
\usepackage{array}
\usepackage{siunitx}
\usepackage{tikz}
\usepackage{pgf}
\DeclareMathSizes{10.0}{17}{12}{12}

\begin{document}
\begin{flushleft}
    \setlength{\parskip}{0pt plus 1fill}
    \setlength{\parfillskip}{0pt}
    \setlength{\tabcolsep}{2\tabcolsep}% make the lines a little longer

    % print 2 numbers
    %
    %     42
    %    + 7
    %
    \newcommand{\allan}{
        \pgfmathsetmacro\RandomA{random(10,99)}%
        \pgfmathsetmacro\RandomB{random(0, int(9 - mod(\RandomA,10)))}%
        \edef\next{%
            & \noexpand\leavevmode
              \ifnum\RandomA<10 \noexpand\hphantom{0}\fi % if \RandomA can be smaller than ten
              \RandomA \noexpand\\%
            + & \RandomB \noexpand\\%
        }%
        \next
    }

    % create 7x9 grid of addition problems
    \foreach \n in {0,...,8}{
        \foreach \n in {0,...,6}{
            \begin{tabular}{>{$}l<{$} @{$\;$} >{$}r<{$}}
                \allan
                \hline
                \vadjust{\vspace{1.1cm}}% place for result
            \end{tabular}%
            \hfill
        }%
        \par
    }
    \flushbottom
    \newpage
\end{flushleft}
\end{document}

Hint: \pgfmathsetseed{<number>} can be used to get reproducible results.

Related Solutions

[Tex/LaTex] Using ifthenelse in pgfmath

This is a problem with the fpu library that is used by pgfplots: The ifthenelse command is not implemented in fpu, so it falls back to the normal pgfmath routine, which then stumbles over the floating point format of the arguments, because numbers are handled in the form 1Y1.0e0].

To circumvent this, the fpu library can be disabled in the newly defined math function using

\pgfkeys{/pgf/fpu=false}

However, the x-value handed over by pgfplots is still in the floating point format, so it has to be converted into a fixed point format:

\pgfmathfloattofixed{\x}
\let\x=\pgfmathresult

In case the fpu library is not active, this will fail because \pgfmathfloattofixed{\x} doesn't know what to do with a fixed point number. So we need to use \pgflibraryfpuifactive to test whether fpu is active, and convert the number only if it is.

Now x is a normal fixed point number, and all the common pgfmath functions should work.

However, the pgfmath engine is less precise than fpu, so it might not be desirable to fall back to it.

As ifthenelse is not a very complicated function, we can just define it ourselves:

\pgfmathdeclarefunction{ifthenelsefpu}{3}{ %}
  \pgfmathparse{#1*#2 + !#1*#3} %
}

Which can be used like the original function.

I've put both approaches into the example document below:

\documentclass{article}
\usepackage{pgfplots}

\pgfmathdeclarefunction{ifthenelsefpu}{3}{%
  \pgfmathparse{#1*#2 + !#1*#3}%
}
\pgfmathdeclarefunction{f}{1}{%
\pgfmathparse{ifthenelsefpu(#1<0,#1^2,#1)}%
}

\pgfmathdeclarefunction{g}{1}{%
  \pgflibraryfpuifactive{%
    \pgfkeys{/pgf/fpu=false}%
    \pgfmathfloattofixed{#1}%
    \let\x=\pgfmathresult%
  }%
  {%
    \pgfmathparse{#1}%
    \let\x=\pgfmathresult%
  }%
  \pgfmathparse{ifthenelse(\x<0,(\x)^2,\x)}%
}

\begin{document}
\begin{tikzpicture}
\begin{axis}[every axis plot post/.append style={
  mark=none,domain=-3:3,smooth}, 
  axis x line*=bottom, axis y line*=left, enlargelimits=upper]
  \addplot {f(x+0.5)};
  \addplot {g(x-1)};
\end{axis}
\end{tikzpicture}

%Code for showing that the functions work outside pgfplots
\pgfmathf{-3}\pgfmathresult

\pgfmathg{-3}\pgfmathresult
\end{document}

pgfplots and ifthenelse

[Tex/LaTex] TikZ \foreach loop evaluate variable using pgfmath function

I think all you need to to do is to add an extra {} around the expression as the comma is probably confusing the parser.

\foreach  \j [evaluate=\j as \jn using {mod(\j,4)}]  in {5,6}

However, I would recommend a slightly different approach and that is to use pagemathtruncatemacro (or \pgfmathsetmacro if you need real number values) instead:

Code:

\documentclass{article}
\usepackage{tikz}
\begin{document}
  \begin{tikzpicture} 
    \foreach  \j  in {5,6} {
       \pgfmathtruncatemacro{\jn}{mod(\j,4)}%
       \node[] at (\j,0) {$\jn$};
    }
  \end{tikzpicture}
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] Using ifthenelse in pgfmath

[Tex/LaTex] TikZ \foreach loop evaluate variable using pgfmath function

Code:

Related Question