Parse simple arithmetics and return the result

Question

I want a command \ca which takes a simple arithmetic calculation as an argument and returns the result with proper decimal places. Additionally I want an boolean argument which decides if only the result is printed or the whole calculation.

For example

\ca{8.12 - 2.2 + 1}

should just print 6.92.

or

\ca[t]{8.12 - 2.2 + 1}

should print 8.12 - 2.2 + 1 = 6.92

Following the question How can I sum two values and store the result in other variable? I did this:

\documentclass{article}
\usepackage[nomessages]{fp}% http://ctan.org/pkg/fp
\usepackage{ifthen}

\newcommand{\ca}[2][f]{
\FPeval{\result}{clip(#2)}
\ifthenelse{\equal{#1}{t}}{
$#2=  \result$}
{
\result
}
}



\begin{document}
\ca[t]{3*(2.2 + 2.3)}

\ca{2.5 + 2.78}
\end{document}

Is it possible to to the same such that the german comma notation is used in what is displayed (i.e. 8,2 instead of 8.2) and in the case the calculation is printed that * is printed as \dcot.

Answer 1

Here is a crude way of modifying the output to be \cdot and ,-specific using xstring. The reason for using xstring is because the argument to fp (#2) would otherwise have to be parsed and separated into operators and operands to enable numprint usage (say).

\documentclass{article}
\usepackage[nomessages]{fp}% http://ctan.org/pkg/fp
\usepackage{xstring}% http://ctan.org/pkg/xstring
\usepackage{xparse}% http://ctan.org/pkg/xparse

\NewDocumentCommand{\ca}{s m}{
  \FPeval{\result}{clip(#2)}
  \IfBooleanTF{#1}% Condition on starred/unstarred version
    {% starred version \ca*{...}
      \StrSubstitute{\result}{.}{,}
    }{% unstarred version \ca{...}
      \StrSubstitute{#2}{.}{,\!}[\temp]% '.' -> ','
      \StrSubstitute{\temp}{*}{\cdot}[\temp]% '*' -> '\cdot'
      $\temp=\StrSubstitute{\result}{.}{,\!}$
    }
}

\begin{document}
\ca{3*(2.2 + 2.3)}

\ca*{2.5 + 2.78}
\end{document}​

xparse was used to provide a starred/unstarred version of \ca where the unstarred version \ca prints the expression, while the starred version \ca* does not.

Answer 2

I think you mean \cdot not \dot. In this case you may use:

\documentclass{article}
\usepackage[nomessages]{fp}% http://ctan.org/pkg/fp
\usepackage{ifthen}

\begingroup
\catcode`\.=\active
\catcode`\*=\active
\newcommand{\germannotation}[1]{%
  \begingroup
    \catcode`\.=\active
    \def.{{,}}%
    \catcode`\*=\active
    \def*{\cdot}%
    \scantokens{#1}%
  \endgroup
}
\global\let\germannotation\germannotation
\endgroup

\newcommand{\ca}[2][f]{%
  \FPeval{\result}{clip(#2)}%
  \edef\result{\noexpand\germannotation{\result}}%
  \ifthenelse{\equal{#1}{t}}{%
    $\germannotation{#2}=\result$%
  }{%
    \result
  }%
}

\begin{document}
\ca[t]{3*(2.2 + 2.3)}

\ca{2.5 + 2.78}
\end{document}

Answer 3

Here is a version that use pgf for the math calculations which allows for more complicated math expressions (such as tan(deg(pi/4)) below), and the numprint package for the formatting of the output:

Notes:

• The german formatting of the input and changing the * in the input to a \cdot (adding pi, \tan, etc...) is adapted form @Werner's solution.

Futher Enhancements:

• Use numprint for the numbers in the input as that allows for more flexibility than just changing the . to a ,.
• Handle formatting of more complex mathematical expressions, for instance change exp(a/b) to \e^{a/b}

Code:

\documentclass{article}
\usepackage{pgf}
\usepackage{xparse}
\usepackage{xstring}
\usepackage{numprint}

\newcommand*{\AdjustInput}[1]{%
    \StrSubstitute{#1}{.}{,\!}[\temp]%
    \StrSubstitute{\temp}{*}{\cdot}[\temp]% 
    \StrSubstitute{\temp}{sin}{\sin}[\temp]% 
    \StrSubstitute{\temp}{cos}{\cos}[\temp]% 
    \StrSubstitute{\temp}{tan}{\tan}[\temp]% 
    \StrSubstitute{\temp}{deg}{}[\temp]% 
    \StrSubstitute{\temp}{((}{(}[\temp]% 
    \StrSubstitute{\temp}{))}{)}[\temp]% 
    \StrSubstitute{\temp}{pi}{\pi}[\temp]% 
    \temp%
}%

\NewDocumentCommand{\ca}{s m}{%
    \pgfmathsetmacro{\var}{#2}%
    \IfBooleanTF{#1}{%
        \ensuremath{\numprint{\var}}%
    }{%
        \ensuremath{\AdjustInput{#2}=\numprint{\var}}%
    }%
}%

\begin{document}
\ca*{8.12 - 2.2 + 1}% starred version only prints result

\ca{3*(2.2 + 2.3)}

\ca{8.12 - 2.2 + tan(deg(pi/4))}
\end{document}

Answer 4

This is a simplified version of Schweinebacke's solution (and a case where \ensuremath can be justified):

\documentclass[a4paper]{article}
\usepackage{xparse,fp}
\def\changecommaandstar{%
  \mathcode`.=\string"8000
  \mathcode`*=\string"8000
  \begingroup\lccode`~=`.\lowercase{\endgroup\def~}{{,}}
  \begingroup\lccode`~=`*\lowercase{\endgroup\def~}{\cdot}
}
\NewDocumentCommand{\ca}{sm}{%
  \ensuremath{\begingroup
  \FPeval{\result}{clip(#2)}
  \changecommaandstar                   
  \IfBooleanT{#1}{#2=}\result
  \endgroup}
}

\begin{document}

\ca*{3*(2.2 + 2.3)}

$\ca{2.5 + 2.78}>5$

\end{document}

This is also a case where a *-version, rather than an optional argument, is perhaps better.

Answer 5

I'm a little hesitant in adding this answer, as I'm merely fumbling my way around with Lua. Feel free to edit and improve the code.

Anyways, as implied above, here is a way that requires compilation with lualatex, as the calculation is done with Lua.

\documentclass{article}
\usepackage{luacode}
\newcommand{\ca}[2][f]{%
\luaexec{
    check = "#1"
    input = #2
    answer = tostring(input)
    answer = string.gsub(answer, "\%.", "{,}")
    calculation = "#2"
    calculation = string.gsub(calculation, "*", "\\cdot ")
    calculation = string.gsub(calculation, "\%.", "{,}")
    if check == "f" then
       tex.sprint("\\ensuremath{", answer, "}")
    else
       tex.sprint("\\ensuremath{", calculation, "=", answer, "}")
    end
}}
\begin{document}
\ca{1+2.2 - 5/2} \par
\ca[t]{3+1-2.34*3}
\end{document}

This could also be expanded to allow sin, cos, etc. by changing the definition of the command to

\newcommand{\ca}[2][f]{%
\luaexec{
    local sin, cos, tan, pi, exp, ln, log = math.sin, math.cos, math.tan, math.pi, math.exp, math.log, math.log10
    check = "#1"
    input = #2
    answer = tostring(input)
    answer = string.gsub(answer, "\%.", "{,}")
    calculation = "#2"
    calculation = string.gsub(calculation, "*", "\\cdot ")
    calculation = string.gsub(calculation, "\%.", "{,}")
    calculation = string.gsub(calculation, "pi*", "\\pi ")
    calculation = string.gsub(calculation, "sin", "\\sin ")
    calculation = string.gsub(calculation, "cos", "\\cos ")
    calculation = string.gsub(calculation, "tan", "\\tan ")
    calculation = string.gsub(calculation, "exp", "\\exp ")
    calculation = string.gsub(calculation, "ln", "\\ln ")
    calculation = string.gsub(calculation, "log", "\\log ")
    if check == "f" then
       tex.sprint("\\ensuremath{", answer, "}")
    else
       tex.sprint("\\ensuremath{", calculation, "=", answer, "}")
    end
}}

Answer 6

Here is something I fooled around with. I became aware of your question afterwards, so it is only a partial answer. It uses the new l3fp package of expl3.

\documentclass{article}
\usepackage{xparse}
\begin{document}

\ExplSyntaxOn

\cs_new:Npn \typeset_eq:n #1 {
  \tl_set:Nn \l_tmpa_tl { #1 }
  \tl_set_eq:NN \l_tmpb_tl \l_tmpa_tl
  \tl_replace_all:Nnn \l_tmpb_tl { * } { \times }
  \tl_replace_all:Nnn \l_tmpb_tl { pi } { \pi }
  \tl_replace_all:Nnn \l_tmpb_tl { sin } { \sin }
  \tl_replace_all:Nnn \l_tmpb_tl { cos } { \cos }
  \tl_replace_all:Nnn \l_tmpb_tl { tan } { \tan }
  $
  \l_tmpb_tl = \fp_eval:n { \l_tmpa_tl }
  $
}

\NewDocumentCommand { \eq } { m } {
  \typeset_eq:n { #1 }
}

\ExplSyntaxOff

\eq{ 1 + 2 * 3 }

\eq{ sin ( pi / 3 ) }

\eq{ cos ( pi / 4 ) }

\eq{ tan ( pi / 6 ) }

\end{document}