Argthtjtr

I'm trying to define a macro to typeset Eulers complex e-power with or without a minus sign in its argument. I would like the macro to automatically detect if its argument starts with a -. I have the following MWE which uses and optional argument:

documentclass[a4paper,12pt,fleqn]{article}



defimaginaryunit{j}                  % the imaginary unit, i for mathematician and theoretical physicist, j for the rest of the world.

defimunit{mathrm{imaginaryunit}}   % ... in upright math

defce{mathrm{e}}                    % the constant e, upright of course

makeatletter

defepowim{@ifnextchar[{epowimi}{epowimi}}       % e to-the-power-of imaginary unit

defepowimi[#1]#2{ce^{#1ifimaginaryunit jrelax,fiimunit#2}}       % e to-the-power-of imaginary unit

makeatother



begin{document}



begin{equation}

epowim{alpha}qquad epowim[-]{alpha} qquad ce^{-imunitalpha}

end{equation}



end{document}

So I would like a macro that detects if its argument starts with a -:

epowim{-alpha}

should detect the - and place it before the imaginary unit instead of placing it after the imaginary unit.

So the question is if it can be done and how.

Something like this?

documentclass[a4paper,12pt,fleqn]{article}

defimaginaryunit{j}                  % the imaginary unit, i for mathematician and theoretical physicist, j for the rest of the world.

defimunit{mathrm{imaginaryunit}}   % ... in upright math

defce{mathrm{e}}                    % the constant e, upright of course

newcommandepowim[1]{ce^{epowimaux#1relaxendep}}

defepowimaux#1#2endep{ifx-#1relax-imunitelse%

  if jimaginaryunitrelax,fiimunit#1fi#2}

begin{document}

[

epowim{alpha}qquad epowim{-alpha} qquad ce^{-imunitalpha}

]

[

epowim{x+t}quadepowim{-x+t}quadepowim{-}quadepowim{}

]

defimaginaryunit{i}

[

epowim{alpha}qquad epowim{-alpha} qquad ce^{-imunitalpha}

]

[

epowim{x+t}quadepowim{-x+t}quadepowim{-}quadepowim{}

]

end{document}

Avoid def, your life will be easier.

Since you seem to know about @ifnextchar:

documentclass[a4paper,12pt,fleqn]{article}



% the imaginary unit, j for engineers and i for the rest of the world

newcommandimaginaryunit{j}

% in upright type as engineers do; also Euler's constant

newcommandimunit{mathrm{imaginaryunit}}

newcommandce{mathrm{e}}



newcommand{fiximunit}{ifimaginaryunit j,fi}



makeatletter

newcommand{epowim}[1]{ce^{epowim@#1}}

newcommand{epowim@}{@ifnextchar-{epowim@@}{epowim@@{fiximunit}}}

newcommand{epowim@@}[1]{#1imunit}

makeatother



begin{document}



begin{equation}

epowim{alpha}qquad epowim{-alpha} qquad ce^{-imunitalpha}

qquad epowim{} qquad epowim{-}

end{equation}



end{document}

Explanation: @ifnextchar- uses the next argument if - is found, the successive one otherwise, but without removing -. So if - is called the result will be

epowim@@-alpha

which passes - as argument to epowim@@. Otherwise epowim@@ is called with fiximunit as argument.

This would not fail with epowim{} or epowim{-} to typeset e^j and e^−j respectively.

A perhaps simpler implementation with xparse:

documentclass[a4paper,12pt,fleqn]{article}



usepackage{xparse}



% the imaginary unit, j for engineers and i for the rest of the world

newcommandimaginaryunit{j}

% in upright type as engineers do; also Euler's constant

newcommandimunit{mathrm{imaginaryunit}}

newcommandce{mathrm{e}}



newcommand{fiximunit}{ifimaginaryunit j,fi}



NewDocumentCommand{epowim}{m}{ce^{powim#1}}

NewDocumentCommand{powim}{t-}{IfBooleanTF{#1}{-imunit}{fiximunitimunit}}



begin{document}



begin{equation}

epowim{alpha}qquad epowim{-alpha} qquad ce^{-imunitalpha}

qquad epowim{} qquad epowim{-}

end{equation}



end{document}