Make command with multiple optional arguments

Question

I wish to make a command \DDF that prints $\delta\Delta\Phi$ with optional scripts. Could you please help me do this?

Here are desired inputs to give desired outputs:

1. \DDF should give $\delta\Delta\Phi$
2. \DDF{a}{b} should give $\delta\Delta\Phi_a^b$
3. \DDF{a}{} should give $\delta\Delta\Phi_a$
4. \DDF{a} should give $\delta\Delta\Phi_a$
5. \DDF{}{b} should give $\delta\Delta\Phi^b$

I think the following may (almost) work -- except for (4) -- but even so I'm not sure it's the rigorous or elegant way to do it:

\newcommand{\DDF}[2]{\delta\Delta\Phi_{#1}^{#2}}

Answer 1

It's not difficult (but with brackets, not braces):

\documentclass{article}
\usepackage{amsmath}

\NewDocumentCommand{\DDF}{oo}{%
  \delta\Delta\Phi
  \IfNoValueTF{#2}{%
    \IfValueT{#1}{_{#1}}
  }{%
   _{#1}^{#2}%
  }%
}

\begin{document}

$\DDF$

$\DDF[a][b]$

$\DDF[a][]$

$\DDF[a]$

$\DDF[][b]$

\end{document}

However, it's not clear what the advantage is over

\newcommand{\DDF}{\delta\Delta\Phi}

and input as

$\DDF$

$\DDF_{a}^{b}$

$\DDF_{a}$

$\DDF_{a}$

$\DDF^{b}$

The coding you propose is much less clear, in my opinion, and you must remember that the subscript comes first, whereas you can do

\DDF^{b}_{a}

and get identical result to \DDF_{a}^{b}.