Passing optional arguments to a command with also optional arguments

Question

I have been struggling with the following implementation for the last couple of days without being able to find a solution.

I have the following minimal working example:

\documentclass{article}
\usepackage{xkeyval}
\usepackage{amssymb, amsmath}
\usepackage{xparse}
\usepackage{etoolbox}
\makeatletter
\define@cmdkey [Notation] {nom} {A} {}
\define@cmdkey [Notation] {nom} {B} {}
\presetkeys [Notation] {nom} {A={},B={}}{}
\NewDocumentCommand{\nom}{ m O{} }{%
    \setkeys[Notation]{nom}{#2}%
        \ifdefempty{\cmdNotation@nom@A}{% Descriptor section
            \ifdefempty{\cmdNotation@nom@B}{% 
                e-\def\subscript{}
            }{%
                f-\def\subscript{\mathtt{\cmdNotation@nom@B}}%
            }%
        }{%
            \ifdefempty{\cmdNotation@nom@B}{%
                g-\def\subscript{\mathtt{\cmdNotation@nom@A}}%
            }{%
                h-\def\subscript{\mathtt{\cmdNotation@nom@A,\cmdNotation@nom@B}}%
            }%
        }%

    \mathcal{#1}_{\subscript}
}% 
\makeatother
\makeatletter
\define@cmdkey [Notation] {test} {of} {}
\define@cmdkey [Notation] {test} {wrt} {}
\presetkeys [Notation] {test} {of={},wrt={}}{}
\NewDocumentCommand{\test}{ m O{} }{%
    \setkeys[Notation]{test}{#2}%
\nom{#1}[A=\cmdNotation@test@of, B=\cmdNotation@test@wrt]
}%

\makeatother
\begin{document}
\begin{align}
\nom{K}[A=A, B=B]\
\nom{K}[A=A] \
\nom{K}[B=B] \
\nom{K} \
\test{K}[of=A, wrt=B] \
\test{K}[of=A] \
\test{K}[wrt=B] \
\test{K}
\end{align}
\end{document}

Basically when I call \nom inside \test and the optional inputs of test are empty, they are received in \nom as non-empty arguments.

So far, the only solution I have found is the following:

\makeatletter
\define@cmdkey [Notation] {test} {of} {}
\define@cmdkey [Notation] {test} {wrt} {}
\presetkeys [Notation] {test} {of={},wrt={}}{}
\NewDocumentCommand{\test}{ m O{} }{%
    \setkeys[Notation]{test}{#2}%
            \ifdefempty{\cmdNotation@test@wrt}{%
                \ifdefempty{\cmdNotation@test@of}{%  
                    \nom{#1}[] 
                }{%
                    \nom{#1}[B=\cmdNotation@test@of] 
                }%
            }{%
                \ifdefempty{\cmdNotation@test@of}{%         
                    \nom{#1}[A=\cmdNotation@test@wrt] 
                }{%
                    \nom{#1}[A=\cmdNotation@test@wrt, B=\cmdNotation@test@of] 
                }%
            }% 
}%          
\makeatother

But this is not feasible because in my real implementation \nom and \test have more than 10 inputs and I cannot create a check for each combination of inputs. Furthermore, I have 10 other fuctions similar to \test that internally call \nom.

I hope you can help me. Thanks in advance!

Edit:

As suggested by @Gaussler and @egreg, working with lists in principle works. But I stumbled accross some cases where the passed arguments are not part of a list, or another form of evaluation is needed instead of simple comma separation (see circled in blue). For instance \dot, \hat in the first case are two optional modifiers \mod and \modd, or K and L are part of a text descriptor where both/one/none of the inputs could exist.

In the case of each of the \test_i i = 1:n, I could use different combinations of inputs and pass them to \nom to produce different equations according to my needs.

Answer 1

I'm not sure why this indirection. Anyway, using expl3 for everything is easier. Note the grouping, so keys set at the same level will not influence each other.

The \test command will not call \nom with an optional argument, because it has already set the options.

\documentclass{article}
\usepackage{amssymb, amsmath}
\usepackage{xparse}
\ExplSyntaxOn
\keys_define:nn { notation/nom }
 {
  A .tl_set:N = \l_wdsgn_notation_A_tl,
  B .tl_set:N = \l_wdsgn_notation_B_tl,
  A .initial:n = {},
  B .initial:n = {},
 }
\keys_define:nn { notation/test }
 {
  of .code:n = \keys_set:nn { notation/nom } { A=#1 },
  wrt .code:n = \keys_set:nn { notation/nom } { B=#1 },
 }
\NewDocumentCommand{\nom}{ m O{} }
 {
  \group_begin:
  \wdsgn_notation_nom:nn { #1 } { #2 }
  \group_end:
 }
\clist_new:N \l__wdsgn_notation_subscript_clist
\cs_new:Nn \wdsgn_notation_nom:nn
 {
  \keys_set:nn { notation/nom } { #2 }
  \tl_if_empty:NTF \l_wdsgn_notation_A_tl
   { % A is empty
    \tl_if_empty:NTF \l_wdsgn_notation_B_tl { e- } { f- }
   }
   { % A is not empty
    \tl_if_empty:NTF \l_wdsgn_notation_B_tl { g- } { h- }
   }
  \mathcal{#1}
  \clist_put_right:NV \l__wdsgn_notation_subscript_clist \l_wdsgn_notation_A_tl
  \clist_put_right:NV \l__wdsgn_notation_subscript_clist \l_wdsgn_notation_B_tl
  \clist_if_empty:NF \l__wdsgn_notation_subscript_clist
   { % here we exploit the fact that \clist_use:Nn disregards empty items
    \sb{\mathtt{\clist_use:Nn \l__wdsgn_notation_subscript_clist {,}}}
   }
 }
\NewDocumentCommand{\test}{ m O{} }
 {
  \group_begin:
  \keys_set:nn { notation/test } { #2 }
  \nom{#1}
  \group_end:
 }
\ExplSyntaxOff
\begin{document}
\begin{align}
\nom{K}[A=A, B=B]\
\nom{K}[A=A] \
\nom{K}[B=B] \
\nom{K} \
\test{K}[of=A, wrt=B] \
\test{K}[of=A] \
\test{K}[wrt=B] \
\test{K}
\end{align}
\end{document}

Note. Thanks to Gaussler who pointed out the need for a fix.

Answer 2

An alternative solution I made because I was bored. (Independently of this, allow me to comment that your syntax seems very counterintuitive to me. Are you sure this is really the way you want to type whatever it is you are writing?)

\documentclass{article}
\usepackage{semantex}
\NewSymbolClass\nom[
    data provide=data A,
    data provide=data B,
    parse options={
        command=\mathcal,
        inner return,
        if blank TF={\SemantexDataGetExpNot{data A}}{
            if blank TF={\SemantexDataGetExpNot{data B}}
            {
                symbol put left={e-},
            }
            {
                symbol put left={f-},
                set keys x={
                    sep lower={\SemantexExpNot\mathtt{\SemantexDataGetExpNot{data B}}},
                },
            },
        }
        {
            if blank TF={\SemantexDataGetExpNot{data B}}
            {
                symbol put left={g-},
                set keys x={
                    sep lower={\SemantexExpNot\mathtt{\SemantexDataGetExpNot{data A}}},
                },
            }
            {
                symbol put left={h-},
                set keys x={
                    sep lower={\SemantexExpNot\mathtt{\SemantexDataGetExpNot{data A}}},
                    sep lower={\SemantexExpNot\mathtt{\SemantexDataGetExpNot{data B}}},
                },
            },
        },
    },
    define keys[1]={
        {A}{ data set={data A}{#1} },
        {B}{ data set={data B}{#1} },
    },
]
\NewSymbolClass\test[
    parent=\nom,
    define keys[1]={
        {of}{ A={#1} },
        {wrt}{ B={#1} },
    },
]
\begin{document}
\begin{align}
    \nom{K}[A=A, B=B]\
    \nom{K}[A=A] \
    \nom{K}[B=B] \
    \nom{K} \
    \test{K}[of=A, wrt=B] \
    \test{K}[of=A] \
    \test{K}[wrt=B] \
    \test{K}
\end{align}
\end{document}

---

I’m not quite sure what you mean by your updated answer. But semantex can also be programmed to handle these kinds of situations. Forgive me for using weird command names in the following, but I’m not quite sure what your notation is really supposed to mean:

\documentclass{article}
\usepackage{semantex}
\NewVariableClass\MyVar[
    output=\MyVar,
]
% First a few variables; the "v" stands for variable:
\NewObject\MyVar\vh{h}
\NewObject\MyVar\vg{g}
\NewObject\MyVar\vf{f}
\NewObject\MyVar\ve{e}
\NewObject\MyVar\vK{K}
\NewObject\MyVar\vL{L}
% Feel free to give the following more descriptive names:
\NewObject\MyVar\guid{\mathrm{guid}} % could also use \operatorname, depending on what "guid" is
\NewObject\MyVar\scriptK{\mathcal{K}}
\NewObject\MyVar\ttA{\mathtt{A}}
\NewObject\MyVar\ttB{\mathtt{B}}
\NewObject\MyVar\ttC{\mathtt{C}}
\NewObject\MyVar\ttD{\mathtt{D}}
\NewObject\MyVar\ttE{\mathtt{E}}
\NewObject\MyVar\ttF{\mathtt{F}}
\NewObject\MyVar\ttG{\mathtt{G}}
\NewObject\MyVar\ttH{\mathtt{H}}
\NewObject\MyVar\ttX{\mathtt{X}}
\NewObject\MyVar\ttY{\mathtt{Y}}
\NewVariableClass\WeirdConstruction[
    parent=\MyVar,
    data provide=data A,
    data provide=data B,
    data provide=data C,
    data provide=data D,
    data provide=data E,
    data provide=data F,
    data provide=data G,
    data provide=data H,
    define keys={
        {mod}{ command=\hat },
        {modd}{ command=\dot },
    },
    define keys[1]={
        {A}{ data set={data A}{#1} },
        {B}{ data set={data B}{#1} },
        {C}{ data set={data C}{#1} },
        {D}{ data set={data D}{#1} },
        {E}{ data set={data E}{#1} },
        {F}{ data set={data F}{#1} },
        {G}{ data set={data G}{#1} },
        {H}{ data set={data H}{#1} },
        {description}{
            parse,
            if blank TF={\SemantexDataGetExpNot{lower}}
            {
                lower={#1},
            }
            {
                lower={_\bgroup #1},
                post lower=\egroup,
            },
        },
    },
    parse options={
        set keys x={
            sep upper left=\SemantexDataGetExpNot{data B},
            sep upper left=\SemantexDataGetExpNot{data A},
            sep lower left=\SemantexDataGetExpNot{data D},
            sep lower left=\SemantexDataGetExpNot{data C},
            sep upper=\SemantexDataGetExpNot{data E},
            sep upper=\SemantexDataGetExpNot{data F},
            sep lower=\SemantexDataGetExpNot{data G},
            sep lower=\SemantexDataGetExpNot{data H},
        },
    },
]
\NewObject\WeirdConstruction\ThetaConstruction{\Theta}
\NewObject\WeirdConstruction\aConstruction{\mathbf{a}}
\begin{document}
[
    \ThetaConstruction[
        A=\ttA, B=\ttB,
        C=\ttC, D=\ttD,
        E=\ttE, F=\ttF,
        G=\ttG, H=\ttH,
        mod, modd,
        description=\vK,
        description=\vL,
    ]
]
[
    \aConstruction[
        A=\ttC,C=\ttX,
        mod, modd,
        description=\guid,
        description=3,
    ]
]
\end{document}