Greek `\chi`'s subscript expressions: how to make it smaller or offset lower?

Question

I am unsatisfied with the way subscript is rendered for the Greek letter \chi. This particular letter is rendered with a small downward offset. I occasionally have to prefix the subscript with \sciptscriptstyle such that, in effect, an expression may look like

\sup{\chi_{\scriptscriptstyle A_n}(x)}[n]

where

\RenewDocumentCommand{\sup}{m O{}}{
    \operatorname{sup}\ifstrempty{#2}{}{\limits_{\mathclap{\substack{\expandafter{\scriptscriptstyle{#2}}}}}}
        \expandafter{#1} 
}

(I admit this snippet is a little messy, especially due to the uncanonical declaration of the optional argument as O{} and testing via \ifstrempty instead of o for the argument type and IfNoValueTF--using the xparse package. I am not entirely clear yet about what syntax is more straightforward.)

Is there a way to redefine \chi keeping the syntax in line with all semantically equivalent concepts, i.e., letters, but having only \chi's subscript expressions smaller or slightly lower? To clarify, I am thinking of redefining the subscript operator _ for \chi only. But I naively suppose TeX' grammar would not let me do that.

An evident work-around would involve defining a new macro using a different syntax like

\newcommand{\Chi}[1]{\chi_{\scriptscriptstyle{#1}}}

So effectively, what I want is just

\chi_{expr}

where expr is rendered smaller or offset lower than default.

Answer 1

Using \scriptscriptstyle is not a good typographical device, because it will make unbalanced symbols.

Here's the way for ensuring the subscript is shifted down as if there was a superscript.

\documentclass{article}
\usepackage{amsmath,xparse}

\let\latexchi\chi
\makeatletter
\renewcommand\chi{\@ifnextchar_\sub@chi\latexchi}
\newcommand{\sub@chi}[2]{% #1 is _, #2 is the subscript
  \@ifnextchar^{\subsup@chi{#2}}{\latexchi^{}_{#2}}%
}
\newcommand{\subsup@chi}[3]{% #1 is the subscript, #2 is ^, #3 is the superscript
  \latexchi_{#1}^{#3}%
}
\makeatother

\begin{document}
\noindent
$\latexchi_{A}\chi_{A}$\\[2ex]
$\latexchi_{A_{n}}\chi_{A_{n}}$\\[2ex]
$\chi_{A}\quad\chi_{A}^{2}\quad\chi^{2}_{A}\quad\chi^{2}\quad\chi$
\end{document}

Answer 2

Yet another possibility one might want to consider: Redefine \chi so that the bottom half of a "math strut" is inserted automatically after the character. (Aside: A mathstrut is a TeX object of zero width -- hence it's invisible -- and the height and depth of a round parenthesis, i.e., ).) That way, the position of any subscripts will be keyed off the {\chi\mathstrut} combo rather than the \chi symbol. Because the depth of the mathstrut exceeds the depth of \chi, the subscript will end up being placed lower -- as desired.

The solution below employs the amsart document class, which loads the amsmath package automatically. For non-AMS document classes, be sure to load the amsmath package so that the \smash[t]{...} macro is available.

\documentclass[a4paper]{amsart}

\makeatletter
\@ifdefinable\@latex@chi{\let\@latex@chi\chi}
\renewcommand*\chi{{\@latex@chi\smash[t]{\mathstrut}}} % want only bottom half of \mathstrut
\makeatletter

\begin{document}
Text before $\chi_{A}$, text after.

Text before $\chi_{S_{i}}$, text after

Another couple of lines of text for testing consistency of the gap between the 
baselines.  Some more text.  Some more text.
\end{document}

Output:

Answer 3

\documentclass{article}
\usepackage{mathtools}

\newcommand{\mychi}{\raisebox{0pt}[1ex][1ex]{$\chi$}}
\newlength{\temp}

\begin{document}
\[ \textrm{before}\quad \chi_A^2 \quad\textrm{after}\quad \mychi_A^2 \]

\settoheight{\temp}{$\chi$}
\noindent\the\temp\newline
\settoheight{\temp}{\mychi}
\the\temp
\end{document}

You can fine tune the \rasisebox parameters as desired.

Answer 4

I just came across the same problem. The solution that works for me is just writing it as a sub-subscript:

\chi_{_{A_n}}

Answer 5

You could use the power of xparse to define new sub- and superscript arguments and pass them as optional arguments. Here is the full code and explanation.

Basically you use a and b arguments in xparse that search for _{#1} and ^{#2} respectively and then do whatever you want with those arguments. I use here the solution from egreg to show you how easy it is.

\let\originalchi\chi
\RenewDocumentCommand\chi{ab}
  {\originalchi
   \IfValueT{#1}{_{#1}}%
   \IfValueTF{#2}{^{#2}}{^{}}}
...
$\originalchi_{A}\chi_{A}$\\[2ex]
$\originalchi_{A_{n}}\chi_{A_{n}}$\\[2ex]
$\chi_{A}\quad\chi_{A}^{2}\quad\chi^{2}_{A}\quad\chi^{2}\quad\chi$

a and b (and A{<default>} and B{<default>}) behave exactly like the rest of xparse arguments.

Here's the full compilable code:

\documentclass{scrartcl}
\usepackage{mathtools,xparse}

\ExplSyntaxOn
\cs_new_protected:Npn \__xparse_count_type_k:w #1
 {
  \__xparse_single_token_check:n { #1 }
  \quark_if_recursion_tail_stop_do:Nn #1 { \__xparse_bad_arg_spec:wn }
  \__xparse_count_mandatory:N
 }
\cs_new_protected:Npn \__xparse_count_type_K:w #1 #2
 {
  \__xparse_single_token_check:n { #1 }
  \quark_if_recursion_tail_stop_do:nn { #2 } { \__xparse_bad_arg_spec:wn }
  \__xparse_count_mandatory:N
 }
\cs_new_protected:Npn \__xparse_add_type_k:w #1
 { \exp_args:NNo \__xparse_add_type_K:w #1 { \c__xparse_no_value_tl } }
\cs_new_protected:Npn \__xparse_add_type_K:w #1 #2
 {
  \__xparse_flush_m_args:
  \__xparse_add_grabber_optional:N K
  \tl_put_right:Nn \l__xparse_signature_tl { #1 { #2 } }
  \__xparse_prepare_signature:N
 }
\cs_new_protected:Npn \__xparse_add_expandable_type_k:w #1
 {
  \exp_args:NNo \__xparse_add_expandable_type_K:w #1 { \c__xparse_no_value_tl }
 }
\cs_new_protected_nopar:Npn \__xparse_add_expandable_type_K:w #1 #2
 {
  \__msg_kernel_error:nnx { xparse } { invalid-expandable-argument-type } { K }
  \__xparse_add_expandable_type_m:w % May be create this?
 }
\cs_new_protected:Npn \__xparse_grab_K:w #1 #2 #3 \l__xparse_args_tl
 {
  \__xparse_grab_K_aux:NnnNn #1 { #2 } { #3 } \cs_set_protected_nopar:Npn
   { _ignore_spaces }
 }
\cs_new_protected:Npn \__xparse_grab_K_long:w #1 #2 #3 \l__xparse_args_tl
 {
  \__xparse_grab_K_aux:NnnNn #1 { #2 } { #3 } \cs_set_protected:Npn
   { _ignore_spaces }
 }
\cs_new_protected:Npn \__xparse_grab_K_trailing:w #1 #2 #3 \l__xparse_args_tl
 {
  \__xparse_grab_K_aux:NnnNn #1 { #2 } { #3 } \cs_set_protected_nopar:Npn
   { _ignore_spaces }
 }
\cs_new_protected:Npn \__xparse_grab_K_long_trailing:w #1 #2 #3 \l__xparse_args_tl
 {
  \__xparse_grab_K_aux:NnnNn #1 { #2 } { #3 } \cs_set_protected:Npn
   { _ignore_spaces }
 }
\cs_new_protected:Npn \__xparse_grab_K_aux:NnnNn #1 #2 #3 #4 #5
 {
  \exp_after:wN #4 \l__xparse_fn_tl ##1
   {
    \__xparse_add_arg:n { ##1 }
    #3 \l__xparse_args_tl
   }    
  \use:c { peek_meaning_remove #5 :NTF } #1
   { \l__xparse_fn_tl }
   {
    \__xparse_add_arg:n { #2 }
    #3 \l__xparse_args_tl
   }
 }

\prop_put:Nnn \c__xparse_shorthands_prop { a } { k \sb }
\prop_put:Nnn \c__xparse_shorthands_prop { b } { k \sp }
\prop_put:Nnn \c__xparse_shorthands_prop { A } { K \sb }
\prop_put:Nnn \c__xparse_shorthands_prop { B } { K \sp }
\ExplSyntaxOff

\let\originalchi\chi
\RenewDocumentCommand\chi{ab}
  {\originalchi
   \IfValueT{#1}{_{#1}}%
   \IfValueTF{#2}{^{#2}}{^{}}}

\begin{document}
\noindent
$\originalchi_{A}\chi_{A}$\\[2ex]
$\originalchi_{A_{n}}\chi_{A_{n}}$\\[2ex]
$\chi_{A}\quad\chi_{A}^{2}\quad\chi^{2}_{A}\quad\chi^{2}\quad\chi$
\end{document}