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Is there any way to reduce the distance inside σ₀ and between sigma and its subscript in general in the following setup automatically? That is, each time you type in sigma_0 (or sigma_1 etc.), you wish the actual output to be more consistent with sigma_!0 (or sigma_!1 etc.).

Input:

documentclassbook
usepackagefontspec
usepackage[american,british,french,norsk,german,ngerman]babel
usepackagemathtools
mathtoolssetmathic=true %%% See http://tex.stackexchange.com/a/3496/
usepackageamssymb
usepackageunicode-math
setmainfont[Ligatures=TeX]TeX Gyre Termes
setsansfontTeX Gyre Heros[Scale=0.88]
setmonofontTeX Gyre Cursor
setmathfont[Ligatures=TeX]TeX Gyre Termes Math
setmathfont[Ligatures=TeX,range=setminus]Asana Math
setmathfont[Ligatures=TeX,Extension=.otf,range="2A3E,BoldFont=XITSMath-Bold]XITSMath-Regular%%% The fat semicolon
usepackage[babel=true,verbose=errors]microtype
begindocument
[sigma_0 sigma_0]
[sigma_!0 sigma_!0]
enddocument

Output so far:

As you see, in the upper line the left zero seems to be more close to the right σ (which doesn't make any sense) than to the left one (which would make sense). The kerning in the lower line makes more sense.

I guess, this would be easier than Subscript kerning for specific letters in XeLaTeX, since we already have sigma as a macro and can redefine it.

For which letters in the subscript position the kerning should be improved is intentionally left unspecified; improving the kerning in sigma_<any single arabic digit or any single Latin small letter> would suffice as a start. Of course, for σ_T we might need less kerning (e.g., only -1mu rather than -3mu), and that's why capital Latin letters would need more work (and are not asked for in the first step).

The following definition does it:

ExplSyntaxOn
cs_new_eq:NN __userxlixk_actual_sigma: sigma
RenewDocumentCommandsigma
 __userxlixk_sigma: 
cs_new_protected:Npn __userxlixk_sigma:
 
 peek_catcode_remove:NTF c_math_subscript_token
 __userxlixk_sigma_check_group:n 
 __userxlixk_actual_sigma: 
 
cs_new_protected:Npn __userxlixk_sigma_check_group:n #1
 
 tl_if_single_token:nTF #1
 __userxlixk_actual_sigma: c_math_subscript_token ! #1 
 __userxlixk_actual_sigma: c_math_subscript_token #1 
 
ExplSyntaxOff

I save the definition of sigma in __userxlixk_actual_sigma: then redefine sigma to check:

1. if it is followed by a c_math_subscript_token: if it is not, then just print __userxlixk_actual_sigma: otherwise;




2. grab what follows the subscript token as argument and check if the argument consists of a single token: if it does, apply a !, otherwise print normally.

Here's the output before and after the redefinition (I used LuaTeX and lua-visual-debug to show the negative kern):

Code:

documentclass[varwidth]standalone
usepackagelua-visual-debug
usepackageluatexbase
usepackageunravel
usepackagefontspec
usepackage[american,british,french,norsk,german,ngerman]babel
usepackagemathtools
mathtoolssetmathic=true %%% See http://tex.stackexchange.com/a/3496/
usepackageamssymb
usepackageunicode-math
setmainfont[Ligatures=TeX]TeX Gyre Termes
setsansfontTeX Gyre Heros[Scale=0.88]
setmonofontTeX Gyre Cursor
setmathfont[Ligatures=TeX]TeX Gyre Termes Math
setmathfont[Ligatures=TeX,range=setminus]Asana Math
setmathfont[Ligatures=TeX,Extension=.otf,range="2A3E,BoldFont=XITSMath-Bold]XITSMath-Regular%%% The fat semicolon
usepackage[babel=true,verbose=errors]microtype
begindocument
$sigma_abc sigma_0 sigma_0$

ExplSyntaxOn
cs_new_eq:NN __userxlixk_actual_sigma: sigma
RenewDocumentCommandsigma
 __userxlixk_sigma: 
cs_new_protected:Npn __userxlixk_sigma:
 
 peek_catcode_remove:NTF c_math_subscript_token
 __userxlixk_sigma_check_group:n 
 __userxlixk_actual_sigma: 
 
cs_new_protected:Npn __userxlixk_sigma_check_group:n #1
 
 tl_if_single_token:nTF #1
 __userxlixk_actual_sigma: c_math_subscript_token ! #1 
 __userxlixk_actual_sigma: c_math_subscript_token #1 
 
ExplSyntaxOff

$sigma_abc sigma_0 sigma_0$
enddocument

Note, however, that this code will work if you use sigma_a^b but not if you use sigma^b_a.

I'd use the e argument type of xparse.

documentclassbook
usepackagefontspec
usepackage[american,british,french,norsk,german,ngerman]babel
usepackagemathtools
usepackageamssymb
usepackageunicode-math
usepackage[babel=true,verbose=errors]microtype

setmainfontTeX Gyre Termes
setsansfontTeX Gyre Heros[Scale=0.88]
setmonofontTeX Gyre Cursor
setmathfontTeX Gyre Termes Math
setmathfontAsana Math[
 range=setminus,
]
setmathfontXITSMath-Regular[
 Extension=.otf,
 range="2A3E,
 BoldFont=XITSMath-Bold,
]

%mathtoolssetmathic=true %%% See http://tex.stackexchange.com/a/3496/

AtBeginDocument%
 letstandardsigmasigma
 letsigmakernedsigma


NewDocumentCommandkernedsigmae_^%
 standardsigma
 IfValueT#1_!#1%
 IfValueT#2^#2%


begindocument

[sigma_0 sigma_0^2 sigma^2_0]
[standardsigma_!0 standardsigma_!0^2 standardsigma^2_!0]

enddocument