\newcommand with adjustable size

Question

I'm soon going to take Live-notes of a course where Tensors are commonly used.

Tensors consist of a Letter, say T, with numerous sub-and superscripts.

Generally, a tensor could look like

T^{i_{1},i{2},i{3}}_ {j_{1},j_{2},j_{3}} 

I would like to know if it is possible to create a \newcommand with 4 parameters,

\Tensor{T}{i}{j}{3}

Which sets the Tensor letter, the name of the super and subscript, and specifically the number of sub-and superscripts. I don't know whether this is possible.

Answer 1

Yes, it's possible in many ways with loops. I prefer LaTeX3 (the experimental kernel and macros):

\documentclass{article}
\usepackage{xparse}

\DeclareMathAlphabet{\mathsfsl}{OT1}{cmss}{m}{sl}

\ExplSyntaxOn
% #1 = tensor
% #2 = number of indices
% #3 = upper index
% #4 = number of lower indices (optional)
% #5 = lower index
\NewDocumentCommand{\Tensor}{mmmom}
 {
  \IfNoValueTF { #4 }
   {
    \tens_make:nnnnn { #1 } { #2 } { #3 } { #2 } { #5 }
   }
   {
    \tens_make:nnnnn { #1 } { #2 } { #3 } { #4 } { #5 }
   }
 }
\cs_new_protected:Npn \tens_make:nnnnn #1 #2 #3 #4 #5
 {
  \tl_clear:N \l__tens_sup_tl
  \tl_clear:N \l__tens_sub_tl
  \tens_create_script:Nnn \l__tens_sup_tl { #2 } { #3 }
  \tens_create_script:Nnn \l__tens_sub_tl { #4 } { #5 }
  \mathsfsl{#1}
  \sp{\l__tens_sup_tl}
  \sb{\l__tens_sub_tl}
 }
\cs_new_protected:Npn \tens_create_script:Nnn #1 #2 #3
 {
  \int_step_inline:nnnn { 1 } { 1 } { #2 }
   {
    \int_compare:nTF { ##1 == 1 }
     {
      \tl_put_right:Nn #1 { #3 \sb {##1} }
     }
     {
      \tl_put_right:Nn #1 { , #3 \sb {##1} }
     }
   }
 }

\tl_new:N \l__tens_sup_tl
\tl_new:N \l__tens_sub_tl

\ExplSyntaxOff

\begin{document}

$\Tensor{T}{3}{i}{j}$

$\Tensor{T}{3}{i}[5]{j}$

$\Tensor{T}{2}{i}[0]{j}$

\end{document}

With a change of syntax, we can accommodate for different numbers of superscripts and subscripts: if there's no optional argument before the subscript variable name, the number will be the same as for the superscript variables. You can even have one (or both) equal to zero.