Make a very large forward slash in math mode

Question

this is the result I'd like to achieve:

I tried various commands to make the forward slash larger, for instance I tried the \left. (...) \right / or composing multiple \mathlarger commands but I couldn't get the desired result, with both of them the forward slash is bigger than normal but not even close to be large enough.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amssymb, amsmath, amsthm}


\title{Big forwardslash}
\author{Niccolò Della Rocca}
\date{July 2021}

\begin{document}

\[\left. 
                 V\otimes_{\mathbb C}W= \mathbb C\left[V\times W\right]\middle\slash
                \text{Span}
                    \begin{Bmatrix}
                        (\underline{v}+\underline{v}',\underline{w}) - (\underline{v},\underline{w}) - (\underline{v}',\underline{w}) \\
                        (\underline{v},\underline{w}+\underline{w}') - (\underline{v},\underline{w}) - (\underline{v},\underline{w}')\\
                        a(\underline{v},\underline{w}) - (a\underline{v},\underline{w})\\ 
                        a(\underline{v},\underline{w}) - (\underline{v},a\underline{w})\\
                        a\in\mathbb C,\:\underline{v}\in V,\:\underline{w}\in W
                    \end{Bmatrix}
                 \right.
            \]

\end{document}

Answer 1

You can do it, but should you? Do you really think this is a good formula to display? I really think it isn't, for several reasons:

1. it's very big and difficult to read;
2. it's not the way tensor products are defined (it is one way, but one never uses it, relying instead on the universal property).

Anyway, here's a way to do it.

First of all:

1. \mathbb C is not proper syntax; use \mathbb{C};
2. better yet, define your own command;
3. underlining symbols for vectors is very old-fashioned markup;
4. better defining an abstract command that can be modified without chasing the document for \underline;
5. \text{Span} is wrong syntax: try it in the statement of a theorem;
6. use \DeclareMathOperator.

Now the promised code:

\documentclass{article}
\usepackage{amssymb, amsmath, amsthm}
\usepackage{l3draw}

\newcommand{\CC}{\mathbb{C}}
\newcommand{\vct}[1]{\underline{#1}}
\DeclareMathOperator{\Span}{Span}

\ExplSyntaxOn
\NewDocumentCommand{\reallybigslash}{O{2em}mm}
 {% #1 = width (default 2em)
  % #2 = left part
  % #3 = right part
  #2\!
  \begin{gathered}
  \bafforasta_reallybigslash:nnn { #1 } { #2 } { #3 }
  \end{gathered}
  \!#3
 }

\cs_new_protected:Nn \bafforasta_reallybigslash:nnn
 {
  \hbox_set:Nn \l_tmpa_box { $\displaystyle#2$ }
  \hbox_set:Nn \l_tmpb_box { $\displaystyle#3$ }
  \dim_set:Nn \l_tmpa_dim
   {
    \dim_max:nn { \box_ht:N \l_tmpa_box + \box_dp:N \l_tmpa_box }
                { \box_ht:N \l_tmpb_box + \box_dp:N \l_tmpb_box }
   }
  \draw_begin:
  \draw_linewidth:n { 0.75pt }
  \draw_path_moveto:n { 0pt , 0pt }
  \draw_path_lineto:n { #1 , \l_tmpa_dim }
  \draw_path_use_clear:n { stroke }
  \draw_end:
 }

\ExplSyntaxOff

\title{Big forwardslash}
\author{Niccolò Della Rocca}
\date{July 2021}

\begin{document}

\[
\reallybigslash{
  V\otimes_{\CC}W= \CC[V\times W]
}{
  \Span\left\{
  \begin{matrix}
    (\vct{v}+\vct{v}',\vct{w}) - (\vct{v},\vct{w}) - (\vct{v}',\vct{w}) \\
    (\vct{v},\vct{w}+\vct{w}') - (\vct{v},\vct{w}) - (\vct{v},\vct{w}')\\
    a(\vct{v},\vct{w}) - (a\vct{v},\vct{w})\\ 
    a(\vct{v},\vct{w}) - (\vct{v},a\vct{w})\\
    a\in\CC,\vct{v}\in V,\vct{w}\in W
  \end{matrix}
  \right\}
}
\]

\end{document}

The \reallybigslash command has an optional argument to set the slash's width. For instance, with

\reallybigslash[1em]{...}{...}

(where the dots stand for the same as before) you get