Repair show for Cayley tables as MathJax does not support setlength

[was]

Define a finite group and its multiplication table:

sage: S = SymmetricGroup(3)
sage: T = S.multiplication_table()

The multiplication table can give latex code to be copy-pasted in a paper:

sage: latex(T)
\setlength{\arraycolsep}{2\ex}
\begin{array}{r|*{6}{r}}
\multicolumn{1}{c|}{\ast}&a&b&c&d&e&f\\\hline
{}a&a&b&c&d&e&f\\
{}b&b&a&d&c&f&e\\
{}c&c&e&a&f&b&d\\
{}d&d&f&b&e&a&c\\
{}e&e&c&f&a&d&b\\
{}f&f&d&e&b&c&a\\
\end{array}}

but is also used for showing the table in a notebook worksheet.

In Sage 4.8 with SageNB we used to have:

sage: show(T)
Unknown control sequence '\setlength'

In Sage 9.2.rc0 with Jupyter, show(T) does display a table but with \setlength displayed in red instead of contributing to the rendering.

[rbeezer]

I thought this was on #10787, but now I see it is not. I'm going to point it here.

I've been waiting on MathJax before tackling this, on the hope it has better support for tables.

[slelievre]

Still a problem in Jupyter Notebook with Sage 9.2.rc0.

[gh-DaveWitteMorris]

The PR adds a variable sage.misc.latex_macros.sage_configurable_mathjax_macros that holds a list of macro definitions that pretty_print will include in all LaTeX code that is sent to MathJax. The PR then solves the problem on this ticket by adding \multicolumn and \setlength to this list as no-ops that swallow their arguments.

---

New commits:

​7381952	trac 11362 configurable mathjax macros
​71b0986	update doctests

[klee]

I don't like the proposed solution. It seems a bandage.

A general solution that would also solve possible future problems would be to introduce a new magic method obj._mathjax_() which provides latex code renderable by mathjax and defaults to an alias of obj._latex_() when it is not defined for obj.

[gh-DaveWitteMorris]

I sympathize with what you are saying, and I considered that solution (except that my idea was to add a keyword (maybe style="MathJax") to the _latex_ command. But I don't see how to make it will work without massive changes, because an object that does not have a _mathjax_ method will presumably call the _latex_ method of its subobjects (or subexpressions) and will therefore not do the right thing for MathJax.

I think of MathJax as being a version of latex, rather than a completely different format, so I think it is reasonable to just add a tweak to make it work better (as in my PR). The variable I added simply makes it possible to add definitions for latex macros that MathJax does not understand, and is completely analogous to the variable sage_configurable_latex_macros that is already in sage, which makes it possible to add definitions for sage macros that vanilla latex does not understand.

[klee]

How about using _rich_repr_? This seems a general mechanism to serve the purpose that I have in mind about _mathjax_. There are many examples in Sage src.

[klee]

Replying to gh-DaveWitteMorris:

I sympathize with what you are saying, and I considered that solution (except that my idea was to add a keyword (maybe style="MathJax") to the _latex_ command. But I don't see how to make it will work without massive changes, because an object that does not have a _mathjax_ method will presumably call the _latex_ method of its subobjects (or subexpressions) and will therefore not do the right thing for MathJax.

I think of MathJax as being a version of latex, rather than a completely different format, ...

MathJax is a javascript renderer for latex in html, and also sometimes means the subset of latex it supports. On the other hand LaTeX is a format for TeX which primarily targets printing.

It seems to me currently there is some unfortunate confused code in this respect in the rich output system in Sage. Perhaps straightening the confused code would give a natural solution of this ticket's problem. I will investigate more.

[slelievre]

Related:

• #31536: Divorce MathJax from LaTeX and let it marry HTML

[klee]

With #31536, the following patch will solve the problem of this ticket.

src/sage/matrix/operation_table.py

@@ -1078 +1078 @@
         table.append('\\end{array}')
         table.append('}')
         return ''.join(table)
+
+    def _html_(self):
+        n = self._n
+        names = self._names
+
+        # Headers
+        table = ['\\begin{array}{r|*{'+str(n)+'}{r}}\n']
+        table.append(self._latex_symbol)
+        table += ['&'+names[i] for i in range(n)]
+        table.append('\\\\\\hline\n')
+
+        # Row label and body of table
+        for g in range(n):
+            table.append('{}')  # Interrupts newline and [], so not line spacing
+            table.append(names[g])
+            for h in range(n):
+                table.append('&'+names[self._table[g][h]])
+            table.append('\\\\\n')
+
+        # Finish
+        table.append('\\end{array}')
+        return ''.join(table)
+