Bug in Mathematica TeXForm generating \left\left

Question

Bug introduced in 9.0 and persisting through 11.3 or later

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I asked about this in the TeX chat. It seems Mathematica generate invalid Latex in this example.

ClearAll[y,x];
ode = D[y[x], x] - (y[x]^2 + 1)/(Abs[y[x] + (1 + y[x])^(1/2)]*(1 + x)^(3/2));
TeXForm[ode]

The output is

y'(x)-\frac{y(x)^2+1}{(x+1)^{3/2} \left\left| y(x)+\sqrt{y(x)+1}\right\right| }

Using \left\left is illegal. TeXLive 2014 will not compile it. MWE

\documentclass{article}
\usepackage{amsmath,mathtools}
\begin{document}
\begin{equation}

y'(x)-\frac{y(x)^2+1}{(x+1)^{3/2} \left\left| y(x)+\sqrt{y(x)+1}\right\right| }

\end{equation}
\end{document}

Compile:

 pdflatex foo.tex

! Missing delimiter (. inserted).
<to be read again> 
                   \left 
l.7 ...eft\left| y(x)+\sqrt{y(x)+1}\right\right| }

? 

Just wanted to confirm with others if this is a bug before send email to [email protected] unless someone finds a smart fix or an option to solve this.

V9.01 and V10.

Update:

If any one gets such a case, the fix in this example is to simply remove the extra \left at the outers. Like this

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

\begin{document}
\begin{equation}
y'(x)-\frac{y(x)^2+1}{(x+1)^{3/2} \left| y(x)+\sqrt{y(x)+1}\right| }
\end{equation}
\end{document} 

Compiles now ok. The output is

fyi, just send an email to [email protected] as well. Experts in Latex at TeX forum confirmed the code generated by Mathematica is wrong.

Answer 1

Why we're getting this buggy result

In process of conversion to $\TeX$, whenever Mathematica encounters "something delimited" i.e. RowBox with something surrounded with Strings matching:

"(" | "[" | "\[LeftModified]" | "\[LeftDoubleBracket]" | "{" | "\[Piecewise]" | "\[LeftFloor]" | "\[LeftCeiling]" | "\[LeftAngleBracket]" | "\[LeftSkeleton]" | "«" | "\[LeftBracketingBar]" | "\[LeftDoubleBracketingBar]" | ")" | "]" | "\[RightModified]" | "\[RightDoubleBracket]" | "}" | "\[RightFloor]" | "\[RightCeiling]" | "\[RightAngleBracket]" | "\[RightSkeleton]" | "»" | "\[RightBracketingBar]" | "\[RightDoubleBracketingBar]" | "/" | "\\" | "|" | "\[VerticalSeparator]" | "||"`

then it tests, whether those delimited boxes can potentially result in something higher then line height, using System`Convert`TeXFormDump`DelimiterBoxQ function.

If System`Convert`TeXFormDump`DelimiterBoxQ returns False, then "ordinary translation" to $\TeX$ occurs and delimiters are converted using System`Convert`TeXFormDump`maketex function, which for Abs TraditionalForm delimiters: "\[LeftBracketingBar]", "\[RightBracketingBar]" returns "\\left| " and "\\right| " respectively.

That's why we get:

Abs[x + 1]//TeXForm
(* \\left| x+1\\right| *)

If System`Convert`TeXFormDump`DelimiterBoxQ returns, True then delimiters are converted using System`Convert`TeXFormDump`InsertDelimiters function which adds \\left or \\right to result of conversion of delimiter with System`Convert`TeXFormDump`$TeXDelimiterReplacements rules.

System`Convert`TeXFormDump`$TeXDelimiterReplacements contains replacement rules for delimiters like "\[LeftAngleBracket]" -> {"\\langle "}. Among them, for unknown reason, two pairs of $\TeX$ delimiters contain additional "\\left" and "\\right" commands:

System`Convert`TeXFormDump`$TeXDelimiterReplacements // TableForm
(*
    ...
    \[LeftBracketingBar] -> {\left| }
    \[LeftDoubleBracketingBar] -> {\left\| }
    ...
    \[RightBracketingBar] -> {\right| }
    \[RightDoubleBracketingBar] -> {\right\| }
    ...
*)

In case of "\[LeftBracketingBar]", "\[LeftDoubleBracketingBar]" and their right counterparts, System`Convert`TeXFormDump`InsertDelimiters function adds additional \\left and \\right to delimiters that already have them from System`Convert`TeXFormDump`$TeXDelimiterReplacements rules.

That's why we get:

Abs[x + 1/2]//TeXForm
(* \left\left| x+\frac{1}{2}\right\right| *)

This bug was introduced in Mathematica version 9. In version 8 there are no additional \\left and \\right commands neither in System`Convert`TeXFormDump`$TeXDelimiterReplacements rules, nor in System`Convert`TeXFormDump`maketex function.

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How to fix this bug

Fixing this bug is easy, we just need to patch System`Convert`TeXFormDump`$TeXDelimiterReplacements rules:

System`Convert`TeXFormDump`$TeXDelimiterReplacements =
    System`Convert`TeXFormDump`$TeXDelimiterReplacements /. {
        "\\left| " | "\\right| " -> "|",
        "\\left\\| " | "\\right\\| " -> "\\| "
    }

Now we get correct $\TeX$ code:

Abs[x] // TeXForm
(* \left| x\right| *)

Abs[x + 1/2] // TeXForm
(* \left|x+\frac{1}{2}\right| *)

D[y[x], x] - (y[x]^2 + 1)/(Abs[y[x] + (1 + y[x])^(1/2)]*(1 + x)^(3/2)) // TeXForm
(* y'(x)-\frac{y(x)^2+1}{(x+1)^{3/2} \left|y(x)+\sqrt{y(x)+1}\right|} *)

Answer 2

This seems to be fixed in 12.1.1:

$Version

(* 12.1.1 for Mac OS X x86 (64-bit) (June 9, 2020) *)

ClearAll[y, x];
ode = D[y[x], x] - (y[x]^2 + 1)/(Abs[y[x] + (1 + y[x])^(1/2)]*(1 + x)^(3/2));
TeXForm[ode]

(* y'(x)-\frac{y(x)^2+1}{(x+1)^{3/2} \left|y(x)+\sqrt{y(x)+1}\right| } *)