Incompatibility of Row and TeXForm
The following works in Version 9.0.1.0 and Version 10.0.1.0
BoxForm`$UseTemplateSlotSequenceForRow = False;
{x^a, Sqrt@b, ArcSin[c]} // Row // TeXForm
(* x^a\sqrt{b}\sin^{-1}(c) *)
Short answer
The TLDR answer is:
System`Convert`CommonDump`templateBoxToDisplay = BoxForm`TemplateBoxToDisplayBoxes
A more long-winded answer follows.
Background
The basic approach used by TeXForm
is to create TraditionalForm
boxes, and then to convert those boxes into a TeXForm
string. The basic internal function that TeXForm
uses to convert boxes into a string is System`Convert`TeXFormDump`maketex
. For example, consider BesselJ[n, x]
. The TraditionalForm
boxes are:
MakeBoxes[BesselJ[n, x], TraditionalForm]
TemplateBox[{"n", "x"}, "BesselJ"]
Notice how System`Convert`TeXFormDump`maketex
is used to convert the above boxes into a string:
TracePrint[
ToString[BesselJ[n, x], TeXForm],
_System`Convert`TeXFormDump`maketex,
TraceInternal->True
]
System`Convert`TeXFormDump`maketex[TemplateBox[{n,x},BesselJ]]
System`Convert`TeXFormDump`maketex[RowBox[{SubscriptBox[J,n],(,x,)}]]
...
"J_n(x)"
By default, System`Convert`TeXFormDump`maketex
uses System`Convert`CommonDump`ExpandTemplateBoxes
to convert TemplateBox
objects into normal boxes:
TracePrint[
System`Convert`TeXFormDump`maketex[TemplateBox[{"n","x"},"BesselJ"]],
_System`Convert`CommonDump`ExpandTemplateBoxes
]
System`Convert`CommonDump`ExpandTemplateBoxes[TemplateBox[{n,x},BesselJ]]
System`Convert`CommonDump`ExpandTemplateBoxes[TemplateBox[{n,x},BesselJ],Display]
"J_n(x)"
and:
System`Convert`CommonDump`ExpandTemplateBoxes[TemplateBox[{"n","x"},"BesselJ"]]
RowBox[{SubscriptBox["J", "n"], "(", "x", ")"}]
Summarizing, TeXForm
does the following:
- Create
TraditionalForm
boxes - Convert
TemplateBox
objects into normal boxes - Convert normal boxes into a
TeXForm
string
The problem with Row
So, where do things go wrong with Row
objects? In Mathematica version 7 and earlier, Row
objects were formatted as RowBox
objects directly, and so there was no need to convert TemplateBox
objects into normal boxes. However, starting in versions 8 or 9, Row
objects were formatted as TemplateBox
objects. For example, in M9 (I don't have ready access to earlier versions):
MakeBoxes[Row[{x, y}], TraditionalForm]
TemplateBox[{"x", "y"}, "RowDefault"]
One possible fix for this issue is to restore the old functionality of formatting Row
objects as normal boxes, and this is what the global variable BoxForm`$UseTemplateSlotSequenceForRow
controls. I don't like this solution, as it means that Row
objects will never use TemplateBox
, which I think is a shame (I think TemplateBox
offers both speed and memory advantages). Also, it only fixes one symptom of the issue, and not the underlying problem. So, let's figure out the underlying problem.
TemplateSlotSequence
Here is the TemplateBox
format for a Row
object:
boxes = MakeBoxes[Row[{x, y}, None], TraditionalForm]
TemplateBox[{"x", "y"}, "RowNoSeparators"]
(I used a Row
object with a separator for reasons I will explain later). These are the normal boxes that TeXForm
creates for this TemplateBox
:
System`Convert`CommonDump`ExpandTemplateBoxes[
TemplateBox[{"x","y"}, "RowNoSeparators"]
]
RowBox[{TemplateSlotSequence[1]}]
Notice the appearance of a TemplateSlotSequence
object. This kind of object is not supported by System`Convert`TeXFormDump`maketex
. Also, just like other Slot
objects, the TemplateSlotSequence
object only has meaning when it is inside of a Function
object, so the above output is not a valid form of normal boxes. This is the reason for the error that gets reported:
ToString[Row[{x, y}, None], TeXForm]
TeXForm::unspt: TeXForm of TemplateSlotSequence[1] is not supported.
""
Single argument Row
The above error doesn't happen for single argument Row
because System`Convert`TeXFormDump`maketex
was hacked to support it. Compare:
TracePrint[
System`Convert`TeXFormDump`maketex[TemplateBox[{"x", "y"}, "RowNoSeparators"]],
_System`Convert`CommonDump`ExpandTemplateBoxes
]
System`Convert`CommonDump`ExpandTemplateBoxes[TemplateBox[{x,y},RowNoSeparators]]
System`Convert`CommonDump`ExpandTemplateBoxes[TemplateBox[{x,y},RowNoSeparators],Display]
TeXForm::unspt: TeXForm of TemplateSlotSequence[1] is not supported.
""
with:
TracePrint[
System`Convert`TeXFormDump`maketex[TemplateBox[{"x", "y"}, "RowDefault"]],
_System`Convert`CommonDump`ExpandTemplateBoxes
]
"xy"
Notice that the "RowDefault" TemplateBox
never gets processed by System`Convert`CommonDump`ExpandTemplateBoxes
because System`Convert`TeXFormDump`maketex
has a special DownValues
for this case.
Non-Row TemplateSlotSequence issues
The failure to support TemplateSlotSequence
is not restricted to Row
objects. For example:
ToString[BellY[a, b, {c, d}], TeXForm]
TeXForm::unspt: TeXForm of TemplateSlotSequence[3,,] is not supported.
"Y_{a,b}()"
ToString[WignerD[{j, m1, m2}, \[Theta]], TeXForm]
TeXForm::unspt: TeXForm of TemplateSlotSequence[4,,] is not supported.
"D_{\text{m1},\text{m2}}^j()"
So, changing the formatting of Row
so that it doesn't use a TemplateBox
is not really sufficient, it won't fix the above errors.
Fix
The function used by TeXForm
to convert TemplateBox
objects into normal boxes is System`Convert`CommonDump`templateBoxToDisplay
:
TracePrint[
System`Convert`CommonDump`ExpandTemplateBoxes[TemplateBox[{"x", "y"}, "RowNoSeparators"]],
_System`Convert`CommonDump`templateBoxToDisplay,
TraceInternal->True
]
System`Convert`CommonDump`templateBoxToDisplay[TemplateBox[{x,y},RowNoSeparators]]
RowBox[{TemplateSlotSequence[1]}]
Instead of using System`Convert`CommonDump`templateBoxToDisplay
one could use BoxForm`TemplateBoxToDisplayBoxes
:
template = TemplateBox[{"x","y"},"RowNoSeparators"];
System`Convert`CommonDump`templateBoxToDisplay[template]
BoxForm`TemplateBoxToDisplayBoxes[template]
RowBox[{TemplateSlotSequence[1]}]
RowBox[{"x", "y"}]
Note that the latter function produces acceptable boxes. I don't know why TeXForm
uses its own custom function to convert TemplateBox
objects. So, a simple fix is to redefine System`Convert`CommonDump`templateBoxToDisplay
:
System`Convert`CommonDump`templateBoxToDisplay = BoxForm`TemplateBoxToDisplayBoxes;
Now, TeXForm
will work properly with any object whose format uses a TemplateSlotSequence
TemplateBox
:
ToString[BellY[a, b, {c, d}], TeXForm] //OutputForm
ToString[WignerD[{j, m1, m2}, θ], TeXForm] //OutputForm
ToString[Row[{a, b}, ","], TeXForm] //OutputForm
$Y_{a,b}(c,d)$
$D_{\operatorname{m1},\operatorname{m2}}^j(0,\theta ,0)$
$a,b$