Some PGbasicmacros.pl no longer work in WW 2.15 (moved from webwork2)

[taniwallach]

@apizer reported in openwebwork/webwork2#1110

The macros
$LTE, $GTE, $LBRACE, $RBRACE, $LB, $RB,
from PGbasicmacros.pl no longer display correctly when viewing problems (HTML mode).

The initial discussion was there...

[taniwallach]

@Alex-Jordan suggested removing the HTML_tth code from pg:

But either way in time for the next release, it would be healthier for the code base to spend time in pg clearing away the references to retired output modes.

Note: since fallback uses HTML_hhh before plain HTML, this will require care to avoid unexpected changes to what will be rendered in the active modes.

[apizer]

I found this bug in testing an .ova version I'm putting together (Ubuntu 20.04 Server, WW 2.15, Apache2, Lighttpd, Rserver, cronjob for temp file removal, timing.log rotation, etc.). Hopefully this will work in a lot of setting. The original version (from VirtualBox) now on the web doesn't work well on other platforms. Hopefully the new one I'm testing (from VMware) will work. My point is I don't like to distribute things with known bugs so I think I'll distribute an edited version of PGbasicmacros.pl with the change:
HTML_MathJax => [ "HTML", "HTML_dpng", "HTML_tth", ],
which (as Nathan suggested) fixes the immediate bug.
When a fix (hot or not) uploaded, this can get over written but probably many people don't apply hot fixes or update their system.

[mgage]

I'm with Alex in that in the long term I'd like to see all of the references to LaTeX2HTML and HTML_tth removed. We are no longer supporting them. (I don't think either of them has implementation code distributed with webwork anymore. I think we should also remove references to jsMath unless someone thinks that still works faster than MathJax in certain cases.

It looks to me as if the assumption was that the tex codes for MathJax (HTML_MathJax) were assumed to be exactly the same as the tex codes for HTML_tth. Hence no specific references for HTML_MathJax were added. Is that not true? what are the correct codes for MathJax for these items? How does that compare to the codes for PTX?

[Alex-Jordan]

I guess I am not so concerned about removing these old display modes and it breaking a problem. Because webwork2 isn't supposed to be supporting these anyway. So if removal breaks a problem, it means that the problem was "supposed" to be broken and was only passing by because of an accident. And we could go the extra mile and proactively examine the OPL problems that mention tth (there are 31, plus 6 macro libraries).

[jwj61]

Most (if not all) of the time it is part of a MODES command, so if the user is not using tth, it will not come up.

[apizer]

To answer Nathan's question, this is an old bug. At least it appears in WW2.13 which is the only older version I tested. My "patch" is to use
HTML_MathJax => [ "HTML_dpng", "HTML", "HTML_tth", ],
In PGbasicmacros.pl, basically the only places HTML_tth appears are in the macros that cause problems (LB, etc) so at least as far as PGbasicmacros.pl is concerned, the above should cause no problems.

[taniwallach]

I think this is more complicated than we had hoped.

@mgage wrote:

It looks to me as if the assumption was that the tex codes for MathJax (HTML_MathJax) were assumed to be exactly the same as the tex codes for HTML_tth. Hence no specific references for HTML_MathJax were added. Is that not true? what are the correct codes for MathJax for these items? How does that compare to the codes for PTX?

@apizer wrote:

In PGbasicmacros.pl, basically the only places HTML_tth appears are in the macros that cause problems (LB, etc) so at least as far as PGbasicmacros.pl is concerned, the above should cause no problems.

Yes, most of the use of a HTML_tth definition seems to be in the macros which were broken, but not all of them. The patch was mainly intended to verify that the fall-back order was the reason that MathJax "mode" was give "tth" output. Thinking about all the macros of this style which have HTML_tth definitions leads me to think that we may be oversimplifying the issue and thus also the patch. There are 8 macros marked with either not for use in math mode or only for use in math mode and these are the macros which have a HTML_tth setting and are making problems.

Four of the macros @apizer had problems with ($LBRACE, $RBRACE, $LB, $RB) are intended for use only outside math mode - so should be generating "plain HTML" and not something to be handled by MathJax inside a WW math block. For those 4 macros, it seems that HTML_MathJax should be acting like plain HTML mode, and that is the effect of the change in fall-back order.

However, the other two ($LTE, $GTE) @apizer mentioned as well as $LTS and $GTS are intended for use in math mode, so apparently should prefer the LaTeX style output - so should behave like HTML_tth did (as in the prior fallback order) and should not be creating "plain HTML" output rather than a LaTeX macro.

It seems that any real fix which handles all 8 macros properly will require adding a HTML_MathJax setting to at least 4 of these 8 MODES based definitions.

[Alex-Jordan]

For some history, those markings (like "for math mode only") are comments I added when adding the PTX output. It did not make sense to me that someone would use something like $LBRACE inside math mode. Why wouldn't they use \{? And in PTX, outside math mode, it would just be { while inside it would be \{, so they are distinguished. These macros are "unaware" of whether they are being executed inside math mode, so the question was how to make them have different outputs depending on use in or out of math?

There were similar issues with the others. It's possible that my declarations for these to be used "only in math mode" (or not) are incorrect. I'm grateful for any second opinions on those declarations.

[apizer]

It has been a very long time since I thought about any of this, but I do not think any of these macros were intended to be used in math mode. In a math expression, people should use LaTeX. There is probably documentation on this somewhere.

[Alex-Jordan]

It has been a very long time since I thought about any of this, but I do not think any of these macros were intended to be used in math mode. In a math expression, people should use LaTeX. There is probably documentation on this somewhere.

That is what I would have thought. But I was led to believe these for are for use inside math:

sub LTS { MODES(TeX => '<', Latex2HTML => '\\lt ', HTML => '&lt;', HTML_tth => '<', PTX => '\lt' ); };  #only for use in math mode
sub GTS { MODES(TeX => '>', Latex2HTML => '\\gt ', HTML => '&gt;', HTML_tth => '>', PTX => '\gt' ); };  #only for use in math mode
sub LTE { MODES(TeX => '\\le ', Latex2HTML => '\\le ', HTML => '<U>&lt;</U>', HTML_tth => '\\le ', PTX => '\leq' ); };  #only for use in math mode
sub GTE { MODES(TeX => '\\ge ', Latex2HTML => '\\ge ', HTML => '<U>&gt;</U>', HTML_tth => '\\ge ', PTX => '\geq' ); };  #only for use in math mode

because of things like the TeX => '\\ge ',. Outside of math in TeX, that macro is undefined by default. And unless you use the math font, are you even going to have a character for $GTE outside of math mode with vanilla pdflatex?

And also TeX => '>',. IIRC, in older pdflatex (contemporary with when these were written), outside of math mode, these come out as inverted question marks or something like that.

[taniwallach]

I agree that there seems to be some confusion about these 4 macros ($LTS, $GTS, $LTE, $GTE). The comment added into PGbasicmaros.ps about them being meant for use in math mode seems not to make much sense, as the we have TeX notation to use. In fact, I did some digging in the Wiki to see what is written about them - and found that all 4 are marked as deprecated in https://webwork.maa.org/wiki/Display_Macros .

A Google search also found
https://query.libretexts.org/Assessment_Gallery/Mathematics/WeBWorK_Import/WeBWorK/WeBWorK_tutorial/Fort_Lewis_tutorial_2011/120-pg-special-characters.pg which does not mention these macros and directs to use math mode.

It does seem that there may be some "legitimate" need for these macros in text mode, for use inside popup menus, which is one of the use cases found in the OPL.

---

I found some 140 occurrences in the OPL using grep and some use these macros inside math and some outside (particular inside Popup answers). The use inside popup's make sense, as as far as I recall math notation can not be used in them, but HTML entities should work. The list of what I found is in a following post.

Wherever these macros are used in the OPL inside Math mode, they could be replaced by the TeX alternative.

---

It seems to me that as long as they exist in the code-base - they should probably be designed to work outside math mode, where they are arguable needed, even if they will not behave as nicely in math mode or in PDF output, For TeX mode we would want some "reasonable" definition that works outside of Math mode (<= for $LTE???).

If we do leave active patched definitions for these 4 macros, I recommend redefining the HTML setting for $LTE and $GTE to take advantage of the Unicode support in modern browsers and just use the HTML entities ≤ and ≥ rather than the old hack using an underline.

I ran into a site with a table of many math symbols from Unicode at https://www.toptal.com/designers/htmlarrows/math/

[taniwallach]

Found in the OPL (note that one hit also used $LBRACE and $RBRACE in math mode):

./Contrib/Keele/NuclearPhysics/Particles/BD_lepton_1_original.pg:66:$GTS \{ $muon->menu() \} 
./Contrib/Keele/NuclearPhysics/Particles/BD_lepton_1_original.pg:67:$GTS \{ $electron->menu() \} 
./Contrib/Keele/NuclearPhysics/Particles/BD_lepton_1_original.pg:68:$GTS \{ $neutrino->menu() \}
./Contrib/PCC/BasicAlgebra/LinearInequalities/SetNotationToGraph10.pg:42:$symbol = $GTS;  #Don't use < or > directly.
./Contrib/PCC/BasicAlgebra/LinearInequalities/SetNotationToGraph20.pg:42:$symbol = $LTS;  #Don't use < or > directly.
./Contrib/PCC/BasicAlgebra/ComparisonsAndBasicInequalities/CompareNumbers20.pg:78:    [`[$frac]\, [$LTS]\,[$integer]`]
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions60.pg:60:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions60.pg:65:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions60.pg:70:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions60.pg:78:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions30.pg:60:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions30.pg:65:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions30.pg:70:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions30.pg:79:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions80.pg:60:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions80.pg:65:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions80.pg:70:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions80.pg:78:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions10.pg:55:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions10.pg:60:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions10.pg:65:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions10.pg:74:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions50.pg:60:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions50.pg:65:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions50.pg:70:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions50.pg:79:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions90.pg:61:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions90.pg:66:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions90.pg:71:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions90.pg:78:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions40.pg:55:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions40.pg:60:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions40.pg:65:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions40.pg:74:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions20.pg:55:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions20.pg:60:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions20.pg:65:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions20.pg:74:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions70.pg:65:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions70.pg:70:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions70.pg:75:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./Contrib/PCC/BasicMath/FractionsCalculation/CompareFractions70.pg:84:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality130.pg:77:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality130.pg:78:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequalityWithFraction60.pg:77:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequalityWithFraction60.pg:78:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/GraphToSetAndIntervalNotation20.pg:133:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/GraphToSetAndIntervalNotation20.pg:134:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SetNotationToGraph10.pg:40:$symbol = $GTS;  #Don't use < or > directly.
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/CompoundInequalityAnd40.pg:81:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/CompoundInequalityAnd40.pg:82:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/GraphToSetAndIntervalNotation30.pg:133:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/GraphToSetAndIntervalNotation30.pg:134:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/CompoundInequalityAnd70.pg:85:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/CompoundInequalityAnd70.pg:86:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/CompoundInequalityAnd80.pg:82:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/CompoundInequalityAnd80.pg:83:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality10.pg:72:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality10.pg:73:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality110.pg:77:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality110.pg:78:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality40.pg:71:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality40.pg:72:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/CompoundInequalityAnd50.pg:83:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/CompoundInequalityAnd50.pg:84:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality310.pg:75:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality310.pg:76:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality170.pg:73:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality170.pg:74:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/GraphToSetAndIntervalNotation10.pg:134:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/GraphToSetAndIntervalNotation10.pg:135:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality240.pg:78:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality240.pg:79:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequalityWithFraction10.pg:77:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequalityWithFraction10.pg:78:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/GraphToSetAndIntervalNotation40.pg:133:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/GraphToSetAndIntervalNotation40.pg:134:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality20.pg:72:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality20.pg:73:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality180.pg:73:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality180.pg:74:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality60.pg:87:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality60.pg:88:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequalityWithFraction70.pg:78:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequalityWithFraction70.pg:79:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality320.pg:78:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality320.pg:79:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality70.pg:71:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequality70.pg:72:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequalityWithFraction30.pg:92:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/SolveInequalityWithFraction30.pg:93:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/CompoundInequalityAnd60.pg:79:* *[$GTS]=* for [`\geq`],
./OpenProblemLibrary/PCC/BasicAlgebra/LinearInequalities/CompoundInequalityAnd60.pg:80:* and *[$LTS]=* for [`\leq`] 
./OpenProblemLibrary/PCC/BasicAlgebra/ComparisonsAndBasicInequalities/CompareNumbers10.pg:50:$popup = PopUp(['?', $LTS, $GTS, '='], $LTS);
./OpenProblemLibrary/PCC/BasicAlgebra/ComparisonsAndBasicInequalities/CompareNumbers10.pg:77:If you have trouble differentiate between [$GTS] and [$LTS], remember this trick: The alligator eats the bigger number. That's why we write [`2[$GTS]1`], or [`1[$LTS]2`].
./OpenProblemLibrary/PCC/BasicAlgebra/ComparisonsAndBasicInequalities/CompareFractionOperations10.pg:60:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./OpenProblemLibrary/PCC/BasicAlgebra/ComparisonsAndBasicInequalities/CompareFractionOperations10.pg:65:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./OpenProblemLibrary/PCC/BasicAlgebra/ComparisonsAndBasicInequalities/CompareFractionOperations10.pg:70:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./OpenProblemLibrary/PCC/BasicAlgebra/ComparisonsAndBasicInequalities/CompareFractionOperations10.pg:89:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./OpenProblemLibrary/PCC/BasicAlgebra/ComparisonsAndBasicInequalities/CompareNumbers20.pg:75:    [`[$frac]\, [$LTS]\,[$integer]`]
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions60.pg:57:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions60.pg:62:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions60.pg:67:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions60.pg:75:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions30.pg:57:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions30.pg:62:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions30.pg:67:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions30.pg:76:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions10.pg:52:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions10.pg:57:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions10.pg:62:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions10.pg:71:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions50.pg:57:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions50.pg:62:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions50.pg:67:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions50.pg:76:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions20.pg:52:    $popup = PopUp(["?", $LTS, $GTS, "="], $LTS);
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions20.pg:57:    $popup = PopUp(["?", $LTS, $GTS, "="], $GTS);
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions20.pg:62:    $popup = PopUp(["?", $LTS, $GTS, "="], "=");
./OpenProblemLibrary/PCC/BasicMath/FractionsCalculation/CompareFractions20.pg:71:Choose [`[$LTS]`], [`[$GTS]`], or [`=`] to make a true statement.
./OpenProblemLibrary/PCC/BasicMath/IntegerAndSquareRoot/CompareNumbers50.pg:78:      $popups[$i] = PopUp(['?', $LTS, $GTS, '='], $GTS);
./OpenProblemLibrary/PCC/BasicMath/IntegerAndSquareRoot/CompareNumbers50.pg:81:      $popups[$i] = PopUp(['?', $LTS, $GTS, '='], $LTS);
./OpenProblemLibrary/270/setDerivatives12MVT/c3s2p1.pg:81:\{ ans_rule(10) \}\(  $LTE \)  \{ ans_rule(10) \}
./OpenProblemLibrary/Rochester/setDiscrete5Algorithms/ur_dis_5_1.pg:35:$BBOLD while $EBOLD n \( $GTS \) 0 $BR
./OpenProblemLibrary/Rochester/setDiscrete5Algorithms/ur_dis_5_1.pg:50:$BBOLD while $EBOLD n \( $GTE \) 0  $BR
./OpenProblemLibrary/Rochester/setDiscrete5Algorithms/ur_dis_5_1.pg:73:$BBOLD while $EBOLD i \( $LTS \) 10 $BR
./OpenProblemLibrary/Rochester/setAlgebra16FunctionGraphs/c0s5p4.pg:30: \(-1 $LTS x $LTS 1\) $BR
./OpenProblemLibrary/Rochester/setAlgebra16FunctionGraphs/c0s5p4.pg:31: and \(x\in[-1,1]\) means \(-1 $LTE x $LTE 1\).
./OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/1_Precalculus_Review/1.3_The_Basic_Classes_of_Functions/1.3.1.pg:32:$mc->qa('Determine the domain of the function.', "\( x $GTE 0 \)");
./OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/1_Precalculus_Review/1.3_The_Basic_Classes_of_Functions/1.3.1.pg:33:$mc->extra("\( x $LTE 0 \)", "all Real numbers");
./OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/1_Precalculus_Review/1.3_The_Basic_Classes_of_Functions/1.3.5.pg:32:$mc->extra("\( x $GTE -$int \)", "\( x $LTE -$int \)", "all Real numbers");
./OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/4_Applications_of_the_Derivative/4.4_The_Shape_of_a_Graph/4.4.9.pg:77:  $int1_fsign = "$GTS 0";
./OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/4_Applications_of_the_Derivative/4.4_The_Shape_of_a_Graph/4.4.9.pg:81:  $int1_fsign = "$LTS 0";
./OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/4_Applications_of_the_Derivative/4.4_The_Shape_of_a_Graph/4.4.9.pg:86:  $int2_fsign = "$GTS 0";
./OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/4_Applications_of_the_Derivative/4.4_The_Shape_of_a_Graph/4.4.9.pg:91:  $int2_fsign = "$LTS 0";
./OpenProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/4_Applications_of_the_Derivative/4.4_The_Shape_of_a_Graph/4.4.47.pg:176:Let \[f(x) = \{$f->reduce->TeX\}, \; 0 $LTE x $LTE 2 \pi\]
./OpenProblemLibrary/NAU/setFoundations/MAT320_0403.pg:53:Determine whether the given equality is true (T) or false (F). We use standard notation for intervals (open, closed, or half-open) in the set of real numbers. For instance, \( [a,b)=$LBRACE x \in {\mathbb R} \ | \ a $LTE x $LTS b $RBRACE \), and \( (a,\infty)=$LBRACE x \in {\mathbb R} \ | \ x $GTS a $RBRACE \). The set of positive integers is denoted by \( {\mathbb N} \). $BR
./OpenProblemLibrary/Michigan/Chap17Sec5/Q15.pg:94:with angle brackets: e.g., as $BBOLD${LTS}${SPACE}1 + s + t, s - t, 3 - t$SPACE$GTS$EBOLD.)$EITALIC
./OpenProblemLibrary/Michigan/Chap17Sec5/Q17.pg:86:$BBOLD${LTS}${SPACE}1 + s + t, s - t, 3 - t$SPACE$GTS$EBOLD.)$EITALIC
./OpenProblemLibrary/Michigan/Chap13Sec2/Q19.pg:84:\( \vec v = ${LTS}$midscores$GTS \).
./OpenProblemLibrary/Michigan/Chap13Sec2/Q19.pg:86:\( \vec w = $LTS$finscores$GTS \).  If the final counts twice as much as the
./OpenProblemLibrary/Dartmouth/setStewartCh13S1/problem_5.pg:48:$LTS, $LTS =, =, $GTS =, $GTS\)

[taniwallach]

Why wouldn't they use \{?

Just for the record and people who Google when they have issues, when coding in the "old" style (not using PGML, ex. using BEGIN_TEXT and END_TEXT) \{ does not work inside math (between \( and \)) as it is used to denote the start of embedded Perl code. Instead use \lbrace in math mode.

Using \{ as in

    \( \displaystyle \left\{ (x,y) \rule{0pt}{12pt} \right|  \)
    \{ $ansA1->ans_rule(8) \}

causes the MathJax no to render and triggers the WeBWorK Warnings similar to

 ERROR in old_safe_ev, PGbasicmacros.pl:

## There is an error occuring inside evaluation brackets \{ ...code... \}
## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
## Code evaluated:
## (x,y) \\rule{0pt}{12pt} \\right| \\)
\\{ $ansA1->ans_rule(8)
##syntax error at line 3 of (eval 8348), at EOF
(Might be a runaway multi-line )) string starting on line 2)
##