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Mathvariant fixes #2292

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merged 10 commits into from
Jan 5, 2024
Merged

Mathvariant fixes #2292

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05bb502
Be careful about propogating the correct font when synthesizing math …
brucemiller Dec 31, 2023
15cb596
Omit mathvariant=normal when it's the default
brucemiller Dec 31, 2023
0cb7fee
Cleanup test cases for missing/erroneous/redundant font or mathvarian…
brucemiller Dec 31, 2023
097c24b
Add class ltx_mathvariant_xxx to MathML tokens whenever the mathvaria…
brucemiller Jan 3, 2024
bddfc1c
Add fallback CSS classes for unhandled mathvariants
brucemiller Jan 3, 2024
e0142e4
Update testcase for additional css classes
brucemiller Jan 3, 2024
8a87fa9
Don't add CSS class for mathvariant=normal
brucemiller Jan 4, 2024
12df8ca
Avoid mathvariant on m:mtext (only use css); avoid visible css effect…
brucemiller Jan 5, 2024
ad4b68e
Update testcase for simplified mathml
brucemiller Jan 5, 2024
e5d7b6a
clarify comment
brucemiller Jan 5, 2024
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13 changes: 8 additions & 5 deletions lib/LaTeXML/MathParser.pm
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Original file line number Diff line number Diff line change
Expand Up @@ -1168,10 +1168,10 @@ sub Absent {
return New('absent'); }

sub InvisibleTimes {
return New('times', "\x{2062}", role => 'MULOP', font => LaTeXML::Common::Font->new()); }
return New('times', "\x{2062}", role => 'MULOP'); }

sub InvisibleComma {
return New(undef, "\x{2063}", role => 'PUNCT', font => LaTeXML::Common::Font->new()); }
return New(undef, "\x{2063}", role => 'PUNCT'); }

# Get n-th arg of an XMApp.
# However, this is really only used to get the script out of a sub/super script
Expand Down Expand Up @@ -1406,19 +1406,22 @@ sub Fence {
return InterpretDelimited(New($op, undef, ($decl_id ? (decl_id => $decl_id) : ())), @stuff); } }

# Compose a complex relational operator from two tokens, such as >=, >>
# (similar to CatSymbols, but specialized to relops)
sub TwoPartRelop {
my ($op1, $op2) = @_;
$op1 = Lookup($op1);
$op2 = Lookup($op2);
my $m1 = p_getTokenMeaning($op1);
my $m2 = p_getTokenMeaning($op2);
my $m1 = p_getTokenMeaning($op1);
my $m2 = p_getTokenMeaning($op2);
my $font = p_getAttribute($op1, '_font');
my $meaning;
if ($m1 eq $m2) {
$meaning = "much-$m1"; }
else {
$meaning = "$m1-or-$m2"; }
my $content = $op1->textContent . $op2->textContent;
return ['ltx:XMTok', { role => "RELOP", meaning => $meaning }, $content]; }
return ['ltx:XMTok', { role => "RELOP", meaning => $meaning, ($font ? (_font => $font) : ()) },
$content]; }

# NOTE: It might be best to separate the multiple Formulae into separate XMath's???
# but only at the top level!
Expand Down
7 changes: 4 additions & 3 deletions lib/LaTeXML/Package.pm
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Expand Up @@ -1619,7 +1619,8 @@ sub defmath_rewrite {

sub defmath_common_constructor_options {
my ($cs, $presentation, %options) = @_;
my $sizer = inferSizer($options{sizer}, $options{reversion});
my $sizer = inferSizer($options{sizer}, $options{reversion});
my $presentation_s = $presentation && ToString($presentation);
return (
alias => $options{alias} || $cs->getString,
(defined $options{reversion} ? (reversion => $options{reversion}) : ()),
Expand All @@ -1645,8 +1646,8 @@ sub defmath_common_constructor_options {
stretchy => $options{stretchy},
operator_stretchy => $options{operator_stretchy},
font => ($options{mathstyle}
? sub { LookupValue('font')->merge(mathstyle => $options{mathstyle})->specialize($presentation); }
: sub { LookupValue('font')->specialize($presentation); }),
? sub { LookupValue('font')->merge(mathstyle => $options{mathstyle})->specialize($presentation_s); }
: sub { LookupValue('font')->specialize($presentation_s); }),
lpadding => $options{lpadding},
rpadding => $options{rpadding} },
scope => $options{scope}); }
Expand Down
4 changes: 3 additions & 1 deletion lib/LaTeXML/Package/LaTeX.pool.ltxml
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Expand Up @@ -3875,7 +3875,9 @@ DefPrimitive('\@array@bindings [] AlignmentTemplate', sub {
if ($str != 1) {
$$attr{rowsep} = Dimension(($str - 1) . 'em'); }
alignmentBindings($template, 'math', attributes => $attr);
MergeFont(mathstyle => 'text');
if (my $font = LookupValue('font')) {
if (($font->getMathstyle || 'text') eq 'display') {
MergeFont(mathstyle => 'text'); } }
Let("\\\\", '\@alignment@newline');
Let('\lx@intercol', '\lx@math@intercol');
return; });
Expand Down
13 changes: 8 additions & 5 deletions lib/LaTeXML/Package/TeX.pool.ltxml
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Expand Up @@ -6859,14 +6859,15 @@ DefConstructor('\lx@hack@bordermatrix{}', sub {
my $n = scalar(@rows) - 1;
$col1->setAttribute(rowspan => $n);
$coln->setAttribute(rowspan => $n);
my $pfont = $STATE->lookupValue('font')->specialize('(');
$document->appendTree($col1,
['ltx:XMWrap', { depth => $d },
['ltx:XMTok', { role => 'OPEN', height => 0, depth => $d, yoffset => $md }, '('],
['ltx:XMTok', { height => $h, yoffset => $md }, ' ']]); # Effectively, a strut
['ltx:XMTok', { role => 'OPEN', height => 0, depth => $d, yoffset => $md, font => $pfont }, '('],
['ltx:XMTok', { height => $h, yoffset => $md, font => $pfont }, ' ']]); # Effectively, a strut
$document->appendTree($coln,
['ltx:XMWrap', {},
['ltx:XMTok', { role => 'CLOSE', height => 0, depth => $d, yoffset => $md }, ')'],
['ltx:XMTok', { height => $h, yoffset => $md }, ' ']]);
['ltx:XMTok', { role => 'CLOSE', height => 0, depth => $d, yoffset => $md, font => $pfont }, ')'],
['ltx:XMTok', { height => $h, yoffset => $md, font => $pfont }, ' ']]);
return; },
reversion => '#1');

Expand Down Expand Up @@ -7291,7 +7292,9 @@ DefConstructor('\lx@apply OptionalKeyVals:XMath {}{}',
DefConstructor('\lx@symbol OptionalKeyVals:XMath {}',
"<ltx:XMTok $XMath_attributes>#2</ltx:XMTok>",
reversion => '#2',
afterDigest => sub { XMath_copy_keyvals(@_); });
afterDigest => sub {
$_[1]->setFont($_[1]->getArg(2)->getFont);
XMath_copy_keyvals(@_); });

# Wrap the contents in an ltx:XMWrap, to stand as a single subtree & providing attributes
# The ltx:XMWrap may be collapsed, later, by parsing
Expand Down
13 changes: 9 additions & 4 deletions lib/LaTeXML/Post/MathML.pm
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Expand Up @@ -18,8 +18,8 @@ use LaTeXML::Util::Unicode;
use LaTeXML::Post;
use LaTeXML::Common::Font;
use List::Util qw(max);
use base qw(LaTeXML::Post::MathProcessor);
use base qw(Exporter);
use base qw(LaTeXML::Post::MathProcessor);
use base qw(Exporter);
our @EXPORT = (
qw( &DefMathML ),
qw( &pmml &pmml_scriptsize &pmml_smaller
Expand Down Expand Up @@ -703,6 +703,8 @@ sub stylizeContent {
elsif (!$variant) { $variant = 'normal'; } } # must say so explicitly.
elsif ($font && !$variant) {
Warn('unexpected', $font, undef, "Unrecognized font variant '$font'"); $variant = ''; }
elsif ($variant eq 'normal') { # normal is default for any other tokens, so omit
$variant = undef; }
# Should we map to Unicode's Plane 1 blocks for Mathematical Alphanumeric Symbols?
# Only upper & lower case latin & greek, and also numerals can be mapped.
# For each mathvariant, and for each of those 5 groups, there is a linear mapping,
Expand All @@ -729,15 +731,18 @@ sub stylizeContent {
$class = ($class ? $class . ' ' : '') . 'ltx_font_oldstyle'; }
elsif ($font =~ /smallcaps/) {
$class = ($class ? $class . ' ' : '') . 'ltx_font_smallcaps'; }
elsif ($variant) { # Any left-over mathvariant? Punt to CSS
$class = ($class ? $class . ' ' : '') . 'ltx_mathvariant_' . $variant; }
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Should this check also unset $variant = undef; after it is moved to a class value?

As it is, I see that one of the tests has both a class and mathvariant attribute, as in:

<mtext class="ltx_mathvariant_italic" mathvariant="italic">

But in MathML Core the only prescribed use of mathvariant is for the normal value. So the class addition should suffice. That was my suggestion in #2051 (comment)

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Right, well as I understood the original issue, and the implications of the (eventually) linked mozilla issue, it was that Core will ignore (most) mathvariants, and that Full may ignore it, and that CSS could be used as a fallback. Moreover, that browsers should be able to cope with there being both CSS and mathvariant.

Keeping the mathvariant at least records for MathML-Full agents which don't support CSS that the token was (apparently) intended to belong to a certain semantic class. Removing it seems somehow wrong, even though in the current scheme of things it is likely always to be ignored (but harmless?)

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Since it is ignored in practice, keeping it until there is some actual issue caused by it is likely harmless, as you say. And indeed it is a MathML Full use.

I've heard rumors of hypothetical MathML Full agents without CSS support, but I wonder if/when we'll have some to test with...

Linking the current MathML Core text on mathvariant just in case:

The mathvariant attribute, if present, must be an ASCII case-insensitive match of normal.

No further comments on the PR, looks good to merge.


if ($opacity) {
$cssstyle = ($cssstyle ? $cssstyle . ';' : '') . "opacity:$opacity"; }

# Now, look up any OperatorDictionary properties
my %props = ($tag eq 'm:mo' ? opdict_lookup($text, $role) : ());

# Resolve stretch & size
$stretchy = undef if ($tag ne 'm:mo'); # Only allowed on m:mo!
$size = undef if $stretchy; # Ignore size, if we're stretching.
$stretchy = undef if ($tag ne 'm:mo'); # Only allowed on m:mo!
$size = undef if $stretchy; # Ignore size, if we're stretching.
my $stretchyhack = undef;
if ($text =~ /^[\x{2061}\x{2062}\x{2063}]*$/) { # invisible get no size or stretchiness
$stretchy = $size = undef; }
Expand Down
16 changes: 16 additions & 0 deletions lib/LaTeXML/resources/CSS/LaTeXML.css
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Expand Up @@ -462,6 +462,22 @@ span.ltx_framed { display:inline-block; text-indent:0; } /* avoid padding/
.ltx_font_smallcaps { font-variant: small-caps; font-style:normal; }
.ltx_font_oldstyle { font-variant-numeric: oldstyle-nums; }
.ltx_font_mathcaligraphic { font-family: "Lucida Calligraphy", "Zapf Chancery","URW Chancery L"; }
/* Fallbacks for when content+mathvariant cannot be mapped to Unicode */
.ltx_mathvariant_italic { font-style: italic; }
.ltx_mathvariant_bold { font-weight: bold; }
.ltx_mathvariant_bold-italic { font-style: italic; font-weight: bold; }
.ltx_mathvariant_sans-serif { font-family: sans-serif; }
.ltx_mathvariant-bold-sans-serif { font-family: sans-serif; font-weight: bold; }
.ltx_mathvariant-sans-serif-italic { font-family: sans-serif; font-style: italic; }
.ltx_mathvariant-bold-sans-serif-italic { font-family: sans-serif; font-style: italic; font-weight: bold; }
.ltx_mathvariant_monospace { font-family: monospace; }
/* Can we say anything generic about double-struck, script or fraktur ? */
.ltx_mathvariant_double-struck { font-weight: bold; }
.ltx_mathvariant_script { font-family: "Lucida Calligraphy", "Zapf Chancery","URW Chancery L", cursive; }
.ltx_mathvariant_bold-script { font-family: "Lucida Calligraphy", "Zapf Chancery","URW Chancery L", cursive; font-weight: bold; }
.ltx_mathvariant-fraktur { }/* ??? */
.ltx_mathvariant_bold-fraktur { font-weight: bold; }

/*

.ltx_font_mathscript { ? }
Expand Down
8 changes: 4 additions & 4 deletions t/alignment/listing.xml
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Expand Up @@ -513,7 +513,7 @@ and with messed up braces <text class="ltx_lst_numbers_left ltx_lstlisting"><tex
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP">⁢</XMTok>
<XMTok color="#000000" meaning="times" role="MULOP">⁢</XMTok>
<XMTok font="italic" fontsize="70%" role="UNKNOWN">i</XMTok>
<XMTok font="italic" fontsize="70%" role="UNKNOWN">j</XMTok>
</XMApp>
Expand Down Expand Up @@ -565,7 +565,7 @@ and with messed up braces <text class="ltx_lst_numbers_left ltx_lstlisting"><tex
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP">⁢</XMTok>
<XMTok color="#000000" meaning="times" role="MULOP">⁢</XMTok>
<XMTok font="italic" fontsize="70%" role="UNKNOWN">i</XMTok>
<XMTok font="italic" fontsize="70%" role="UNKNOWN">j</XMTok>
</XMApp>
Expand Down Expand Up @@ -622,7 +622,7 @@ and with messed up braces <text class="ltx_lst_numbers_left ltx_lstlisting"><tex
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP">⁢</XMTok>
<XMTok color="#000000" meaning="times" role="MULOP">⁢</XMTok>
<XMTok font="italic" fontsize="70%" role="UNKNOWN">i</XMTok>
<XMTok font="italic" fontsize="70%" role="UNKNOWN">j</XMTok>
</XMApp>
Expand Down Expand Up @@ -671,7 +671,7 @@ and with messed up braces <text class="ltx_lst_numbers_left ltx_lstlisting"><tex
<XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
<XMTok role="UNKNOWN">a</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP">⁢</XMTok>
<XMTok font="upright" meaning="times" role="MULOP">⁢</XMTok>
<XMTok fontsize="70%" role="UNKNOWN">i</XMTok>
<XMTok fontsize="70%" role="UNKNOWN">j</XMTok>
</XMApp>
Expand Down
8 changes: 4 additions & 4 deletions t/alignment/plainmath.xml
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Expand Up @@ -54,8 +54,8 @@
</XMCell>
<XMCell rowspan="2">
<XMWrap depth="6.8pt">
<XMTok depth="6.8pt" font="italic" height="0" role="OPEN" yoffset="-6.8pt">(</XMTok>
<XMTok font="italic" height="6.8pt" yoffset="-6.8pt"> </XMTok>
<XMTok depth="6.8pt" height="0" role="OPEN" yoffset="-6.8pt">(</XMTok>
<XMTok height="6.8pt" yoffset="-6.8pt"> </XMTok>
</XMWrap>
</XMCell>
<XMCell align="center">
Expand All @@ -66,8 +66,8 @@
</XMCell>
<XMCell rowspan="2">
<XMWrap>
<XMTok depth="6.8pt" font="italic" height="0" role="CLOSE" yoffset="-6.8pt">)</XMTok>
<XMTok font="italic" height="6.8pt" yoffset="-6.8pt"> </XMTok>
<XMTok depth="6.8pt" height="0" role="CLOSE" yoffset="-6.8pt">)</XMTok>
<XMTok height="6.8pt" yoffset="-6.8pt"> </XMTok>
</XMWrap>
</XMCell>
</XMRow>
Expand Down
4 changes: 2 additions & 2 deletions t/babel/numprints.xml
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Expand Up @@ -1212,7 +1212,7 @@ vs.
<XMDual>
<XMTok color="#0000FF" font="italic" meaning="123456.23e1" role="NUMBER">123456.23e1</XMTok>
<XMApp color="#0000FF">
<XMTok meaning="times" role="MULOP">⁢</XMTok>
<XMTok color="#000000" meaning="times" role="MULOP">⁢</XMTok>
<XMText><text align="right" width="68.3pt"><Math mode="inline" tex="\textstyle 123{,}456" text="list@(123, 456)" xml:id="S3.p6.m3.m1">
<XMath>
<XMDual>
Expand Down Expand Up @@ -1317,7 +1317,7 @@ vs.
<XMDual>
<XMTok color="#0000FF" font="italic" meaning="14561234.562e12" role="NUMBER">14561234.562e12</XMTok>
<XMApp color="#0000FF">
<XMTok meaning="times" role="MULOP">⁢</XMTok>
<XMTok color="#000000" meaning="times" role="MULOP">⁢</XMTok>
<XMText><text align="right" width="68.3pt"><Math mode="inline" tex="\textstyle 14{,}561{,}234" text="list@(14, 561, 234)" xml:id="S3.p6.m6.m1">
<XMath>
<XMDual>
Expand Down
2 changes: 1 addition & 1 deletion t/complex/si.xml
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Expand Up @@ -2877,7 +2877,7 @@ Some text <break/><Math mode="inline" tex="4\text{\,}\mathrm{m}\text{\,}{\mathrm
<XMTok lpadding="0pt" meaning="arcminute" role="UNKNOWN">′</XMTok>
</XMApp>
<XMApp>
<XMTok meaning="times" role="MULOP">⁢</XMTok>
<XMTok color="#000000" meaning="times" role="MULOP">⁢</XMTok>
<XMTok meaning="6" role="NUMBER">6</XMTok>
<XMTok font="italic" width="0pt">.</XMTok>
<XMTok lpadding="0pt" meaning="arcsecond" role="UNKNOWN">″</XMTok>
Expand Down
2 changes: 1 addition & 1 deletion t/daemon/formats/lexmath.xml
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Expand Up @@ -32,7 +32,7 @@ Also <math id="p4.m3" class="ltx_Math" alttext="\mathit{func}" display="inline">

<tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline">
<td class="ltx_eqn_cell ltx_eqn_center_padleft"></td>
<td class="ltx_eqn_cell ltx_align_center"><math id="S0.Ex3.m1" class="ltx_Math" alttext="\int_{0}^{\infty}x\,dx=\text{zero, \it yes 0}" display="block"><semantics><mrow><mrow><msubsup><mo>∫</mo><mn>0</mn><mi mathvariant="normal">∞</mi></msubsup><mrow><mi>x</mi><mo lspace="0.170em">⁢</mo><mrow><mo rspace="0em">𝑑</mo><mi>x</mi></mrow></mrow></mrow><mo>=</mo><mrow><mtext>zero, </mtext><mtext mathvariant="italic">yes 0</mtext></mrow></mrow><annotation encoding="application/x-llamapun">∫ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ∞ end_POSTSUPERSCRIPT italic_x italic_d italic_x = zero, italic_yes italic_0</annotation></semantics></math></td>
<td class="ltx_eqn_cell ltx_align_center"><math id="S0.Ex3.m1" class="ltx_Math" alttext="\int_{0}^{\infty}x\,dx=\text{zero, \it yes 0}" display="block"><semantics><mrow><mrow><msubsup><mo>∫</mo><mn>0</mn><mi mathvariant="normal">∞</mi></msubsup><mrow><mi>x</mi><mo lspace="0.170em">⁢</mo><mrow><mo rspace="0em">𝑑</mo><mi>x</mi></mrow></mrow></mrow><mo>=</mo><mrow><mtext>zero, </mtext><mtext class="ltx_mathvariant_italic" mathvariant="italic">yes 0</mtext></mrow></mrow><annotation encoding="application/x-llamapun">∫ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ∞ end_POSTSUPERSCRIPT italic_x italic_d italic_x = zero, italic_yes italic_0</annotation></semantics></math></td>
<td class="ltx_eqn_cell ltx_eqn_center_padright"></td></tr></tbody>
</table>
</div>
Expand Down
4 changes: 2 additions & 2 deletions t/fonts/mathcolor.xml
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Expand Up @@ -17,7 +17,7 @@
<p><Math mode="inline" tex="r{\color[rgb]{0,1,0}g\color[rgb]{1,1,0}y}" text="r * g * y" xml:id="p2.m1">
<XMath>
<XMApp color="#FF0000">
<XMTok meaning="times" role="MULOP">⁢</XMTok>
<XMTok color="#000000" meaning="times" role="MULOP">⁢</XMTok>
<XMTok font="italic" role="UNKNOWN">r</XMTok>
<XMTok color="#00FF00" font="italic" role="UNKNOWN">g</XMTok>
<XMTok color="#FFFF00" font="italic" role="UNKNOWN">y</XMTok>
Expand All @@ -29,7 +29,7 @@
<p><text color="#FF0000">R <Math mode="inline" tex="r\mbox{R}{\color[rgb]{0,1,0}g\mbox{G}\color[rgb]{1,1,0}y\mbox{Y}}r\mbox{R}" text="r * [R] * g * [G] * y * [Y] * r * [R]" xml:id="p3.m1">
<XMath>
<XMApp>
<XMTok meaning="times" role="MULOP">⁢</XMTok>
<XMTok color="#000000" meaning="times" role="MULOP">⁢</XMTok>
<XMTok font="italic" role="UNKNOWN">r</XMTok>
<XMText>R</XMText>
<XMTok color="#00FF00" font="italic" role="UNKNOWN">g</XMTok>
Expand Down
14 changes: 7 additions & 7 deletions t/math/ambiguous_relations.xml
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Expand Up @@ -9,7 +9,7 @@
<Math mode="display" tex="x&gt;=0" text="x &gt;= 0" xml:id="S0.Ex1.m1">
<XMath>
<XMApp>
<XMTok font="italic" meaning="greater-than-or-equals" role="RELOP">&gt;=</XMTok>
<XMTok meaning="greater-than-or-equals" role="RELOP">&gt;=</XMTok>
<XMTok font="italic" role="UNKNOWN">x</XMTok>
<XMTok meaning="0" role="NUMBER">0</XMTok>
</XMApp>
Expand All @@ -22,7 +22,7 @@
<Math mode="display" tex="x&lt;=0" text="x &lt;= 0" xml:id="S0.Ex2.m1">
<XMath>
<XMApp>
<XMTok font="italic" meaning="less-than-or-equals" role="RELOP">&lt;=</XMTok>
<XMTok meaning="less-than-or-equals" role="RELOP">&lt;=</XMTok>
<XMTok font="italic" role="UNKNOWN">x</XMTok>
<XMTok meaning="0" role="NUMBER">0</XMTok>
</XMApp>
Expand All @@ -48,7 +48,7 @@
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S0.Ex3.m1.4">
<XMTok font="italic" meaning="greater-than-or-equals" role="RELOP">&gt;=</XMTok>
<XMTok meaning="greater-than-or-equals" role="RELOP">&gt;=</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S0.Ex3.m1.2">y</XMTok>
<XMTok meaning="0" role="NUMBER">0</XMTok>
</XMApp>
Expand Down Expand Up @@ -91,7 +91,7 @@
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S0.Ex5.m1.4">
<XMTok font="italic" meaning="greater-than-or-equals" role="RELOP">&gt;=</XMTok>
<XMTok meaning="greater-than-or-equals" role="RELOP">&gt;=</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S0.Ex5.m1.2">y</XMTok>
<XMTok font="italic" role="UNKNOWN">z</XMTok>
</XMApp>
Expand Down Expand Up @@ -122,7 +122,7 @@
<Math mode="display" tex="a&lt;&lt;b" text="a &lt;&lt; b" xml:id="S0.Ex7.m1">
<XMath>
<XMApp>
<XMTok font="italic" meaning="much-less-than" role="RELOP">&lt;&lt;</XMTok>
<XMTok meaning="much-less-than" role="RELOP">&lt;&lt;</XMTok>
<XMTok font="italic" role="UNKNOWN">a</XMTok>
<XMTok font="italic" role="UNKNOWN">b</XMTok>
</XMApp>
Expand All @@ -142,13 +142,13 @@
</XMApp>
<XMWrap>
<XMApp xml:id="S0.Ex8.m1.3">
<XMTok font="italic" meaning="much-less-than" role="RELOP">&lt;&lt;</XMTok>
<XMTok meaning="much-less-than" role="RELOP">&lt;&lt;</XMTok>
<XMTok meaning="0" role="NUMBER">0</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S0.Ex8.m1.1">a</XMTok>
</XMApp>
<XMTok role="PUNCT">,</XMTok>
<XMApp xml:id="S0.Ex8.m1.4">
<XMTok font="italic" meaning="much-greater-than" role="RELOP">&gt;&gt;</XMTok>
<XMTok meaning="much-greater-than" role="RELOP">&gt;&gt;</XMTok>
<XMTok font="italic" role="UNKNOWN" xml:id="S0.Ex8.m1.2">b</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
Expand Down
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