This repository has been archived by the owner on Jan 3, 2020. It is now read-only.
forked from w3c/mathml.old
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Overview-d.html
1871 lines (1717 loc) · 123 KB
/
Overview-d.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!DOCTYPE HTML>
<html lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>Mathematical Markup Language (MathML) Version 4.0 -- Diff Marked Version</title>
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
<style type="text/css">
/** Table of Contents taken from html 5.2 spec
stop flicker in toc **/
.toc a {
/* More spacing; use padding to make it part of the click target. */
padding-top: 0.1rem;
/* Larger, more consistently-sized click target */
display: block;
/* Reverse color scheme */
color: black;
border-color: #3980B5;
border-bottom-width: 3px !important;
margin-bottom: 0px !important;
}
.egmeta {
color:#5555AA;font-style:italic;font-family:serif;font-weight:bold;
}
div.graphic{margin-left:2em}
table.syntax {
font-size: 75%;
background-color: #DDDDDD;
border: thin solid;
}
table.syntax td {
border: solid thin;
}
table.syntax th {
text-align: left;
}
table.attributes td { padding-left:0.5em; padding-right:0.5em; border: solid thin; }
table.attributes td.attname { white-space:nowrap; vertical-align:top;}
table.attributes td.attdesc { background-color:#F0F0FF; padding-left:2em; padding-right:2em}
th.uname {font-size: 50%; text-align:left;}
code { font-family: monospace; }
div.constraint,
div.issue,
div.note,
div.notice { margin-left: 2em; }
li p { margin-top: 0.3em;
margin-bottom: 0.3em; }
div.exampleInner pre { margin-left: 1em;
margin-top: 0em; margin-bottom: 0em}
div.exampleOuter {border: 4px double gray;
margin: 0em; padding: 0em}
div.exampleInner { background-color: #d5dee3;
border-top-width: 4px;
border-top-style: double;
border-top-color: #d3d3d3;
border-bottom-width: 4px;
border-bottom-style: double;
border-bottom-color: #d3d3d3;
padding: 4px; margin: 0em }
div.exampleWrapper { margin: 4px }
div.exampleHeader { font-weight: bold;
margin: 4px}
a.mainindex {font-weight: bold;}
li.sitem {list-style-type: none;}
.error { color: red }
div.mathml-example {border:solid thin black;
padding: 0.5em;
margin: 0.5em 0 0.5em 0;
}
div.strict-mathml-example {border:solid thin black;
padding: 0.5em;
margin: 0.5em 0 0.5em 0;
}
div.strict-mathml-example h5 {
margin-top: -0.3em;
margin-bottom: -0.5em;}
var.meta {background-color:green}
var.transmeta {background-color:red}
pre.mathml {padding: 0.5em;
background-color: #FFFFDD;}
pre.mathml-fragment {padding: 0.5em;
background-color: #FFFFDD;}
pre.strict-mathml {padding: 0.5em;
background-color: #FFFFDD;}
span.uname {color:#999900;font-size:75%;font-family:sans-serif;}
.minitoc { border-style: solid;
border-color: #0050B2;
border-width: 1px ;
padding: 0.3em;}
.attention { border-style: solid;
border-width: 1px ;
color: #5D0091;
background: #F9F5DE;
border-color: red;
margin-left: 1em;
margin-right: 1em;
margin-top: 0.25em;
margin-bottom: 0.25em; }
.attribute-Name { background: #F9F5C0; }
.method-Name { background: #C0C0F9; }
.IDL-definition { border-style: solid;
border-width: 1px ;
color: #001000;
background: #E0FFE0;
border-color: #206020;
margin-left: 1em;
margin-right: 1em;
margin-top: 0.25em;
margin-bottom: 0.25em; }
.baseline {vertical-align: baseline}
#eqnoc1 {width: 10%}
#eqnoc2 {width: 80%; text-align: center; }
#eqnoc3 {width: 10%; text-align: right; }
div.div1 {margin-bottom: 1em;}
.h3style {
text-align: left;
font-family: sans-serif;
font-weight: normal;
color: #0050B2;
font-size: 125%;
}
h4 { text-align: left;
font-family: sans-serif;
font-weight: normal;
color: #0050B2; }
h5 { text-align: left;
font-family: sans-serif;
font-weight: bold;
color: #0050B2; }
th {background: #E0FFE0;}
p, blockquote, h4 { font-family: sans-serif; }
dt, dd, dl, ul, li { font-family: sans-serif; }
pre, code { font-family: monospace }
a.termref {
text-decoration: none;
color: black;
}
sub.diff-link {background-color: black; color: white; font-family:
sans-serif; font-weight: bold;}
.diff-add { background-color: #FFFF99}
.diff-del { background-color: #FF9999; text-decoration: line-through }
.diff-chg { background-color: #99FF99 }
.diff-off { }
.mathml-render {
font-family: serif;
font-size: 130%;
border: solid 4px green;
padding-left: 1em;
padding-right: 1em;
}
</style>
<link rel="stylesheet" type="text/css" href="https://www.w3.org/StyleSheets/TR/2016/W3C-ED.css"><script src="//www.w3.org/scripts/TR/2016/fixup.js"> </script></head>
<body>
<div>
<p>The presentation of this document has been augmented to
identify changes since the previous draft of MathML 3.0.
Three kinds of changes are highlighted: <span class="diff-add">new, added text</span>,
<span class="diff-chg">changed text</span>, and
<span class="diff-del">deleted text</span>.</p>
<hr>
</div>
<div class="head">
<p><a href="https://www.w3.org/"><img src="https://www.w3.org/StyleSheets/TR/2016/logos/W3C" alt="W3C" height="48" width="72"></a></p>
<h1><a id="title"></a>Mathematical Markup Language (MathML) Version 4.0</h1>
<h2><a id="w3c-doctype"></a>W3C Working Draft 26 January 2019</h2>
<dl>
<dt>This version:</dt>
<dd><a href="https://w3c.github.io/mathml/">https://w3c.github.io/mathml/</a></dd>
<dt>Latest MathML 3 version:</dt>
<dd>
<a href="https://www.w3.org/TR/MathML4/">https://www.w3.org/TR/MathML4/</a>
</dd>
<dt>Latest MathML Recommendation:</dt>
<dd>
<a href="https://www.w3.org/TR/MathML/">https://www.w3.org/TR/MathML/</a>
</dd>
<dt>Previous version:</dt>
<dd><a href="https://www.w3.org/TR/2014/REC-MathML3-20140410/">https://www.w3.org/TR/2014/REC-MathML3-20140410/</a></dd>
<dt>
Editors' version:</dt>
<dd><a href="https://w3c.github.io/mathml/">https://w3c.github.io/mathml/</a></dd>
<dt>Editors:</dt>
<dd>David Carlisle, NAG</dd>
<dd>Patrick Ion, Mathematical Reviews, American Mathematical Society</dd>
<dd>Robert Miner (deceased), Design Science, Inc.</dd>
<dt id="authors">Principal Authors:</dt>
<dd>Ron Ausbrooks, Stephen Buswell, David Carlisle, Giorgi Chavchanidze, Stéphane Dalmas, Stan Devitt, Angel Diaz, Sam Dooley, Roger Hunter, Patrick Ion, Michael Kohlhase, Azzeddine Lazrek, Paul Libbrecht, Bruce Miller, Robert Miner (deceased), Chris Rowley, Murray Sargent, Bruce Smith, Neil Soiffer, Robert Sutor, Stephen Watt</dd>
</dl>
<p>Please refer to the <a href="https://www.w3.org/Math/Documents/mathml3-errata.html"><strong>errata</strong></a>
for this document, which may include some normative corrections.</p>
<p>In addition to the <a href="Overview.html">HTML</a> version, this document is also available in these non-normative formats: <a href="Overview-d.html">diff marked HTML version</a>, <a href="Overview.xml">XHTML+MathML version</a>, <a href="mathml.html">single page HTML5+MathML version</a>, and <a href="mathml.pdf">PDF version</a>.</p>
<p>See also <a href="https://www.w3.org/2005/11/Translations/Query?titleMatch=MathML3"><strong>translations</strong></a>.</p>
<p class="copyright"><a href="https://www.w3.org/Consortium/Legal/ipr-notice#Copyright">Copyright</a> © 1998-2017 <a href="https://www.w3.org/"><abbr title="World Wide Web Consortium">W3C</abbr></a><sup>®</sup> (<a href="https://www.csail.mit.edu/"><abbr title="Massachusetts Institute of Technology">MIT</abbr></a>, <a href="https://www.ercim.eu/"><abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr></a>, <a href="https://www.keio.ac.jp/">Keio</a>, <a href="http://ev.buaa.edu.cn/">Beihang</a>). W3C <a href="https://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>, <a href="https://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a> and <a href="https://www.w3.org/Consortium/Legal/copyright-documents">document use</a> rules apply.</p>
<hr title="Separator for header">
</div>
<div>
<h2><a id="abstract"></a>Abstract</h2>
<p>
This specification defines the Mathematical Markup Language, or
<a id="td-mathml"></a>MathML. MathML is a markup language
for describing mathematical notation and capturing
both its structure and content. The goal of MathML is to enable
mathematics to be served, received, and processed on the World Wide
Web, just as <a id="td-html"></a>HTML has
enabled this functionality for text.
</p>
<p>
This specification of the markup language MathML is intended
primarily for a readership consisting of those who will be
developing or implementing renderers or editors using it, or
software that will communicate using MathML as a protocol for input
or output. It is <em>not</em> a User's Guide but rather a
reference document.
</p>
<p>
MathML can be used to encode both mathematical notation and
mathematical content. About thirty-eight of the MathML tags describe
abstract notational structures, while another about one hundred and
seventy provide a way of unambiguously specifying the intended
meaning of an expression. Additional chapters discuss how the MathML
content and presentation elements interact, and how MathML renderers
might be implemented and should interact with browsers. Finally,
this document addresses the issue of special characters used for
mathematics, their handling in MathML, their presence in Unicode,
and their relation to fonts.
</p>
<p>
While MathML is human-readable, authors typically will
use equation editors, conversion
programs, and other specialized software tools to generate
MathML. Several versions of such MathML tools exist,
both freely available software and commercial
products, and more are under development.
</p>
<p>MathML was originally specified as an XML application and most of the
examples in this specification assume that syntax. Other syntaxes are possible most
notably
<a href="appendixg-d.html#HTML5">[HTML5]</a> specifies the syntax for MathML in HTML. Unless explictly noted,
the examples in this specification are also valid HTML syntax.</p>
</div>
<div>
<h2><a id="status"></a>Status of this Document</h2>
<p><strong>This document is an editors' copy that has no official standing. (Date: 2019-01-26)</strong></p>
<p><em> This section describes the status of this document at the time
of its publication. Other documents may supersede this document. A
list of current W3C publications and the latest revision of this
technical report can be found in the <a href="https://www.w3.org/TR/">W3C technical reports index</a> at
https://www.w3.org/TR/.</em>
</p>
<p>
This document was produced by the <a href="https://www.w3.org/Math/">W3C Math Working Group</a> as
a <a href="https://www.w3.org/Consortium/Process/tr#RecsW3C">Recommendation</a>
and is part of the
W3C <a href="https://www.w3.org/Math/Activity">Math Activity</a>.
The goals of the W3C Math Working Group are discussed in the <a href="https://www.w3.org/Math/Documents/Charter2006.html"> W3C Math WG
Charter</a> (revised July 2006). The authors of this document are
the W3C Math Working Group members. A list of <a href="appendixe-d.html">participants in the W3C Math Working Group</a>
is available.
</p>
<p>This document has been reviewed by W3C Members, by software
developers, and by other W3C groups and interested parties, and is
endorsed by the Director as a W3C Recommendation. It is a stable
document and may be used as reference material or cited from another
document. W3C's role in making the Recommendation is to draw attention
to the specification and to promote its widespread deployment. This
enhances the functionality and interoperability of the Web.</p>
<p>
All reported errata to
the first edition have been addressed in this addition, and a full change log appears
in
<a href="appendixf-d.html">Appendix F Changes</a>. The diff-marked version linked in the frontmatter highlights all changes between
the first and second editions. In addition to incorporating errata, the main change
in this addition is to recognise that MathML parsing is also specified in <a href="appendixg-d.html#HTML5">[HTML5]</a> and where necessary to note where HTML and XML usage differ.
</p>
<p>
The Working Group maintains a comprehensive
<a href="https://www.w3.org/Math/testsuite/">Test Suite</a>. This
is publicly available and developers are encouraged to submit their results for display.
The <a href="https://www.w3.org/Math/testsuite/results/tests.html">Test Results</a>
are public. They show at least two interoperable implementations for each
essential test. Further details may be found in the
<a href="https://www.w3.org/Math/Documents/mml3-implementation-report.html">Implementation Report</a>.</p>
<p>
The MathML 2.0 (Second Edition) specification has been a W3C
Recommendation since 2001. After its
recommendation, a W3C Math Interest Group collected
reports of experience
with the deployment of MathML and identified issues with MathML that
might be ameliorated. The rechartering of a Math Working Group
did not signal any change in the overall design of MathML.
The major additions in MathML 3 are support for
bidirectional layout, better linebreaking and explicit positioning,
elementary math notations, and a new strict content MathML vocabulary
with well-defined semantics. The MathML 3 Specification has also been
restructured.
</p>
<p> This document was produced by a group operating under
the <a href="https://www.w3.org/Consortium/Patent-Policy-20040205/">5 February 2004 W3C Patent Policy</a>. W3C maintains a
<a href="https://www.w3.org/2004/01/pp-impl/35549/status" rel="disclosure">public list of any patent disclosures</a> made in connection with
the deliverables of the group; that page also includes instructions
for disclosing a patent. An individual who has actual knowledge of
a patent which the individual believes contains
<a href="https://www.w3.org/Consortium/Patent-Policy-20040205/#def-essential">Essential Claim(s)</a>
must disclose the information in accordance with
<a href="https://www.w3.org/Consortium/Patent-Policy-20040205/#sec-Disclosure">section 6 of the W3C Patent Policy</a>.</p>
<p>Public discussion of MathML and issues of support through the W3C
for mathematics on the Web takes place on <a href="mailto:[email protected]"> the public mailing list of the Math Working
Group</a> (<a href="https://lists.w3.org/Archives/Public/www-math/">list archives</a>).
To subscribe send an email to <a href="mailto:[email protected]">[email protected]</a>
with the word <code>subscribe</code> in the subject line.
<span class="diff-add">Alternatively, report an issue at this specification's
<a href="https://github.com/w3c/mathml">GitHub repository</a>.<a href="appendixf-d.html#d7e27703"><sub class="diff-link">F</sub></a></span>
</p>
<p>
The basic chapter structure of this document is based on the earlier
MathML 2.0 Recommendation <a href="appendixh-d.html#MathML2">[MathML2]</a>. That MathML 2.0
itself was a revision of the earlier W3C Recommendation MathML 1.01
<a href="appendixh-d.html#MathML1">[MathML1]</a>; MathML 3.0 is a revision of the W3C
Recommendation MathML 2.0. It differs from it in that all previous
chapters have been updated, some new
elements and attributes added and some
deprecated.
Much has been moved to separate documents containing explanatory
material, material on characters and entities and on the MathML DOM.
The discussion of character entities has led to the document
<em>XML Entity Definitions for Characters</em> <a href="appendixg-d.html#Entities">[Entities]</a>,
which is now a W3C Recommendation. The concern with
use of CSS with MathML has led to the document <em>A MathML for CSS Profile</em>
<a href="appendixh-d.html#MathMLforCSS">[MathMLforCSS]</a>, which was a W3C Recommendation
accompanying MathML 3.0.
</p>
<p>
The biggest differences from MathML 2.0 (Second Edition) are in Chapters 4 and 5,
although there have been
smaller improvements throughout the specification. A more detailed
description of changes from the previous Recommendation follows.
</p>
<ul>
<li>
<p>
Much of the non-normative explication
that formerly was found in Chapters 1 and 2, and many examples from
elsewhere in the previous MathML specifications, were removed
from the MathML3 specification and planned to be incorporated into a MathML Primer
to be prepared as a separate document. It is expected this will help
the use of this formal MathML3 specification as a reference document
in implementations, and offer the new user better help in
understanding MathML's deployment. The remaining content of Chapters 1
and 2 has been edited to reflect the changes elsewhere in the
document, and in the rapidly evolving Web environment. Some of the
text in them went back to early days of the Web and XML, and its
explanations are now commonplace.
</p>
</li>
<li>
<p>
Chapter 3, on presentation-oriented markup, adds new material on linebreaking,
and on markup for elementary math notations used in many
countries (<code>mstack</code>, <code>mlongdiv</code> and other
associated elements). Other changes include revisions to
the <code>mglyph</code>, <code>mpadded</code> and <code>maction</code>
elements and significant unification and cleanup of attribute
values.
Earlier work, as recorded in the W3C Note <a href="https://www.w3.org/TR/2006/NOTE-arabic-math-20060131/">Arabic
mathematical notation</a>, has allowed clarification of the
relationship with bidirectional text and examples
with RTL text have been added.
</p>
</li>
<li>
<p>
Chapter 4, on content-oriented markup, contains major changes and additions.
The meaning of the actual content remains as before in principle,
but a lot of work has been done on expressing it better. A few new elements have been
added.
</p>
</li>
<li>
<p>
Chapter 5 has been refined as its purpose has been further
clarified to deal with the mixing of markup languages. This chapter deals,
in particular, with interrelations of parts of the
MathML specification, especially with presentation and content
markup.
</p>
</li>
<li>
<p>
Chapter 6 is a new addition which deals with the issues of interaction
of MathML with a host environment. This chapter deals with interrelations
of the MathML specification with XML and HTML, but in the context of deployment
on the Web. In particular there is a discussion of the interaction of CSS
with MathML.
</p>
</li>
<li>
<p>
Chapter 7 replaces the previous Chapter 6, and has been rewritten
and reorganized to reflect the new
situation in regard to Unicode, and the changed
W3C context with regard to named character entities. The
new W3C specification <em>XML Entity Definitions for
Characters</em>, which incorporates those used for mathematics has
become a a W3C Recommendation, <a href="appendixg-d.html#Entities">[Entities]</a>.</p>
</li>
<li>
<p>
The Appendices, of which there are eight shown, have been
reworked.
Appendix A now contains the new RelaxNG schema
for MathML3 as well as discussion of MathML3 DTD issues.
Appendix B addresses media types associated with MathML and
implicitly constitutes a request for the registration of three new ones,
as is now standard for work from the W3C.
Appendix C contains a new simplified and reconsidered Operator Dictionary.
Appendices D, E, F, G and H contain similar non-normative material to
that in the previous specification, now appropriately updated.
</p>
</li>
<li>
<p>
A fuller discussion of the document's evolution can be found in
<a href="appendixf-d.html">Appendix F Changes</a>.
</p>
</li>
</ul>
</div>
<nav id="toc">
<h2 id="tochead">Table of Contents</h2>
<ol class="toc">
<li><a href="chapter1-d.html"><span class="secno">1 </span> Introduction</a>
<ol class="toc">
<li><a href="chapter1-d.html#intro.notation"><span class="secno">1.1 </span> Mathematics and its Notation</a>
</li>
<li><a href="chapter1-d.html#intro.origin"><span class="secno">1.2 </span> Origins and Goals</a>
<ol class="toc">
<li><a href="chapter1-d.html#intro.goals"><span class="secno">1.2.1 </span> Design Goals of MathML</a>
</li>
</ol>
</li>
<li><a href="chapter1-d.html#intro.overview"><span class="secno">1.3 </span> Overview</a>
</li>
<li><a href="chapter1-d.html#intro.example"><span class="secno">1.4 </span> A First Example</a>
</li>
</ol>
</li>
<li><a href="chapter2-d.html"><span class="secno">2 </span> MathML Fundamentals</a>
<ol class="toc">
<li><a href="chapter2-d.html#fund.syntax"><span class="secno">2.1 </span> MathML Syntax and Grammar</a>
<ol class="toc">
<li><a href="chapter2-d.html#fund.xmlgeneral"><span class="secno">2.1.1 </span> General Considerations</a>
</li>
<li><a href="chapter2-d.html#interf.namespace"><span class="secno">2.1.2 </span> MathML and Namespaces</a>
</li>
<li><a href="chapter2-d.html#fund.xmlsyntax"><span class="secno">2.1.3 </span> Children versus Arguments</a>
</li>
<li><a href="chapter2-d.html#fund.renderingmodel"><span class="secno">2.1.4 </span> MathML and Rendering</a>
</li>
<li><a href="chapter2-d.html#fund.attval"><span class="secno">2.1.5 </span> MathML Attribute Values</a>
<ol class="toc">
<li><a href="chapter2-d.html#id.2.1.5.1"><span class="secno">2.1.5.1 </span> Syntax notation used in the MathML specification</a>
</li>
<li><a href="chapter2-d.html#fund.units"><span class="secno">2.1.5.2 </span> Length Valued Attributes</a>
</li>
<li><a href="chapter2-d.html#fund.color"><span class="secno">2.1.5.3 </span> Color Valued Attributes</a>
</li>
<li><a href="chapter2-d.html#fund.defaults"><span class="secno">2.1.5.4 </span> Default values of attributes</a>
</li>
</ol>
</li>
<li><a href="chapter2-d.html#fund.globatt"><span class="secno">2.1.6 </span> Attributes Shared by all MathML Elements</a>
</li>
<li><a href="chapter2-d.html#fund.collapse"><span class="secno">2.1.7 </span> Collapsing Whitespace in Input</a>
</li>
</ol>
</li>
<li><a href="chapter2-d.html#interf.toplevel"><span class="secno">2.2 </span> The Top-Level
<code><math></code> Element</a>
<ol class="toc">
<li><a href="chapter2-d.html#interf.toplevel.atts"><span class="secno">2.2.1 </span> Attributes</a>
</li>
<li><a href="chapter2-d.html#id.2.2.2"><span class="secno">2.2.2 </span> Deprecated Attributes</a>
</li>
</ol>
</li>
<li><a href="chapter2-d.html#interf.genproc"><span class="secno">2.3 </span> Conformance</a>
<ol class="toc">
<li><a href="chapter2-d.html#fund.mathmlconf"><span class="secno">2.3.1 </span> MathML Conformance</a>
<ol class="toc">
<li><a href="chapter2-d.html#interf.testsuite"><span class="secno">2.3.1.1 </span> MathML Test Suite and Validator</a>
</li>
<li><a href="chapter2-d.html#interf.deprec"><span class="secno">2.3.1.2 </span> Deprecated MathML 1.x and MathML 2.x Features</a>
</li>
<li><a href="chapter2-d.html#interf.extension"><span class="secno">2.3.1.3 </span> MathML
Extension Mechanisms and Conformance</a>
</li>
</ol>
</li>
<li><a href="chapter2-d.html#interf.error"><span class="secno">2.3.2 </span> Handling of Errors</a>
</li>
<li><a href="chapter2-d.html#interf.unspecified"><span class="secno">2.3.3 </span> Attributes for unspecified data</a>
</li>
</ol>
</li>
</ol>
</li>
<li><a href="chapter3-d.html"><span class="secno">3 </span> Presentation Markup</a>
<ol class="toc">
<li><a href="chapter3-d.html#presm.intro"><span class="secno">3.1 </span> Introduction</a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.1.1"><span class="secno">3.1.1 </span> What Presentation Elements Represent</a>
</li>
<li><a href="chapter3-d.html#id.3.1.2"><span class="secno">3.1.2 </span> Terminology Used In This Chapter</a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.1.2.1"><span class="secno">3.1.2.1 </span> Types of presentation elements</a>
</li>
<li><a href="chapter3-d.html#id.3.1.2.2"><span class="secno">3.1.2.2 </span> Terminology for other classes of elements and their relationships</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.reqarg"><span class="secno">3.1.3 </span> Required Arguments</a>
<ol class="toc">
<li><a href="chapter3-d.html#presm.inferredmrow"><span class="secno">3.1.3.1 </span> Inferred <code><mrow></code>s</a>
</li>
<li><a href="chapter3-d.html#id.3.1.3.2"><span class="secno">3.1.3.2 </span> Table of argument requirements</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#id.3.1.4"><span class="secno">3.1.4 </span> Elements with Special Behaviors</a>
</li>
<li><a href="chapter3-d.html#presm.bidi"><span class="secno">3.1.5 </span> Directionality</a>
<ol class="toc">
<li><a href="chapter3-d.html#presm.bidi.math"><span class="secno">3.1.5.1 </span> Overall Directionality of Mathematics Formulas</a>
</li>
<li><a href="chapter3-d.html#presm.bidi.token"><span class="secno">3.1.5.2 </span> Bidirectional Layout in Token Elements</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.scriptlevel"><span class="secno">3.1.6 </span> Displaystyle and Scriptlevel</a>
</li>
<li><a href="chapter3-d.html#presm.linebreaking"><span class="secno">3.1.7 </span> Linebreaking of Expressions</a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.1.7.1"><span class="secno">3.1.7.1 </span> Control of Linebreaks</a>
</li>
<li><a href="chapter3-d.html#presm.lbalgorithm"><span class="secno">3.1.7.2 </span> Automatic Linebreaking Algorithm (Informative)</a>
</li>
<li><a href="chapter3-d.html#presm.inline.lbalgorithm"><span class="secno">3.1.7.3 </span> Linebreaking Algorithm for Inline Expressions (Informative)</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.warnfinetuning"><span class="secno">3.1.8 </span> Warning about fine-tuning of presentation</a>
<ol class="toc">
<li><a href="chapter3-d.html#presm.warntweaking"><span class="secno">3.1.8.1 </span> Warning: non-portability of tweaking</a>
</li>
<li><a href="chapter3-d.html#presm.warnspacing"><span class="secno">3.1.8.2 </span> Warning: spacing should not be used to convey meaning</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.summary"><span class="secno">3.1.9 </span> Summary of Presentation Elements</a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.1.9.1"><span class="secno">3.1.9.1 </span> Token Elements</a>
</li>
<li><a href="chapter3-d.html#id.3.1.9.2"><span class="secno">3.1.9.2 </span> General Layout Schemata</a>
</li>
<li><a href="chapter3-d.html#id.3.1.9.3"><span class="secno">3.1.9.3 </span> Script and Limit Schemata</a>
</li>
<li><a href="chapter3-d.html#id.3.1.9.4"><span class="secno">3.1.9.4 </span> Tables and Matrices</a>
</li>
<li><a href="chapter3-d.html#id.3.1.9.5"><span class="secno">3.1.9.5 </span> Elementary Math Layout</a>
</li>
<li><a href="chapter3-d.html#id.3.1.9.6"><span class="secno">3.1.9.6 </span> Enlivening Expressions</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.presatt"><span class="secno">3.1.10 </span> Mathematics style attributes common to presentation elements</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.tokel"><span class="secno">3.2 </span> Token Elements</a>
<ol class="toc">
<li><a href="chapter3-d.html#presm.tokenchars"><span class="secno">3.2.1 </span>
Token Element Content Characters, <code><mglyph/></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#presm.symbolchars"><span class="secno">3.2.1.1 </span> Alphanumeric symbol characters</a>
</li>
<li><a href="chapter3-d.html#presm.mglyph"><span class="secno">3.2.1.2 </span> Using images to represent
symbols <code><mglyph/></code></a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.commatt"><span class="secno">3.2.2 </span> Mathematics style attributes common to token elements</a>
<ol class="toc">
<li><a href="chapter3-d.html#presm.deprecatt"><span class="secno">3.2.2.1 </span> Deprecated style attributes on token elements</a>
</li>
<li><a href="chapter3-d.html#presm.html.insertion"><span class="secno">3.2.2.2 </span> Embedding HTML in MathML</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mi"><span class="secno">3.2.3 </span> Identifier <code><mi></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.2.3.1"><span class="secno">3.2.3.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.2.3.2"><span class="secno">3.2.3.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#presm.mi.examples"><span class="secno">3.2.3.3 </span> Examples</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mn"><span class="secno">3.2.4 </span> Number <code><mn></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.2.4.1"><span class="secno">3.2.4.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.2.4.2"><span class="secno">3.2.4.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#presm.mn.examples"><span class="secno">3.2.4.3 </span> Examples</a>
</li>
<li><a href="chapter3-d.html#presm.not.single.mn"><span class="secno">3.2.4.4 </span> Numbers that should not be written
using <code><mn></code> alone</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mo"><span class="secno">3.2.5 </span> Operator, Fence, Separator or Accent
<code><mo></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.2.5.1"><span class="secno">3.2.5.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#presm.mo.attrs"><span class="secno">3.2.5.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.2.5.3"><span class="secno">3.2.5.3 </span> Examples with ordinary operators</a>
</li>
<li><a href="chapter3-d.html#id.3.2.5.4"><span class="secno">3.2.5.4 </span> Examples with fences and separators</a>
</li>
<li><a href="chapter3-d.html#presm.invisibleops"><span class="secno">3.2.5.5 </span> Invisible operators</a>
</li>
<li><a href="chapter3-d.html#id.3.2.5.6"><span class="secno">3.2.5.6 </span> Names for other special operators</a>
</li>
<li><a href="chapter3-d.html#id.3.2.5.7"><span class="secno">3.2.5.7 </span> Detailed rendering rules for <code><mo></code> elements</a>
</li>
<li><a href="chapter3-d.html#presm.op.stretch"><span class="secno">3.2.5.8 </span> Stretching of operators, fences and accents</a>
</li>
<li><a href="chapter3-d.html#presm.mo.linebreaks"><span class="secno">3.2.5.9 </span> Examples of Linebreaking</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mtext"><span class="secno">3.2.6 </span> Text <code><mtext></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.2.6.1"><span class="secno">3.2.6.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.2.6.2"><span class="secno">3.2.6.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.2.6.3"><span class="secno">3.2.6.3 </span> Examples</a>
</li>
<li><a href="chapter3-d.html#presm.mixtextmath"><span class="secno">3.2.6.4 </span> Mixing text and mathematics</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mspace"><span class="secno">3.2.7 </span> Space <code><mspace/></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.2.7.1"><span class="secno">3.2.7.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.2.7.2"><span class="secno">3.2.7.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.2.7.3"><span class="secno">3.2.7.3 </span> Examples</a>
</li>
<li><a href="chapter3-d.html#id.3.2.7.4"><span class="secno">3.2.7.4 </span> Definition of space-like elements</a>
</li>
<li><a href="chapter3-d.html#id.3.2.7.5"><span class="secno">3.2.7.5 </span> Legal grouping of space-like elements</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.ms"><span class="secno">3.2.8 </span> String Literal <code><ms></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.2.8.1"><span class="secno">3.2.8.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.2.8.2"><span class="secno">3.2.8.2 </span> Attributes</a>
</li>
</ol>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.genlayout"><span class="secno">3.3 </span> General Layout Schemata</a>
<ol class="toc">
<li><a href="chapter3-d.html#presm.mrow"><span class="secno">3.3.1 </span> Horizontally Group Sub-Expressions
<code><mrow></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.3.1.1"><span class="secno">3.3.1.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.3.1.2"><span class="secno">3.3.1.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.3.1.3"><span class="secno">3.3.1.3 </span> Proper grouping of sub-expressions using <code><mrow></code></a>
</li>
<li><a href="chapter3-d.html#id.3.3.1.4"><span class="secno">3.3.1.4 </span> Examples</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mfrac"><span class="secno">3.3.2 </span> Fractions <code><mfrac></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.3.2.1"><span class="secno">3.3.2.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.3.2.2"><span class="secno">3.3.2.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.3.2.3"><span class="secno">3.3.2.3 </span> Examples</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mroot"><span class="secno">3.3.3 </span> Radicals <code><msqrt></code>, <code><mroot></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.3.3.1"><span class="secno">3.3.3.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.3.3.2"><span class="secno">3.3.3.2 </span> Attributes</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mstyle"><span class="secno">3.3.4 </span> Style Change <code><mstyle></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.3.4.1"><span class="secno">3.3.4.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#presm.mstyle.attrs"><span class="secno">3.3.4.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.3.4.3"><span class="secno">3.3.4.3 </span> Examples</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.merror"><span class="secno">3.3.5 </span> Error Message <code><merror></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.3.5.1"><span class="secno">3.3.5.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.3.5.2"><span class="secno">3.3.5.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.3.5.3"><span class="secno">3.3.5.3 </span> Example</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mpadded"><span class="secno">3.3.6 </span> Adjust Space Around Content
<code><mpadded></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.3.6.1"><span class="secno">3.3.6.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#presm.mpaddedatt"><span class="secno">3.3.6.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.3.6.3"><span class="secno">3.3.6.3 </span> Meanings of size and position attributes</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mphantom"><span class="secno">3.3.7 </span> Making Sub-Expressions Invisible <code><mphantom></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.3.7.1"><span class="secno">3.3.7.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.3.7.2"><span class="secno">3.3.7.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.3.7.3"><span class="secno">3.3.7.3 </span> Examples</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mfenced"><span class="secno">3.3.8 </span> Expression Inside Pair of Fences
<code><mfenced></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.3.8.1"><span class="secno">3.3.8.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.3.8.2"><span class="secno">3.3.8.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.3.8.3"><span class="secno">3.3.8.3 </span> Examples</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.menclose"><span class="secno">3.3.9 </span> Enclose Expression Inside Notation
<code><menclose></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.3.9.1"><span class="secno">3.3.9.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.3.9.2"><span class="secno">3.3.9.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.3.9.3"><span class="secno">3.3.9.3 </span> Examples</a>
</li>
</ol>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.scrlim"><span class="secno">3.4 </span> Script and Limit Schemata</a>
<ol class="toc">
<li><a href="chapter3-d.html#presm.msub"><span class="secno">3.4.1 </span> Subscript <code><msub></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.4.1.1"><span class="secno">3.4.1.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.4.1.2"><span class="secno">3.4.1.2 </span> Attributes</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.msup"><span class="secno">3.4.2 </span> Superscript <code><msup></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.4.2.1"><span class="secno">3.4.2.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.4.2.2"><span class="secno">3.4.2.2 </span> Attributes</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.msubsup"><span class="secno">3.4.3 </span> Subscript-superscript Pair <code><msubsup></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.4.3.1"><span class="secno">3.4.3.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#presm.subsupatt"><span class="secno">3.4.3.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.4.3.3"><span class="secno">3.4.3.3 </span> Examples</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.munder"><span class="secno">3.4.4 </span> Underscript <code><munder></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.4.4.1"><span class="secno">3.4.4.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.4.4.2"><span class="secno">3.4.4.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.4.4.3"><span class="secno">3.4.4.3 </span> Examples</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mover"><span class="secno">3.4.5 </span> Overscript <code><mover></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.4.5.1"><span class="secno">3.4.5.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.4.5.2"><span class="secno">3.4.5.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.4.5.3"><span class="secno">3.4.5.3 </span> Examples</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.munderover"><span class="secno">3.4.6 </span> Underscript-overscript Pair
<code><munderover></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.4.6.1"><span class="secno">3.4.6.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.4.6.2"><span class="secno">3.4.6.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.4.6.3"><span class="secno">3.4.6.3 </span> Examples</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mmultiscripts"><span class="secno">3.4.7 </span> Prescripts and Tensor Indices
<code><mmultiscripts></code>,
<code><mprescripts/></code>,
<code><none/></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.4.7.1"><span class="secno">3.4.7.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.4.7.2"><span class="secno">3.4.7.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.4.7.3"><span class="secno">3.4.7.3 </span> Examples</a>
</li>
</ol>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.tabmat"><span class="secno">3.5 </span> Tabular Math</a>
<ol class="toc">
<li><a href="chapter3-d.html#presm.mtable"><span class="secno">3.5.1 </span> Table or Matrix
<code><mtable></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.5.1.1"><span class="secno">3.5.1.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#presm.mtable.attrs"><span class="secno">3.5.1.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.5.1.3"><span class="secno">3.5.1.3 </span> Examples</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mtr"><span class="secno">3.5.2 </span> Row in Table or Matrix <code><mtr></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.5.2.1"><span class="secno">3.5.2.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.5.2.2"><span class="secno">3.5.2.2 </span> Attributes</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mlabeledtr"><span class="secno">3.5.3 </span> Labeled Row in Table or Matrix
<code><mlabeledtr></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.5.3.1"><span class="secno">3.5.3.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.5.3.2"><span class="secno">3.5.3.2 </span> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.5.3.3"><span class="secno">3.5.3.3 </span> Equation Numbering</a>
</li>
<li><a href="chapter3-d.html#id.3.5.3.4"><span class="secno">3.5.3.4 </span> Example</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.mtd"><span class="secno">3.5.4 </span> Entry in Table or Matrix <code><mtd></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.5.4.1"><span class="secno">3.5.4.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#presm.mtdatts"><span class="secno">3.5.4.2 </span> Attributes</a>
</li>
</ol>
</li>
<li><a href="chapter3-d.html#presm.malign"><span class="secno">3.5.5 </span> Alignment Markers
<code><maligngroup/></code>, <code><malignmark/></code></a>
<ol class="toc">
<li><a href="chapter3-d.html#id.3.5.5.1"><span class="secno">3.5.5.1 </span> Description</a>
</li>
<li><a href="chapter3-d.html#id.3.5.5.2"><span class="secno">3.5.5.2 </span> Specifying alignment groups</a>
</li>
<li><a href="chapter3-d.html#id.3.5.5.3"><span class="secno">3.5.5.3 </span> Table cells that are not divided into alignment groups</a>
</li>
<li><a href="chapter3-d.html#id.3.5.5.4"><span class="secno">3.5.5.4 </span> Specifying alignment points using <code><malignmark/></code></a>
</li>
<li><a href="chapter3-d.html#id.3.5.5.5"><span class="secno">3.5.5.5 </span> <code><malignmark/></code> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.5.5.6"><span class="secno">3.5.5.6 </span> <code><maligngroup/></code> Attributes</a>
</li>
<li><a href="chapter3-d.html#id.3.5.5.7"><span class="secno">3.5.5.7 </span> Inheritance of groupalign values</a>
</li>
<li><a href="chapter3-d.html#id.3.5.5.8"><span class="secno">3.5.5.8 </span> MathML representation of an alignment example</a>
</li>
<li><a href="chapter3-d.html#id.3.5.5.9"><span class="secno">3.5.5.9 </span> Further details of alignment elements</a>
</li>