forked from latex3/unicode-math
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathunicode-math-doc.tex
1493 lines (1245 loc) · 66.1 KB
/
unicode-math-doc.tex
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
% !TEX TS-program = XeLaTeX
\providecommand\DOCUMENTEND{T}
\documentclass[a4paper]{ltxdoc}
\if \DOCUMENTEND T \OnlyDescription \fi
\makeatletter
\GetFileInfo{unicode-math.dtx}
\let\umfiledate\filedate
\let\umfileversion\fileversion
\CheckSum{0}
\EnableCrossrefs
\CodelineIndex
\errorcontextlines=999
\def\@dotsep{1000}
\setcounter{tocdepth}{2}
\setlength\columnseprule{0.4pt}
\renewcommand\tableofcontents{\relax
\begin{multicols}{2}[\section*{\contentsname}]\relax
\@starttoc{toc}\relax
\end{multicols}}
\setcounter{IndexColumns}{2}
\renewenvironment{theglossary}
{\small\list{}{}
\item\relax
\glossary@prologue\GlossaryParms
\let\item\@idxitem \ignorespaces
\def\pfill{\hspace*{\fill}}}
{\endlist}
\usepackage[svgnames]{xcolor}
\usepackage{array,booktabs,calc,enumitem,fancyvrb,graphicx,ifthen,longtable,refstyle,subfig,topcapt,url,varioref,underscore}
\setcounter{LTchunksize}{100}
\usepackage[slash-delimiter=frac,nabla=literal]{unicode-math}
\usepackage{metalogo,hologo}
\fvset{fontsize=\small,xleftmargin=2em}
\usepackage[it]{titlesec}
\setmainfont{texgyrepagella}%
[
Extension = .otf ,
UprightFont = *-regular ,
ItalicFont = *-italic ,
BoldFont = *-bold ,
BoldItalicFont = *-bolditalic ,
]
\setsansfont{Iwona}%
[
Scale=MatchLowercase,
Extension = .otf,
UprightFont = *-Regular,
ItalicFont = *-Italic,
BoldFont = *-Bold,
BoldItalicFont = *-BoldItalic,
]
\setmonofont{Inconsolatazi4-Regular.otf}%
[
Scale=MatchLowercase,
BoldFont=Inconsolatazi4-Bold.otf
]
\setmathfont{texgyrepagella-math.otf}
\setmathfont[version=xits]{xits-math.otf}
\newfontface\umfont{xits-math.otf}
\usepackage{hypdoc}
\hypersetup{linktocpage}
% work around some issue turning | into "j" inside mathsf in the definition of \Module:
% (also prettify)
\def\Module#1{{\footnotesize\color{red}$\langle$\texttt{#1}$\rangle$}}
\usepackage{minitoc}
\linespread{1.1}
\frenchspacing
\definecolor{niceblue}{rgb}{0.2,0.4,0.8}
\def\theCodelineNo{\textcolor{niceblue}{\sffamily\tiny\arabic{CodelineNo}}}
\newcommand*\name[1]{{#1}}
\newcommand*\pkg[1]{\textsf{#1}}
\newcommand*\feat[1]{\texttt{#1}}
\newcommand*\opt[1]{\texttt{#1}}
\newcommand*\note[1]{\unskip\footnote{#1}}
\let\latin\textit
\def\eg{\latin{e.g.}}
\def\Eg{\latin{E.g.}}
\def\ie{\latin{i.e.}}
\def\etc{\@ifnextchar.{\latin{etc}}{\latin{etc.}\@}}
\def\STIX{\textsc{stix}}
\def\MacOSX{Mac~OS~X}
\def\ascii{\textsc{ascii}}
\def\OMEGA{Omega}
\newcounter{argument}
\makeatletter
\g@addto@macro\endmacro{\setcounter{argument}{0}}
\makeatother
\newcommand*\darg[1]{%
\stepcounter{argument}%
{\ttfamily\char`\#\theargument~:~}#1\par\noindent\ignorespaces
}
\newcommand*\doarg[1]{%
\stepcounter{argument}%
{\ttfamily\makebox[0pt][r]{[}\char`\#\theargument]:~}#1\par\noindent\ignorespaces
}
\newcommand\codeline[1]{\par{\centering#1\par\noindent}\ignorespaces}
\newcommand\unichar[1]{\textsc{u}+\texttt{\small#1}}
\setlength\parindent{2em}
\def \MakePrivateLetters {%
\catcode`\@=11\relax
\catcode`\_=11\relax
\catcode`\:=11\relax
}
\def\partname{Part}
\makeatother
\begin{document}
\title{Experimental Unicode mathematical typesetting: The \pkg{unicode-math} package}
\author{Will Robertson, Philipp Stephani and Khaled Hosny\\
\texttt{[email protected]}}
\date{\umfiledate \qquad \umfileversion}
\maketitle
\begin{abstract}
\noindent
This document describes the \pkg{unicode-math} package, which is
intended as an implementation of Unicode
maths for \LaTeX\ using the \XeTeX\ and Lua\TeX\ typesetting engines.
With this package, changing maths fonts is as easy as changing
text fonts --- and there are more and more maths fonts appearing now.
Maths input can also be simplified with Unicode since literal glyphs may be
entered instead of control sequences in your document source.
The package provides support for both \XeTeX\ and Lua\TeX. The different
engines provide differing levels of support for Unicode maths.
Please let us know of any troubles.
Alongside this documentation file, you should be able to find a minimal
example demonstrating the use of the package,
`\texttt{unimath-example.ltx}'. It also comes with a separate document,
`\texttt{unimath-symbols.pdf}',
containing a complete listing of mathematical symbols defined by
\pkg{unicode-math}, including comparisons between different fonts.
Finally, while the STIX fonts may be used with this package, accessing
their alphabets in their `private user area' is not yet supported.
(Of these additional alphabets there is a separate caligraphic design
distinct to the script design already included.)
Better support for the STIX fonts is planned for an upcoming revision of the
package after any problems have been ironed out with the initial version.
\end{abstract}
\doparttoc\faketableofcontents
\newpage
\part{User documentation}
\parttoc
\clearpage
\section{Introduction}
This document describes the \pkg{unicode-math} package, which is an
\emph{experimental} implementation of a macro to Unicode glyph encoding for
mathematical characters.
Users who desire to specify maths alphabets only (Greek and Latin letters,
and Arabic numerals)
may wish to use Andrew Moschou's \pkg{mathspec} package instead.
(\XeTeX-only at time of writing.)
\section{Acknowledgements}
Many thanks to:
Microsoft for developing the mathematics extension to OpenType as part of
Microsoft Office~2007;
Jonathan Kew for implementing Unicode math support in \XeTeX;
Taco Hoekwater for implementing Unicode math support in \LuaTeX;
Barbara Beeton for her prodigious effort compiling the definitive list of Unicode math
glyphs and their \LaTeX\ names (inventing them where necessary), and also
for her thoughtful replies to my sometimes incessant questions;
Philipp Stephani for extending the package to support \LuaTeX.
Ross Moore and Chris Rowley have provided moral and technical support
from the very early days with great insight into the issues we face trying
to extend and use \TeX\ in the future.
Apostolos Syropoulos, Joel Salomon, Khaled Hosny, and Mariusz Wodzicki
have been fantastic beta testers.
\section{Getting started}
Load \pkg{unicode-math} as a regular \LaTeX\ package. It should be loaded
after any other maths or font-related package in case it needs to overwrite
their definitions. Here's an example:
\begin{Verbatim}
\usepackage{amsmath} % if desired
\usepackage{unicode-math}
\setmathfont{Asana-Math.otf}
\end{Verbatim}
Three OpenType maths fonts are included by default in \TeX\ Live 2011:
Latin Modern Math, Asana Math, and XITS Math.
These can be loaded directly with their filename
with both \XeLaTeX\ and \LuaLaTeX; resp.,
\begin{Verbatim}
\setmathfont{latinmodern-math.otf}
\setmathfont{Asana-Math.otf}
\setmathfont{xits-math.otf}
\end{Verbatim}
Other OpenType maths fonts may be loaded in the usual way; please see the
\pkg{fontspec} documentation for more information.
Once the package is loaded, traditional TFM-based fonts are not supported any more;
you can only switch to a different OpenType math font using the \cs{setmathfont} command.
If you do not load an OpenType maths font before |\begin{document}|, Latin Modern Math (see above) will be loaded automatically.
\subsection{New commands}
\textbf{New v0.8:}
\pkg{unicode-math} provides the following commands to select specific `alphabets' within the unicode maths font: (usage, e.g.: |$\symbfsf{g}$|${}\to\symbfsf{g}$)
\begin{quote}
\ExplSyntaxOn
\clist_map_inline:nn {
normal, literal, up, bfup, bfit, sfup, sfit, bfsfup, bfsfit, bfsf,
bb, bbit, scr, bfscr, cal, bfcal, frak, bffrak,
up, sf, bf, tt, it,
}{\cs{sym#1}~}
\ExplSyntaxOff
\end{quote}
Many of these are also defined with `familiar' synonyms:
\begin{quote}
\ExplSyntaxOn
\clist_map_inline:nn {
normal, bb, bbit, scr, bfscr, cal, bfcal, frak, bffrak,
bfup, bfit, sfup, sfit, bfsfup, bfsfit, bfsf
}{\mbox{\cs{math#1}}~}
\ExplSyntaxOff
\end{quote}
So what about \cs{mathup}, \cs{mathit}, \cs{mathbf}, \cs{mathsf}, and \cs{mathtt}?
(N.B.: \cs{mathrm} is defined as a synonym for \cs{mathup}, but the latter is prefered as it is a script-agnostic term.)
These commands have `overloaded' meanings in \LaTeX, and it's important to consider the subtle differences between, e.g., \cs{symbf} and \cs{mathbf}.
The former switches to single-letter mathematical symbols, whereas the second switches to a text font that behaves correctly in mathematics but should be used for multi-letter identifiers.
These four commands (and \cs{mathrm}) are defined in the traditional \LaTeX\ manner.
Further details are discussed in \secref{mathselect}.
Additional similar commands can be defined using
\begin{Verbatim}
\setmathfontface\mathfoo{...}
\end{Verbatim}
\subsection{Package options}
Package options may be set when the package as loaded or at any later
stage with the \cs{unimathsetup} command. Therefore, the following two
examples are equivalent:
\begin{Verbatim}
\usepackage[math-style=TeX]{unicode-math}
% OR
\usepackage{unicode-math}
\unimathsetup{math-style=TeX}
\end{Verbatim}
Note, however, that some package options affects how maths is initialised
and changing an option such as |math-style| will not take effect until a
new maths font is set up.
Package options may \emph{also} be used when declaring new maths fonts,
passed via options to the \cs{setmathfont} command.
Therefore, the following two examples are equivalent:
\begin{Verbatim}
\unimathsetup{math-style=TeX}
\setmathfont{Cambria Math}
% OR
\setmathfont{Cambria Math}[math-style=TeX]
\end{Verbatim}
A short list of package options is shown in \tabref{pkgopt}.
See following sections for more information.
\begin{table}\centering
\topcaption{Package options.}
\tablabel{pkgopt}
\begin{tabular}{lll}
\toprule
Option & Description & See\dots \\
\midrule
|math-style| & Style of letters & \secref{math-style} \\
|bold-style| & Style of bold letters & \secref{bold-style} \\
|sans-style| & Style of sans serif letters & \secref{sans-style} \\
|nabla| & Style of the nabla symbol & \secref{nabla} \\
|partial| & Style of the partial symbol & \secref{partial} \\
|colon| & Behaviour of \cs{colon} & \secref{colon} \\
|slash-delimiter| & Glyph to use for `stretchy' slash & \secref{slash-delimiter} \\
\bottomrule
\end{tabular}
\end{table}
\section{Unicode maths font setup}
In the ideal case, a single Unicode font will contain all maths glyphs we
need. The file |unicode-math-table.tex| (based on Barbara Beeton's \STIX\ table)
provides the mapping between Unicode
maths glyphs and macro names (all 3298 — or however many — of them!). A
single command
\codeline{\cmd\setmathfont\marg{font name}\oarg{font features}}
implements this for every every symbol and alphabetic variant.
That means |x| to $x$, |\xi| to $\xi$, |\leq| to $\leq$, etc., |\symscr{H}|
to $\symscr{H}$ and so on, all for Unicode glyphs within a single font.
This package deals well with Unicode characters for maths
input. This includes using literal Greek letters in formulae,
resolving to upright or italic depending on preference.
Font features specific to \pkg{unicode-math} are shown in \tabref{mathfontfeatures}.
Package options (see \tabref{pkgopt}) may also be used.
Other \pkg{fontspec} features are also valid.
\begin{table}\centering
\topcaption{Maths font options.}
\tablabel{mathfontfeatures}
\begin{tabular}{lll}
\toprule
Option & Description & See\dots \\
\midrule
|range| & Style of letters & \secref{range} \\
|script-font| & Font to use for sub- and super-scripts & \secref{sscript} \\
|script-features| & Font features for sub- and super-scripts & \secref{sscript} \\
|sscript-font| & Font to use for nested sub- and super-scripts & \secref{sscript} \\
|sscript-features| & Font features for nested sub- and super-scripts & \secref{sscript} \\
\bottomrule
\end{tabular}
\end{table}
\subsection{Using multiple fonts}
\seclabel{range}
There will probably be few cases where a single Unicode maths font suffices
(simply due to glyph coverage). The \STIX\ font comes to mind as a
possible exception. It will therefore be necessary to delegate specific
Unicode ranges of glyphs to separate fonts:
\codeline{\cmd\setmathfont\marg{font name}|[range=|\meta{unicode range}|,|\meta{font features}|]|}
where \meta{unicode range} is a comma-separated list of Unicode slot numbers and ranges such as |{"27D0-"27EB,"27FF,"295B-"297F}|.
Note that \TeX's syntax for accessing the slot number of a character, such as |`\+|, will also work here.
You may also use the macro for accessing the glyph, such as \cs{int}, or whole collection of symbols with the same math type, such as \cs{mathopen}, or complete math styles such as \cs{symbb}.
(Only numerical slots, however, can be used in ranged declarations.)
\subsubsection{Control over alphabet ranges}
As discussed earlier, Unicode mathematics consists of a number of `alphabet styles' within a single font. In \pkg{unicode-math}, these ranges are indicated with the following (hopefully self-explanatory) labels:
\begin{quote}\ttfamily
\ExplSyntaxOn
\clist_use:Nn \g__um_named_ranges_clist {\,,\,~}
\ExplSyntaxOff
\end{quote}
Fonts can be selected for specified ranges only using the following syntax, in which case all other maths font setup remains untouched:
\begin{itemize}
\item |[range=bb]| to use the font for `|bb|' letters only.
\item |[range=bfsfit/{greek,Greek}]| for Greek lowercase and uppercase only (also with |latin|, |Latin|, |num| as possible options for Latin lower-/upper-case and numbers, resp.).
\item |[range=up->sfup]| to map to different output styles.
\end{itemize}
Note that `meta-styles' such as `|bf|' and `|sf|' are not included here since they are context dependent. Use |[range=bfup]| and |[range=bfit]| to effect changes to the particular ranges selected by `|bf|' (and similarly for `|sf|').
If a particular math style is not defined in the font, we fall back onto the lower-base plane (i.e., `upright') glyphs.
Therefore, to use an \ascii-encoded fractur font, for example, write
\begin{Verbatim}
\setmathfont{SomeFracturFont}[range=frak]
\end{Verbatim}
and because the math plane fractur glyphs will be missing, \pkg{unicode-math} will know to use the \ascii\ ones instead.
If necessary this behaviour can be forced with |[range=frak->up]|, since the `|up|' range corresponds to \ascii\ letters.
%If you wanted to swap the maths symbols with sans serif forms, it would be possible to write |[range={up->sfup,it->sfit}]|.
%Note, however, that at present Unicode does not encode glyphs for sans serif Greek (\tabref{mathalphabets}).
Users of the impressive Minion Math fonts (commercial) may use remapping to access the bold glyphs using:
\begin{Verbatim}
\setmathfont{MinionMath-Regular.otf}
\setmathfont{MinionMath-Bold.otf}[range={bfup->up,bfit->it}]
\end{Verbatim}
To set up the complete range of optical sizes for these fonts, a font declaration such as the following may be used: (adjust may be desired according to the font size of the document)
\begin{Verbatim}
\setmathfont{Minion Math}[
SizeFeatures = {
{Size = -6.01, Font = MinionMath-Tiny},
{Size = 6.01-8.41, Font = MinionMath-Capt},
{Size = 8.41-13.01, Font = MinionMath-Regular},
{Size = 13.01-19.91, Font = MinionMath-Subh},
{Size = 19.91-, Font = MinionMath-Disp}
}]
\setmathfont{Minion Math}[range = {bfup->up,bfit->it},
SizeFeatures = {
{Size = -6.01, Font = MinionMath-BoldTiny},
{Size = 6.01-8.41, Font = MinionMath-BoldCapt},
{Size = 8.41-13.01, Font = MinionMath-Bold},
{Size = 13.01-19.91, Font = MinionMath-BoldSubh},
{Size = 19.91-, Font = MinionMath-BoldDisp}
}]
\end{Verbatim}
\textbf{v0.8:} Note that in previous versions of \pkg{unicode-math}, these features were labelled |[range=\mathbb]| and so on. This old syntax is still supported for backwards compatibility, but is now discouraged.
\subsection{Script and scriptscript fonts/features}
\seclabel{sscript}
Cambria Math uses OpenType font features to activate smaller optical sizes
for scriptsize and scriptscriptsize symbols (the $B$ and $C$, respectively,
in $A_{B_C}$).
Other typefaces (such as Minion Math) may use entirely separate font files.
The features |script-font| and |sscript-font| allow alternate fonts to be
selected for the script and scriptscript sizes, and |script-features| and
|sscript-features| to apply different OpenType features to them.
By default |script-features| is defined as |Style=MathScript| and |sscript-features| is |Style=MathScriptScript|.
These correspond to the two levels of OpenType's |ssty| feature tag.
If the |(s)script-features| options are specified manually, you must
additionally specify the |Style| options as above.
\subsection{Maths `versions'}
\LaTeX\ uses a concept known as `maths versions' to switch math fonts
mid-document.
This is useful because it is more efficient than loading a complete maths
font from scratch every time---especially with thousands of glyphs in the case of Unicode maths!
The canonical example for maths versions is to select a `bold' maths font
which might be suitable for section headings, say.
(Not everyone agrees with this typesetting choice, though; be careful.)
To select a new maths font in a particular version, use the syntax
\codeline{\cmd\setmathfont\marg{font name}|[version=|\meta{version name}|,|\meta{font features}|]|}
and to switch between maths versions mid-document use the standard \LaTeX\ command
\cmd\mathversion\marg{version name}.
\subsection{Legacy maths `alphabet' commands}
\seclabel{mathselect}
\LaTeX\ traditionally uses \cs{DeclareMathAlphabet} and \cs{SetMathAlphabet} to define document commands such as \cs{mathit}, \cs{mathbf}, and so on.
While these commands can still be used, \pkg{unicode-math} defines a wrapper command to assist with the creation of new such maths alphabet commands.
This command is known as \cs{setmathface} in symmetry with \pkg{fontspec}'s \cs{newfontface} command; it takes syntax:
\begin{quote}
\cmd\setmathfontface\meta{command}\marg{font name}|[|\meta{font features}|]|
\makebox[0pt][l]{\cmd\setmathfontface\meta{command}\marg{font name}|[||version=|\meta{version name}|,|\meta{font features}|]|}
\end{quote}
For example, if you want to define a new legacy maths alphabet font \cs{mathittt}:
\begin{verbatim}
\setmathfontface\mathittt{texgyrecursor-italic.otf}
...
$\mathittt{foo} = \mathittt{a} + \mathittt{b}$
\end{verbatim}
\subsubsection{Default `text math' fonts}
The five `text math' fonts, discussed above, are: \cs{mathrm}, \cs{mathbf}, \cs{mathit}, \cs{mathsf}, and \cs{mathtt}.
These commands are also defined with their original definition under synonyms \cs{mathtextrm}, \cs{mathtextbf}, and so on.
When selecting document fonts using \pkg{fontspec} commands such as \cs{setmainfont}, \pkg{unicode-math} inserts some additional that keeps the current default fonts `in sync' with their corresponding \cs{mathrm} commands, etc.
For example, in standard \LaTeX, \cs{mathsf} doesn't change even if the main document font is changed using |\renewcommand\sfdefault{...}|. With \pkg{unicode-math} loaded, after writing |\setsansfont{Helvetica}|, \cs{mathsf} will now be set in Helvetica.
If the \cs{mathsf} font is set explicitly at any time in the preamble, this `auto-following' does not occur. The legacy math font switches can be defined either with commands defined by \pkg{fontspec} (|\setmathrm|, |\setmathsf|, etc.) or using the more general |\setmathfontface\mathsf| interface defined by \pkg{unicode-math}.
\subsubsection{Replacing `text math' fonts by symbols}
For certain types of documents that use legacy input syntax (say you're typesetting a new version of a book written in the 1990s), it would be preferable to use |\symbf| rather than |\mathbf| en masse.
For example, if bold maths is used only for vectors and matrices, a dedicated symbol font will produce better spacing and will better match the main math font.
Alternatively, you may have used an old version of \pkg{unicode-math} (pre-v0.8), when the \cs{symXYZ} commands were not defined and \cs{mathbf} behaved like \cs{symbf} does now.
A series of package options (\tabref{legacyfontswitch}) are provided to facilitate switching the definition of \cs{mathXYZ} for the five legacy text math font definitions.
\begin{table}
\centering
\topcaption{Maths text font configuration options. Note that \cs{mathup} and \cs{mathrm} are aliases of each other and cannot be configured separately.}
\tablabel{legacyfontswitch}
\begin{tabular}{lll}
\toprule
Defaults (from `text' font) & From `maths symbols' \\
\midrule
|mathrm=text| & |mathrm=sym | \\
|mathup=text|\rlap{$^\ast$} & |mathup=sym|{}\rlap{$^\ast$} \\
|mathit=text| & |mathit=sym | \\
|mathsf=text| & |mathsf=sym | \\
|mathbf=text| & |mathbf=sym | \\
|mathtt=text| & |mathtt=sym | \\
\bottomrule
\end{tabular}
\end{table}
A `smart' macro is intended for a future version of \pkg{unicode-math} that can automatically distinguish between single- and multi-letter arguments to \cs{mathbf} and use either the maths symbol or the `text math' font as appropriate.
\subsubsection{Operator font}
\LaTeX\ defines an internal command \cs{operator@font} for typesetting elements such as |\sin| and |\cos|.
This font is selected from the legacy |operators| NFSS `MathAlphabet', which is no longer relevant in the context of \pkg{unicode-math}.
By default, the \cs{operator@font} command is defined to switch to the \cs{mathrm} font.
You may now change these using the command:
\begin{Verbatim}
\setoperatorfont\mathit
\end{Verbatim}
Or, to select a \pkg{unicode-math} range:
\begin{Verbatim}
\setoperatorfont\symscr
\end{Verbatim}
\setoperatorfont\symscr
For example, after the latter above, |$\sin x$| will produce `$\sin x$'.
\mathversion{normal}
\setoperatorfont\mathrm
\section{Maths input}
\XeTeX's Unicode support allows maths input through two methods. Like
classical \TeX, macros such as \cmd\alpha, \cmd\sum, \cmd\pm, \cmd\leq, and
so on, provide verbose access to the entire repertoire of characters defined
by Unicode. The literal characters themselves may be used instead, for more
readable input files.
\subsection{Math `style'}
\seclabel{math-style}
Classically, \TeX\ uses italic lowercase Greek letters and \emph{upright}
uppercase Greek letters for variables in mathematics. This is contrary to
the \textsc{iso} standards of using italic forms for both upper- and lowercase.
Furthermore, in various historical contexts, often associated with French typesetting, it was common to use upright uppercase \emph{Latin} letters as well as upright
upper- and lowercase Greek, but italic lowercase latin. Finally, it is not unknown to use upright letters
for all characters, as seen in the Euler fonts.
The \pkg{unicode-math} package accommodates these possibilities with the
option \opt{math-style} that takes one of four (case sensitive) arguments:
\opt{TeX}, \opt{ISO}, \opt{french}, or \opt{upright}.\footnote{Interface inspired by Walter Schmidt's \pkg{lucimatx} package.}
The \opt{math-style} options' effects are shown in brief in \tabref{math-style}.
The philosophy behind the interface to the mathematical symbols
lies in \LaTeX's attempt of separating content and formatting. Because input
source text may come from a variety of places, the upright and
`mathematical' italic Latin and Greek alphabets are \emph{unified} from the
point of view of having a specified meaning in the source text. That is, to
get a mathematical ‘$x$’, either the \ascii\ (`keyboard') letter |x| may
be typed, or the actual Unicode character may be used. Similarly for Greek
letters. The upright or italic forms are then chosen based on the
|math-style| package option.
If glyphs are desired that do not map as per the package option (for
example, an upright `g' is desired but typing |$g$| yields `$g$'),
\emph{markup} is required to specify this; to follow from the example:
|\symup{g}|.
Maths style commands such as \cmd\symup\ are detailed later.
\paragraph{`Literal' interface}
Some may not like this convention of normalising their input.
For them, an upright |x| is an upright `x' and that's that.
(This will be the case when obtaining source text from copy/pasting PDF or
Microsoft Word documents, for example.)
For these users, the |literal| option to |math-style| will effect this behaviour.
The \cs{symliteral}\marg{syms} command can also be used, regardless of package setting, to force the style to match the literal input characters.
This is a `mirror' to \cs{symnormal}\marg{syms} (also alias \cs{mathnormal}) which `resets' the character mapping in its argument to that originally set up through package options.
\begin{table}
\centering
\topcaption{Effects of the \opt{math-style} package option.}
\tablabel{math-style}
\begin{tabular}{@{}>{\ttfamily}lcc@{}}
\toprule
& \multicolumn{2}{c}{Example} \\
\cmidrule(l){2-3}
\rmfamily Package option & Latin & Greek \\
\midrule
math-style=ISO & $(a,z,B,X)$ & $\symit{(\alpha,\beta,\Gamma,\Xi)}$ \\
math-style=TeX & $(a,z,B,X)$ & $(\symit\alpha,\symit\beta,\symup\Gamma,\symup\Xi)$ \\
math-style=french & $(a,z,\symup B,\symup X)$ & $(\symup\alpha,\symup\beta,\symup\Gamma,\symup\Xi)$ \\
math-style=upright & $(\symup a,\symup z,\symup B,\symup X)$ & $(\symup\alpha,\symup\beta,\symup\Gamma,\symup\Xi)$ \\
\bottomrule
\end{tabular}
\end{table}
\subsection{Bold style}
\seclabel{bold-style}
Similar as in the previous section, ISO standards differ somewhat to \TeX's
conventions (and classical typesetting) for `boldness' in mathematics. In
the past, it has been customary to use bold \emph{upright} letters to denote
things like vectors and matrices. For example, \( \symbfup{M} =
(\mitM_x,\mitM_y,\mitM_z) \). Presumably, this was due to the relatively
scarcity of bold italic fonts in the pre-digital typesetting era.
It has been suggested by some that \emph{italic} bold symbols should be used nowadays instead, but this practise is certainly not widespread.
Bold Greek letters have simply been bold variant glyphs of their regular
weight, as in \( \mbfitxi = (\mitxi_\mitr,\mitxi_\mitphi,\mitxi_\mittheta)
\).
Confusingly, the syntax in \LaTeX\ traditionally has been different for obtaining `normal' bold symbols in Latin and Greek: \cmd\mathbf\ in the former (`$\symbfup{M}$'), and \cmd\bm\ (or
\cmd\boldsymbol, deprecated) in the latter (`$\mbfitxi$').
In \pkg{unicode-math}, the \cmd\symbf\ command works directly with both
Greek and Latin maths characters and depending on package option
either switches to upright for Latin letters (|bold-style=TeX|) as well or
keeps them italic (|bold-style=ISO|).
To match the package options for non-bold characters, with option
|bold-style=upright| all bold characters are upright, and
|bold-style=literal| does not change the upright/italic shape of the letter.
The \opt{bold-style} options' effects are shown in brief in \tabref{bold-style}.
Upright and italic bold mathematical letters input as direct Unicode
characters are normalised with the same rules. For example, with
|bold-style=TeX|, a literal bold italic latin character will be typeset
upright.
Note that \opt{bold-style} is independent of \opt{math-style}, although if
the former is not specified then matching defaults are chosen based on the
latter.
\begin{table}
\centering
\topcaption{Effects of the \opt{bold-style} package option.}
\tablabel{bold-style}
\begin{tabular}{@{}>{\ttfamily}lcc@{}}
\toprule
& \multicolumn{2}{c}{Example} \\
\cmidrule(l){2-3}
\rmfamily Package option & Latin & Greek \\
\midrule
bold-style=ISO & $(\symbfit a, \symbfit z, \symbfit B, \symbfit X)$ & $(\symbfit\alpha, \symbfit\beta, \symbfit\Gamma, \symbfit\Xi)$ \\
bold-style=TeX & $(\symbfup a,\symbfup z,\symbfup B,\symbfup X)$ & $(\symbfit\alpha, \symbfit\beta,\symbfup \Gamma,\symbfup \Xi)$ \\
bold-style=upright & $(\symbfup a,\symbfup z,\symbfup B,\symbfup X)$ & $(\symbfup \alpha,\symbfup \beta,\symbfup \Gamma,\symbfup \Xi)$ \\
\bottomrule
\end{tabular}
\end{table}
\subsection{Sans serif style}
\seclabel{sans-style}
Unicode contains upright and italic, medium and bold mathematical style characters.
These may be explicitly selected with the \cs{mathsfup}, \cs{mathsfit}, \cs{mathbfsfup}, and \cs{mathbfsfit}
commands discussed in \secref{all-math-alphabets}.
How should the generic \cs{mathsf} behave? Unlike bold, sans serif is used much more sparingly
in mathematics. I've seen recommendations to typeset tensors in sans serif italic
or sans serif italic bold (e.g., examples in the \pkg{isomath} and \pkg{mattens} packages).
But \LaTeX's \cs{mathsf} is \textsl{upright} sans serif.
Therefore I reluctantly add the package options |[sans-style=upright]| and |[sans-style=italic]| to control the behaviour of \cs{mathsf}.
The |upright| style sets up the command to use upright sans serif, including Greek;
the |italic| style switches to using italic in both Latin and Greek.
In other words, this option simply changes the meaning of \cs{mathsf} to either \cs{mathsfup} or \cs{mathsfit}, respectively.
Please let me know if more granular control is necessary here.
There is also a |[sans-style=literal]| setting, set automatically with |[math-style=literal]|, which retains the uprightness of the input characters used when selecting the sans serif output.
\subsubsection{What about bold sans serif?}
While you might want your bold upright and your sans serif italic, I don't believe you'd also want
your bold sans serif upright (or all vice versa, if that's even conceivable). Therefore, bold sans
serif follows from the setting for sans serif; it is completely independent of the setting for bold.
In other words, \cs{mathbfsf} is either \cs{mathbfsfup} or \cs{mathbfsfit} based on |[sans-style=upright]| or |[sans-style=italic]|, respectively. And \texttt{[sans-style = literal]} causes \cs{mathbfsf} to retain the same italic or upright shape as the input, and turns it bold sans serif.
N.B.: there is no medium-weight sans serif Greek range in Unicode.
Therefore, |\symsf{\alpha}| does not make sense (it produces `$\symsf{\alpha}$'), while |\symbfsf{\alpha}| gives `$\symbfsfup{\alpha}$' or `$\symbfsfit{\alpha}$' according to the |sans-style|.
\subsection{All (the rest) of the mathematical styles}
\seclabel{all-math-alphabets}
Unicode contains separate codepoints for most if not all variations of style
shape one may wish to use in mathematical notation. The complete list is shown
in \tabref{mathalphabets}. Some of these have been covered in the previous sections.
The math font switching commands do not nest; therefore if you want
sans serif bold, you must write |\symbfsf{...}| rather than |\symbf{\symsf{...}}|.
This may change in the future.
\begin{table}
\caption{Mathematical styles defined in Unicode. Black dots indicate an style exists in the font specified; blue dots indicate shapes that should always be taken from the upright font even in the italic style. See main text for description of \cs{mathbbit}.}
\tablabel{mathalphabets}
\centering
\def\Y{\textbullet}
\def\M{\textcolor[rgb]{0.5,0.5,1}{\textbullet}}
\begin{tabular}{@{} lll l ccc @{}}
\toprule
\multicolumn{3}{c}{Font} & & \multicolumn{3}{c}{Alphabet} \\
\cmidrule(r){1-3}
\cmidrule(l){5-7}
Style & Shape & Series & Switch & Latin & Greek & Numerals \\
\midrule
Serif & Upright & Normal & \cs{mathup} & \Y & \Y & \Y \\
& & Bold & \cs{mathbfup} & \Y & \Y & \Y \\
& Italic & Normal & \cs{mathit} & \Y & \Y & \M \\
& & Bold & \cs{mathbfit} & \Y & \Y & \M \\
Sans serif & Upright & Normal & \cs{mathsfup} & \Y & & \Y \\
& Italic & Normal & \cs{mathsfit} & \Y & & \M \\
& Upright & Bold & \cs{mathbfsfup} & \Y & \Y & \Y \\
& Italic & Bold & \cs{mathbfsfit} & \Y & \Y & \M \\
Typewriter & Upright & Normal & \cs{mathtt} & \Y & & \Y \\
Double-struck & Upright & Normal & \cs{mathbb} & \Y & & \Y \\
& Italic & Normal & \cs{mathbbit} & \Y & & \\
Script & Upright & Normal & \cs{mathscr} & \Y & & \\
& & Bold & \cs{mathbfscr} & \Y & & \\
Fraktur & Upright & Normal & \cs{mathfrak} & \Y & & \\
& & Bold & \cs{mathbffrac} & \Y & & \\
\bottomrule
\end{tabular}
\end{table}
\subsubsection{Double-struck}
The double-struck style (also known as `blackboard bold') consists of
upright Latin letters $\{\symbb{a}$--$\symbb{z}$,$\symbb{A}$$\symbb{Z}\}$,
numerals $\symbb{0}$--$\symbb{9}$, summation symbol $\symbb\sum$, and four
Greek letters only: $\{\symbb{\gamma\pi\Gamma\Pi}\}$.
While |\symbb{\sum}| does produce a double-struck summation symbol,
its limits aren't properly aligned. Therefore,
either the literal character or the control sequence \cs{Bbbsum} are
recommended instead.
There are also five Latin \emph{italic} double-struck letters: $\symbbit{Ddeij}$.
These can be accessed (if not with their literal characters or control sequences)
with the \cs{mathbbit} style switch, but note that only those five letters
will give the expected output.
\subsubsection{Caligraphic vs.\ Script variants}
The Unicode maths encoding contains a style for `Script' letters,
and while by default \cs{mathcal} and \cs{mathscr}
are synonyms, there are some situations when a
separate `Caligraphic' style is needed as well.
If a font contains alternate glyphs for a separat caligraphic style,
they can be selected explicitly as shown below.
This feature is currently only supported by the XITS~Math font, where
the caligraphic letters are accessed with the same glyph slots as the
script letters but with the first stylistic set feature (|ss01|) applied.
\begin{verbatim}
\setmathfont{xits-math.otf}[range={cal,bfcal},StylisticSet=1]
\end{verbatim}
An example is shown below.
\begin{quote}
\setmathfont{xits-math.otf}[range=scr]
\setmathfont{xits-math.otf}[range=cal,StylisticSet=1]
The Script style (\cs{mathscr}) in XITS Math is: $\symscr{ABCXYZ}$\par
The Caligraphic style (\cs{mathcal}) in XITS Math is: $\symcal{ABCXYZ}$
\end{quote}
\subsection{Miscellanea}
\subsubsection{Nabla}
\seclabel{nabla}
The symbol $\nabla$ comes in the six forms shown in \tabref{nabla}.
We want an individual option to specify whether we want upright or italic
nabla by default (when either upright or italic nabla is used in the
source). \TeX\ classically uses an upright nabla, and \textsc{iso}
standards agree with this convention.
The package options |nabla=upright| and
|nabla=italic| switch between the two choices, and |nabla=literal| respects
the shape of the input character. This is then inherited
through \cmd\symbf; \cmd\symit\ and \cmd\symup\ can be used to force one
way or the other.
|nabla=italic| is the default. |nabla=literal| is
activated automatically after |math-style=literal|.
\begin{table}
\begin{minipage}[b]{0.49\textwidth}
\centering
\topcaption{The various forms of nabla.}
\tablabel{nabla}
\let \tmpshow\empty
\begin{tabular}{@{}llc@{}}
\toprule
\multicolumn{2}{@{}l}{Description} & Glyph
\\ \cmidrule(r){1-2}\cmidrule(l){3-3}
Upright & Serif & $\symup\nabla$ \\
& Bold serif & $\symbfup\nabla$ \\
& Bold sans & $\symbfsfup\nabla$ \\
\cmidrule(lr){1-2}\cmidrule(lr){3-3}
Italic & Serif & $\symit\nabla$ \\
& Bold serif & $\symbfit\nabla$ \\
& Bold sans & $\symbfsfit\nabla$ \\
\bottomrule
\end{tabular}
\end{minipage}\hfill
\begin{minipage}[b]{0.49\textwidth}
\centering
\topcaption{The partial differential.}
\tablabel{partial}
\begin{tabular}{@{}llc@{}}
\toprule
\multicolumn{2}{@{}l}{Description} & Glyph
\\ \cmidrule(r){1-2}\cmidrule(l){3-3}
Regular & Upright & $\symup\partial$ \\
& Italic & $\symit\partial$ \\
Bold & Upright & $\symbfup\partial$ \\
& Italic & $\symbfit\partial$ \\
Sans bold & Upright & $\symbfsfup\partial$ \\
& Italic & $\symbfsfit\partial$ \\
\bottomrule
\end{tabular}
\end{minipage}
\end{table}
\subsubsection{Partial}
\seclabel{partial}
The same applies to the symbols \unichar{2202} partial differential and
\unichar{1D715} math italic partial differential.
At time of writing, both the Cambria Math and STIX fonts display these
two glyphs in the same italic style, but this is hopefully a bug that will
be corrected in the future~--- the `plain' partial differential should
really have an upright shape.
Use the |partial=upright| or |partial=italic| package options to specify
which one you would like, or |partial=literal| to have the same character
used in the output as was used for the input.
The default is (always, unless someone requests and
argues otherwise) |partial=italic|.\footnote{A good argument would revolve
around some international standards body recommending upright over italic.
I just don't have the time right now to look it up.} |partial=literal|
is activated following |math-style=literal|.
See \tabref{partial} for the variations on the partial differential symbol.
\subsubsection{Primes}
Primes ($x'$) may be input in several ways. You may use any combination
the \ascii\ straight quote (\texttt{\char`\'}) or the Unicode prime \unichar{2032}
($'$); when multiple primes occur next to each other, they chain
together to form double, triple, or quadruple primes if the font contains
pre-drawn glyphs. The individual prime glyphs are accessed, as usual,
with the \cs{prime} command, and the double-, triple-, and quadruple-prime
glyphs are available with \cs{dprime}, \cs{trprime}, and \cs{qprime},
respectively.
If the font does not contain the pre-drawn glyphs or more than four primes
are used, the single prime glyph is used multiple times with a negative
kern to get the spacing right. There is no user interface to adjust this
negative kern yet (because I haven't decided what it should look like);
if you need to, write something like this:
\begin{Verbatim}
\ExplSyntaxOn
\muskip_gset:Nn \g_@@_primekern_muskip { -\thinmuskip/2 }
\ExplySyntaxOff
\end{Verbatim}
Backwards or reverse primes behave in exactly the same way; use the \ascii\
back tick (\texttt{\char`\`}) or the Unicode reverse prime \unichar{2035}
({\umfont\char"2035}).
The command to access the backprime is \cs{backprime}, and
multiple backwards primes can accessed with \cs{backdprime},
\cs{backtrprime}, and \cs{backqprime}.
In all cases above, no error checking is performed if you attempt to
access a multi-prime glyph in a font that doesn't contain one. For this
reason, it may be safer to write |x''''| instead of |x\qprime|
in general.
If you ever need to enter the straight quote |'| or the backtick |`| in
maths mode, these glyphs can be accessed with \cs{mathstraightquote} and
\cs{mathbacktick}.
\subsubsection{Unicode subscripts and superscripts}
You may, if you wish, use Unicode subscripts and superscripts in your
source document. For basic expressions, the use of these characters
can make the input more readable.
Adjacent sub- or super-scripts will be concatenated into a single
expression.
The range of subscripts and superscripts supported by this package
are shown in \figref{superscripts,subscripts}. Please request more if
you think it is appropriate.
\begin{figure}\centering
\fbox{\fontspec{Charis SIL}\Large
A
^^^^2070 ^^^^00b9 ^^^^00b2 ^^^^00b3 ^^^^2074 ^^^^2075 ^^^^2076 ^^^^2077
^^^^2078 ^^^^2079 ^^^^207a ^^^^207b ^^^^207c ^^^^207d ^^^^207e ^^^^2071
^^^^207f ^^^^207f ^^^^02b0 ^^^^02b2 ^^^^02b3 ^^^^02b7 ^^^^02b8
Z}
\caption{
The Unicode superscripts supported as input characters.
These are the literal glyphs from Charis SIL,
not the output seen when used for maths input.
The `A' and `Z' are to provide context for the size and
location of the superscript glyphs.
}
\figlabel{superscripts}
\end{figure}
\begin{figure}\centering
\fbox{\fontspec{Charis SIL}\Large
A
^^^^2080 ^^^^2081 ^^^^2082 ^^^^2083 ^^^^2084 ^^^^2085 ^^^^2086 ^^^^2087
^^^^2088 ^^^^2089 ^^^^208a ^^^^208b ^^^^208c ^^^^208d ^^^^208e ^^^^2090
^^^^2091 ^^^^1d62 ^^^^2092 ^^^^1d63 ^^^^1d64 ^^^^1d65 ^^^^2093 ^^^^1d66
^^^^1d67 ^^^^1d68 ^^^^1d69 ^^^^1d6a
Z}
\caption{
The Unicode subscripts supported as input characters.
See note from \figref{superscripts}.
}
\figlabel{subscripts}
\end{figure}
\subsubsection{Colon}
\seclabel{colon}
The colon is one of the few confusing characters of Unicode maths.
In \TeX, \texttt{:} is defined as a colon with relation spacing: `$a:b$'.
While \cs{colon} is defined as a colon with punctuation spacing: `$a\colon b$'.
In Unicode, \unichar{003A} {colon} is defined as a punctuation symbol,
while \unichar{2236} {ratio} is the colon-like symbol used in mathematics to denote
ratios and other things.
This breaks the usual straightforward mapping from control sequence to Unicode input character
to (the same) Unicode glyph.
To preserve input compatibility, we remap the \ascii\ input character `\texttt{:}' to \unichar{2236}.
Typing a literal \unichar{2236} char will result in the same output.
If \pkg{amsmath} is loaded, then the definition of \cs{colon} is inherited from there
(it looks like a punctuation colon with additional space around it).
Otherwise, \cs{colon} is made to output a colon with \cs{mathpunct} spacing.
The package option |colon=literal| forces \ascii\ input `|:|' to be printed as \cs{mathcolon} instead.
\subsubsection{Slashes and backslashes}
\seclabel{slash-delimiter}
There are several slash-like symbols defined in Unicode. The complete list is shown in \tabref{slashes}.
\begin{table}\centering
\caption{Slashes and backslashes.}
\tablabel{slashes}
\begin{tabular}{@{}cl@{}cl@{}}
\toprule
Slot & Name & Glyph & Command \\
\midrule
\unichar{002F} & \textsc{solidus} & \umfont \char"002F & \cs{slash} \\
\unichar{2044} & \textsc{fraction slash} & \umfont \char"2044 & \cs{fracslash} \\
\unichar{2215} & \textsc{division slash} & \umfont \char"2215 & \cs{divslash} \\
\unichar{29F8} & \textsc{big solidus} & \umfont \char"29F8 & \cs{xsol} \\
\midrule
\unichar{005C} & \textsc{reverse solidus} & \umfont \char"005C & \cs{backslash} \\
\unichar{2216} & \textsc{set minus} & \umfont \char"2216 & \cs{smallsetminus} \\
\unichar{29F5} & \textsc{reverse solidus operator}& \umfont \char"29F5 & \cs{setminus} \\
\unichar{29F9} & \textsc{big reverse solidus} & \umfont \char"29F9 & \cs{xbsol} \\
\bottomrule
\end{tabular}
\end{table}
In regular \LaTeX\ we can write \cs{left}\cs{slash}\dots\cs{right}\cs{backslash}
and so on and obtain extensible delimiter-like symbols. Not all of the Unicode slashes
are suitable for this (and do not have the font support to do it).
\paragraph{Slash}
Of \unichar{2044} {fraction slash}, TR25 says that it is:
\begin{quote}
\dots used to build up simple fractions in running text\dots
however parsers of mathematical texts should be prepared to handle fraction slash
when it is received from other sources.
\end{quote}
\unichar{2215} {division slash} should be used when division is represented
without a built-up fraction; $\pi\approx22/7$, for example.
\unichar{29F8} {big solidus} is a `big operator' (like $\sum$).
\paragraph{Backslash}