1<TeXmacs|1.0.7.9>
2
3<style|tmdoc>
4
5<\body>
6  <tmdoc-title|Typing mathematical symbols>
7
8  The Greek characters are obtained in <TeXmacs> using the
9  <prefix|math:greek>-key. For instance, <key|math:greek a>
10  yields<nbsp><math|\<alpha\>> and <key|math:greek G> yields
11  <math|\<Gamma\>>. Similarly, <prefix|math:bold>, <prefix|math:cal>,
12  <prefix|math:frak> and <prefix|math:bbb> can be used in order to type bold,
13  calligraphic, fraktur and blackboard bold characters. For instance,
14  <shortcut|\<frak-m\>> yields<nbsp><math|\<frak-m\>>, <key|S-F6 R>
15  yields<nbsp><math|\<bbb-R\>> and <shortcut|\<b-cal-Z\>> yields
16  <math|\<b-cal-Z\>>.
17
18  Greek characters can also be obtained as ``variants'' of Latin characters
19  using the <key|var>-key. For instance, <key|p var> yields <math|\<pi\>>.
20  The <key|var>-key is also used for obtaining variants of the Greek letters
21  themselves. For instance, both <key|math:greek p var> and <key|p var var>
22  yield <math|\<varpi\>>. An alternative way to enter blackboard bold
23  characters is to type the same capital twice. For instance, <key|Z Z>
24  yields<nbsp><math|\<bbb-Z\>>.
25
26  Some symbols admit many variants. For instance, <key|\<less\>> yields
27  <math|\<less\>>, <key|\<less\> var> yields <math|\<in\>>, <key|\<less\> var
28  var> yields <math|\<subset\>>, <key|\<less\> var var var> yields
29  <math|\<prec\>>, and so on. You may ``cycle back'' among the variants
30  using<nbsp><key|S-var>. For instance, <key|\<less\> var var S-var> is
31  equivalent to <key|\<less\> var>.
32
33  Many other mathematical symbols are obtained by ``natural''
34  key-combinations. For instance, <key|- \<gtr\>> yields
35  <math|<op|\<rightarrow\>>>, <key|- - \<gtr\>> yields
36  <math|<op|\<longrightarrow\>>> and <key|\<gtr\> => yields
37  <math|<op|\<geqslant\>>>. Similarly, <key|\| var -> yields
38  <math|<op|\<vdash\>>>, <key|\| - \<gtr\>> yields <math|<op|\<mapsto\>>> and
39  <key|- \<gtr\> \<less\> -> yields <math|<op|\<rightleftarrows\>>>. The
40  following general rules hold in order to enter mathematical symbols:
41
42  <\description>
43    <item*|<key|tab>>is the main key for obtaining variants. For instance,
44    <key|\<gtr\> => yields <math|<op|\<geqslant\>>>, but <key|\<gtr\> = var>
45    yields<nbsp><math|<op|\<geq\>>>. Similarly, <key|\<less\> var var> yields
46    <math|<op|\<subset\>>>, <key|\<less\> var var => yields
47    <math|<op|\<subseteq\>>> and <key|\<less\> var var = var> yields
48    <math|<op|\<subseteqq\>>>. Also, <key|P var> yields<nbsp><math|\<wp\>>
49    and <key|e var> yields the constant <math|\<mathe\>=exp<around|(|1|)>>.
50
51    <item*|<key|@>>is used for putting symbols into circles or boxes. For
52    instance, <key|@ +> yields <math|<op|\<oplus\>>> and <key|@ x> yields
53    <math|<op|\<otimes\>>>. Similarly, <key|@ var +> yields
54    <math|<op|\<boxplus\>>>.
55
56    <item*|<key|/>>is used for negations. For instance, <key|= /> yields
57    <math|<op|\<neq\>>> and <key|\<less\> = /> yields
58    <math|<neg|\<leqslant\>>>. Notice that <key|\<less\> = var var /> yields
59    <math|<op|\<nleqq\>>>, while <key|\<less\> = var var / var> yields
60    <math|<op|\<lneqq\>>>.
61
62    <item*|<key|!>>is used after arrows in order to force scripts to be
63    placed above or below the arrow. For instance, <key|- - \<gtr\> ^ x>
64    yields <math|<op|\<longrightarrow\><rsup|x> >>, but <key|- - \<gtr\> ! ^
65    x> yields <math|\<longrightarrowlim\><rsup|x>>.
66  </description>
67
68  The logical relations <math|\<wedge\>> and <math|\<vee\>> are obtained
69  using <key|&> and <key|%>. The operators <math|\<cap\>> and <math|\<cup\>>
70  are natural variants <key|& var> and <key|% var>. Various miscellaneous
71  symbols can be optained using the <prefix|math:symbol> prefix.
72
73  Notice that certain symbols with a different mathematical meaning are
74  sometimes denoted in a<nbsp>similar way; such symbols are called
75  <em|homoglyphs>. For instance, the vertical bar <math|\|> can be used as
76  a<nbsp>separator for defining sets <math|R<rsup|\<gtr\>>=<around*|{|x\<in\>R\|x\<gtr\>0|}>>,
77  but also as the binary relation ``divides''<nbsp><rigid|<math|11\<divides\>1001>>.
78  Often, but not always, homoglyphs admit a different spacing. The most
79  annoying ambiguity is between invisible multiplication <math|x*y> and
80  function application <math|sin x>, which are entered using the shortcuts
81  <key|*> <abbr|resp.> <key|space>.
82
83  In order to facilitate certain automated treatments of your documents, such
84  as mathematical syntax checking, we incite authors to pay attention to the
85  homoglyph problem when entering formulas. For more information on this
86  issue and how <TeXmacs> can assist you to use the appropriate notations, we
87  refer to our section on the <hlink|semantics of mathematical
88  symbols|../semantics/man-semantics-symbols.en.tm>.
89
90  <tmdoc-copyright|1998--2010|Joris van der Hoeven>
91
92  <tmdoc-license|Permission is granted to copy, distribute and/or modify this
93  document under the terms of the GNU Free Documentation License, Version 1.1
94  or any later version published by the Free Software Foundation; with no
95  Invariant Sections, with no Front-Cover Texts, and with no Back-Cover
96  Texts. A copy of the license is included in the section entitled "GNU Free
97  Documentation License".>
98</body>
99
100<\initial>
101  <\collection>
102    <associate|language|english>
103  </collection>
104</initial>