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>