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  1. <inform-div1 id="oper-dict" role="appendixf"><head>Operator Dictionary</head>
  2. <!-- $Id: operator-dict.xml,v 1.19 2001/01/04 15:08:55 davidc Exp $ -->
  3.  
  4. <p>The following table gives the suggested dictionary of rendering
  5. properties for operators, fences, separators, and accents in MathML, all of
  6. which are represented by <kw role="element">mo</kw> elements. For brevity,
  7. all such elements will be called simply <quote>operators</quote> in this
  8. Appendix.</p>
  9.  
  10. <div2 id="oper-dict_format"><head>Format of operator dictionary entries</head>
  11.  
  12. <p>The operators are divided into groups, which are separated by blank
  13. lines in the listing below. The grouping, and the order of the groups, is
  14. significant for the proper grouping of sub-expressions using <kw
  15. role="starttag">mrow</kw> (<specref ref="presm_mrow"/>); the rule described
  16. there is especially relevant to the automatic generation of MathML by
  17. conversion from other formats for displayed mathematics, such as &TeX;,
  18. which do not always specify how sub-expressions nest.</p>
  19.  
  20. <p>The format of the table entries is: the <kw role="starttag">mo</kw>
  21. element content between double quotes (start and end tags not shown),
  22. followed by the attribute list in XML format, starting with the
  23. <kw role="attrib">form</kw> attribute, followed by the default rendering
  24. attributes which should be used for <kw role="element">mo</kw> elements
  25. with the given content and <kw role="attrib">form</kw> attribute.</p>
  26.  
  27. <p>Any attribute not listed for some entry has its default value,
  28. which is given in parentheses in the table of attributes in <specref
  29. ref="presm_mo"/>.</p>
  30.  
  31. <p>Note that the characters & and < are represented in the
  32. following table entries by the entity references
  33. <kw role="entity">amp</kw> and <kw role="entity">lt</kw> respectively,
  34. as would be necessary if they appeared in the content of an actual
  35. <kw role="element">mo</kw> element (or any other MathML or XML
  36. element).</p>
  37.  
  38. <!-- It would be nice to show them as themselves, for clarity   -->
  39. <!-- but this would use & inconsistently, since some        -->
  40. <!-- extended characters have to be shown as entity references. -->
  41.  
  42. <p>For example, the first entry,
  43. <eg><![CDATA[
  44. "(" form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em"
  45. ]]></eg>
  46. could be expressed as an <kw role="element">mo</kw> element by:
  47. <eg role='mathml'><![CDATA[
  48. <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em"> ( </mo>
  49. ]]></eg>
  50. (note the lack of double quotes around the content, and the
  51. whitespace added around the content for readability, which is optional
  52. in MathML).</p>
  53.  
  54. <p>This entry means that, for MathML renderers which use this
  55. suggested operator dictionary, giving the element
  56. <code><mo form="prefix"> ( </mo></code>
  57. alone, or simply
  58. <code><mo> ( </mo></code>
  59. in a position for which
  60. <code>form="prefix"</code>
  61. would be inferred (see below), is equivalent to giving the element
  62. with all attributes as shown above.</p>
  63. </div2>
  64.  
  65. <div2 id="oper-dict_index"><head>Indexing of operator dictionary</head>
  66.  
  67. <p>Note that the dictionary is indexed not just by the element
  68. content, but by the element content and <kw role="attrib">form</kw> attribute
  69. value, together. Operators with more than one possible form have more
  70. than one entry. The MathML specification describes how the renderer
  71. chooses (<quote>infers</quote>) which form to use when no <kw role="attrib">form</kw>
  72. attribute is given; see <specref ref="presm_formdefval"/>. </p>
  73.  
  74. <p>Having made that choice, or with the <kw role="attrib">form</kw> attribute
  75. explicitly specified in the <kw role="starttag">mo</kw> element's start
  76. tag, the MathML renderer uses the remaining attributes from the
  77. dictionary entry for the appropriate single form of that operator,
  78. ignoring the entries for the other possible forms.</p>
  79. </div2>
  80.  
  81. <div2 id="oper-dict_names"><head>Choice of entity names</head>
  82.  
  83. <p>Extended characters in MathML (and in the operator dictionary
  84. below) are represented by XML-style entity references using the syntax
  85. <kw role="entity">character-name</kw> the complete list of characters and
  86. character names is given in <specref ref="chars"/>. Many characters can be referred
  87. to by more than one name; often, memorable names composed of full
  88. words have been provided in MathML, as well as one or more names used
  89. in other standards, such as Unicode. The characters in the operators
  90. in this dictionary are generally listed under their full-word names
  91. when these exist. For example, the integral operator is named below by
  92. the one-character sequence <kw role="entity">Integral</kw>, but
  93. could equally well be named <kw role="entity">int</kw>. The choice
  94. of name for a given character in MathML has no effect on its
  95. rendering.</p>
  96.  
  97. <p>It is intended that every entity named below appears somewhere in
  98. <specref ref="chars"/>. If this is not true, it is an error in this
  99. specification. If such an error exists, the abovementioned chapter should
  100. be taken as definitive, rather than this appendix.</p>
  101. </div2>
  102.  
  103. <div2 id="oper-dict_space"><head>Notes on <kw role="attrib">lspace</kw> and 
  104. <kw role="attrib">rspace</kw> attributes</head>
  105.  
  106. <p>The values for <kw role="attrib">lspace</kw> and <kw
  107. role="attrib">rspace</kw> given here range from 0 to 
  108. <kw role="attval">verythickmathspace</kw>, which has a default value
  109. of 6/18 em.
  110. For the invisible operators whose content is <kw
  111. role="entity">InvisibleTimes</kw> or <kw role="entity">ApplyFunction</kw>,
  112. it is suggested that MathML renderers choose spacing in a context-sensitive
  113. way (which is an exception to the static values given in the following
  114. table). For <code><![CDATA[<mo>⁡</mo>]]></code>, the total
  115. spacing (<kw role="attval">lspace</kw>+<kw role="attval">rspace</kw>) in
  116. expressions such as <quote>sin <mi>x</mi></quote> (where the right operand
  117. doesn't start with a fence) should be greater than zero; for
  118. <code><![CDATA[<mo>⁢</mo>]]></code>, the total spacing
  119. should be greater than zero when both operands (or the nearest tokens on
  120. either side, if on the baseline) are identifiers displayed in a non-slanted
  121. font (i.e. under the suggested rules, when both operands are
  122. multi-character identifiers).</p>
  123.  
  124. <p>Some renderers may wish to use no spacing for most operators
  125. appearing in scripts (i.e. when <kw role="attrib">scriptlevel</kw> is greater
  126. than 0; see <specref ref="presm_mstyle"/>), as is the case in &TeX;.</p>
  127. </div2>
  128.  
  129. <div2 id="oper-dict_entries"><head>Operator dictionary entries</head>
  130. <eg><![CDATA[
  131. "("                                  form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
  132. ")"                                  form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
  133. "["                                  form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
  134. "]"                                  form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
  135. "{"                                  form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
  136. "}"                                  form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
  137. "”"            form="postfix" fence="true"  lspace="0em" rspace="0em"
  138. "’"                  form="postfix" fence="true"  lspace="0em" rspace="0em"
  139. "⟨"                 form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
  140. "&LeftBracketingBar;"                form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
  141. "⌈"                      form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
  142. "⟦"                form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
  143. "&LeftDoubleBracketingBar;"          form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
  144. "⌊"                        form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
  145. "“"             form="prefix"  fence="true"  lspace="0em" rspace="0em"
  146. "‘"                   form="prefix"  fence="true"  lspace="0em" rspace="0em"
  147. "⟩"                form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
  148. "&RightBracketingBar;"               form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
  149. "⌉"                     form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
  150. "⟧"               form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
  151. "&RightDoubleBracketingBar;"         form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
  152. "⌋"                       form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
  153. "&LeftSkeleton;"                     form="prefix"  fence="true"  lspace="0em" rspace="0em"
  154. "&RightSkeleton;"                    form="postfix" fence="true"  lspace="0em" rspace="0em"
  155. "⁣"                   form="infix"   separator="true"  lspace="0em" rspace="0em"
  156. ","                                  form="infix"   separator="true"  lspace="0em" rspace="verythickmathspace"
  157. "─"                   form="infix"   stretchy="true" minsize="0"  lspace="0em" rspace="0em"
  158. "|"                     form="infix"   stretchy="true" minsize="0"  lspace="0em" rspace="0em"
  159. ";"                                  form="infix"   separator="true"  lspace="0em" rspace="thickmathspace"
  160. ";"                                  form="postfix" separator="true"  lspace="0em" rspace="0em"
  161. ":="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  162. "≔"                           form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  163. "∵"                          form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  164. "∴"                        form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  165. "❘"                form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  166. "//"                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  167. "∷"                            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  168. "&"                              form="prefix"   lspace="0em" rspace="thickmathspace"
  169. "&"                              form="postfix"  lspace="thickmathspace" rspace="0em"
  170. "*="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  171. "-="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  172. "+="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  173. "/="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  174. "->"                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  175. ":"                                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  176. ".."                                 form="postfix"  lspace="mediummathspace" rspace="0em"
  177. "..."                                form="postfix"  lspace="mediummathspace" rspace="0em"
  178. "∋"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  179. "⫤"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  180. "⊨"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  181. "⊤"                          form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  182. "⊣"                          form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  183. "⊢"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  184. "⇒"                          form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  185. "⥰"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  186. "|"                                  form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  187. "||"                                 form="infix"    lspace="mediummathspace" rspace="mediummathspace"
  188. "⩔"                               form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
  189. "&&"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  190. "⩓"                              form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
  191. "&"                              form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  192. "!"                                  form="prefix"   lspace="0em" rspace="thickmathspace"
  193. "⫬"                              form="prefix"   lspace="0em" rspace="thickmathspace"
  194. "∃"                           form="prefix"   lspace="0em" rspace="thickmathspace"
  195. "∀"                           form="prefix"   lspace="0em" rspace="thickmathspace"
  196. "∄"                        form="prefix"   lspace="0em" rspace="thickmathspace"
  197. "∈"                          form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  198. "∉"                       form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  199. "∌"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  200. "⊏̸"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  201. "⋢"             form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  202. "⊐̸"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  203. "⋣"           form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  204. "⊂⃒"                        form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  205. "⊈"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  206. "⊃⃒"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  207. "⊉"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  208. "∋"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  209. "⊏"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  210. "⊑"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  211. "⊐"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  212. "⊒"              form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  213. "⋐"                           form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  214. "⊆"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  215. "⊃"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  216. "⊇"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  217. "⇐"                  form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  218. "⇔"             form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  219. "⇒"                 form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  220. "⥐"              form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  221. "⥞"                form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  222. "↽"                   form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  223. "⥖"                form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  224. "⥟"               form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  225. "⇁"                  form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  226. "⥗"               form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  227. "←"                        form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  228. "⇤"                     form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  229. "⇆"              form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  230. "↔"                   form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  231. "⥎"                  form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  232. "↤"                     form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  233. "⥚"                    form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  234. "↼"                       form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  235. "⥒"                    form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  236. "↙"                   form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  237. "↘"                  form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  238. "→"                       form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  239. "⇥"                    form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  240. "⇄"              form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  241. "↦"                    form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  242. "⥛"                   form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  243. "⇀"                      form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  244. "⥓"                   form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  245. "←"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  246. "→"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  247. "↖"                   form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  248. "↗"                  form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  249. "="                                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  250. "<"                               form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  251. ">"                                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  252. "!="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  253. "=="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  254. "<="                              form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  255. ">="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  256. "≡"                        form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  257. "≍"                           form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  258. "≐"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  259. "∥"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  260. "⩵"                            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  261. "≂"                       form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  262. "⇌"                      form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  263. "≥"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  264. "⋛"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  265. "≧"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  266. "⪢"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  267. "≷"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  268. "⩾"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  269. "≳"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  270. "≎"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  271. "≏"                        form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  272. "⊲"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  273. "⧏"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  274. "⊴"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  275. "≤"                               form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  276. "⋚"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  277. "≦"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  278. "≶"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  279. "⪡"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  280. "⩽"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  281. "≲"                        form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  282. "≫"             form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  283. "≪"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  284. "≢"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  285. "≭"                        form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  286. "∦"             form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  287. "≠"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  288. "≂̸"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  289. "≯"                       form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  290. "≱"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  291. "≧̸"              form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  292. "≫̸"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  293. "≹"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  294. "⩾̸"             form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  295. "≵"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  296. "≎̸"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  297. "≏̸"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  298. "⋪"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  299. "⧏̸"               form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  300. "⋬"             form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  301. "≮"                          form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  302. "≰"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  303. "&NotLessFullEqual;"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  304. "≸"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  305. "≪̸"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  306. "⩽̸"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  307. "≴"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  308. "⪢̸"          form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  309. "⪡̸"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  310. "⊀"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  311. "⪯̸"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  312. "⋠"            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  313. "&NotPrecedesTilde;"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  314. "⋫"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  315. "⧐̸"              form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  316. "⋭"            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  317. "⊁"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  318. "⪰̸"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  319. "⋡"            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  320. "≿̸"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  321. "≁"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  322. "≄"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  323. "≇"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  324. "≉"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  325. "∤"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  326. "≺"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  327. "⪯"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  328. "≼"               form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  329. "≾"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  330. "∷"                       form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  331. "∝"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  332. "⇋"               form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
  333. "⊳"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  334. "⧐"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  335. "⊵"               form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  336. "≻"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  337. "⪰"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  338. "≽"               form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  339. "≿"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  340. "∼"                            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  341. "≃"                       form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  342. "≅"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  343. "≈"                       form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  344. "⊥"                            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  345. "∣"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
  346. "⊔"                      form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
  347. "⋃"                            form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
  348. "⊎"                        form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
  349. "-"                                  form="infix"    lspace="mediummathspace" rspace="mediummathspace"
  350. "+"                                  form="infix"    lspace="mediummathspace" rspace="mediummathspace"
  351. "⋂"                     form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
  352. "∓"                        form="infix"    lspace="mediummathspace" rspace="mediummathspace"
  353. "±"                        form="infix"    lspace="mediummathspace" rspace="mediummathspace"
  354. "⊓"               form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
  355. "⋁"                              form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
  356. "⊖"                      form="prefix"  largeop="true" movablelimits="true"  lspace="0em" rspace="thinmathspace"
  357. "⊕"                       form="prefix"  largeop="true" movablelimits="true"  lspace="0em" rspace="thinmathspace"
  358. "∑"                              form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
  359. "⋃"                            form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
  360. "⊎"                        form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
  361. "lim"                                form="prefix"  movablelimits="true"  lspace="0em" rspace="thinmathspace"
  362. "max"                                form="prefix"  movablelimits="true"  lspace="0em" rspace="thinmathspace"
  363. "min"                                form="prefix"  movablelimits="true"  lspace="0em" rspace="thinmathspace"
  364. "⊖"                      form="infix"    lspace="thinmathspace" rspace="thinmathspace"
  365. "⊕"                       form="infix"    lspace="thinmathspace" rspace="thinmathspace"
  366. "∲"         form="prefix"  largeop="true" stretchy="true"  lspace="0em" rspace="0em"
  367. "∮"                  form="prefix"  largeop="true" stretchy="true"  lspace="0em" rspace="0em"
  368. "∳"  form="prefix"  largeop="true" stretchy="true"  lspace="0em" rspace="0em"
  369. "∯"            form="prefix"  largeop="true" stretchy="true"  lspace="0em" rspace="0em"
  370. "∫"                         form="prefix"  largeop="true" stretchy="true"  lspace="0em" rspace="0em"
  371. "⋓"                              form="infix"    lspace="thinmathspace" rspace="thinmathspace"
  372. "⋒"                              form="infix"    lspace="thinmathspace" rspace="thinmathspace"
  373. "≀"                    form="infix"    lspace="thinmathspace" rspace="thinmathspace"
  374. "⋀"                            form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
  375. "⊗"                      form="prefix"  largeop="true" movablelimits="true"  lspace="0em" rspace="thinmathspace"
  376. "∐"                        form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
  377. "∏"                          form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
  378. "⋂"                     form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
  379. "∐"                        form="infix"    lspace="thinmathspace" rspace="thinmathspace"
  380. "⋆"                             form="infix"    lspace="thinmathspace" rspace="thinmathspace"
  381. "⊙"                        form="prefix"  largeop="true" movablelimits="true"  lspace="0em" rspace="thinmathspace"
  382. "*"                                  form="infix"    lspace="thinmathspace" rspace="thinmathspace"
  383. "⁢"                   form="infix"    lspace="0em" rspace="0em"
  384. "·"                        form="infix"    lspace="thinmathspace" rspace="thinmathspace"
  385. "⊗"                      form="infix"    lspace="thinmathspace" rspace="thinmathspace"
  386. "⋁"                              form="infix"    lspace="thinmathspace" rspace="thinmathspace"
  387. "⋀"                            form="infix"    lspace="thinmathspace" rspace="thinmathspace"
  388. "⋄"                          form="infix"    lspace="thinmathspace" rspace="thinmathspace"
  389. "∖"                        form="infix"   stretchy="true"  lspace="thinmathspace" rspace="thinmathspace"
  390. "/"                                  form="infix"   stretchy="true"  lspace="thinmathspace" rspace="thinmathspace"
  391. "-"                                  form="prefix"   lspace="0em" rspace="veryverythinmathspace"
  392. "+"                                  form="prefix"   lspace="0em" rspace="veryverythinmathspace"
  393. "∓"                        form="prefix"   lspace="0em" rspace="veryverythinmathspace"
  394. "±"                        form="prefix"   lspace="0em" rspace="veryverythinmathspace"
  395. "."                                  form="infix"    lspace="0em" rspace="0em"
  396. "⨯"                            form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
  397. "**"                                 form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
  398. "⊙"                        form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
  399. "∘"                      form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
  400. "□"                           form="prefix"   lspace="0em" rspace="verythinmathspace"
  401. "∇"                              form="prefix"   lspace="0em" rspace="verythinmathspace"
  402. "∂"                         form="prefix"   lspace="0em" rspace="verythinmathspace"
  403. "ⅅ"             form="prefix"   lspace="0em" rspace="verythinmathspace"
  404. "ⅆ"                    form="prefix"   lspace="0em" rspace="verythinmathspace"
  405. "√"                             form="prefix"  stretchy="true"  lspace="0em" rspace="verythinmathspace"
  406. "⇓"                  form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  407. "⟸"              form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  408. "⟺"         form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  409. "⟹"             form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  410. "⇑"                    form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  411. "⇕"                form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  412. "↓"                        form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  413. "⤓"                     form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  414. "⇵"                 form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  415. "↧"                     form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  416. "⥡"                form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  417. "⇃"                   form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  418. "⥙"                form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  419. "⥑"                 form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  420. "⥠"                  form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  421. "↿"                     form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  422. "⥘"                  form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  423. "⟵"                    form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  424. "⟷"               form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  425. "⟶"                   form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  426. "⥯"             form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  427. "⥝"               form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  428. "⇂"                  form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  429. "⥕"               form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  430. "⥏"                form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  431. "⥜"                 form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  432. "↾"                    form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  433. "⥔"                 form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  434. "↓"                   form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
  435. "↑"                     form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
  436. "↑"                          form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  437. "⤒"                       form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  438. "⇅"                 form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  439. "↕"                      form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  440. "⥮"                    form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  441. "↥"                       form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
  442. "^"                                  form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
  443. "<>"                              form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
  444. "'"                                  form="postfix"  lspace="verythinmathspace" rspace="0em"
  445. "!"                                  form="postfix"  lspace="verythinmathspace" rspace="0em"
  446. "!!"                                 form="postfix"  lspace="verythinmathspace" rspace="0em"
  447. "~"                                  form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
  448. "@"                                  form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
  449. "--"                                 form="postfix"  lspace="verythinmathspace" rspace="0em"
  450. "--"                                 form="prefix"   lspace="0em" rspace="verythinmathspace"
  451. "++"                                 form="postfix"  lspace="verythinmathspace" rspace="0em"
  452. "++"                                 form="prefix"   lspace="0em" rspace="verythinmathspace"
  453. "⁡"                    form="infix"    lspace="0em" rspace="0em"
  454. "?"                                  form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
  455. "_"                                  form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
  456. "˘"                            form="postfix" accent="true"  lspace="0em" rspace="0em"
  457. "¸"                          form="postfix" accent="true"  lspace="0em" rspace="0em"
  458. "`"                 form="postfix" accent="true"  lspace="0em" rspace="0em"
  459. "˙"                   form="postfix" accent="true"  lspace="0em" rspace="0em"
  460. "˝"           form="postfix" accent="true"  lspace="0em" rspace="0em"
  461. "&DiacriticalLeftArrow;"             form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  462. "&DiacriticalLeftRightArrow;"        form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  463. "&DiacriticalLeftRightVector;"       form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  464. "&DiacriticalLeftVector;"            form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  465. "´"                 form="postfix" accent="true"  lspace="0em" rspace="0em"
  466. "&DiacriticalRightArrow;"            form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  467. "&DiacriticalRightVector;"           form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  468. "˜"                 form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  469. "¨"                        form="postfix" accent="true"  lspace="0em" rspace="0em"
  470. "̑"                        form="postfix" accent="true"  lspace="0em" rspace="0em"
  471. "ˇ"                            form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  472. "^"                              form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  473. "‾"                          form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  474. "⏞"                        form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  475. "⎴"                      form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  476. "⏜"                  form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  477. "⃛"                        form="postfix" accent="true"  lspace="0em" rspace="0em"
  478. "_"                         form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  479. "⏟"                       form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  480. "⎵"                     form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  481. "⏝"                 form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
  482. ]]></eg>
  483.  
  484. </div2>
  485. </inform-div1>
  486.