# F Operator Dictionary (Non-Normative)

Overview: Mathematical Markup Language (MathML) Version 2.0
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F Operator Dictionary (Non-normative)
F.1 Format of operator dictionary entries
F.2 Indexing of operator dictionary
F.3 Choice of entity names
F.4 Notes on `lspace` and `rspace` attributes
F.5 Operator dictionary entries

The following table gives the suggested dictionary of rendering properties for operators, fences, separators, and accents in MathML, all of which are represented by `mo` elements. For brevity, all such elements will be called simply `operators' in this Appendix.

## F.1 Format of operator dictionary entries

The operators are divided into groups, which are separated by blank lines in the listing below. The grouping, and the order of the groups, is significant for the proper grouping of sub-expressions using `<mrow>` (Section 3.3.1 [Horizontally Group Sub-Expressions (`mrow`)]); the rule described there is especially relevant to the automatic generation of MathML by conversion from other formats for displayed mathematics, such as TEX, which do not always specify how sub-expressions nest.

The format of the table entries is: the `<mo>` element content between double quotes (start and end tags not shown), followed by the attribute list in XML format, starting with the `form` attribute, followed by the default rendering attributes which should be used for `mo` elements with the given content and `form` attribute.

Any attribute not listed for some entry has its default value, which is given in parentheses in the table of attributes in Section 3.2.5 [Operator, Fence, Separator or Accent (`mo`)].

Note that the characters & and < are represented in the following table entries by the entity references `&amp;` and `&lt;` respectively, as would be necessary if they appeared in the content of an actual `mo` element (or any other MathML or XML element).

For example, the first entry,

    "(" form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em"

could be expressed as an `mo` element by:

    <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em"> ( </mo>

(note the lack of double quotes around the content, and the whitespace added around the content for readability, which is optional in MathML).

This entry means that, for MathML renderers which use this suggested operator dictionary, giving the element `<mo form="prefix"> ( </mo>` alone, or simply `<mo> ( </mo>` in a position for which `form="prefix"` would be inferred (see below), is equivalent to giving the element with all attributes as shown above.

## F.2 Indexing of operator dictionary

Note that the dictionary is indexed not just by the element content, but by the element content and `form` attribute value, together. Operators with more than one possible form have more than one entry. The MathML specification describes how the renderer chooses (`infers') which form to use when no `form` attribute is given; see Section 3.2.5.7.2 [Default value of the `form` attribute].

Having made that choice, or with the `form` attribute explicitly specified in the `<mo>` element's start tag, the MathML renderer uses the remaining attributes from the dictionary entry for the appropriate single form of that operator, ignoring the entries for the other possible forms.

## F.3 Choice of entity names

Extended characters in MathML (and in the operator dictionary below) are represented by XML-style entity references using the syntax `&character-name;` the complete list of characters and character names is given in Chapter 6 [Characters, Entities and Fonts]. Many characters can be referred to by more than one name; often, memorable names composed of full words have been provided in MathML, as well as one or more names used in other standards, such as Unicode. The characters in the operators in this dictionary are generally listed under their full-word names when these exist. For example, the integral operator is named below by the one-character sequence `&Integral;`, but could equally well be named `&int;`. The choice of name for a given character in MathML has no effect on its rendering.

It is intended that every entity named below appears somewhere in Chapter 6 [Characters, Entities and Fonts]. If this is not true, it is an error in this specification. If such an error exists, the abovementioned chapter should be taken as definitive, rather than this appendix.

## F.4 Notes on `lspace` and `rspace` attributes

The values for `lspace` and `rspace` given here range from 0 to `verythickmathspace`, which has a default value of 6/18 em. For the invisible operators whose content is `&InvisibleTimes;` or `&ApplyFunction;`, it is suggested that MathML renderers choose spacing in a context-sensitive way (which is an exception to the static values given in the following table). For `<mo>&ApplyFunction;</mo>`, the total spacing (`lspace`+`rspace`) in expressions such as `sin x' (where the right operand doesn't start with a fence) should be greater than zero; for `<mo>&InvisibleTimes;</mo>`, the total spacing should be greater than zero when both operands (or the nearest tokens on either side, if on the baseline) are identifiers displayed in a non-slanted font (i.e. under the suggested rules, when both operands are multi-character identifiers).

Some renderers may wish to use no spacing for most operators appearing in scripts (i.e. when `scriptlevel` is greater than 0; see Section 3.3.4 [Style Change (`mstyle`)]), as is the case in TEX.

## F.5 Operator dictionary entries

    "("                                  form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
    ")"                                  form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "["                                  form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "]"                                  form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "{"                                  form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "}"                                  form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "&CloseCurlyDoubleQuote;"            form="postfix" fence="true"  lspace="0em" rspace="0em"
    "&CloseCurlyQuote;"                  form="postfix" fence="true"  lspace="0em" rspace="0em"
    "&LeftAngleBracket;"                 form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "&LeftBracketingBar;"                form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "&LeftCeiling;"                      form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "&LeftDoubleBracket;"                form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "&LeftDoubleBracketingBar;"          form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "&LeftFloor;"                        form="prefix"  fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "&OpenCurlyDoubleQuote;"             form="prefix"  fence="true"  lspace="0em" rspace="0em"
    "&OpenCurlyQuote;"                   form="prefix"  fence="true"  lspace="0em" rspace="0em"
    "&RightAngleBracket;"                form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "&RightBracketingBar;"               form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "&RightCeiling;"                     form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "&RightDoubleBracket;"               form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "&RightDoubleBracketingBar;"         form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "&RightFloor;"                       form="postfix" fence="true" stretchy="true"  lspace="0em" rspace="0em"
    "&LeftSkeleton;"                     form="prefix"  fence="true"  lspace="0em" rspace="0em"
    "&RightSkeleton;"                    form="postfix" fence="true"  lspace="0em" rspace="0em"
    "&InvisibleComma;"                   form="infix"   separator="true"  lspace="0em" rspace="0em"
    ","                                  form="infix"   separator="true"  lspace="0em" rspace="verythickmathspace"
    "&HorizontalLine;"                   form="infix"   stretchy="true" minsize="0"  lspace="0em" rspace="0em"
    "&VerticalLine;"                     form="infix"   stretchy="true" minsize="0"  lspace="0em" rspace="0em"
    ";"                                  form="infix"   separator="true"  lspace="0em" rspace="thickmathspace"
    ";"                                  form="postfix" separator="true"  lspace="0em" rspace="0em"
    ":="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Assign;"                           form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Because;"                          form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Therefore;"                        form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&VerticalSeparator;"                form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "//"                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Colon;"                            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&"                              form="prefix"   lspace="0em" rspace="thickmathspace"
    "&"                              form="postfix"  lspace="thickmathspace" rspace="0em"
    "*="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "-="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "+="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "/="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "->"                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    ":"                                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    ".."                                 form="postfix"  lspace="mediummathspace" rspace="0em"
    "..."                                form="postfix"  lspace="mediummathspace" rspace="0em"
    "&SuchThat;"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&DoubleLeftTee;"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&DoubleRightTee;"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&DownTee;"                          form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&LeftTee;"                          form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&RightTee;"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Implies;"                          form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&RoundImplies;"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "|"                                  form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "||"                                 form="infix"    lspace="mediummathspace" rspace="mediummathspace"
    "&Or;"                               form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
    "&&"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&And;"                              form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
    "&"                              form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "!"                                  form="prefix"   lspace="0em" rspace="thickmathspace"
    "&Not;"                              form="prefix"   lspace="0em" rspace="thickmathspace"
    "&Exists;"                           form="prefix"   lspace="0em" rspace="thickmathspace"
    "&ForAll;"                           form="prefix"   lspace="0em" rspace="thickmathspace"
    "&NotExists;"                        form="prefix"   lspace="0em" rspace="thickmathspace"
    "&Element;"                          form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotElement;"                       form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotReverseElement;"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotSquareSubset;"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotSquareSubsetEqual;"             form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotSquareSuperset;"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotSquareSupersetEqual;"           form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotSubset;"                        form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotSubsetEqual;"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotSuperset;"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotSupersetEqual;"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&ReverseElement;"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&SquareSubset;"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&SquareSubsetEqual;"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&SquareSuperset;"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&SquareSupersetEqual;"              form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Subset;"                           form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&SubsetEqual;"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Superset;"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&SupersetEqual;"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&DoubleLeftArrow;"                  form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&DoubleLeftRightArrow;"             form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&DoubleRightArrow;"                 form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&DownLeftRightVector;"              form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&DownLeftTeeVector;"                form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&DownLeftVector;"                   form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&DownLeftVectorBar;"                form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&DownRightTeeVector;"               form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&DownRightVector;"                  form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&DownRightVectorBar;"               form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&LeftArrow;"                        form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&LeftArrowBar;"                     form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&LeftArrowRightArrow;"              form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&LeftRightArrow;"                   form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&LeftRightVector;"                  form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&LeftTeeArrow;"                     form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&LeftTeeVector;"                    form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&LeftVector;"                       form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&LeftVectorBar;"                    form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&LowerLeftArrow;"                   form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&LowerRightArrow;"                  form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&RightArrow;"                       form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&RightArrowBar;"                    form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&RightArrowLeftArrow;"              form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&RightTeeArrow;"                    form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&RightTeeVector;"                   form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&RightVector;"                      form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&RightVectorBar;"                   form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&ShortLeftArrow;"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&ShortRightArrow;"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&UpperLeftArrow;"                   form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&UpperRightArrow;"                  form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "="                                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "<"                               form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    ">"                                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "!="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "=="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "<="                              form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    ">="                                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Congruent;"                        form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&CupCap;"                           form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&DotEqual;"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&DoubleVerticalBar;"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Equal;"                            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&EqualTilde;"                       form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Equilibrium;"                      form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&GreaterEqual;"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&GreaterEqualLess;"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&GreaterFullEqual;"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&GreaterGreater;"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&GreaterLess;"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&GreaterSlantEqual;"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&GreaterTilde;"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&HumpDownHump;"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&HumpEqual;"                        form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&LeftTriangle;"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&LeftTriangleBar;"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&LeftTriangleEqual;"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&le;"                               form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&LessEqualGreater;"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&LessFullEqual;"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&LessGreater;"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&LessLess;"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&LessSlantEqual;"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&LessTilde;"                        form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NestedGreaterGreater;"             form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NestedLessLess;"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotCongruent;"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotCupCap;"                        form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotDoubleVerticalBar;"             form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotEqual;"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotEqualTilde;"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotGreater;"                       form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotGreaterEqual;"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotGreaterFullEqual;"              form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotGreaterGreater;"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotGreaterLess;"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotGreaterSlantEqual;"             form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotGreaterTilde;"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotHumpDownHump;"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotHumpEqual;"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotLeftTriangle;"                  form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotLeftTriangleBar;"               form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotLeftTriangleEqual;"             form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotLess;"                          form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotLessEqual;"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotLessFullEqual;"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotLessGreater;"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotLessLess;"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotLessSlantEqual;"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotLessTilde;"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotNestedGreaterGreater;"          form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotNestedLessLess;"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotPrecedes;"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotPrecedesEqual;"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotPrecedesSlantEqual;"            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotPrecedesTilde;"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotRightTriangle;"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotRightTriangleBar;"              form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotRightTriangleEqual;"            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotSucceeds;"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotSucceedsEqual;"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotSucceedsSlantEqual;"            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotSucceedsTilde;"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotTilde;"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotTildeEqual;"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotTildeFullEqual;"                form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotTildeTilde;"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&NotVerticalBar;"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Precedes;"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&PrecedesEqual;"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&PrecedesSlantEqual;"               form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&PrecedesTilde;"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Proportion;"                       form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Proportional;"                     form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&ReverseEquilibrium;"               form="infix"   stretchy="true"  lspace="thickmathspace" rspace="thickmathspace"
    "&RightTriangle;"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&RightTriangleBar;"                 form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&RightTriangleEqual;"               form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Succeeds;"                         form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&SucceedsEqual;"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&SucceedsSlantEqual;"               form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&SucceedsTilde;"                    form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&Tilde;"                            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&TildeEqual;"                       form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&TildeFullEqual;"                   form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&TildeTilde;"                       form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&UpTee;"                            form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&VerticalBar;"                      form="infix"    lspace="thickmathspace" rspace="thickmathspace"
    "&SquareUnion;"                      form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
    "&Union;"                            form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
    "&UnionPlus;"                        form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
    "-"                                  form="infix"    lspace="mediummathspace" rspace="mediummathspace"
    "+"                                  form="infix"    lspace="mediummathspace" rspace="mediummathspace"
    "&Intersection;"                     form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
    "&MinusPlus;"                        form="infix"    lspace="mediummathspace" rspace="mediummathspace"
    "&PlusMinus;"                        form="infix"    lspace="mediummathspace" rspace="mediummathspace"
    "&SquareIntersection;"               form="infix"   stretchy="true"  lspace="mediummathspace" rspace="mediummathspace"
    "&Vee;"                              form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
    "&CircleMinus;"                      form="prefix"  largeop="true" movablelimits="true"  lspace="0em" rspace="thinmathspace"
    "&CirclePlus;"                       form="prefix"  largeop="true" movablelimits="true"  lspace="0em" rspace="thinmathspace"
    "&Sum;"                              form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
    "&Union;"                            form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
    "&UnionPlus;"                        form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
    "lim"                                form="prefix"  movablelimits="true"  lspace="0em" rspace="thinmathspace"
    "max"                                form="prefix"  movablelimits="true"  lspace="0em" rspace="thinmathspace"
    "min"                                form="prefix"  movablelimits="true"  lspace="0em" rspace="thinmathspace"
    "&CircleMinus;"                      form="infix"    lspace="thinmathspace" rspace="thinmathspace"
    "&CirclePlus;"                       form="infix"    lspace="thinmathspace" rspace="thinmathspace"
    "&ClockwiseContourIntegral;"         form="prefix"  largeop="true" stretchy="true"  lspace="0em" rspace="0em"
    "&ContourIntegral;"                  form="prefix"  largeop="true" stretchy="true"  lspace="0em" rspace="0em"
    "&CounterClockwiseContourIntegral;"  form="prefix"  largeop="true" stretchy="true"  lspace="0em" rspace="0em"
    "&DoubleContourIntegral;"            form="prefix"  largeop="true" stretchy="true"  lspace="0em" rspace="0em"
    "&Integral;"                         form="prefix"  largeop="true" stretchy="true"  lspace="0em" rspace="0em"
    "&Cup;"                              form="infix"    lspace="thinmathspace" rspace="thinmathspace"
    "&Cap;"                              form="infix"    lspace="thinmathspace" rspace="thinmathspace"
    "&VerticalTilde;"                    form="infix"    lspace="thinmathspace" rspace="thinmathspace"
    "&Wedge;"                            form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
    "&CircleTimes;"                      form="prefix"  largeop="true" movablelimits="true"  lspace="0em" rspace="thinmathspace"
    "&Coproduct;"                        form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
    "&Product;"                          form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
    "&Intersection;"                     form="prefix"  largeop="true" movablelimits="true" stretchy="true"  lspace="0em" rspace="thinmathspace"
    "&Coproduct;"                        form="infix"    lspace="thinmathspace" rspace="thinmathspace"
    "&Star;"                             form="infix"    lspace="thinmathspace" rspace="thinmathspace"
    "&CircleDot;"                        form="prefix"  largeop="true" movablelimits="true"  lspace="0em" rspace="thinmathspace"
    "*"                                  form="infix"    lspace="thinmathspace" rspace="thinmathspace"
    "&InvisibleTimes;"                   form="infix"    lspace="0em" rspace="0em"
    "&CenterDot;"                        form="infix"    lspace="thinmathspace" rspace="thinmathspace"
    "&CircleTimes;"                      form="infix"    lspace="thinmathspace" rspace="thinmathspace"
    "&Vee;"                              form="infix"    lspace="thinmathspace" rspace="thinmathspace"
    "&Wedge;"                            form="infix"    lspace="thinmathspace" rspace="thinmathspace"
    "&Diamond;"                          form="infix"    lspace="thinmathspace" rspace="thinmathspace"
    "&Backslash;"                        form="infix"   stretchy="true"  lspace="thinmathspace" rspace="thinmathspace"
    "/"                                  form="infix"   stretchy="true"  lspace="thinmathspace" rspace="thinmathspace"
    "-"                                  form="prefix"   lspace="0em" rspace="veryverythinmathspace"
    "+"                                  form="prefix"   lspace="0em" rspace="veryverythinmathspace"
    "&MinusPlus;"                        form="prefix"   lspace="0em" rspace="veryverythinmathspace"
    "&PlusMinus;"                        form="prefix"   lspace="0em" rspace="veryverythinmathspace"
    "."                                  form="infix"    lspace="0em" rspace="0em"
    "&Cross;"                            form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
    "**"                                 form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
    "&CircleDot;"                        form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
    "&SmallCircle;"                      form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
    "&Square;"                           form="prefix"   lspace="0em" rspace="verythinmathspace"
    "&Del;"                              form="prefix"   lspace="0em" rspace="verythinmathspace"
    "&PartialD;"                         form="prefix"   lspace="0em" rspace="verythinmathspace"
    "&CapitalDifferentialD;"             form="prefix"   lspace="0em" rspace="verythinmathspace"
    "&DifferentialD;"                    form="prefix"   lspace="0em" rspace="verythinmathspace"
    "&Sqrt;"                             form="prefix"  stretchy="true"  lspace="0em" rspace="verythinmathspace"
    "&DoubleDownArrow;"                  form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&DoubleLongLeftArrow;"              form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&DoubleLongLeftRightArrow;"         form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&DoubleLongRightArrow;"             form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&DoubleUpArrow;"                    form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&DoubleUpDownArrow;"                form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&DownArrow;"                        form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&DownArrowBar;"                     form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&DownArrowUpArrow;"                 form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&DownTeeArrow;"                     form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&LeftDownTeeVector;"                form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&LeftDownVector;"                   form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&LeftDownVectorBar;"                form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&LeftUpDownVector;"                 form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&LeftUpTeeVector;"                  form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&LeftUpVector;"                     form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&LeftUpVectorBar;"                  form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&LongLeftArrow;"                    form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&LongLeftRightArrow;"               form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&LongRightArrow;"                   form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&ReverseUpEquilibrium;"             form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&RightDownTeeVector;"               form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&RightDownVector;"                  form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&RightDownVectorBar;"               form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&RightUpDownVector;"                form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&RightUpTeeVector;"                 form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&RightUpVector;"                    form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&RightUpVectorBar;"                 form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&ShortDownArrow;"                   form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
    "&ShortUpArrow;"                     form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
    "&UpArrow;"                          form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&UpArrowBar;"                       form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&UpArrowDownArrow;"                 form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&UpDownArrow;"                      form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&UpEquilibrium;"                    form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "&UpTeeArrow;"                       form="infix"   stretchy="true"  lspace="verythinmathspace" rspace="verythinmathspace"
    "^"                                  form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
    "<>"                              form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
    "'"                                  form="postfix"  lspace="verythinmathspace" rspace="0em"
    "!"                                  form="postfix"  lspace="verythinmathspace" rspace="0em"
    "!!"                                 form="postfix"  lspace="verythinmathspace" rspace="0em"
    "~"                                  form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
    "@"                                  form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
    "--"                                 form="postfix"  lspace="verythinmathspace" rspace="0em"
    "--"                                 form="prefix"   lspace="0em" rspace="verythinmathspace"
    "++"                                 form="postfix"  lspace="verythinmathspace" rspace="0em"
    "++"                                 form="prefix"   lspace="0em" rspace="verythinmathspace"
    "&ApplyFunction;"                    form="infix"    lspace="0em" rspace="0em"
    "?"                                  form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
    "_"                                  form="infix"    lspace="verythinmathspace" rspace="verythinmathspace"
    "&Breve;"                            form="postfix" accent="true"  lspace="0em" rspace="0em"
    "&Cedilla;"                          form="postfix" accent="true"  lspace="0em" rspace="0em"
    "&DiacriticalGrave;"                 form="postfix" accent="true"  lspace="0em" rspace="0em"
    "&DiacriticalDot;"                   form="postfix" accent="true"  lspace="0em" rspace="0em"
    "&DiacriticalDoubleAcute;"           form="postfix" accent="true"  lspace="0em" rspace="0em"
    "&DiacriticalLeftArrow;"             form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&DiacriticalLeftRightArrow;"        form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&DiacriticalLeftRightVector;"       form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&DiacriticalLeftVector;"            form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&DiacriticalAcute;"                 form="postfix" accent="true"  lspace="0em" rspace="0em"
    "&DiacriticalRightArrow;"            form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&DiacriticalRightVector;"           form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&DiacriticalTilde;"                 form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&DoubleDot;"                        form="postfix" accent="true"  lspace="0em" rspace="0em"
    "&DownBreve;"                        form="postfix" accent="true"  lspace="0em" rspace="0em"
    "&Hacek;"                            form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&Hat;"                              form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&OverBar;"                          form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&OverBrace;"                        form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&OverBracket;"                      form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&OverParenthesis;"                  form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&TripleDot;"                        form="postfix" accent="true"  lspace="0em" rspace="0em"
    "&UnderBar;"                         form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&UnderBrace;"                       form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&UnderBracket;"                     form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"
    "&UnderParenthesis;"                 form="postfix" accent="true" stretchy="true"  lspace="0em" rspace="0em"

Overview: Mathematical Markup Language (MathML) Version 2.0
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