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1 | - | + | The Wiki supports LaTeX markup:
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2 | + | |||
3 | + | <math>pi=\frac{3}{4} \sqrt{3}+24 \int_0^{1/4}{\sqrt{x-x^2}dx}</math>
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4 | + | |||
5 | + | Mathematical Formula (LaTeX) can be inserted into text like this:
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6 | + | {{{
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7 | + | <math>Insert formula here</math>
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8 | + | }}}
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9 | + | |||
10 | + | For example:
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11 | + | {{{
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12 | + | <math>\alpha^2+\beta^2=1</math>
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13 | + | }}}
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14 | + | |||
15 | + | ...displays <math>\alpha^2+\beta^2=1</math>
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16 | + | |||
17 | + | == Displaying a Formula ==
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18 | + | |||
19 | + | The Wiki uses a subset of TeX markup, including some extensions from LaTeX and AMSLaTeX, for mathematical formulae. It generates either PNG images or simple HTML markup, depending on the complexity of the expression. While it can generate MathML, it is not currently used due to limited browser support. As browsers become more advanced and support for MathML becomes more wide-spread, this could be the preferred method of output as images have very real disadvantages.
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20 | + | |||
21 | + | === Syntax ===
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22 | + | |||
23 | + | Math markup goes inside `<math> ... </math>`.
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24 | + | |||
25 | + | ===Pros of HTML===
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26 | + | # In-line HTML formulae always align properly with the rest of the HTML text.
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27 | + | # The formula's background, font size and face match the rest of HTML contents and the appearance respects CSS and browser settings.
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28 | + | # Pages using HTML will load faster.
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29 | + | |||
30 | + | === Pros of TeX ===
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31 | + | # TeX is semantically superior to HTML. In TeX, "`x`" means "mathematical variable <math>x</math>", whereas in HTML "`x`" could mean anything. Information has been irrevocably lost.
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32 | + | # TeX has been specifically designed for typesetting formulae, so input is easier and more natural, and output is more aesthetically pleasing.
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33 | + | # One consequence of point 1 is that TeX can be transformed into HTML, but not vice-versa. This means that on the server side we can always transform a formula, based on its complexity and location within the text, user preferences, type of browser, etc. Therefore, where possible, all the benefits of HTML can be retained, together with the benefits of TeX. It's true that the current situation is not ideal, but that's not a good reason to drop information/contents. It's more a reason to help improve the situation.
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34 | + | # Another consequence of point 1 is that TeX can be converted to !MathML for browsers which support it, thus keeping its semantics and allowing it to be rendered vectorially.
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35 | + | # When writing in TeX, editors need not worry about whether this or that version of this or that browser supports this or that HTML entity. The burden of these decisions is put on the server. This doesn't hold for HTML formulae, which can easily end up being rendered wrongly or differently from the editor's intentions on a different browser.
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36 | + | # TeX is the preferred text formatting language of most professional mathematicians, scientists, and engineers. It is easier to persuade them to contribute if they can write in TeX.
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37 | + | |||
38 | + | === Example Formulas ===
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39 | + | |||
40 | + | The following are a few examples of formulas:
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41 | + | |||
42 | + | {{{
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43 | + | <math>\sqrt{1-e^2}</math>
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44 | + | }}}
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45 | + | <math>\sqrt{1-e^2}</math>
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46 | + | |||
47 | + | {{{
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48 | + | <math>\overbrace{ 1+2+\cdots+100 }^{5050}</math>
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49 | + | }}}
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50 | + | <math>\overbrace{ 1+2+\cdots+100 }^{5050}</math>
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51 | + | |||
52 | + | {{{
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53 | + | <math>ax^2 + bx + c = 0</math>
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54 | + | }}}
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55 | + | <math>ax^2 + bx + c = 0</math>
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56 | + | |||
57 | + | {{{
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58 | + | <math>\int_{-N}^{N} e^x\, dx</math>
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59 | + | }}}
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60 | + | <math>\int_{-N}^{N} e^x\, dx</math>
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61 | + | |||
62 | + | == Functions, symbols, special characters ==
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63 | + | |||
64 | + | === Accents/Diacritics ===
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65 | + | |||
66 | + | || `\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}` || <math>\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}</math> ||
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67 | + | || `\check{a} \bar{a} \ddot{a} \dot{a}` ||<math>\ \check{a} \bar{a} \ddot{a} \dot{a}</math> ||
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68 | + | |||
69 | + | === Standard functions ===
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70 | + | |||
71 | + | || `\sin a \cos b \tan c`|| <math>\ \sin a \cos b \tan c</math> ||
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72 | + | || `\sec d \csc e \cot f`|| <math>\sec d \csc e \cot f\,\!</math> ||
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73 | + | || `\arcsin h \arccos i \arctan j`|| <math>\arcsin h \arccos i \arctan j\,\!</math> ||
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74 | + | || `\sinh k \cosh l \tanh m \coth n`|| <math>\ \sinh k \cosh l \tanh m \coth n</math> ||
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75 | + | || `\operatorname{sh}\,o\,\operatorname{ch}\,p\,\operatorname{th}\,q`|| <math>\ \operatorname{sh}\,o\,\operatorname{ch}\,p\,\operatorname{th}\,q</math> ||
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76 | + | || `\operatorname{arsinh}\,r\,\operatorname{arcosh}\,s\,\operatorname{artanh}\,t`|| <math>\operatorname{arsinh}\,r\,\operatorname{arcosh}\,s\,\operatorname{artanh}\,t\,\!</math> ||
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77 | + | || `\lim u \limsup v \liminf w \min x \max y` || <math>\ \lim u \limsup v \liminf w \min x \max y</math> ||
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78 | + | || `\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g` ||<math>\ \inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g</math> ||
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79 | + | || `\deg h \gcd i \Pr j \det k \hom l \arg m \dim n` || <math>\deg h \gcd i \Pr j \det k \hom l \arg m \dim n\,\!</math> ||
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80 | + | |||
81 | + | === Modular arithmetic ===
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82 | + | |||
83 | + | || `s_k \equiv 0 \pmod{m}` || <math>s_k \equiv 0 \pmod{m}\,\! </math> ||
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84 | + | || `a\,\bmod\,b` || <math>a\,\bmod\,b\,\!</math> ||
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85 | + | |||
86 | + | === Derivatives ===
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87 | + | |||
88 | + | || `\nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2}` || <math>\nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2}</math> ||
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89 | + | |||
90 | + | === Sets ===
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91 | + | |||
92 | + | || `\forall \exists \empty \emptyset \varnothing` || <math>\forall \exists \empty \emptyset \varnothing\,\!</math> ||
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93 | + | || `\in \ni \not \in \notin \subset \subseteq \supset \supseteq` || <math>\in \ni \not \in \notin \subset \subseteq \supset \supseteq\,\!</math> ||
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94 | + | || `\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus` || <math>\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus\,\!</math> ||
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95 | + | || `\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup` || <math>\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup\,\!</math> ||
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96 | + | |||
97 | + | === Operators ===
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98 | + | |||
99 | + | || `+ \oplus \bigoplus \pm \mp - ` || <math>+ \oplus \bigoplus \pm \mp - \,\!</math> ||
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100 | + | || `\times \otimes \bigotimes \cdot \circ \bullet \bigodot` || <math>\times \otimes \bigotimes \cdot \circ \bullet \bigodot\,\!</math> ||
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101 | + | || `\star * / \div \frac{1}{2}` || <math>\star * / \div \frac{1}{2}\,\!</math> ||
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102 | + | |||
103 | + | === Logic ===
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104 | + | || `\land (or \and) \wedge \bigwedge \bar{q} \to p` || <math>\land \wedge \bigwedge \bar{q} \to p\,\!</math> ||
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105 | + | || `\lor \vee \bigvee \lnot \neg q \And` || <math>\lor \vee \bigvee \lnot \neg q \And\,\!</math> ||
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106 | + | |||
107 | + | === Root ===
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108 | + | |||
109 | + | || `\sqrt{2} \sqrt[n]{x}` || <math>\sqrt{2} \sqrt[n]{x}\,\!</math> ||
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110 | + | |||
111 | + | === Relations ===
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112 | + | |||
113 | + | || `\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}` || <math>\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}\,\!</math> ||
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114 | + | || `\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto` || <math>\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto\,\!</math> ||
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115 | + | |||
116 | + | === Geometric ===
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117 | + | |||
118 | + | || `\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ` || <math>\Diamond \, \Box \, \triangle \, \angle \perp \, \mid \; \nmid \, \| 45^\circ\,\!</math> ||
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119 | + | |||
120 | + | === Arrows ===
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121 | + | |||
122 | + | || `\leftarrow (or \gets) \rightarrow (or \to) \nleftarrow \not\to \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow` || <math>\leftarrow \rightarrow \nleftarrow \not\to \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow \,\!</math> ||
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123 | + | || `\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow (or \iff)` || <math>\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow \,\!</math> ||
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124 | + | || `\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow` || <math>\ \uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow</math> ||
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125 | + | || `\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons` || <math>\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons \,\!</math> ||
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126 | + | || `\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright` || <math>\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright \,\!</math> ||
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127 | + | || `\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft` || <math>\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft \,\!</math> ||
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128 | + | || `\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow ` || <math>\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \,\!</math> ||
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129 | + | |||
130 | + | === Special ===
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131 | + | |||
132 | + | || `\And \eth \S \P \% \dagger \ddagger \ldots \cdots` || <math>\And \eth \S \P \% \dagger \ddagger \ldots \cdots\,\!</math> ||
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133 | + | || `\smile \frown \wr \triangleleft \triangleright \infty \bot \top` || <math>\smile \frown \wr \triangleleft \triangleright \infty \bot \top\,\!</math> ||
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134 | + | || `\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar` || <math>\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar\,\!</math> ||
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135 | + | || `\ell \mho \Finv \Re \Im \wp \complement` || <math>\ell \mho \Finv \Re \Im \wp \complement\,\!</math> ||
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136 | + | || `\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp` || <math>\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp\,\!</math> ||
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137 | + | |||
138 | + | === Unsorted (new stuff) ===
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139 | + | |||
140 | + | || `\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown` || <math> \vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown</math> ||
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141 | + | || `\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge` || <math>\ \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge</math> ||
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142 | + | || `\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes` || <math> \veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes</math> ||
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143 | + | || `\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant` || <math> \rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant</math> ||
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144 | + | || `\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq` || <math> \eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq</math> ||
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145 | + | || `\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft` || <math> \fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft</math> ||
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146 | + | || `\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot` || <math> \Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot</math> ||
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147 | + | || `\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq` || <math> \ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq</math> ||
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148 | + | || `\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork` || <math> \Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork</math> ||
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149 | + | || `\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq` || <math> \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq</math> ||
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150 | + | || `\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid` || <math> \lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid</math> ||
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151 | + | || `\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr` || <math> \nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr</math> ||
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152 | + | || `\subsetneq` || <math>\subsetneq</math> ||
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153 | + | || `\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq` || <math> \ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq</math> ||
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154 | + | || `\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq` || <math> \succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq</math> ||
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155 | + | || `\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq` || <math> \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq</math> ||
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156 | + | || `\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus` || <math>\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus\,\!</math> ||
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157 | + | || `\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq` || <math>\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq\,\!</math> ||
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158 | + | || `\dashv \asymp \doteq \parallel` || <math>\dashv \asymp \doteq \parallel\,\!</math> ||
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159 | + | || `\ulcorner \urcorner \llcorner \lrcorner` || <math>\ulcorner \urcorner \llcorner \lrcorner</math> ||
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160 | + | |||
161 | + | == Larger Expressions ==
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162 | + | |||
163 | + | === Parenthesizing big expressions, brackets, bars ===
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164 | + | |||
165 | + | || '''Feature''' || '''Syntax''' || '''How it looks rendered''' ||
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166 | + | || Bad || `( \frac{1}{2} )` || <math>( \frac{1}{2} )</math> ||
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167 | + | || Good || `\left ( \frac{1}{2} \right )` || <math>\left ( \frac{1}{2} \right )</math> ||
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168 | + | |||
169 | + | You can use various delimiters with \left and \right:
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170 | + | |||
171 | + | || '''Feature''' || '''Syntax''' || '''How it looks rendered''' ||
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172 | + | || Parentheses || `\left ( \frac{a}{b} \right )` || <math>\left ( \frac{a}{b} \right )</math> ||
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173 | + | || Brackets || `\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack` || <math>\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack</math> ||
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174 | + | || Braces || `\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace` || <math>\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace</math> ||
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175 | + | || Angle brackets || `\left \langle \frac{a}{b} \right \rangle` || <math>\left \langle \frac{a}{b} \right \rangle</math> ||
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176 | + | || Bars and double bars || `\left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|` || <math>\left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|</math> ||
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177 | + | || Floor and ceiling functions: || `\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil` || <math>\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil</math> ||
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178 | + | || Slashes and backslashes || `\left / \frac{a}{b} \right \backslash` || <math>\left / \frac{a}{b} \right \backslash</math> ||
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179 | + | || Up, down and up-down arrows || `\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow` || <math>\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow</math> ||
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180 | + | || Delimiters can be mixed,[[BR]]as long as \left and \right match || `\left [ 0,1 \right )` [[BR]] `\left \langle \psi \right |` || <math>\left [ 0,1 \right )</math> [[BR]] <math>\left \langle \psi \right |</math> ||
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181 | + | || Use \left. and \right. if you don't[[BR]]want a delimiter to appear: || `\left . \frac{A}{B} \right \} \to X` || <math>\left . \frac{A}{B} \right \} \to X</math> ||
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182 | + | || Size of the delimiters || `\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]/` || <math>\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]</math> ||
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183 | + | || . || `\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle` || <math>\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle</math> ||
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184 | + | || . || `\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big|` || <math>\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big|</math> ||
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185 | + | || . || `\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil` || <math>\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil</math> ||
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186 | + | || . || `\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow` || <math>\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow</math> ||
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187 | + | || . || `\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow` || <math>\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow</math> ||
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188 | + | || . || `\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash` || <math>\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash</math> ||
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189 | + | |||
190 | + | == Alphabets and typefaces ==
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191 | + | |||
192 | + | Texvc cannot render arbitrary Unicode characters. Those it can handle can be entered by the expressions below. For others, such as Cyrillic, they can be entered as Unicode or HTML entities in running text, but cannot be used in displayed formulas.
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193 | + | |||
194 | + | ||_\2. '''Greek alphabet''' ||
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195 | + | || `\Alpha \Beta \Gamma \Delta \Epsilon \Zeta` || <math>\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \,\!</math> ||
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196 | + | || `\Eta \Theta \Iota \Kappa \Lambda \Mu` || <math>\Eta \Theta \Iota \Kappa \Lambda \Mu \,\!</math> ||
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197 | + | || `\Nu \Xi \Pi \Rho \Sigma \Tau` || <math>\Nu \Xi \Pi \Rho \Sigma \Tau\,\!</math> ||
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||
198 | + | || `\Upsilon \Phi \Chi \Psi \Omega` || <math>\Upsilon \Phi \Chi \Psi \Omega \,\!</math> ||
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||
199 | + | || `\alpha \beta \gamma \delta \epsilon \zeta` || <math>\alpha \beta \gamma \delta \epsilon \zeta \,\!</math> ||
|
||
200 | + | || `\eta \theta \iota \kappa \lambda \mu` || <math>\eta \theta \iota \kappa \lambda \mu \,\!</math> ||
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||
201 | + | || `\nu \xi \pi \rho \sigma \tau` || <math>\nu \xi \pi \rho \sigma \tau \,\!</math> ||
|
||
202 | + | || `\upsilon \phi \chi \psi \omega` || <math>\upsilon \phi \chi \psi \omega \,\!</math> ||
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203 | + | || `\varepsilon \digamma \vartheta \varkappa` || <math>\varepsilon \digamma \vartheta \varkappa \,\!</math> ||
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204 | + | || `\varpi \varrho \varsigma \varphi` || <math>\varpi \varrho \varsigma \varphi\,\!</math> ||
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205 | + | ||_\2. '''Blackboard Bold/Scripts''' ||
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||
206 | + | || `\mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G}` || <math>\mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G} \,\!</math> ||
|
||
207 | + | || `\mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M}` || <math>\mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M} \,\!</math> ||
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||
208 | + | || `\mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T}` || <math>\mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T} \,\!</math> ||
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||
209 | + | || `\mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z}` || <math>\mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z}\,\!</math> ||
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||
210 | + | ||_\2. '''boldface (vectors)''' ||
|
||
211 | + | || `\mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G}` || <math>\mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G} \,\!</math> ||
|
||
212 | + | || `\mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M}` || <math>\mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M} \,\!</math> ||
|
||
213 | + | || `\mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T}` || <math>\mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T} \,\!</math> ||
|
||
214 | + | || `\mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z}` || <math>\mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z} \,\!</math> ||
|
||
215 | + | || `\mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g}` || <math>\mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g} \,\!</math> ||
|
||
216 | + | || `\mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m}` || <math>\mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m} \,\!</math> ||
|
||
217 | + | || `\mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t}` || <math>\mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t} \,\!</math> ||
|
||
218 | + | || `\mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z}` || <math>\mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z} \,\!</math> ||
|
||
219 | + | || `\mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4}` || <math>\mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4} \,\!</math> ||
|
||
220 | + | || `\mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9}` || <math>\mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9}\,\!</math> ||
|
||
221 | + | ||_\2. '''Boldface (greek)''' ||
|
||
222 | + | || `\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta}` || <math>\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta} \,\!</math> ||
|
||
223 | + | || `\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu}` || <math>\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu}\,\!</math> ||
|
||
224 | + | || `\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau}` || <math>\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau}\,\!</math> ||
|
||
225 | + | || `\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}` || <math>\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}\,\!</math> ||
|
||
226 | + | || `\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta}` || <math>\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta}\,\!</math> ||
|
||
227 | + | || `\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu}` || <math>\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu}\,\!</math> ||
|
||
228 | + | || `\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau}` || <math>\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau}\,\!</math> ||
|
||
229 | + | || `\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}` || <math>\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}\,\!</math> ||
|
||
230 | + | || `\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa}` || <math>\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa} \,\!</math> ||
|
||
231 | + | || `\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}` || <math>\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}\,\!</math> ||
|
||
232 | + | ||_\2. '''Italics''' ||
|
||
233 | + | || `\mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G}` || <math>\mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G} \,\!</math> ||
|
||
234 | + | || `\mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M}` || <math>\mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M} \,\!</math> ||
|
||
235 | + | || `\mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T}` || <math>\mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T} \,\!</math> ||
|
||
236 | + | || `\mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z}` || <math>\mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z} \,\!</math> ||
|
||
237 | + | || `\mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g}` || <math>\mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g} \,\!</math> ||
|
||
238 | + | || `\mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m}` || <math>\mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m} \,\!</math> ||
|
||
239 | + | || `\mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t}` || <math>\mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t} \,\!</math> ||
|
||
240 | + | || `\mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z}` || <math>\mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z} \,\!</math> ||
|
||
241 | + | || `\mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4}` || <math>\mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4} \,\!</math> ||
|
||
242 | + | || `\mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9}` || <math>\mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9}\,\!</math> ||
|
||
243 | + | ||_\2. '''Roman typeface''' ||
|
||
244 | + | || `\mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G}` || <math>\mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G} \,\!</math> ||
|
||
245 | + | || `\mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M}` || <math>\mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M} \,\!</math> ||
|
||
246 | + | || `\mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T}` || <math>\mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T} \,\!</math> ||
|
||
247 | + | || `\mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z}` || <math>\mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z} \,\!</math> ||
|
||
248 | + | || `\mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g}` || <math>\mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g}\,\!</math> ||
|
||
249 | + | || `\mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m}` || <math>\mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m} \,\!</math> ||
|
||
250 | + | || `\mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t}` || <math>\mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t} \,\!</math> ||
|
||
251 | + | || `\mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z}` || <math>\mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z} \,\!</math> ||
|
||
252 | + | || `\mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4}` || <math>\mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4} \,\!</math> ||
|
||
253 | + | || `\mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9}` || <math>\mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9}\,\!</math> ||
|
||
254 | + | ||_\2. '''Fraktur typeface''' ||
|
||
255 | + | || `\mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G}` || <math>\mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G} \,\!</math> ||
|
||
256 | + | || `\mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M}` || <math>\mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M} \,\!</math> ||
|
||
257 | + | || `\mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T}` || <math>\mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T} \,\!</math> ||
|
||
258 | + | || `\mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z}` || <math>\mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z} \,\!</math> ||
|
||
259 | + | || `\mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g}` || <math>\mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g} \,\!</math> ||
|
||
260 | + | || `\mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m}` || <math>\mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m} \,\!</math> ||
|
||
261 | + | || `\mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t}` || <math>\mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t} \,\!</math> ||
|
||
262 | + | || `\mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z}` || <math>\mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z} \,\!</math> ||
|
||
263 | + | || `\mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4}` || <math>\mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4} \,\!</math> ||
|
||
264 | + | || `\mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9}` || <math>\mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9}\,\!</math> ||
|
||
265 | + | ||_\2. '''Calligraphy/Script''' ||
|
||
266 | + | || `\mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G}` || <math>\mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G} \,\!</math> ||
|
||
267 | + | || `\mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M}` || <math>\mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M} \,\!</math> ||
|
||
268 | + | || `\mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T}` || <math>\mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T} \,\!</math> ||
|
||
269 | + | || `\mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z}` || <math>\mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z}\,\!</math> ||
|
||
270 | + | ||_\2. '''Hebrew''' ||
|
||
271 | + | || `\aleph \beth \gimel \daleth` || <math>\aleph \beth \gimel \daleth\,\!</math> ||
|
||
272 | + | |||
273 | + | == Formatting issues ==
|
||
274 | + | |||
275 | + | === Spacing ===
|
||
276 | + | |||
277 | + | Note that TeX handles most spacing automatically, but you may sometimes want manual control.
|
||
278 | + | |||
279 | + | || '''Feature''' || '''Syntax''' || '''How it looks rendered''' ||
|
||
280 | + | || double quad space || a \qquad b || <math>a \qquad b</math> ||
|
||
281 | + | || quad space || a \quad b || <math>a \quad b</math> ||
|
||
282 | + | || text space || a\ b || <math>a\ b</math> ||
|
||
283 | + | || text space without PNG conversion || a \mbox{ } b || <math>a \mbox{ } b</math> ||
|
||
284 | + | || large space || a\;b || <math>a\;b</math> ||
|
||
285 | + | || medium space || a\>b || (not supported) ||
|
||
286 | + | || small space || a\,b || <math>a\,b</math> ||
|
||
287 | + | || no space || ab || <math>ab\,</math> ||
|
||
288 | + | || small negative space || a\!b || <math>a\!b</math> || |