Extension:Math/Native MathML/Reported Cases

Some reported cases. Vesion on Beta https://en.wikipedia.beta.wmflabs.org/wiki/Extension:Math/Native_MathML/Reported_Cases

Cases

Reported Phabricator bugs

Number	LaTex	Rendering	Notes
1a	\text{let}\ {n \to +\infty}	$\text{let}n\to +\mathrm{\infty }$ ${\text{let}}\ {n\to +\infty }$	task T377057 spaces needed here
1b	\lim_{n\to +\infty}\left(1+\frac 1n\right)^n	$\underset{n\to +\mathrm{\infty }}{\lim }{(1+\frac{1}{n})}^n$ $\lim _{n\to +\infty }\left(1+{\frac {1}{n}}\right)^{n}$	task T377057 Too much space around operators when used in limits in MathML mode
2	\lim_{n \to +\infty}\frac{\sqrt{2\pi n} }{n!}\left(\frac{n}{e}\right)^n = 1	$\underset{n\to +\mathrm{\infty }}{\lim }\frac{\sqrt{2\pi n}}{n!}{\left(\frac{n}{e}\right)}^n=1$ $\lim _{n\to +\infty }{\frac {\sqrt {2\pi n}}{n!}}\left({\frac {n}{e}}\right)^{n}=1$	task T375935 The factorial symbol ! should be upright, it is sloping in Clients-side mathjax mode.
3	\det(A)=\sum_{\sigma\in S_n} e(\sigma)\prod_{i=1}^n a_{i,\sigma_i}	$\det (A)={\sum }_{\sigma \in S_n}e(\sigma )\prod _{i=1}^n{a}_{i,{\sigma }_i}$ $\det(A)=\sum _{\sigma \in S_{n}}e(\sigma )\prod _{i=1}^{n}a_{i,\sigma _{i}}$	task T375907 \sum_condition puts condition in the in wrong position in MathML and client-side MathJax modes
4a	\textstyle \int\limits_{-N}^{N} e^x dx	$\underset{-N}{\overset{N}{\int }}{e}^{x}dx$ $\textstyle \int \limits _{-N}^{N}e^{x}dx$	task T375349 \int_a^b limits in incorrect position in MathML mode.
4b	\textstyle \int_{-N}^{N} e^x dx	${\int }_{-N}^N{e}^{x}dx$ $\textstyle \int _{-N}^{N}e^{x}dx$
4c	\displaystyle \int\limits_{-N}^{N} e^x dx	$\underset{-N}{\overset{N}{\int }}{e}^{x}dx$ $\displaystyle \int \limits _{-N}^{N}e^{x}dx$
4d	\displaystyle \int_{-N}^{N} e^x dx	$\underset{-N}{\overset{N}{\int }}{e}^{x}dx$ $\displaystyle \int _{-N}^{N}e^{x}dx$
4e	\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx	$\underset{1}{\overset{3}{\int }}\frac{e^3/x}{x^2}dx$ $\int \limits _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx$
4f	\int_{1}^{3}\frac{e^3/x}{x^2}\, dx	$\underset{1}{\overset{3}{\int }}\frac{e^3/x}{x^2}dx$ $\int _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx$
4h	\int\limits_{1}^{3}\frac{\frac{e^3}{x} }{\frac{x^2}{5} }\, dx	$\underset{1}{\overset{3}{\int }}\frac{\frac{e^3}{x}}{\frac{x^2}{5}}dx$ $\int \limits _{1}^{3}{\frac {\frac {e^{3}}{x}}{\frac {x^{2}}{5}}}\,dx$
4i	\int_{1}^{3}\frac{\frac{e^3}{x} }{\frac{x^2}{5} }\, dx	$\underset{1}{\overset{3}{\int }}\frac{\frac{e^3}{x}}{\frac{x^2}{5}}dx$ $\int _{1}^{3}{\frac {\frac {e^{3}}{x}}{\frac {x^{2}}{5}}}\,dx$
5a	\begin{align} \frac{dy}{du} &= f'(u) = e^u, \\ \frac{du}{dv} &= g'(v) = \cos v, \\ \frac{dv}{dx} &= h'(x) = 2x. \end{align}	$\begin{array}{ll}\frac{dy}{du}& =f^{\prime }(u)=e^u,\\ \frac{du}{dv}& =g^{\prime }(v)=\cos v,\\ \frac{dv}{dx}& =h^{\prime }(x)=2x.\end{array}$ ${\begin{aligned}{\frac {dy}{du}}&=f'(u)=e^{u},\\{\frac {du}{dv}}&=g'(v)=\cos v,\\{\frac {dv}{dx}}&=h'(x)=2x.\end{aligned}}$	task T375317 \align aligns fields in the centre rather that on the left in MathML mode
5b	\begin{align} z & = a \\ f(x,y,z) & = x + y + z \end{align}	$\begin{array}{ll}z& =a\\ f(x,y,z)& =x+y+z\end{array}$ ${\begin{aligned}z&=a\\f(x,y,z)&=x+y+z\end{aligned}}$
5c	f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases}	$f(n)=\{\begin{array}{ll}n/2,& \text{if }n\text{ is even}\\ 3n+1,& \text{if }n\text{ is odd}\end{array}$ $f(n)={\begin{cases}n/2,&{\text{if }}n{\text{ is even}}\\3n+1,&{\text{if }}n{\text{ is odd}}\end{cases}}$
5d	\begin{align} a&=b & c&=d & e&=f\\ aa&=bb & cc&=dd & ee&=ff\\ aaa&=bbb & ccc&=ddd & eee&=fff \end{align}	$\begin{array}{llllll}a& =b& c& =d& e& =f\\ aa& =bb& cc& =dd& ee& =ff\\ aaa& =bbb& ccc& =ddd& eee& =fff\end{array}$ ${\begin{aligned}a&=b&c&=d&e&=f\\aa&=bb&cc&=dd&ee&=ff\\aaa&=bbb&ccc&=ddd&eee&=fff\end{aligned}}$
5e	\begin{align} x&=y & X&=Y & a&=b+c\\ x'&=y' & X'&=Y' & a'&=b\\ x+x'&=y+y' & X+X'&=Y+Y' & a'b&=c'b \end{align}	$\begin{array}{llllll}x& =y& X& =Y& a& =b+c\\ x^{\prime }& =y^{\prime }& X^{\prime }& =Y^{\prime }& a^{\prime }& =b\\ x+x^{\prime }& =y+y^{\prime }& X+X^{\prime }& =Y+Y^{\prime }& a^{\prime }b& =c^{\prime }b\end{array}$ ${\begin{aligned}x&=y&X&=Y&a&=b+c\\x'&=y'&X'&=Y'&a'&=b\\x+x'&=y+y'&X+X'&=Y+Y'&a'b&=c'b\end{aligned}}$
6a  Done	\begin{align} \frac{dy}{du} &= f'(u) = e^u, \\[6pt] \frac{du}{dv} &= g'(v) = \cos v, \\[6pt] \frac{dv}{dx} &= h'(x) = 2x. \end{align}	$\begin{array}{ll}\frac{dy}{du}& =f^{\prime }(u)=e^u,\\ \frac{du}{dv}& =g^{\prime }(v)=\cos v,\\ \frac{dv}{dx}& =h^{\prime }(x)=2x.\end{array}$ ${\begin{aligned}{\frac {dy}{du}}&=f'(u)=e^{u},\\[6pt]{\frac {du}{dv}}&=g'(v)=\cos v,\\[6pt]{\frac {dv}{dx}}&=h'(x)=2x.\end{aligned}}$	task T375295 \begin{align} with font sizes specified show font size annotation [6pt] in MathML mode
6b	\begin{align} \varpi &= [2,1,1,1,1,1,4,1,2,\ldots], \\[8mu] 2\varpi &= [5,4,10,2,1,2,3,29,\ldots], \\[5mu] \frac{\varpi}{2} &= [1,3,4,1,1,1,5,2,\ldots], \\[2mu] \frac{\varpi}{\pi} &= [0,1,5,21,3,4,14,\ldots]. \end{align}	$\begin{array}{ll}\varpi & =[2,1,1,1,1,1,4,1,2,\dots ],\\ 2\varpi & =[5,4,10,2,1,2,3,29,\dots ],\\ \frac{\varpi }{2}& =[1,3,4,1,1,1,5,2,\dots ],\\ \frac{\varpi }{\pi }& =[0,1,5,21,3,4,14,\dots ].\end{array}$ ${\begin{aligned}\varpi &=[2,1,1,1,1,1,4,1,2,\ldots ],\\[8mu]2\varpi &=[5,4,10,2,1,2,3,29,\ldots ],\\[5mu]{\frac {\varpi }{2}}&=[1,3,4,1,1,1,5,2,\ldots ],\\[2mu]{\frac {\varpi }{\pi }}&=[0,1,5,21,3,4,14,\ldots ].\end{aligned}}$
7a	a\operatorname{sn}b	$a\mathrm{s}\mathrm{n}b$ $a\operatorname {sn} b$	task T375861 a\operatorname{sn}b rendered with no spaces before and after operator in MathML mode
7b	a(\operatorname{sn}(b)), a[\operatorname{sn}[b]], a\{\operatorname{sn}\{b\}\}	$a(\mathrm{s}\mathrm{n}(b)),a[\mathrm{s}\mathrm{n}[b]],a\{\mathrm{s}\mathrm{n}\{b\}\}$ $a(\operatorname {sn} (b)),a[\operatorname {sn} [b]],a\{\operatorname {sn} \{b\}\}$	no space need here
7c	\operatorname{G}(V, g)	$\mathrm{G}(V,g)$ $\operatorname {G} (V,g)$	no space need here
8a	\displaystyle\sum_{n\in\mathbb{Z} }	${\sum }_{n\in \mathbb{\mathbb{Z}}}$ $\displaystyle \sum _{n\in \mathbb {Z} }$	task T375907 \sum_condition puts condition in the in wrong position in MathML and client-side MathJax modes
8b	\displaystyle\prod_{n\in\mathbb{Z} }	${\prod }_{n\in \mathbb{\mathbb{Z}}}$ $\displaystyle \prod _{n\in \mathbb {Z} }$
8b	\displaystyle\prod_{n\in\mathbb{Z} }^{n\ne 5}	$\prod _{n\in \mathbb{\mathbb{Z}}}^{n\ne 5}$ $\displaystyle \prod _{n\in \mathbb {Z} }^{n\neq 5}$	with superscript rendered below
8c	\sum_{n>k} R \quad \prod_{n>k} P \quad \coprod_{n>k} RR	${\sum }_{n>k}R{\prod }_{n>k}P{\coprod }_{n>k}RR$ $\sum _{n>k}R\quad \prod _{n>k}P\quad \coprod _{n>k}RR$
8d	\bigcup_{n>k} J \quad \biguplus_{n>k} L \quad \bigcap_{n>k} N	${\bigcup }_{n>k}J{⨄}_{n>k}L{\bigcap }_{n>k}N$ $\bigcup _{n>k}J\quad \biguplus _{n>k}L\quad \bigcap _{n>k}N$
8e	\bigoplus_{n>k} W \quad \bigotimes_{n>k} V \quad \bigodot_{n>k} F	${⨁}_{n>k}W{⨂}_{n>k}V{⨀}_{n>k}F$ $\bigoplus _{n>k}W\quad \bigotimes _{n>k}V\quad \bigodot _{n>k}F$
8f	\bigvee_{n>k} V \quad \bigwedge_{n>k} W \quad \bigsqcup_{n>k} S	${\bigvee }_{n>k}V{\bigwedge }_{n>k}W{⨆}_{n>k}S$ $\bigvee _{n>k}V\quad \bigwedge _{n>k}W\quad \bigsqcup _{n>k}S$
8g	\int_{n>k} U \quad \oint_{n>k} T \quad \iint_{n>k} S	${\int }_{n>k}U{\oint }_{n>k}T{\iint }_{n>k}S$ $\int _{n>k}U\quad \oint _{n>k}T\quad \iint _{n>k}S$	Default for integrals is to the side
9a  Done	\arccot(x), \arccsc(x), \arcsec(x), \sen(x), \sgn(x)	$\mathrm{arccot}(x),\mathrm{arccsc}(x),\mathrm{arcsec}(x),\mathrm{sen}(x),\mathrm{sgn}(x)$ $\operatorname {arccot}(x),\operatorname {arccsc}(x),\operatorname {arcsec}(x),\operatorname {sen}(x),\operatorname {sgn}(x)$	task T375274 mediawiki_function_names math functions eat the following paren in native MML mode
9b	\arcsin(x), \sin(x)	$\arcsin (x),\sin (x)$ $\arcsin(x),\sin(x)$
9c	\operatorname{arccot}(x), \operatorname{arcsin}(x), \operatorname{sgn}(x), \operatorname{sin}(x)	$\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{c}\mathrm{o}\mathrm{t}(x),\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{s}\mathrm{i}\mathrm{n}(x),\mathrm{s}\mathrm{g}\mathrm{n}(x),\mathrm{s}\mathrm{i}\mathrm{n}(x)$ $\operatorname {arccot} (x),\operatorname {arcsin} (x),\operatorname {sgn} (x),\operatorname {sin} (x)$
10a	B^b |\psi\rangle	$B^b|\psi ⟩$ $B^{b}|\psi \rangle$
10a	\langle \psi | B^b \quad \lbrace \psi | B^b \quad \lbrack \psi | B^b	$⟨\psi \left|B^b\right\{\psi \left|B^b\right[\psi |B^b$ $\langle \psi |B^{b}\quad \lbrace \psi |B^{b}\quad \lbrack \psi |B^{b}$	task T375959 Use stretchy="false" for \langle and \rangle in MathML mode
10b	B^b |\psi\rangle \quad B^b | \psi \rbrace \quad B^b | \psi \rbrack \quad B^b \vert\psi\rangle	$B^b|\psi ⟩B^b|\psi \left\}{B}^b\right|\psi \left]B^b\right|\psi ⟩$ $B^{b}|\psi \rangle \quad B^{b}|\psi \rbrace \quad B^{b}|\psi \rbrack \quad B^{b}\vert \psi \rangle$
10c	B^b \left|\psi\right\rangle \quad \psi \left|B^b\right\rangle	$B^b|\psi ⟩\psi |B^b⟩$ $B^{b}\left|\psi \right\rangle \quad \psi \left|B^{b}\right\rangle$	Explicitly specifying \left and \right work
11a Partially done	\updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow	$\updownarrow \updownarrow \updownarrow \updownarrow \updownarrow \dots \Updownarrow \Updownarrow \Updownarrow \Updownarrow \Updownarrow$ $\updownarrow {\big \updownarrow }{\Big \updownarrow }{\bigg \updownarrow }{\Bigg \updownarrow }\dots {\Bigg \Updownarrow }{\bigg \Updownarrow }{\Big \Updownarrow }{\big \Updownarrow }\Updownarrow$	task T375960 \Big/ and \Big\backslash etc are too small in MathML mode.
11b	/ \big/ \Big/ \bigg/ \Bigg/ \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash	$/////\dots \backslash \backslash \backslash \backslash \mathrm{\setminus }$ $/{\big /}{\Big /}{\bigg /}{\Bigg /}\dots {\Bigg \backslash }{\bigg \backslash }{\Big \backslash }{\big \backslash }\backslash$	Partially works in Firefox, upstream problems in chrome, some have almost zero use case
12a	f:X\to Y	$f:X\to Y$ $f:X\to Y$	task T375974 Colon in f : X \to Y should be an operator in MathML mode.
12b	D \And E	$D\mathrm{\&}E$ $D\And E$	Has more space in LaTeX
12c	A \smile B \frown B	$A⌣B⌢B$ $A\smile B\frown B$
12d	A \therefore B \because B	$A\therefore B\because B$ $A\therefore B\because B$
12e	B \overset{\underset{\mathrm{def} }{} }{=} B	$B\stackrel{\mathrm{d}\mathrm{e}\mathrm{f}}{=}B$ $B{\overset {\underset {\mathrm {def} }{}}{=}}B$
12f	A \ulcorner B \urcorner B \llcorner B \lrcorner C	$A⌜B⌝B⌞B⌟C$ $A\ulcorner B\urcorner B\llcorner B\lrcorner C$
12g	A \blacktriangle B \blacktriangledown B	$A▴B▾B$ $A\blacktriangle B\blacktriangledown B$
12h	\forall(\ulcorner\phi\urcorner\in\Sigma^0_n\cup\Pi^0_n) \implies\mathrm{Tr}_n(\ulcorner\phi(y_0,\ldots,y_n)^*\urcorner))	$\mathrm{\forall }(⌜\varphi ⌝\in {\mathrm{\Sigma }}_n^0\cup {\mathrm{\Pi }}_n^0)⟹{\mathrm{T}\mathrm{r}}_n(⌜\varphi (y_0,\dots ,y_n{)}^{*}⌝))$ $\forall (\ulcorner \phi \urcorner \in \Sigma _{n}^{0}\cup \Pi _{n}^{0})\implies \mathrm {Tr} _{n}(\ulcorner \phi (y_{0},\ldots ,y_{n})^{*}\urcorner ))$	en:Reflection principle
13  Done	\|A\|, D(p\|q)	$\Vert A\Vert ,D(p\Vert q)$ $\|A\|,D(p\|q)$	task T376546 \| should render as a double pipe || rather than a single one |. In MathML and Client-side MathJax modes.
14  Done	q(v)=|v|^2\quad q(v)=\|v\|^2 \quad q(v)=\|v\|_A	$q(v)=|v{|}^{2}q(v)=\Vert v{\Vert }^{2}q(v)=\Vert v{\Vert }_A$ $q(v)=|v|^{2}\quad q(v)=\|v\|^{2}\quad q(v)=\|v\|_{A}$	task T376558 Vertical alignment of pipes with superscripts wrong in mathml mode
15	\cancel{y}	$\cancel{y}$ ${\cancel {y}}$	task T376829 \cancel{y} the strike is not visable in native mathml mode
16  Done	\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}	$\begin{array}{lcr}z& =& a\\ f(x,y,z)& =& x+y+z\end{array}$ ${\begin{array}{lcr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}$	task T376838 \begin{array}{lcr} does not respect the optional alignment argument in MathML mode
17	\frac{x}{x}\quad\frac{x}{y}\quad\frac{x}{l}\quad\frac{x}{2}\quad\frac{x}{x}\quad\frac{y}x\quad\frac{l}x\quad\frac{2}x	$\frac{x}{x}\frac{x}{y}\frac{x}{l}\frac{x}{2}\frac{x}{x}\frac{y}{x}\frac{l}{x}\frac{2}{x}$ ${\frac {x}{x}}\quad {\frac {x}{y}}\quad {\frac {x}{l}}\quad {\frac {x}{2}}\quad {\frac {x}{x}}\quad {\frac {y}{x}}\quad {\frac {l}{x}}\quad {\frac {2}{x}}$	task T376883 Bad spacing for fractions with Safari in MathML mode
18	<math>\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}</math> <math>\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}</math>	MediaWiki MathML: $\frac{x}{1+\frac{\cancel{y}}{\cancel{y}}}=\frac{x}{2}$ $\begin{array}{lcr}z& =& a\\ f(x,y,z)& =& x+y+z\end{array}$ MathJax SVG: ${\cfrac {x}{1+{\cfrac {\cancel {y}}{\cancel {y}}}}}={\cfrac {x}{2}}$ ${\begin{array}{lcr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}$	task T376887 Formula in separate paragraphs displayed on the same line in Safari on Mac OS in MathML mode
19a	\lim_{n\to +\infty}\left(1+\frac 1n\right)^n	$\underset{n\to +\mathrm{\infty }}{\lim }{(1+\frac{1}{n})}^n$ $\lim _{n\to +\infty }\left(1+{\frac {1}{n}}\right)^{n}$	task T377057 Too much space around operators when used in limits in MathML mode
19b	\text{let}\ {n \to +\infty}	$\text{let}n\to +\mathrm{\infty }$ ${\text{let}}\ {n\to +\infty }$	More space used when not in a script

Operators

Reported Operators

12c	A + B - C \pm D \mp E \dotplus F	$A+B-C\pm D\mp E\dotplus F$ $A+B-C\pm D\mp E\dotplus F$
12d	A \times B \div C \divideontimes D / E \backslash F	$A\times B÷C\divideontimes D/E\mathrm{\setminus }F$ $A\times B\div C\divideontimes D/E\backslash F$
12e	A\cdot B * C \ast D \star E \circ F \bullet G	$A\cdot B*C\ast D\star E\circ F\bullet G$ $A\cdot B*C\ast D\star E\circ F\bullet G$
12f	A \boxplus B \boxminus C \boxtimes D \boxdot E	$A⊞B\boxminus C⊠D⊡E$ $A\boxplus B\boxminus C\boxtimes D\boxdot E$
12g	A \oplus B \ominus C \otimes D \oslash E \odot F	$A\oplus B\ominus C\otimes D\oslash E\odot F$ $A\oplus B\ominus C\otimes D\oslash E\odot F$
12h	A \circleddash B \circledcirc C \circledast D	$A⊝B⊚C⊛D$ $A\circleddash B\circledcirc C\circledast D$
12i	A \in B \notin A \not\in B \ni B \not\ni C	$A\in B\notin A\in ̸B\ni B\ni ̸C$ $A\in B\notin A\not \in B\ni B\not \ni C$
12j	A \cap B \Cap B \sqcap B \bigcap C	$A\cap B⋒B\sqcap B\bigcap C$ $A\cap B\Cap B\sqcap B\bigcap C$
12k	A \cup B \Cup B \sqcup B \bigcup B \bigsqcup B \uplus B \biguplus C	$A\cup B⋓B\bigsqcup B\bigcup B⨆B\uplus B⨄C$ $A\cup B\Cup B\sqcup B\bigcup B\bigsqcup B\uplus B\biguplus C$
12l	A \setminus B \smallsetminus B \times C	$A\setminus B\setminus B\times C$ $A\setminus B\smallsetminus B\times C$
12m	A \subset B \Subset B \sqsubset C	$A\subset B⋐B⊏C$ $A\subset B\Subset B\sqsubset C$
12n	A \supset B \Supset B \sqsupset C	$A\supset B⋑B⊐C$ $A\supset B\Supset B\sqsupset C$
12o	A \subseteq B \nsubseteq B \subsetneq B \varsubsetneq B \sqsubseteq C	$A\subseteq B⊈B⊊B⊊B⊑C$ $A\subseteq B\nsubseteq B\subsetneq B\varsubsetneq B\sqsubseteq C$
12p	A \supseteq B \nsupseteq B \supsetneq B \varsupsetneq B \sqsupseteq C	$A\supseteq B⊉B⊋B⊋B⊒C$ $A\supseteq B\nsupseteq B\supsetneq B\varsupsetneq B\sqsupseteq C$
12q	A \subseteqq B \nsubseteqq B \subsetneqq B \varsubsetneqq C	$A⫅B⊈B⫋B⫋C$ $A\subseteqq B\nsubseteqq B\subsetneqq B\varsubsetneqq C$
12r	A \supseteqq B \nsupseteqq B \supsetneqq B \varsupsetneqq C	$A⫆B⊉B⫌B⫌C$ $A\supseteqq B\nsupseteqq B\supsetneqq B\varsupsetneqq C$
12s	A = B \ne B \neq B \equiv B \not\equiv C	$A=B\ne B\ne B\equiv B\equiv ̸C$ $A=B\neq B\neq B\equiv B\not \equiv C$
12t	A \doteq B \doteqdot B \overset{\underset{\mathrm{def} }{} }{=} B := C	$A\doteq B\doteqdot B\stackrel{\mathrm{d}\mathrm{e}\mathrm{f}}{=}B:=C$ $A\doteq B\doteqdot B{\overset {\underset {\mathrm {def} }{}}{=}}B:=C$
12u	A \sim B \nsim B \backsim B \thicksim B \simeq B \backsimeq B \eqsim B \cong B \ncong C	$A\sim B\nsim B\backsim B\sim B\simeq B\backsimeq B\eqsim B\cong B≆C$ $A\sim B\nsim B\backsim B\thicksim B\simeq B\backsimeq B\eqsim B\cong B\ncong C$
12v	A \approx B \thickapprox B \approxeq B \asymp B \propto B \varpropto C	$A\approx B\approx B\approxeq B\asymp B\propto B\propto C$ $A\approx B\thickapprox B\approxeq B\asymp B\propto B\varpropto C$
12w	A < B \nless B \ll B \not\ll B \lll B \not\lll B \lessdot C	$A<B\nless B\ll B\ll ̸B⋘B⋘̸B⋖C$ $A<B\nless B\ll B\not \ll B\lll B\not \lll B\lessdot C$
12x	A > B \ngtr B \gg B \not\gg B \ggg B \not\ggg B \gtrdot C	$A>B\ngtr B\gg B\gg ̸B⋙B⋙̸B⋗C$ $A>B\ngtr B\gg B\not \gg B\ggg B\not \ggg B\gtrdot C$
12y	A \le B \leq B \lneq B \leqq B \nleq B \nleqq B \lneqq B \lvertneqq C	$A\le B\le B⪇B\leqq B\nleqq B\nleqq B\lneqq B\lneqq C$ $A\leq B\leq B\lneq B\leqq B\nleq B\nleqq B\lneqq B\lvertneqq C$
12z	A \ge B \geq B \gneq B \geqq B \ngeq B \ngeqq B \gneqq B \gvertneqq C	$A\ge B\ge B⪈B\geqq B\ngeqq B\ngeqq B\gneqq B\gneqq C$ $A\geq B\geq B\gneq B\geqq B\ngeq B\ngeqq B\gneqq B\gvertneqq C$
12aa	A \lessgtr B \lesseqgtr B \lesseqqgtr B \gtrless B \gtreqless B \gtreqqless C	$A\lessgtr B⋚B⪋B\gtrless B⋛B⪌C$ $A\lessgtr B\lesseqgtr B\lesseqqgtr B\gtrless B\gtreqless B\gtreqqless C$
12ab	A \leqslant B \nleqslant B \eqslantless C	$A⩽B⪇B⪕C$ $A\leqslant B\nleqslant B\eqslantless C$
12ac	A \geqslant B \ngeqslant B \eqslantgtr C	$A⩾B⪈B⪖C$ $A\geqslant B\ngeqslant B\eqslantgtr C$
12ad	A \lesssim B \lnsim B \lessapprox B \lnapprox C	$A\lesssim B⋦B⪅B⪉C$ $A\lesssim B\lnsim B\lessapprox B\lnapprox C$
12ae	A \gtrsim B \gnsim B \gtrapprox B \gnapprox C	$A\gtrsim B⋧B⪆B⪊C$ $A\gtrsim B\gnsim B\gtrapprox B\gnapprox C$
12af	A \prec B \nprec B \preceq B \npreceq B \precneqq C	$A\prec B\nprec B⪯B⋠B⪵C$ $A\prec B\nprec B\preceq B\npreceq B\precneqq C$
12ag	A \succ B \nsucc B \succeq B \nsucceq B \succneqq C	$A\succ B\nsucc B⪰B⋡B⪶C$ $A\succ B\nsucc B\succeq B\nsucceq B\succneqq C$
12ah	A \preccurlyeq B \curlyeqprec C	$A\preccurlyeq B⋞C$ $A\preccurlyeq B\curlyeqprec C$
12ai	A \succcurlyeq B \curlyeqsucc C	$A\succcurlyeq B⋟C$ $A\succcurlyeq B\curlyeqsucc C$
12aj	A \precsim B \precnsim B \precapprox B \precnapprox C	$A\precsim B⋨B⪷B⪹C$ $A\precsim B\precnsim B\precapprox B\precnapprox C$
12ak	A \succsim B \succnsim B \succapprox B \succnapprox C	$A\succsim B⋩B⪸B⪺C$ $A\succsim B\succnsim B\succapprox B\succnapprox C$
12al	A \parallel B \nparallel B \shortparallel B \nshortparallel C	$A\parallel B\nparallel B\parallel B\nparallel C$ $A\parallel B\nparallel B\shortparallel B\nshortparallel C$
12am	A \perp B \angle B \sphericalangle B \measuredangle B 45^\circ C	$A\perp B\mathrm{\angle }B\sphericalangle B\measuredangle B45^{\circ }C$ $A\perp B\angle B\sphericalangle B\measuredangle B45^{\circ }C$
12an	A \Box B \square B \blacksquare B \diamond B \Diamond B \lozenge B \blacklozenge B \bigstar C	$A◻B◻B◼B\diamond B◊B◊B⧫B★C$ $A\Box B\square B\blacksquare B\diamond B\Diamond B\lozenge B\blacklozenge B\bigstar C$
12ao	A \bigcirc B \triangle B \bigtriangleup B \bigtriangledown C	$A◯B\mathrm{△}B△B▽C$ $A\bigcirc B\triangle B\bigtriangleup B\bigtriangledown C$
12ap	A \vartriangle B \triangledown C	$A△B▽C$ $A\vartriangle B\triangledown C$
12aq	A \blacktriangle B \blacktriangledown B \blacktriangleleft B \blacktriangleright C	$A▴B▾B◂B▸C$ $A\blacktriangle B\blacktriangledown B\blacktriangleleft B\blacktriangleright C$
12ar	A \forall B \exists B \nexists C	$A\mathrm{\forall }B\mathrm{\exists }B\nexists C$ $A\forall B\exists B\nexists C$
12as	A \therefore B \because B \And C	$A\therefore B\because B\mathrm{\&}C$ $A\therefore B\because B\And C$
12at	A \lor B \vee B \curlyvee B \bigvee C	$A\vee B\vee B⋎B\bigvee C$ $A\lor B\vee B\curlyvee B\bigvee C$
12au	A \land B \wedge B \curlywedge B \bigwedge C	$A\wedge B\wedge B⋏B\bigwedge C$ $A\land B\wedge B\curlywedge B\bigwedge C$
12av	A \lnot B \neg B \not\operatorname{R} B \bot B \top C	$A\mathrm{\neg }B\mathrm{\neg }B\text{⧸}\mathrm{R}B\mathrm{\perp }B\mathrm{\top }C$ $A\lnot B\neg B\not \operatorname {R} B\bot B\top C$
12aw	A \vdash B \dashv B \vDash B \Vdash B \models C	$A⊢B⊣B\models B⊩B\models C$ $A\vdash B\dashv B\vDash B\Vdash B\models C$
12ax	A \Vvdash B \nvdash B \nVdash B \nvDash B \nVDash C	$A\Vvdash B⊬B⊮B⊭B⊯C$ $A\Vvdash B\nvdash B\nVdash B\nvDash B\nVDash C$
12ay	A \ulcorner B \urcorner B \llcorner B \lrcorner C	$A⌜B⌝B⌞B⌟C$ $A\ulcorner B\urcorner B\llcorner B\lrcorner C$
12az	A \Rrightarrow B \Lleftarrow C	$A\Rrightarrow B\Lleftarrow C$ $A\Rrightarrow B\Lleftarrow C$
12ba	A \Rightarrow B \nRightarrow B \Longrightarrow B \implies C	$A\Rightarrow B\nRightarrow B⟹B⟹C$ $A\Rightarrow B\nRightarrow B\Longrightarrow B\implies C$
12bb	A \Leftarrow B \nLeftarrow B \Longleftarrow C	$A\Leftarrow B\nLeftarrow B⟸C$ $A\Leftarrow B\nLeftarrow B\Longleftarrow C$
12bc	A \Leftrightarrow B \nLeftrightarrow B \Longleftrightarrow B \iff C	$A\iff B\nLeftrightarrow B⟺B⟺C$ $A\Leftrightarrow B\nLeftrightarrow B\Longleftrightarrow B\iff C$
12bd	A \Uparrow B \Downarrow B \Updownarrow C	$A\Uparrow B\Downarrow B\Updownarrow C$ $A\Uparrow B\Downarrow B\Updownarrow C$
12be	A \rightarrow B \to B \nrightarrow B \longrightarrow C	$A\to B\to B\nrightarrow B⟶C$ $A\rightarrow B\to B\nrightarrow B\longrightarrow C$
12bf	A \leftarrow B \gets B \nleftarrow B \longleftarrow C	$A\leftarrow B\leftarrow B\nleftarrow B⟵C$ $A\leftarrow B\gets B\nleftarrow B\longleftarrow C$
12bg	A \leftrightarrow B \nleftrightarrow B \longleftrightarrow C	$A\leftrightarrow B\nleftrightarrow B⟷C$ $A\leftrightarrow B\nleftrightarrow B\longleftrightarrow C$
12bh	A \uparrow B \downarrow B \updownarrow C	$A\uparrow B\downarrow B\updownarrow C$ $A\uparrow B\downarrow B\updownarrow C$
12bi	A \nearrow B \swarrow B \nwarrow B \searrow C	$A\nearrow B\swarrow B\nwarrow B\searrow C$ $A\nearrow B\swarrow B\nwarrow B\searrow C$
12bj	A \mapsto B \longmapsto C	$A\mapsto B⟼C$ $A\mapsto B\longmapsto C$
12bk	A \rightharpoonup B \rightharpoondown B \leftharpoonup B \leftharpoondown B \upharpoonleft B \upharpoonright C \downharpoonleft C |- C	$A\rightharpoonup B\rightharpoondown B\leftharpoonup B\leftharpoondown B\upharpoonleft B\upharpoonright C\downharpoonleft C|-C$ $A\rightharpoonup B\rightharpoondown B\leftharpoonup B\leftharpoondown B\upharpoonleft B\upharpoonright C\downharpoonleft C|-C$
12bl	A \downharpoonright B \rightleftharpoons B \leftrightharpoons C	$A\downharpoonright B\rightleftharpoons B\leftrightharpoons C$ $A\downharpoonright B\rightleftharpoons B\leftrightharpoons C$
12bm	A \curvearrowleft B \circlearrowleft B \Lsh B \upuparrows B \rightrightarrows B \rightleftarrows B \rightarrowtail B \looparrowright C	$A\curvearrowleft B\circlearrowleft B\Lsh B\upuparrows B\rightrightarrows B\rightleftarrows B\rightarrowtail B\looparrowright C$ $A\curvearrowleft B\circlearrowleft B\Lsh B\upuparrows B\rightrightarrows B\rightleftarrows B\rightarrowtail B\looparrowright C$
12bn	A \curvearrowright B \circlearrowright B \Rsh B \downdownarrows B \leftleftarrows B \leftrightarrows B \leftarrowtail B \looparrowleft C	$A\curvearrowright B\circlearrowright B\Rsh B\downdownarrows B\leftleftarrows B\leftrightarrows B\leftarrowtail B\looparrowleft C$ $A\curvearrowright B\circlearrowright B\Rsh B\downdownarrows B\leftleftarrows B\leftrightarrows B\leftarrowtail B\looparrowleft C$
12bo	A \hookrightarrow B \hookleftarrow B \multimap B \leftrightsquigarrow B \rightsquigarrow B \twoheadrightarrow B \twoheadleftarrow C	$A\hookrightarrow B\hookleftarrow B⊸B\leftrightsquigarrow B⇝B\twoheadrightarrow B\twoheadleftarrow C$ $A\hookrightarrow B\hookleftarrow B\multimap B\leftrightsquigarrow B\rightsquigarrow B\twoheadrightarrow B\twoheadleftarrow C$
12bp	A \amalg B \P B \S B \% B \dagger B \ddagger B \ldots B \cdots B \vdots B \ddots C	$A⨿B\P B\mathrm{\S }B\%B†B‡B\dots B\cdots B⋮B\ddots C$ $A\amalg B\P B\S B\%B\dagger B\ddagger B\ldots B\cdots B\vdots B\ddots C$
12bq	A \smile B \frown B \wr B \triangleleft B \triangleright C	$A⌣B⌢B\wr B◃B▹C$ $A\smile B\frown B\wr B\triangleleft B\triangleright C$
12br	A \diamondsuit B \heartsuit B \clubsuit B \spadesuit B \Game B \flat B \natural B \sharp C	$A\mathrm{♢}B\mathrm{♡}B\mathrm{♣}B\mathrm{♠}B⅁B\mathrm{♭}B\mathrm{♮}B\mathrm{♯}C$ $A\diamondsuit B\heartsuit B\clubsuit B\spadesuit B\Game B\flat B\natural B\sharp C$
12bs	A \diagup B \diagdown B \centerdot B \ltimes B \rtimes B \leftthreetimes B \rightthreetimes C	$A╱B╲B\cdot B⋉B⋊B⋋B⋌C$ $A\diagup B\diagdown B\centerdot B\ltimes B\rtimes B\leftthreetimes B\rightthreetimes C$
12bt	A \eqcirc B \circeq B \triangleq B \bumpeq B \Bumpeq B \doteqdot B \risingdotseq B \fallingdotseq C	$A\eqcirc B\circeq B\triangleq B\bumpeq B\Bumpeq B\doteqdot B\risingdotseq B\fallingdotseq C$ $A\eqcirc B\circeq B\triangleq B\bumpeq B\Bumpeq B\doteqdot B\risingdotseq B\fallingdotseq C$
12bu	A \intercal B \barwedge B \veebar B \doublebarwedge B \between B \pitchfork C	$A⊺B⊼B⊻B⩞B\between B⋔C$ $A\intercal B\barwedge B\veebar B\doublebarwedge B\between B\pitchfork C$
12bv	A \vartriangleleft B \ntriangleleft B \vartriangleright B \ntriangleright C	$A⊲B⋪B⊳B⋫C$ $A\vartriangleleft B\ntriangleleft B\vartriangleright B\ntriangleright C$
12bw	A \trianglelefteq B \ntrianglelefteq B \trianglerighteq B \ntrianglerighteq C	$A⊴B⋬B⊵B⋭C$ $A\trianglelefteq B\ntrianglelefteq B\trianglerighteq B\ntrianglerighteq C$
12c	A \mid B \smile C \frown D \in E \ni F \vdash G \dashv H \models J \propto K	$A\mid B⌣C⌢D\in E\ni F⊢G⊣H\models J\propto K$ $A\mid B\smile C\frown D\in E\ni F\vdash G\dashv H\models J\propto K$	Other binary relations