1 Sums and Limits

mathclap & friends

X=\sum_{1\leq i\leq j\leq n}X_{ij}

X=\sum_{\mathclap{1\leq i\leq j\leq n}}X_{ij}

X=\sum_{\mathrlap{1\leq i\leq j\leq n}}X_{ij}

X=\sum_{\mathllap{1\leq i\leq j\leq n}}X_{ij}

Cramped

\cramped{x^{2}}\leftrightarrow x^{2}\quad\cramped[\scriptstyle]{x^{2}}% \leftrightarrow{\scriptstyle x^{2}}

Smashoperator

V=\sum_{1\leq i\leq j\leq n}^{\infty}V_{ij}\quad X=\sum_{1\leq i\leq j\leq n}^% {3456}X_{ij}\quad Y=\sum\limits_{1\leq i\leq j\leq n}Y_{ij}\quad Z=\mathop{T}_% {1\leq i\leq j\leq n}Z_{ij}

V=\sum_{1\leq i\leq j\leq n}^{\infty}V_{ij}\quad X=\smashoperator[]{\sum_{1% \leq i\leq j\leq n}^{3456}}X_{ij}\quad Y=\smashoperator[r]{\sum_{1\leq i\leq j% \leq n}^{}}Y_{ij}\quad Z=\smashoperator[l]{\mathop{T}_{1\leq i\leq j\leq n}^{}% }Z_{ij}

Adjustlimits

\text{a)}\lim_{n\to\infty}\max_{p\geq n}\quad\text{b)}\lim_{n\to\infty}\max_{p% ^{2}\geq n}\quad\text{c)}\lim_{n\to\infty}\sup_{p^{2}\geq nK}\quad\text{d)}% \limsup_{n\to\infty}\max_{p\geq n}

\text{a)}\adjustlimits{\lim}_{n\to\infty}{\max}_{p\geq n}\quad\text{b)}% \adjustlimits{\lim}_{n\to\infty}{\max}_{p^{2}\geq n}\quad\text{c)}% \adjustlimits{\lim}_{n\to\infty}{\sup}_{p^{2}\geq nK}\quad\text{d)}% \adjustlimits{\limsup}_{n\to\infty}{\max}_{p\geq n}

2 Tags

equation Q&A Q&A
$a=b$

See Q&A or is it better with Q&A? In the star form \ref* becomes Q&A (\refeq* is not defined).

equation Q&A Q&A

a=b

equation [Q&A] [Q&A]

a=b

Normal tags.

equation (1) (1)

a=a

That was equation (1).

OK tags.

equation [2] [2]

a=a

That was equation [2], but recall [1]

odd tag.

equation {3} {3}

a=a

That was equation {3}, but recall {1} and {2}.

weird tag.

equation ((4)) ((4))

b=b

That was equation ((4)), but recall ((1)), ((2)) and ((3)).

Normal tags again.

equation (5) (5)

c=c

Non-textual

equation (n^th) (n^th)

d=d

That was equation (5), but recall (1), (2), (3), (4) and (n^th).

equation (6) (6)

\displaystyle a=a

equation (**) (**)

\displaystyle b=b

This should refer to the equation containing $a=a$ : (6). Then a switch of tag forms.

equation (7) (7)

\displaystyle c

\displaystyle=c

equation (8) (8)

\displaystyle d

\displaystyle=d

This should refer to the equation containing $d=d$ : (8) (but recall (6)).

equation (9) (9)

e=e

equation (10) (10)

f=f

1+1=2

2+2=4

Blabla (2).

3 Arrows

A\xLeftarrow[under]{over}B\xRightarrow[under]{over}C

x\xleftrightarrow[under]{overlooooooong}y\xLeftrightarrow[underloooooooong]{% over}z

x\xhookleftarrow[bar]{foo}y\xhookrightarrow[bluuuuuuuuub]{baz}t\xmapsto{% heeereee}k

k\xleftharpoonup[.]{}l\xleftharpoondown{..}m\xrightharpoondown[...]{}n% \xrightharpoonup{....}o

x\xrightleftharpoons{bluuuuub}y\xleftrightharpoons[blaaaaaab]{}z

z=\overbrace{\underbracket{x}_{\text{real}}+i\underbracket{y}_{\text{imaginary% }}}^{\text{complex number}}\quad\underbrace{1+1}_{=2}

4 Matrices

\begin{matrix}c&cocococococo\\ c&c\end{matrix}

\begin{matrix}[l]lalalalalala&l\\ l&l\end{matrix}

\begin{matrix}[r]rererererere&r\\ r&r\end{matrix}

\begin{pmatrix}[l]ppppppp&foo\\ l&ppppppppppppppp\end{pmatrix}

\begin{bmatrix}b&b\\ b&b\end{bmatrix}

\begin{Bmatrix}[r]B&B\\ B&BBBBBBBrBBBBBB\end{Bmatrix}

\begin{vmatrix}v&v\\ v&v\end{vmatrix}

\begin{Vmatrix}[c]V&V\\ VVVVVVcVVVVVV&bar\end{Vmatrix}

\begin{vmatrix}[l]a&blblblbllbblblblblblblbl\\ c&d\end{vmatrix}

\begin{bmatrix}a&-b\\ -c&d\end{bmatrix}\begin{bmatrix}[r]a&-b\\ -c&d\end{bmatrix}

\begin{Vmatrix}e&-f\\ -g&h\end{Vmatrix}\begin{Vmatrix}[r]e&-f\\ -g&h\end{Vmatrix}

\begin{bmatrix}a&-bbbbb\\ -c&d\end{bmatrix}\begin{bmatrix}[r]a&-bbbbb\\ -c&d\end{bmatrix}

\begin{Vmatrix}e&-fffff\\ -g&h\end{Vmatrix}\begin{Vmatrix}[r]e&-fffff\\ -g&h\end{Vmatrix}

\begin{bmatrix}[l]a&-bbbbb\\ -c&d\end{bmatrix}\begin{bmatrix}[r]a&-bbbbb\\ -c&d\end{bmatrix}

\begin{Vmatrix}[l]e&-fffff\\ -g&h\end{Vmatrix}\begin{Vmatrix}[r]e&-fffff\\ -g&h\end{Vmatrix}

5 Cases

\begin{cases}E=mc^{2}&\text{Nothing to see here}\\ \int x-3\,dx&\text{Integral is text style}\end{cases}

\begin{dcases}E=mc^{2}&c\approx 3.00\times 10^{8}\,\mathrm{m}/\mathrm{s}\\ \int x-3\,dx&\text{Integral is display style}\end{dcases}

a=\begin{dcases*}E=mc^{2}&Nothing to see here (text in math)\\ \int x-3\,dx&Integral is display style (text in math)\end{dcases*}

\begin{rcases}E=mc^{2}&5^{6}\quad\text{and so on}\\ \int x-3\,dx&\int x\,dx\end{rcases}=b

\begin{rcases*}x^{2}&for $\int x\,dx>0$\\ x^{3}&else\end{rcases*}\Rightarrow\cdots

\begin{drcases}E=mc^{2}&5^{6}\quad\text{and so on}\\ \int x-3\,dx&\int x\,dx\end{drcases}=b

\begin{drcases*}x^{2}&for $\int x\,dx>0$\\ \int x^{3}\,x&else\end{drcases*}\Rightarrow\cdots

\text{foo}=\begin{cases*}\pi&if something\\ \int\Omega^{\Xi}\,\Omega&otherwise\end{cases*}

6 Gathered

A=\begin{gathered}\framebox[113.81102pt]{first}\\ \framebox[113.81102pt]{last}\end{gathered}B

\begin{gathered}a=b+c\\ b=c+d\\ ...\end{gathered}

\boxed{hello}

\displaystyle f(x)

\displaystyle=\int h(x)\,dx

\displaystyle=g(x)

equation (11) (11)

\displaystyle a

\displaystyle=b

Some text

equation (12) (12)

\displaystyle c

\displaystyle=d

Some short text

equation (13) (13)

\displaystyle e

\displaystyle=f

7 Delimiters

\lvert\frac{a}{c}\rvert\quad\left\lvert\frac{a}{c}\right\rvert\quad\Bigg{% \lvert}\frac{a}{b}\Bigg{\rvert}

\lvert\frac{a}{b}\rvert\quad\left\lvert\frac{a}{b}\right\rvert\quad\big{\lvert% }\frac{a}{b}\big{\rvert}\quad\Bigg{\lvert}\frac{a}{b}\Bigg{\rvert}

\lvert\pi\rvert\quad\left\lvert\_\phi\_\right\rvert

\left\langle A,\frac{1}{2}\right\rangle\quad\Big{\langle}B\,\Big{|}\,\sum_{k}f% _{k}\,\Big{|}\,C\Big{\rangle}

\left\{x\in X\middle|\allowbreak\frac{\sqrt{x}}{x^{2}+1}>1\right\}

$\langle 1\,|\,\frac{8}{\frac{4}{1}}\,|\,3\rangle$ $\left\langle 1\,\middle|\,\frac{8}{\frac{4}{1}}\,\middle|\,3\right\rangle$ $\big{\langle}1\,\big{|}\,\frac{8}{\frac{4}{1}}\,\big{|}\,3\big{\rangle}$

\left(\frac{\pi}{\omega}\right)\cdot\left[\int xdx\right]\ldots[\sqrt{\frac{% \sin x}{\cos z}}]\cdots\lparen\frac{\frac{foo}{bar}}{\frac{baz}{qux}}\rparen

Operators

a:=b\quad a\vcentcolon=b\quad a\ordinarycolon=b

a\coloneqq b\quad c\Colonapprox d\quad e\dblcolon f

\bigtimes\times\nuparrow\ndownarrow\otimes\bigotimes

8 Prescripts

{}^{4}_{12}\mathbf{C}^{5+}_{2}\quad\prescript{14}{2}{\mathbf{C}}^{5+}_{2}\quad% \prescript{4}{12}{\mathbf{C}}^{5+}_{2}\quad\prescript{14}{}{\mathbf{C}}^{5+}_{% 2}\quad\prescript{}{2}{\mathbf{C}}^{5+}_{2}

\prescript{A}{Z}{X}\to\prescript{A-4}{Z-2}{Y}+\prescript{4}{2}{\alpha}

a=\frac{\begin{multlined}xy+xy+\int xy\,\text{dx}+xy+xy\\ +xy+xy+xy+xy\end{multlined}xy+xy+\int xy\,\text{dx}+xy+xy\\ +xy+xy+xy+xy}{z}=\frac{\displaystyle\begin{multlined}xy+xy+\int xy\,\text{dx}+% xy+xy\\ +xy+xy+xy+xy\end{multlined}xy+xy+\int xy\,\text{dx}+xy+xy\\ +xy+xy+xy+xy}{z}

9 Multlines

p(x)=3x^{6}+14x^{5}y+590x^{4}y^{2}+19x^{3}y^{3}\\ -12x^{2}y^{4}-12xy^{5}+2y^{6}-a^{3}b^{3}

A=\begin{multlined}\boxed{first}\\ \boxed{last}\end{multlined}\boxed{first}\\ \boxed{last}B

A=\begin{multlined}\boxed{first}\\ \boxed{last}\end{multlined}\boxed{first}\\ \boxed{last}B

A=\begin{multlined}\boxed{first}\\ \boxed{last}\end{multlined}\boxed{first}\\ \boxed{last}B

A=\begin{multlined}\boxed{first}\\ \boxed{last}\end{multlined}\boxed{first}\\ \boxed{last}B

A=\begin{multlined}\boxed{first}\\ \boxed{last}\end{multlined}\boxed{first}\\ \boxed{last}B

A=\begin{multlined}\boxed{first}\\ \boxed{last}\end{multlined}\boxed{first}\\ \boxed{last}B

A=\begin{multlined}\boxed{first}\\ \boxed{last}\end{multlined}\boxed{first}\\ \boxed{last}B

A=\begin{multlined}\boxed{first}\\ \boxed{last}\end{multlined}\boxed{first}\\ \boxed{last}B

A=\begin{multlined}\boxed{first}\\ \boxed{last}\end{multlined}\boxed{first}\\ \boxed{last}B

equation (14) (14)

foo\Coloneqq\begin{lgathered}x=1,\quad x+1=2\\ y=2\end{lgathered}x=1,\quad x+1=2\\ y=2

equation (15) (15)

bar\Coloneqq\begin{rgathered}x=1,\quad x+1=2\\ y=2\end{rgathered}x=1,\quad x+1=2\\ y=2

10 Spread-lines

Spread it

\begin{matrix}a&b&c\\ d&e&f\\ g&h&i\end{matrix}

\begin{pmatrix}a_{1,1}&a_{1,2}&\cdots&a_{1,n}\\ a_{2,1}&a_{2,2}&\cdots&a_{2,n}\\ \vdots&\vdots&\ddots&\vdots\\ a_{m,1}&a_{m,2}&\cdots&a_{m,n}\end{pmatrix}

$\begin{smallmatrix}a&b\\ c&d\end{smallmatrix}$

$\begin{cases}n/2&\quad\text{if }n\text{ is even}\\ -(n+1)/2&\quad\text{if }n\text{ is odd}\\ \end{cases}$

equation (16) (16)

\begin{split}a&=b+c-d\\ &\quad+e-f\\ &=g+h\\ &=i\end{split}

equation (17) (17)

a+b+c+d+e+f\\ +i+j+k+l+m+n

equation (18) (18)

\displaystyle a=b

equation (19) (19)

\displaystyle c=d

equation (20) (20)

\displaystyle a_{1}

\displaystyle=b_{1}+c_{1}

equation (21) (21)

\displaystyle a_{2}

\displaystyle=b_{2}+c_{2}-d_{2}+e_{2}

\displaystyle a_{11}

\displaystyle=b_{11}

\displaystyle a_{12}

\displaystyle=b_{12}

\displaystyle a_{21}

\displaystyle=b_{21}

\displaystyle a_{22}

\displaystyle=b_{22}+c_{22}

equation (22) (22)

\displaystyle x

\displaystyle=y_{1}-y_{2}+y_{3}-y_{5}+y_{8}-\dots

by foo

equation (23) (23)

\displaystyle=y^{\prime}\circ y^{*}

by baz

equation (24) (24)

\displaystyle=y(0)y^{\prime}

by Axiom 1.

\left.\begin{aligned} B^{\prime}&=-\partial\times E,\\ E^{\prime}&=\partial\times B-4\pi j,\end{aligned}\right\}\qquad\text{Maxwell's% equations}

\bigl{(}\begin{smallmatrix}a&b\\ c&d\end{smallmatrix}\bigr{)}

\bigl{(}\begin{matrix}[l]a&b\\ c&d\end{matrix}\bigr{)}

\sum_{\begin{subarray}{l}i\in\Lambda\\ 0<j<n\end{subarray}}P(i,j)

equation (25) (25)

\displaystyle y

\displaystyle=

\displaystyle ax^{2}+bx+c

equation (26) (26)

\displaystyle f(x)

\displaystyle=

\displaystyle x^{2}+2xy+y^{2}

\begin{multlined}\boxed{Firstline}\\ \boxed{Secondline}\\ L+E+F+T\\ R+I+G+H+T\\ L+E+F+T\\ R+I+G+H+T\\ \boxed{WupWup}\\ \boxed{Lastline}\end{multlined}\boxed{Firstline}\\ \boxed{Secondline}\\ L+E+F+T\\ R+I+G+H+T\\ L+E+F+T\\ R+I+G+H+T\\ \boxed{WupWup}\\ \boxed{Lastline}

11 Stepped lines

\begin{gathered}x=1,\quad x+1=2\\ y=2\end{gathered}

42

\begin{gathered}s=2.8,\quad s+0.2=3\\ t=4.5\end{gathered}

1337

12 Shifting equations

Part 1

\displaystyle={}

2nd line

\displaystyle 19

\displaystyle+\framebox[113.81102pt][c]{ last part}

equation (27) (27)

1

\displaystyle=\framebox[85.35826pt]{2}

equation (28) (28)

3

\displaystyle=\framebox[56.9055pt]{4}

\displaystyle a

\displaystyle=b

\displaystyle\mathmakebox[\widthof{{}={}}][c]{\vdots}

\displaystyle=c

\displaystyle\mathmakebox[\widthof{{}={}}][c]{\vdots}

\displaystyle=d

13 Additional BookML tests

13.1 Nesting

equation (29) (29)

\displaystyle a

\displaystyle=b

\displaystyle=c

\displaystyle=d

equation (30) (30)

\begin{gathered}\begin{aligned} a&=b\\ &=c\\ &=d\end{aligned}\\ x^{2}\end{gathered}\begin{aligned} a&=b\\ &=c\\ &=d\end{aligned}

13.2 Cases

equation (31) (31)

\displaystyle|x|=

\displaystyle x,

for

x\geq 0

equation (32) (32)

\displaystyle|x|=

\displaystyle-x,

for

x<0

equation (33a) (33a)

\displaystyle w\equiv

\displaystyle 0

for

c=d=0

equation (33b) (33b)

\displaystyle w\equiv

\displaystyle\sqrt{|c|}\,\sqrt{\frac{1+\sqrt{1+(d/c)^{2}}}{2}}

for

|c|\geq|d|

equation (33c) (33c)

\displaystyle w\equiv

\displaystyle\sqrt{|d|}\,\sqrt{\frac{|c/d|+\sqrt{1+(c/d)^{2}}}{2}}

for

|c|<|d|

equation (34a) (34a)

\displaystyle\sqrt{c+id}=

\displaystyle 0\,,

w=0

(case 33a)

equation (34b) (34b)

\displaystyle\sqrt{c+id}=

\displaystyle w+i\frac{d}{2w}\,,

w\neq 0

,

c\geq 0

equation (34c) (34c)

\displaystyle\sqrt{c+id}=

\displaystyle\frac{|d|}{2w}+iw\,,

w\neq 0

,

c<0

,

d\geq 0

equation (34d) (34d)

\displaystyle\sqrt{c+id}=

\displaystyle\frac{|d|}{2w}-iw\,,

w\neq 0

,

c<0

,

d<0