BookML test: amsmath user guide, displayed equations

American Mathematical Society,  Project

1999-12-13
(revised 2002-02-25, 2016-11-14, 2018-04-05, 2019-10-14, 2020-02-18)

BookML

v0.28.5

0.8.8

2018/12/01

Chapter 1 Displayed equations

1.1 Introduction

a=ba=b
equation (1.1) (1.1)
a=ba=b
equation (1.2) (1.2)
a=b+c−d+e−f=g+h=i\begin{split}a&=b+c-d\\ &\quad+e-f\\ &=g+h\\ &=i\end{split}
equation (1.3) (1.3)
a+b+c+d+e+f+i+j+k+l+m+na+b+c+d+e+f\\ +i+j+k+l+m+n
equation (1.4) (1.4)
a1=b1+c1\displaystyle a_{1}=b_{1}+c_{1}
equation (1.5) (1.5)
a2=b2+c2−d2+e2\displaystyle a_{2}=b_{2}+c_{2}-d_{2}+e_{2}
equation (1.6) (1.6)
a1\displaystyle a_{1}
=b1+c1\displaystyle=b_{1}+c_{1}
equation (1.7) (1.7)
a2\displaystyle a_{2}
=b2+c2−d2+e2\displaystyle=b_{2}+c_{2}-d_{2}+e_{2}
equation (1.8) (1.8)
a11\displaystyle a_{11}
=b11\displaystyle=b_{11}
a12\displaystyle a_{12}
=b12\displaystyle=b_{12}
equation (1.9) (1.9)
a21\displaystyle a_{21}
=b21\displaystyle=b_{21}
a22\displaystyle a_{22}
=b22+c22\displaystyle=b_{22}+c_{22}
a11+b11\displaystyle a_{11}+b_{11}
=c11\displaystyle=c_{11}
a12\displaystyle a_{12}
=b12\displaystyle=b_{12}
b21\displaystyle b_{21}
=c21\displaystyle=c_{21}
a22\displaystyle a_{22}
=b22+c22\displaystyle=b_{22}+c_{22}

1.2 Split equations without alignment

equation (1.10) (1.10)
ABCD\framebox[281.85034pt]{A}\\ \framebox[216.81pt]{B}\\ \framebox[238.49231pt]{C}\\ \framebox[281.85034pt]{D}

1.3 Split equations with alignment

equation (1.11) (1.11)
Hc=12⁢n⁢∑l=0n(−1)l⁢(n−l)p−2⁢∑l1+⋯+lp=l∏i=1p(nili)⋅[(n−l)−(ni−li)]ni−li⋅[(n−l)2−∑j=1p(ni−li)2].\begin{split}H_{c}&=\frac{1}{2n}\sum^{n}_{l=0}(-1)^{l}(n-{l})^{p-2}\sum_{l_{1}% +\dots+l_{p}=l}\prod^{p}_{i=1}\binom{n_{i}}{l_{i}}\\ &\quad\cdot[(n-l)-(n_{i}-l_{i})]^{n_{i}-l_{i}}\cdot\Bigl{[}(n-l)^{2}-\sum^{p}_% {j=1}(n_{i}-l_{i})^{2}\Bigr{]}.\kern-20.00003pt\end{split}

1.4 Equation groups without alignment

equation (1.12) (1.12)
f⁢i⁢r⁢s⁢t⁢e⁢q⁢u⁢a⁢t⁢i⁢o⁢n\displaystyle firstequation
equation (1.13) (1.13)
s⁢e⁢c⁢o⁢n⁢de⁢q⁢u⁢a⁢t⁢i⁢o⁢no⁢n⁢t⁢w⁢o⁢l⁢i⁢n⁢e⁢s\displaystyle\begin{split}second&equation\\ &ontwolines\end{split}
equation (1.14) (1.14)
t⁢h⁢i⁢r⁢d⁢e⁢q⁢u⁢a⁢t⁢i⁢o⁢n\displaystyle thirdequation

1.5 Equation groups with mutual alignment

equation (1.15) (1.15)
x\displaystyle x
=y\displaystyle=y
X\displaystyle X
=Y\displaystyle=Y
a\displaystyle a
=b+c\displaystyle=b+c
equation (1.16) (1.16)
x′\displaystyle x^{\prime}
=y′\displaystyle=y^{\prime}
X′\displaystyle X^{\prime}
=Y′\displaystyle=Y^{\prime}
a′\displaystyle a^{\prime}
=b\displaystyle=b
equation (1.17) (1.17)
x+x′\displaystyle x+x^{\prime}
=y+y′\displaystyle=y+y^{\prime}
X+X′\displaystyle X+X^{\prime}
=Y+Y′\displaystyle=Y+Y^{\prime}
a′⁢b\displaystyle a^{\prime}b
=c′⁢b\displaystyle=c^{\prime}b
equation (1.18) (1.18)
x\displaystyle x
=y1−y2+y3−y5+y8−…\displaystyle=y_{1}-y_{2}+y_{3}-y_{5}+y_{8}-\dots
by (1.27)
equation (1.19) (1.19)
=y′∘y∗\displaystyle=y^{\prime}\circ y^{*}
by (2.1)
equation (1.20) (1.20)
=y⁢(0)⁢y′\displaystyle=y(0)y^{\prime}
by Axiom 1.
equation (1.21) (1.21)
x\displaystyle x
=y1−y2+y3−y5+y8−…\displaystyle=y_{1}-y_{2}+y_{3}-y_{5}+y_{8}-\dots
by (1.27)
equation (1.22) (1.22)
=y′∘y∗\displaystyle=y^{\prime}\circ y^{*}
by (2.1)
equation (1.23) (1.23)
=y⁢(0)⁢y′\displaystyle=y(0)y^{\prime}
by Axiom 1.
equation (1.24) (1.24)
x\displaystyle x
=y\displaystyle=y
X\displaystyle X
=Y\displaystyle=Y
equation (1.25) (1.25)
x′\displaystyle x^{\prime}
=y′\displaystyle=y^{\prime}
X′\displaystyle X^{\prime}
=Y′\displaystyle=Y^{\prime}
equation (1.26) (1.26)
x+x′\displaystyle x+x^{\prime}
=y+y′\displaystyle=y+y^{\prime}
X+X′\displaystyle X+X^{\prime}
=Y+Y′\displaystyle=Y+Y^{\prime}
x\displaystyle x
=y\displaystyle=y
X\displaystyle X
=Y\displaystyle=Y
x′\displaystyle x^{\prime}
=y′\displaystyle=y^{\prime}
X′\displaystyle X^{\prime}
=Y′\displaystyle=Y^{\prime}
x+x′\displaystyle x+x^{\prime}
=y+y′\displaystyle=y+y^{\prime}
X+X′\displaystyle X+X^{\prime}
=Y+Y′\displaystyle=Y+Y^{\prime}

1.6 Alignment building blocks

B′=−∂×E,E′=∂×B−4⁢π⁢j,}Maxwell’s equations\left.\begin{aligned} B^{\prime}&=-\partial\times E,\\ E^{\prime}&=\partial\times B-4\pi j,\end{aligned}\right\}\qquad\text{Maxwell's% equations}
equation (1.27) (1.27)
Pr−j={0if r−j is odd,r!⁢(−1)(r−j)/2if r−j is even.P_{r-j}=\begin{cases}0&\text{if $r-j$ is odd},\\ r!\,(-1)^{(r-j)/2}&\text{if $r-j$ is even}.\end{cases}

1.7 Interrupting a display

equation (1.28) (1.28)
A1\displaystyle A_{1}
=N0⁢(λ;Ω′)−ϕ⁢(λ;Ω′),\displaystyle=N_{0}(\lambda;\Omega^{\prime})-\phi(\lambda;\Omega^{\prime}),
equation (1.29) (1.29)
A2\displaystyle A_{2}
=ϕ⁢(λ;Ω′)−ϕ⁢(λ;Ω),\displaystyle=\phi(\lambda;\Omega^{\prime})-\phi(\lambda;\Omega),
and
equation (1.30) (1.30)
A3\displaystyle A_{3}
=𝒩︀⁢(λ;ω).\displaystyle=\mathcal{N}(\lambda;\omega).

Chapter 2 Miscellaneous mathematical features

2.1 Matrices

equation (2.1) (2.1)
(D1⁢t−a12⁢t2…−a1⁢n⁢tn−a21⁢t1D2⁢t…−a2⁢n⁢tn[2]⁢4−an⁢1⁢t1−an⁢2⁢t2…Dn⁢t),\begin{pmatrix}D_{1}t&-a_{12}t_{2}&\dots&-a_{1n}t_{n}\\ -a_{21}t_{1}&D_{2}t&\dots&-a_{2n}t_{n}\\ [2]{4}\\ -a_{n1}t_{1}&-a_{n2}t_{2}&\dots&D_{n}t\end{pmatrix},

Chapter 3 Additional BookML tests

3.1 Subequations

equation (3.1a) (3.1a)
a1\displaystyle a_{1}
=b1+c1\displaystyle=b_{1}+c_{1}
equation (3.1b) (3.1b)
a2\displaystyle a_{2}
=b2+c2−d2+e2\displaystyle=b_{2}+c_{2}-d_{2}+e_{2}
equation (3.1c) (3.1c)
a11\displaystyle a_{11}
=b11\displaystyle=b_{11}
a12\displaystyle a_{12}
=b12\displaystyle=b_{12}
equation (3.1d) (3.1d)
a21\displaystyle a_{21}
=b21\displaystyle=b_{21}
a22\displaystyle a_{22}
=b22+c22\displaystyle=b_{22}+c_{22}