分子 \over 分母
。如:$$
a+1 \over b+1
$$
编译为
a + 1 b + 1 a+1 \over b+1 b+1a+1
\frac {分子} {分母}
。如:$$
\frac {\frac ab +1} {\frac {c+2}{d+4} +8}
$$
编译为
a b + 1 c + 2 d + 4 + 8 \frac {\frac ab +1} {\frac {c+2}{d+4} +8} d+4c+2+8ba+1
\sqrt [根指数] {被开方数}
,缺省根指数时默认为 2。如:$$
\sqrt [n] {x+y}
$$
编译为
x + y n \sqrt [n] {x+y} nx+y
\log_{对数底数}{表达式}
。如:$$
\log_{10}{(x+y)}
$$
编译为
log 10 ( x + y ) \log_{10}{(x+y)} log10(x+y)
\max_{下标表达式}{最值表达式}
;\min_{下标表达式}{最值表达式}
;$$
\max_{1\leq i\leq n}{|x_i|}
$$
编译为
max 1 ≤ i ≤ n ∣ x i ∣ \max_{1\leq i\leq n}{|x_i|} 1≤i≤nmax∣xi∣
\begin{cases}
和 \end{cases}
包裹每个等式。如:$$
\begin{cases}
a+b+c=2 \\
a-b=4 \\
\end{cases}
$$
编译为
{ a + b + c = 2 a − b = 4 a + c = 5 \begin{cases} a+b+c=2 \\ a-b=4 \\ a+c=5 \end{cases} ⎩ ⎨ ⎧a+b+c=2a−b=4a+c=5
\begin{aligned}
进行对齐,&
表示对齐位置,需要人为加上大号括号。如:$$
\left\{
\begin{aligned}
a+b&=2 \\
a-b&=4 \\
\end{aligned}
\right.
$$
编译为
{ a + b + c = 2 a − b = 4 a + c = 5 \left\{ \begin{aligned} a+b+c&=2 \\ a-b&=4 \\ a+c&=5 \end{aligned} \right. ⎩ ⎨ ⎧a+b+ca−ba+c=2=4=5
$$
y =
\begin{cases}
\sin(x) & x<0 \\
x^2 + 2x +4 & 0 \leq x < 1 \\
x^3 & x \geq 1 \\
\end{cases}
$$
编译为
y = { sin ( x ) x < 0 x 2 + 2 x + 4 0 ≤ x < 1 x 3 x ≥ 1 y = \begin{cases} \sin(x) & x<0 \\ x^2 + 2x +4 & 0 \leq x < 1 \\ x^3 & x \geq 1 \\ \end{cases} y=⎩ ⎨ ⎧sin(x)x2+2x+4x3x<00≤x<1x≥1
\sum_{下标表达式}^{上标表达式}{累加表达式}
;\prod_{下标表达式}^{上标表达式}{累加表达式}
;$$
\sum_{i=1}^n \frac{1}{i^2}
$$
编译为
∑ i = 1 n 1 i 2 \sum_{i=1}^n \frac{1}{i^2} i=1∑ni21
\bigcap_{下标表达式}^{上标表达式}{累加表达式}
;\bigcup_{下标表达式}^{上标表达式}{累加表达式}
;$$
\bigcap_{i=1}^n {A_i}
$$
编译为
⋂ i = 1 n A i \bigcap_{i=1}^n {A_i} i=1⋂nAi
\lim_{变量 \to 变量极限} 表达式
。如:$$
\lim_{x \to +\infty} \frac{1}{x(x+1)}
$$
编译为
lim x → + ∞ 1 x ( x + 1 ) \lim_{x \to +\infty} \frac{1}{x(x+1)} x→+∞limx(x+1)1
{\rm d}x
或 f^\prime
;$\frac{\partial y}{\partial x}$
;\nabla f(x)
;$$
f^\prime(x)=\frac{{\rm d}y}{{\rm d}x}
$$
编译为
f ′ ( x ) = d y d x f^\prime(x)=\frac{{\rm d}y}{{\rm d}x} f′(x)=dxdy
\int {被积表达式}
;\int_{积分下限}^{积分上限} {被积表达式}
;\oint_{积分下限}^{积分上限} {被积表达式}
;$\iint$
;$\iiint$
;$$
\int_0^1 {x^2} {\rm d}x
$$
编译为
∫ 0 1 x 2 d x \int_0^1 {x^2} {\rm d}x ∫01x2dx
\left(\begin{array}{ccc}x_1 &\cdots &x_n\end{array}\right)
。如:\vec{x}=
\left(
\begin{array}{ccc}
x_1 &
\cdots &
x_n
\end{array}
\right)
编译为
x ⃗ = ( x 1 ⋯ x n ) \vec{x}= \left( \begin{array}{ccc} x_1 & \cdots & x_n \end{array} \right) x=(x1⋯xn)
\left(\begin{array}{ccc}x_1 &\cdots &x_n\end{array}\right)
。如:\vec{x}=
\left(
\begin{array}{ccc}
x_1 &
\cdots &
x_n
\end{array}
\right)
编译为
y ⃗ = ( y 1 ⋮ y m ) \vec{y}= \left( \begin{array}{c} y_1 \\ \vdots \\ y_m \end{array} \right) y= y1⋮ym
如果向量的字母不止一个,使用 \vec
会导致箭头过小,无法盖住整个向量名,这是可以采用右箭头 $\overrightarrow{AB}$
: A B → \overrightarrow{AB} AB 。其实向量更常见的写法是黑体加粗,即 $\boldsymbol{x}$
: x \boldsymbol{x} x;
$$
D=
\left|
\begin{array}{cccc}
{a_{11}} & {a_{12}} & {\cdots} & {a_{1 n}} \\
{a_{21}} & {a_{22}} & {\cdots} & {a_{2 n}} \\
{\vdots} & {\vdots} & {\ddots} & {\vdots} \\
{a_{n 1}} & {a_{n 2}} & {\cdots} & {a_{n n}}
\end{array}
\right|
$$
编译为
D = ∣ a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋮ ⋮ ⋱ ⋮ a n 1 a n 2 ⋯ a n n ∣ D= \left| \begin{array}{cccc} {a_{11}} & {a_{12}} & {\cdots} & {a_{1 n}} \\ {a_{21}} & {a_{22}} & {\cdots} & {a_{2 n}} \\ {\vdots} & {\vdots} & {\ddots} & {\vdots} \\ {a_{n 1}} & {a_{n 2}} & {\cdots} & {a_{n n}} \end{array} \right| D= a11a21⋮an1a12a22⋮an2⋯⋯⋱⋯a1na2n⋮ann
$$
A_{m×n}=
\left[
\begin{array}{cccc}
{a_{11}} & {a_{12}} & {\cdots} & {a_{1 n}} \\
{a_{21}} & {a_{22}} & {\cdots} & {a_{2 n}} \\
{\vdots} & {\vdots} & {\ddots} & {\vdots} \\
{a_{m 1}} & {a_{m 2}} & {\cdots} & {a_{m n}}
\end{array}
\right]
$$
编译为
A m × n = [ a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋮ ⋮ ⋱ ⋮ a m 1 a m 2 ⋯ a m n ] A_{m×n}= \left[ \begin{array}{cccc} {a_{11}} & {a_{12}} & {\cdots} & {a_{1 n}} \\ {a_{21}} & {a_{22}} & {\cdots} & {a_{2 n}} \\ {\vdots} & {\vdots} & {\ddots} & {\vdots} \\ {a_{m 1}} & {a_{m 2}} & {\cdots} & {a_{m n}} \end{array} \right] Am×n= a11a21⋮am1a12a22⋮am2⋯⋯⋱⋯a1na2n⋮amn
$$
\left[
\begin{array} {c c | c} %竖线表示2、3列间插入竖线
1 & 2 & 3 \\
4 & 5 & 6
\end{array}
\right]
$$
编译为
[ 1 2 3 4 5 6 ] \left[ \begin{array} {c c | c} %竖线表示2、3列间插入竖线 1 & 2 & 3 \\ 4 & 5 & 6 \end{array} \right] [142536]
$$
\left[
\begin{array} {c}
1 & 2 & 3 \\
\hline %插入横线
4 & 5 & 6
\end{array}
\right]
$$
编译为
[ 1 2 3 4 5 6 ] \left[ \begin{array} {c} 1 & 2 & 3 \\ \hline %插入横线 4 & 5 & 6 \end{array} \right] [142536]
$$A \cong B$$
编译为
A ≅ B A \cong B A≅B
$$A \sim B$$
编译为
A ∼ B A \sim B A∼B
$$A \simeq B$$
编译为
A ≃ B A \simeq B A≃B