Apa itu LaTeX

LaTeX adalah bahasa markup yang dapat dengan indah menghasilkan dokumen yang berisi struktur kompleks seperti ekspresi matematika, dan sering digunakan dalam bidang ilmiah seperti matematika dan fisika. Ekspresi matematika dapat direpresentasikan dalam teks LaTeX dengan menyisipkan string di antara simbol $ dan $.

Ekspresi matematika di LaTeX

Ekspresi matematis	LaTeX
$\equiv$	$\equiv$
$\approx$	$\approx$
$\fallingdotseq$	$\fallingdotseq$
$\risingdotseq$	$\risingdotseq$
$\sim$	`$\simeq`
$\geq$	`$\geq`
$\geqq$	`$\geqq`
$\leq$	`$\leq`
$\leqq$	`$\leqq`
$\gg$	`$\gg`
$\ll$	`$\ll`
$\N$	`$\N`
$\Z$	`$\Z`
$\R$	`$\R`
$\exist$	`$\exist`
$\forall$	`$\forall`
$\times$	`$\times`
$\ast$	`$\ast`
$\div$	`$\div`
$\pm$	`$\pm`
$\mp$	`$\mp`
$\oplus$	`$\oplus`
$\ominus$	`$\ominus`
$\otimes$	`$\otimes`
$\oslash$	`$\oslash`
$\circ$	`$\circ`
$\ltimes$	`$\ltimes`
$\rtimes$	`$\rtimes`
$\in$	`$\in`
$\ni$	`$\ni`
$\notin$	`$\notin`
$\subset$	`$\subset`
$\supset$	`$\supset`
$\subseteq$	`$\subseteq`
$\supseteq$	`$\supseteq`
$\nsubseteq$	`$\nsubseteq`
$\nsupseteq$	`$\nsupseteq`
$\cap$	`$\cap`
$\cup$	`$\cup`
$\emptyset$	`$\emptyset`
$\varnothing$	`$\varnothing`
$\parallel$	`$\parallel`
$x^2$	$x^2$
$x^{10}$	$x^{10}$
$x^{y+1}$	$x^{y+1}$
$x_i$	$x_i$
$x_i^2$	$x_i^2$
$_n C _r$	$_n C _r$
$\mathrm{e}^x$	$\mathrm{e}^x$
$\pi$	$\pi$
$\alpha$	$\alpha$
$\beta$	$\beta$
$\gamma$	$\gamma$
$\mu$	$\mu$
$\nu$	$\nu$
$\theta$	$\theta$
$\eta$	$\eta$
$\delta$	$\delta$
$\zeta$	$\zeta$
$\ell$	$\ell$
$\epsilon$	$\epsilon$
$\sigma$	$\sigma$
$\lambda$	$\lambda$
$\tau$	$\tau$
$\omega$	$\omega$
$\phi$	$\phi$
$\chi$	$\chi$
$\nabla$	$\nabla$
$\psi$	$\psi$
$\kappa$	$\kappa$
$\xi$	$\xi$
$\varepsilon$	$\varepsilon$
$\vartheta$	$\vartheta$
$\varpi$	$\varpi$
$\varsigma$	$\varsigma$
$\varphi$	$\varphi$
$\Gamma$	$\Gamma$
$\Delta$	$\Delta$
$\Omega$	$\Omega$
$\to$	$\to$
$\rightarrow$	$\rightarrow$
$\Rightarrow$	$\Rightarrow$
$\leftarrow$	$\leftarrow$
$\Leftarrow$	$\Leftarrow$
$\leftrightarrow$	$\leftrightarrow$
$\Leftrightarrow$	$\Leftrightarrow$
$\models$	$\models$
$\cdots$	$\cdots$
$\sin(x)$	$\sin(x)$
$\cos(x)$	$\cos(x)$
$\tan(x)$	$\tan(x)$
$\neq$	$\neq$
$x_1, x_2, \cdots, x_n$	$x_1, x_2, \cdots, x_n$
$\dot{x}$	$\dot{x}$
$\ddot{x}$	$\ddot{x}$
$\vec{x}$	$\vec{x}$
$\hat{x}$	$\hat{x}$
$\bar{x}$	$\bar{x}$
$\tilde{x}$	$\tilde{x}$
$\overrightarrow{x}$	$\overrightarrow{x}$
$\overleftarrow{x}$	$\overleftarrow{x}$
$\infty$	$\infty$
$\int$	$\int$
$\lim$	$\lim$
$\lim_{n\to \infty} a_n$	$\lim_{n\to \infty} a_n$
$\mathrm{d} x$	$\mathrm{d} x$
$F(x)=\int f(x) \mathrm{d} x$	$F(x) = \int f(x) \mathrm{d} x$
$\sqrt{x}$	$\sqrt{x}$
$\sqrt[n]{a}$	$\sqrt[n]{a}$
$\int_{-\infty}^{\infty} \mathrm{e}^{-x^2} \mathrm{d} x$	$\int_{-\infty}^{\infty} \mathrm{e}^{-x^2} \mathrm{d} x$
$\sum$	$\sum$
$\sum_i^N x_i$	$\sum_i^N x_i$
$\prod$	$\prod$
$\prod_i x_i$	$\prod_i x_i$
$\frac{1}{2}$	$\frac{1}{2}$
$\sum_{k=0}^\infty \frac{h^k f^{k}(x)}{k!}$	$\sum_{k=0}^\infty \frac{h^k f^{k}(x)}{k!}$
$a \mathrm{a}$	$a \mathrm{a}$
$\left( \right)$	$\left \right)$
$\left( \frac{x}{y} \right)$	$\left( \frac{x}{y} \right)$
$\left[ \frac{x}{y} \right]$	$\left[ \frac{x}{y} \right]$
$\left( \frac{x}{y} \right.$	$\left( \frac{x}{y} \right.$
$\partial$	$\partial$
$\frac{\partial f}{\partial x}$	$\frac{\partial f}{\partial x}$
$\\$	$\\$
$\quad$	$\quad$
$\underset{k}{\textrm{argmax}}$	$\underset{k}{\textrm{argmax}}$
$\textrm{precision} × \textrm{recall}$	$\textrm{precision} × \textrm{recall}$

Diferensial

\left. \frac{dy}{dx} \right|_{x=1}

$$
\left. \frac{dy}{dx} \right|_{x=1}
$$

Persamaan Multiline

\begin{aligned} (x+y)^2 &= (x+y) (x+y) \\ &= x(x+y) + y (x+y) \\ &= x^2 + xy + yx + y^2 \\ &= x^2 + 2xy+y^2 \end{aligned}

$$
\begin{aligned}
  (x+y)^2 &= (x+y) (x+y) \\
  &= x(x+y) + y (x+y) \\
  &= x^2 + xy + yx + y^2 \\
  &= x^2 + 2xy+y^2
\end{aligned}
$$

Matriks

\begin{pmatrix} a & b\\ c & d \end{pmatrix}

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

\begin{bmatrix} a & b\\ c & d \end{bmatrix}

\begin{bmatrix}
a & b\\
c & d
\end{bmatrix}

\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}

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

\left( \begin{array}{c} (x^{1})^T\\ \vdots\\ (x^{N})^T\\ \end{array} \right)

$$
\left(
  \begin{array}{c}
    (x^{1})^T\\
    \vdots\\
    (x^{N})^T\\
  \end{array}
\right)
$$

A = \left( \begin{array}{ccccc} 1 & 1 & 4 & 5 & 1 \\ 1 & 0 & 5 & 0 & 4 \\ 4 & 5 & 1 & 4 & 0 \end{array} \right)

$$
A = \left(
  \begin{array}{ccccc}
    1 & 1 & 4 & 5 & 1 \\
    1 & 0 & 5 & 0 & 4 \\
    4 & 5 & 1 & 4 & 0
  \end{array}
\right)
$$

\begin{pmatrix} a_{11} & \cdots & a_{1i} & \cdots & a_{1n}\\ \vdots & \ddots & & & \vdots \\ a_{i1} & & a_{ii} & & a_{in} \\ \vdots & & & \ddots & \vdots \\ a_{n1} & \cdots & a_{ni} & \cdots & a_{nn} \end{pmatrix} \times \begin{vmatrix} a_{11} & \cdots & a_{1i} & \cdots & a_{1n}\\ \vdots & \ddots & & & \vdots \\ a_{i1} & & a_{ii} & & a_{in} \\ \vdots & & & \ddots & \vdots \\ a_{n1} & \cdots & a_{ni} & \cdots & a_{nn} \end{vmatrix}

$$
\begin{pmatrix}
  a_{11} & \cdots & a_{1i} & \cdots & a_{1n}\\
  \vdots & \ddots &        &        & \vdots \\
  a_{i1} &        & a_{ii} &        & a_{in} \\
  \vdots &        &        & \ddots & \vdots \\
  a_{n1} & \cdots & a_{ni} & \cdots & a_{nn}
\end{pmatrix}

\times

\begin{vmatrix}
  a_{11} & \cdots & a_{1i} & \cdots & a_{1n}\\
  \vdots & \ddots &        &        & \vdots \\
  a_{i1} &        & a_{ii} &        & a_{in} \\
  \vdots &        &        & \ddots & \vdots \\
  a_{n1} & \cdots & a_{ni} & \cdots & a_{nn}
\end{vmatrix}
$$

Conditional Branch

f(x) = \left\{ \begin{array}{ll} 1 & (x = 1) \\ 0 & (otherwise) \end{array} \right.

$$
f(x) = \left\{
  \begin{array}{ll}
    1 & (x = 1) \\
    0 & (otherwise)
  \end{array}
\right.
$$

Nomor Persamaan

\tag{1.0.2} x_i = \sigma (W_i + \beta)

$$
\tag{1.0.2}
x_i = \sigma (W_i + \beta)
$$

Pemrograman Linier

\begin{equation*} \begin{aligned} & \text{minimize} & {\bf c}^T{\bf x} \\ & \text{s.t.} & A{\bf x} \le {\bf b} \\ & & {\bf x} \ge {\bf 0} \\ \end{aligned} \end{equation*}

$$
\begin{equation*}
  \begin{aligned}
    & \text{minimize}
      & {\bf c}^T{\bf x} \\
    & \text{s.t.}
      & A{\bf x} \le {\bf b} \\
      & & {\bf x} \ge {\bf 0} \\
  \end{aligned}
\end{equation*}
$$

Metode Simpleks

\begin{array}{rrrrrrr} x_3 & = & 1 & + & x_1 & - & x_2 \\ x_4 & = & 3 & - & x_1 & & \\ x_5 & = & 2 & & & - & x_2 \\ \hline z & = & & & x_1 & + & x_2 \end{array}

$$
\begin{array}{rrrrrrr}
  x_3 & = & 1 & + & x_1 & - & x_2 \\
  x_4 & = & 3 & - & x_1 &   &     \\
  x_5 & = & 2 &   &     & - & x_2 \\ \hline
  z   & = &   &   & x_1 & + & x_2
\end{array}
$$

Ekspresi matematika di LaTeX

Apa itu LaTeX

Ekspresi matematika di LaTeX

Diferensial

Persamaan Multiline

Matriks

Conditional Branch

Nomor Persamaan

Pemrograman Linier

Metode Simpleks

CPU dan GPU

Ansible Vault

Ryusei Kakujo