Formatting Engee scripts with LaTeX

This example provides a set of commands in the document markup language $\LaTeX{}$, which allow you to format mathematical expressions, text and graphics in user interactive scripts Engee in a convenient and presentable way.

When layout scripts in Engee you should keep in mind that the display of mathematical symbols in expressions embedded in a string, for example: $\int \frac{1}{\sigma {\sqrt {2\pi }}}\,e^{-{(x-\mu )^{2}/2\sigma ^{2}}}\;dx$ may differ from the display of symbols switched off from the string: $$\int \frac{1}{\sigma {\sqrt {2\pi }}}},e^{-{-{(x-\mu )^{2}/2\sigma ^{2}}}}\;dx$$$.

The list of commands in the example $\LaTeX{}$ is not exhaustive.

1. Signs and symbols

1.1 Number systems

Natural $\mathbb N$

Natural with zero $\mathbb N_0$

Plain $\mathbb P$

Whole $\mathbb Z$

Rational $\mathbb Q$

Algebraic $\overline{\mathbb Q}$, $\mathbb A$

Irrational $\mathbb I$

Real $\mathbb R$

Complex $\mathbb C$

Quaternions $\mathbb H$

Octonions (Caley numbers) $\mathbb O$

Cedenions $\mathbb S$

1.2 Greek alphabet

$A\ \alpha$
$B\ \beta$
$\Gamma\ \gamma$
$\Delta\ \delta$
$E\ \epsilon\ \varepsilon$
$Z\ \zeta$ $H\ \eta$
$\Theta\ \theta\ \vartheta$ $I\ \iota$ $K\ \kappa\ \varkappa$ $\Lambda\ \lambda$ $M\ \mu$
$N\ \nu$
$\Xi\ \xi$ $O\ o$ $\Pi\ \pi\ \varpi$ $P\ \rho\ \varrho$ $\Sigma\ \sigma\ \varsigma$
$T\ \tau$
$\Upsilon\ \upsilon$
$\Phi\ \phi\ \varphi$
$X\ \chi$
$\Psi\ \psi$
$\Omega\ \omega$

1.3 Multiple dots and matrices

Multiple dots at the bottom
$k = 1, 2, \dots, n-1$ $k = 1, 2, \ldots, n-1$

Centred dots
$k = 1, 2, \cdots, n-1$

Vertical dotted line
$\vdots$

Diagonal punctuation
$\ddots$

Matrices

$\begin{matrix} x_{11} & x_{12} & x_{13} \\ x_{21} & x_{22} & x_{23} \\ x_{31} & x_{32} & x_{33} \\ \end{matrix}$

$M = \left[ \begin{matrix} x_{11} & x_{12} & x_{13} \\ x_{21} & x_{22} & x_{23} \\ x_{31} & x_{32} & x_{33} \\ \end{matrix} \right]$

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

1.4 Brackets, stoppers

Horizontal braces
$\underbrace{1+2+\ldots+x}_{n} \quad$ $\overbrace{1+2+\ldots+x}^{n}$

Parentheses
$(\frac{A^2}{B_i})$

$\Bigg( \bigg( \Big( \big( \, ( \quad ) \, \big) \Big) \bigg) \Bigg)$

Automatic scaling of brackets
$\left( \frac{A^2}{B_i} \right)$

Brackets
$\Bigg\{ \bigg\{ \Big\{ \big\{ \{ \quad \} \big\} \Big\} \bigg\} \Bigg\}$

Square brackets
$\Bigg[ \bigg[ \Big[ \big[ \, [ \quad ] \, \big] \Big] \bigg] \Bigg]$

Angle brackets
$\Bigg\langle \bigg\langle \Big\langle \big\langle \langle \quad \rangle \big\rangle \Big\rangle \bigg\rangle \Bigg\rangle$

Straight brackets
$\Bigg| \bigg| \Big| \big| | \quad | \big| \Big| \bigg| \Bigg|$

Double straight brackets
$\Bigg\| \bigg\| \Big\| \big\| \| \quad \| \big\| \Big\| \bigg\| \Bigg\|$

1.5 Indices and accents

Indices
$x_{i^2}$
Indices and degrees
$x_{i_n^2}^{n_2^i}$

Ordinary Emphases
$\hat{x}, \check{x}, \tilde{x}, \acute{x}, \grave{x}$
$\dot{x}, \ddot{x}, \breve{x}, \bar{x}, \vec{x}$

Wide accents
$\widehat{xyz}, \widetilde{xyz}$
$\overrightarrow{AB}$

1.6 Other

Hebrew symbols
$\aleph, \, \beth, \, \gimel$

Planck's reduced constant (Dirac constant)
$\hbar = 1,054571800(13) \times 10^{-34} \ Дж \cdot с$

Some of the more specific signs not given in this example can be found in the documentation of Engee.

2. arithmetic and elementary algebra

Not equal
$a \ne b$
$a \neq b$

Approximate equality
$x \approx y$

Identity
$m \equiv n$

Proportionality
$x \sim y$
$x \propto y$

Give or take
$\pm$
Minus-plus
$\mp$

Amount
$\sum _{i=1} ^{n} x_i$
$\sum \limits _{i=1} ^{n} x_i$

The product of a dot
$a \cdot b$

Vector and matrix product
$A \times B$

Tensor product
$A \otimes B$

Element product
$A \odot B$

Work
$\prod \limits ^{n} _{i=0} x_i$

Fractions
$\frac{3}{4}$

$T = T_0 {g H \over {g_0 H_0}}$

Obelus
$\div$

Square root
$i = \sqrt{-1}$

Root of nth degree
$\sqrt[n]{a+b}$

Elevation
$x^{n_0}$

Infinity
$\infty$

Actual part
$\Re(z)$
imaginary part
$\Im(z)$

3. set theory

An empty set
$\emptyset$, $\varnothing$

Belongs to $n \in \mathbb C$ Does not belong $n \notin \mathbb C$

Subset
$A \subseteq B$
$A \subset B$

Superset
$A \supseteq B$
$A \supset B$

Own subset
$A \subsetneq B$

Eigenset
$A \supsetneq B$

union
$A \cup B$

Intersection
$A \cap B$

Difference of sets
$A \setminus B$

function
$f:X \to Y$

Display
$f:x \mapsto f(x)$

4. Comparisons and mathematical logic

Less than or equal to
$A \leq B$
$A \leqslant B$

Greater than or equal to
$A \geq B$
$A \geqslant B$

A lot less
$A \ll B$

Much more
$A \gg B$

Implication
$A \Rightarrow B$ $A \rightarrow B$ $A \supset B$

Equivalence
$A \Leftrightarrow B$

Quantifier of universality ("for everyone...")
$\forall n \in \mathbb{N}$

Quantor of existence
$\exists z \in \mathbb{Z} \quad$ ("exists...")
$\nexists z \in \mathbb{Z} \quad$ ("does not exist...")

Definition
$x:=y$ $P :\Leftrightarrow Q$ $P \stackrel{\rm{def}}{=} Q$

Negation "NOT."
$\bar{A}$
$\lnot A$
$\neg A$

OR disjunction
$A \lor B$ $A \vee B$

"And" conjunction
$A \land B$ $A \wedge B$

Negation of disjunction (Pierce's arrow) OR-NE
$A \downarrow B$

Negation of conjunction (Schaeffer's stroke) "AND-NE"
$A | B$
$A \uparrow B$

"EXCLUDING OR"
$A \oplus B$

5. Trigonometry and geometry

5.1 Signs

Angle
$\angle ABC$

Perpendicular
$AB \bot CD$

Parallel
$AB \parallel CD$

Proportionality
$AB \sim CD$
$AB \propto CD$

Gradus
$\alpha = 90^\circ$

Vector
$\vec a$
$\overrightarrow{AB}$

5.2 Functions

Sine
$\sin{\frac{\pi}{2}}$

Cosine
$\cos{\frac{\pi}{2}}$

tangent
$\tan{\frac{\pi}{2}}$

Cotangent
$\cot{\frac{\pi}{2}}$

arcsinus
$\arcsin{\frac{\sqrt{3}}{2}}$

Arccosine
$\arccos{\frac{\sqrt{3}}{2}}$

Arctangent
$\arctan{\frac{\sqrt{2}}{2}}$

Sekans
$\sec{\alpha}$

Cosecans
$\csc{\alpha}$

5.3 Hyperbolic functions

Hyperbolic sine
$\sinh{x}$

Hyperbolic cosine
$\cosh{x}$

Hyperbolic tangent
$\tanh{x}$

Hyperbolic tangent
$\coth{x}$

6. Mathematical analysis

Indefinite integral (within a paragraph)
$\int f(x) dx$

Undefined integral (off)
$$\int f(x) dx$$

Definite integral (within a paragraph)
$\int_{a}^{b}f(x)dx$
$\int\limits_{a}^{b}f(x)dx$

Double, triple integrals
$\iint f(x) dx$
$\iiint f(x) dx$

Integral over a closed contour
$\oint dl$

partial derivative
${\partial\over{\partial y}}f(x)$

Limit
$\lim \limits_{x \to \infty} f(x) = 0$

Maximum, minimum
$\max X$
$\min X$

Supremum, infimum
$\sup X$
$\inf X$

Nabla operator (Hamilton operator)
$\nabla = \frac{\partial}{\partial x} \vec \imath +\frac{\partial}{\partial y} \vec \jmath + \frac{\partial}{\partial z} \vec k$

7. $\LaTeX{}$ in graphs

Using the library LaTeXStrings.jl you can simplify the design of labels and symbols in graphs in the markup $\LaTeX{}$.

using Plots, LaTeXStrings
gr(size=([500, 300]))

default(fontfamily="Computer Modern", linewidth=2, framestyle=:nothing, grid=true)

F = collect(1:10);
m = 2;
a = F.*m;

Plots.plot(F, a, label = L"a=f(F)", legend = :topleft)
xlabel!(L"Сила\ F,\ [Н \cdot м]")
ylabel!(L"Ускорение\ a,\ [\frac{м}{с^2}]")
title!(L"График\ зависимости\ ускорения\ от\ силы")

To learn more about the layout of Engee charts in $\LaTeX{}$, see documentation.

8. Formatting

8.1 Spaces

$Текст и формула без пробелов.$ $f(x)=x^2+3x+2$

$Пробелы\ как\ в\ тексте.$ $f(x)=x^2\ +\ 3x\ +\ 2$

$Пробелы,\qquad эквивалентные\qquad двойному\qquad размеру\qquad шрифта.\qquad(36\qquad mu)$ $f(x)=x^2\qquad +\qquad 3x\qquad +\qquad 2$

$Пробелы,\quad эквивалентные\quad размеру\quad шрифта.\quad(18\quad mu)$ $f(x)=x^2\quad +\quad 3x\quad +\quad 2$

$Пробелы,\; эквивалентные\; \frac{5}{18}\; размера \;шрифта.\; (5\; mu)$ $f(x)=x^2\; +\; 3x\; +\; 2$

$Пробелы,\: эквивалентные\: \frac{4}{18}\: размера \:шрифта.\: (4\: mu)$ $f(x)=x^2\: +\: 3x\: +\: 2$

$Пробелы,\, эквивалентные\, \frac{3}{18}\, размера \,шрифта.\, (3\, mu)$ $f(x)=x^2\, +\, 3x\, +\, 2$

$Пробелы,\! эквивалентные\! -\frac{3}{18}\! размера \! шрифта.\! (-3 \! mu)$ $f(x)=x^2\!+\!3x\!+\!2$