Mirai Math Reference

Table of contents

Natural input
Toolbar input
General
Operators
Symbols
Functions
Copy TeX to Wiki
Create pdf from TeX
Note on file encoding

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Natural Input

Natural input aims to allow formula input in the same
way as it would be done in text mode, in an attempt to
achieve maximum effectiveness of input.

Type the formula using characters, numbers and symbols.
Use [Home], [End], [Up], [Down], [<-], [->] cursor keys.

* / + -	operators

\	for fraction
^	for power
_	for subscript

{	insert empty array
[	insert empty vector

[F1]	for general toolbar
[F2]	for operator toolbar
[F3]	for symbol toolbar
[F4]	for function toolbar

[Backspace]	remove content before cursor
[Delete]	remove content after cursor

[Enter]	to evaluate expression
[Up], [Down]	to select a formula

Toolbar Input

Toolbar input represents opposite concept to natural input.
It aims to allow the most intuitive, though still comfortable
input for less experienced users and children.

General

Toolbar is activated by [F1]. Use cursor keys and
[Enter] to select symbol. Press [F1] for next tab.

	^n - power
	sqrt(x) - square root
	nthroot(x, n) - nth root
	factorial(x) - n factorial

Functions that follow are meta functions. These are math
functions, that are not easily expressible in terms of octave
vocabulary. These are emulated by combining multiple
octave commands or defining new runtime functions.

	_i - subscript
	frac(x, y) - fraction
	sum(v, fm, to, x) - sum
	prod(v, fm, to, x) - product
	int(fm, to, x, v) - numerical integration / quadrature
	nint(x, v) - integration - no implementation - TeX only
	lim(v, to, x) - limit of function - no implementation - TeX only
	function(name, v, x) - math function definition

Functions shown blue have no implementation - to be used with TeX only.

Operators

Toolbar is activated by [F2]. Use cursor keys and
[Enter] to select symbol. Press [F1] for next tab.

a-b	a<b	subset [Esc]	leftarrow [Esc]
a+b	a>b	supset [Esc]	rightarrow [Esc]
a*b	leq [Esc]	subseteq [Esc]	leftrightarrow [Esc]
a/b	geq [Esc]	supseteq [Esc]	notrightarrow [Esc]
times [Esc]	ll [Esc]	cup [Esc]	notleftrightarrow [Esc]
div [Esc]	gg [Esc]	cap [Esc]
a=b	sim [Esc]	in [Esc]
ne [Esc]	approx [Esc]	empty [Esc]
equiv [Esc]	simeq [Esc]	pm [Esc]
neg [Esc]	propto [Esc]	prime [Esc]

Operators shown blue have no implementation - to be used with TeX only.

Symbols

Toolbar is activated by [F3]. Use cursor keys and
[Enter] to select symbol. Press [F1] for next tab.

inf [Esc]	varth [Esc]	sigma [Esc]	Lambda [Esc]
ii [Esc]	iota [Esc]	varsigma [Esc]	Xi [Esc]
jj [Esc]	kappa [Esc]	tau [Esc]	Pi [Esc]
alpha [Esc]	lambda [Esc]	upsilon [Esc]	Sigma [Esc]
beta [Esc]	mu [Esc]	phi [Esc]	Upsilon [Esc]
gamma [Esc]	nu [Esc]	varphi [Esc]	Phi [Esc]
delta [Esc]	xi [Esc]	chi [Esc]	Psi [Esc]
epsilon [Esc]	omicron [Esc]	psi [Esc]	Omega [Esc]
vareps [Esc]	pi [Esc]	omega [Esc]	nabla [Esc]
zeta [Esc]	varpi [Esc]	Gamma [Esc]	hbar [Esc]
eta [Esc]	rho [Esc]	Delta [Esc]	ddagger [Esc]
theta [Esc]	varrho [Esc]	Theta [Esc]	paragraph [Esc]

Functions

Toolbar is activated by [F4]. Use cursor keys and
[Enter] to select symbol. Press [F1] for first tab.

Operators

Functions can also be input from keyboard.
For example sin() can be inserted by typing sin(.

ln(x) - natural logarithm

log10(x) - base 10 logarithm

exp(x) - exponential

Trigonometric functions

sin(x) - sine

cos(x) - cosine

tan(x) - tangent

asin(x) - arc sinus

acos(x) - arc cosine

atan(x) - arc tangent

sinh(x) - hyperbolic sine

cosh(x) - hyperbolic cosine

tanh(x) - hyperbolic tangent

asinh(x) - hyperbolic arc sine

acosh(x) - hyperbolic arc cosine

atanh(x) - hyperbolic arc tangent

Statistic functions

corrcoef(x, y) - correlation coefficient

cov(x, y) - covariance

median(a) - median value

mean(a) - mean value

std(a) - standard deviation

var(a) - variance

cov(a) - covariance

Matrix Operations

eye(n, m) - create n by m identity matrix

transpose(a) - transpose a matrix

inverse(a) - invert a square matrix

det(a) - determinant of a matrix

min(a) - minimum value in a matrix

max(a) - maximum value in a matrix

rows(a) - returns number of rows

columns(a) - returns number of columns

Graphic Operations

plot(x, y) - 2D plot

meshgrid(x, y) - grid for 3D mesh

mesh(x, y, z) - 3D mesh

title "s" - title of a figure

xlabel "s" - x-axis description

ylabel "s" - y-axis description

zlabel "s" - z-axis description

print -deps "s" - print to .eps file

print -dpng "s" - print to .png file

figure - new figure

Miscellaneous Functions

mod(n, m) - modulo

floor(x) - round down to whole number

ceil(x) - round up to next whole number

abs(x) - absolute value

sign(x) - sign of x

gcd(x, y) - greatest common divisor

lcm(x, y) - least common multiple

rand() - random number

Copy TeX to wiki

Wiki servers such as wikipedia.org allows math formulas in TeX format.

To add formula in wiki, copy TeX including the math xml tag:

<math>TeX formula</math>

Create pdf from TeX

Install latex package such as tetex-latex-3.0.

Run following command on exported tex file on the command line:

pdflatex file.tex

Note on file encoding

Mirai Documents are xml documents and use UTF-8 encoding.

LaTeX Documents can be stored either default encoding or UTF-8.

For HTML and Plain Text default system encoding is used.
Encoding can be changed by adding java option to start script.

-Dfile.encoding=UTF-8

List of availabe encodings can be found on following site:
http://java.sun.com/j2se/1.5.0/docs/guide/intl/encoding.doc.html

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