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5.1 Skriva matematiska formler i LaTeX

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LaTeX matematik

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Skriva formler i LaTeX
Undvika vanliga misstag när man kodar matematik i LaTeX

För att effektivt kunna skriva matematik på din dator i den individuella uppgiften och gruppuppgiften så behöver du koda matematiken med hjälp av LaTeX. I detta avsnitt kommer du få lära dig grunderna i att konstruera LaTeX-kod för att skriva matematiska formler.

How to write basic expressions

To indicate the start of math formatting, use the tag <math>. To end math formatting, use the tag </math>. For example, if you want the formula \displaystyle a+b, in the text box write <math>a+b</math>.

Simple mathematical formulas are written in a straight-forward manner.

Example 1

\displaystyle 1+2-3\quad is written <math>1+2-3</math>
\displaystyle 5/2\quad is written <math>5/2</math>
\displaystyle 4/(2+x)\quad is written <math>4/(2+x)</math>
\displaystyle 4 < 5\quad is written <math>4 < 5</math>

When you need to use symbols that are not available on the keyboard or construct formulas that are not simple you use special commands that start with a backslash, e.g. \le is a command that gives you \displaystyle \le.

The table below shows some of the most commonly used maths commands in LaTeX.

	Example	LaTeX-code	Comment
Simple operations	a+b	`a+b`
	a-b	`a-b`
	a\pm b	`a\pm b`
	a\times b	`a\times b`
	a/b	`a/b`
	\frac{a}{b}	`\frac{a}{b}`	Use \dfrac{a}{b} for a larger sized fraction
	(a)	`(a)`	Scalable parantheses \left(...\right)
Relation signs	a=b	`a=b`
	a\ne b	`a\ne b`	Alternatively: a\not= b
	a< b	`a< b`	NB: Space after "<"
	a\le b	`a\le b`
	a> b	`a>b`
	a\ge b	`a\ge b`
Powers and roots	x^{n}	`x^{n}`
	\sqrt{x}	`\sqrt{x}`
	\sqrt[n]{x}	`\sqrt[n]{x}`	Write \sqrt[\scriptstyle n]{x} for bigger n
Index	x_n	`x_{n}`
Logarithms	\ln x	`\ln x`
	\log x	`\log x`
	\log_{a} x	`\log_{a} x`
Trigonometry	30^{\circ}	`30^{\circ}`
	\cos x	`\cos x`
	\sin x	`\sin x`
	\tan x	`\tan x`
	\cot x	`\cot x`
Arrows	\Rightarrow	`\Rightarrow`
	\Leftarrow	`\Leftarrow`
	\Leftrightarrow	`\Leftrightarrow`
Various symbols	\pi	`\pi`

Example 2

\displaystyle 1\pm3\times 5\quad is written <math>1\pm 3\times 5</math>
\displaystyle \tfrac{1}{2}y\ne x\le z\quad is written <math>\frac{1}{2}y\ne x\le z</math>
\displaystyle 2^{13}\sqrt{3}+\ln y\quad is written <math>2^{13}\sqrt{3}+\ln y</math>
\displaystyle \tan 30^{\circ}+\cot\pi\quad is written <math>\tan 30^{\circ}+\cot\pi</math>

How to write complex expressions

By combining simple expressions, we may form more complex expressions.

Example 3

\displaystyle \sqrt{x+2}\quad is written <math>\sqrt{x+2}</math>
\displaystyle (a^2)^3=a^6\quad is written <math>(a^2)^3=a^6</math>
\displaystyle 2^{2^2}\quad is written <math>2^{2^2}</math>
\displaystyle \sin\sqrt{x}\quad is written <math>\sin\sqrt{x}</math>

Example 4

\displaystyle \sqrt{x+\sqrt{x}}\quad is written <math>\sqrt{x+\sqrt{x}}</math>
\displaystyle \dfrac{x-x^2}{\sqrt{3}}\quad is written <math>\dfrac{x-x^2}{\sqrt{3}}</math>
\displaystyle \dfrac{x}{x+\dfrac{1}{x}}\quad is written <math>\dfrac{x}{x+\dfrac{1}{x}}</math>
\displaystyle x_{1,2}=-\dfrac{p}{2}\pm\sqrt{\left(\dfrac{p}{2}\right)^2-q}\quad is written <math>x_{1,2}=-\dfrac{p}{2}\pm\sqrt{\left(\dfrac{p}{2}\right)^2-q}</math>

How to avoid common mistakes

One of the most common mistakes when editing math in the wiki is to forget the start <math> tag and the end </math> tag.

Remember also to start commands with a backslash (\) and to add a space after the commands (unless they are followed immediately by a new command).

Another frequent mistake is to use an asterisk (*) instead of a proper multiplication sign \displaystyle \times (\times in TeX).

Example 5

	LaTeX	Result
Don't write	`sin x`	\displaystyle sin x
Don't write	`\sinx`	Error
Do write	`\sin x`	\displaystyle \sin x
Don't write	`4*3`	\displaystyle 4*3
Do write	`4\times 3`	\displaystyle 4\times 3
Don't write	`a\times b`	\displaystyle a\times b
Do write	`ab`	\displaystyle ab

Exponents and indices

When writing exponents you use ^ followed by the exponent and to write indices you use _ followed by the index. If the exponent or index consists of more than one symbol it must be enclosed with braces {}.

A special kind of exponent is the degree sign (°) which is written as ^{\circ}.

Example 6

	LaTeX	Result
Don't write	`a2`	\displaystyle a2
Do write	`a^2`	\displaystyle a^2
Don't write	`x1`	\displaystyle x1
Do write	`x_1`	\displaystyle x_1
Don't write	`a^22`	\displaystyle a^22
Do write	`a^{22}`	\displaystyle a^{22}
Don't write	`30^{o}`	\displaystyle 30^{o}
Don't write	`30^{0}`	\displaystyle 30^{0}
Do write	`30^{\circ}`	\displaystyle 30^{\circ}

Delimiters

In more complex expressions you need to make sure to balance each opening parenthesis ( with a closing parenthesis ).

A pair of parenthesis that delimits a tall expression should be as large as the expression. You should therefore prefix the opening parenthesis with \left and the closing parenthesis with \right to get a pair of extensible parentheses that adjust its height to the expression.

Note also that braces {} and not parentheses () are used in commands to delimits arguments.

Example 7

	LaTeX	Result
Don't write	`(1-(1-x)`	\displaystyle (1-(1-x)
Do write	`(1-(1-x))`	\displaystyle (1-(1-x))
Don't write	`(\dfrac{a}{b}+c)`	\displaystyle (\dfrac{a}{b}+c)
Do write	`\left(\dfrac{a}{b}+c\right)`	\displaystyle \left(\dfrac{a}{b}+c\right)
Don't write	`\frac(1)(2)`	\displaystyle \tfrac(1)(2)
Do write	`\frac{1}{2}`	\displaystyle \tfrac{1}{2}
Don't write	`\sqrt(a+b)`	\displaystyle \sqrt(a+b)
Don't write	`\sqrt{(a+b)}`	\displaystyle \sqrt{(a+b)}
Do write	`\sqrt{a+b}`	\displaystyle \sqrt{a+b}

Fractions

As a rule of thumb you should write fractions where the numerator and denominator consist only of a few digits as a small fraction (i.e. with \frac), while other fractions should be large (i.e. with \dfrac).

If an exponent or index contains a fraction then that fraction should be written in a slashed form (e.g. \displaystyle 5/2 instead of \displaystyle \tfrac{5}{2}) to enhance the legibility.

Example 8

	LaTeX	Result
Don't write	`\dfrac{1}{2}`	\displaystyle \dfrac{1}{2}
Do write	`\frac{1}{2}`	\displaystyle \tfrac{1}{2}
(Exception: If the fraction is next to a large expression you should, however, write the fraction as a large fraction.)
Don't write	`\frac{a}{b}`	\displaystyle \tfrac{a}{b}
Do write	`\dfrac{a}{b}`	\displaystyle \dfrac{a}{b}
Don't write	`\frac{\sqrt{3}}{2}`	\displaystyle \tfrac{\sqrt{3}}{2}
Do write	`\dfrac{\sqrt{3}}{2}`	\displaystyle \dfrac{\sqrt{3}}{2}
Don't write	`a^{\frac{1}{2}}`	\displaystyle a^{\frac{1}{2}}
Do write	`a^{1/2}`	\displaystyle a^{1/2}

Study advice

A tip is to try out your maths formulas in the forum or in the wiki where you work on your individual assignment.

Useful web sites

A more thorough list of LaTeX maths commands can be found on Wikipedias help page

Two more thorough texts om LaTeX maths can be found in a chapter of the book The LaTeX Companion and a text by Herbert Voss.

If you want to know more about LaTeX you can visit these sites: Wikipedia, The not so Short Introduction to LaTeX and LaTeX Wikibook.

The actual implementation of LaTeX math that is used in the wiki is jsMath.

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