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Math Guide
The OpenOffice.org Equation Editor
This PDF is designed to be read onscreen, two pages at atime. If you want to print a copy, your PDF viewer shouldhave an option for printing two pages on one sheet ofpaper, but you may need to start with page 2 to get it toprint facing pages correctly. (Print this cover pageseparately.
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Copyright
This document is !opyright 2""#$2"%" by its contributors as listedin the section titledAuthors. &ou may distribute it and'or modify itunder the terms of either the )* eneral Public +icense, version or
later, or the !reative !ommons -ttribution +icense, version ." orlater. -ll trademars within this guide belong to their legitimateowners.
Authors
Daniel !arrera-gnes /el0uncePeter 1upferIan +aurenson
anet 3. 4wisherean 5ollis 6eber3ichele 7arri
Feedback
Please direct any comments or suggestions about this document to8authors9user:fa;.openoffice.org
Publication date and software version
Published 2< 3arch 2"%". /ased on =pen=ffice.org .2.
You can downloadan editable version of this document from
http://oooauthors.org/english/userguide3/published/
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ntering a for!ula
The e;uation editor uses a marup language to represent formulas. ForeGample, 'betacreates the ree character beta ( . This marup isdesigned to read similar to >nglish whenever possible. For eGample, a
over bproduces a fraction8 ab
.
&ou can enter a formula in three ways8
K 4elect a symbol from the Formula >lements window.
K ?ight:clic on the e;uation editor and select the symbol from theconteGt menu.
K Type marup in the e;uation editor.
The conteGt menu and the Formula >lements window insert the
marup corresponding to a symbol. This provides a convenient way tolearn the ==o 3ath marup.
Note!lic on the document body to eGit the formula editor.
Double:clic on a formula to enter the formula editor again.
"he For!ula le!ents window
The simplest method for entering a formula is the Formula >lements
window, shown in Figure %.
#igure (. )*mbols are divided into categories
Note
In ==o 3ath before L.2.", the Formula >lements window was
called the 4election window.
Entering a formula +
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The Formula >lements window is divided into two main parts.
K The to,shows the symbol categories. !lic on these to changethe list of symbols.
K The ottomshows the symbols available in the current category.
"ip&ou can hide or show the Formula >lements window with-ie) Formula Elements.
Example 1: 54For this eGample we will enter a simple formula8 54 . =n the Formula>lements window (Figure 8
% 4elect the top:left button of the categories (top section.
2 !lic on the multiplication symbol.
#igure 3. )electing the multiplication s*mbol
6hen you select the multiplication symbol on the Formula >lementswindow, two things happen8
K The e;uation editor shows the marup8 times
K The body of the document shows a gray boG lie this8
#igure &. ,esult of selecting the multiplication s*mbol
- OOo3_boo_template
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The MBN symbols shown in Figure
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Markup
&ou can type the marup directly in the e;uation editor. For eGample,you can type 5 times 4to obtain 54 . If you now the marup, thiscan be the fastest way to enter a formula.
"ipThe formula marup resembles the way the formula reads in>nglish.
/elow is a short list of common e;uations and their correspondingmarup.
Display Command Display Command
a=b a O b a s;rt aQ
a2 aR2 a n aSn
fx dx int f(G dG an sum aSn
ab a MO b infinity
ab a times b xy G cdot y
Greek characters
ree characters ( , ,, , etc are common in mathematical
formulas. These characters are not available in the #ormula Elementswindow or the right0clic menu. Fortunately, the marup for reecharacters is simple8 Type a sign followed the name of the character,in >nglish.
K To write a lowercasecharacter, type the name of the character inlowercase.
K To write an uppercasecharacter, type the name of the characterin uppercase.
4ee the table below for some eGamples.
Lowercase Uppercase
%alpha %ALPHA A
%beta %BETA B
%gamma %GAMMA
%psi %PSI
%phi %PHI
%theta %THETA
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Note - complete table of ree characters is provided on page 2A.
-nother way to enter ree characters is by using the 4ymbols catalogwindow. !hoose ools ) Catalog. This window is shown in Figure @.*nder )*mbol set, select reeand double:clic on a ree letter
from the list.
#igure 1. )*mbols catalog 0 used for entering "ree characters
Example 2: 3.14159For this eGample we will suppose that8
K 6e want to enter the above formula (the value of pi rounded to #decimal places.
K 6e now the name of the ree character (pi.
K /ut we do not now the marup associated with the symbol.
3te, 18 Type %followed by the teGt pi. This displays the reecharacter .
3te, 28 =pen the Formula >lements window (-ie ) Formula
Elements.3te, 8 The symbol is a relation, so we clic on the ?elationsbutton. If you hover the mouse over this button you see the tooltip,elations(Figure A.
Figure shows the 4election window after clicing the ?elationsbutton. The symbol we want is circled.
Entering a formula
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#igure 2. Tooltip indicatesthe ,elations button.
#igure . fter selecting ,elations.
3te, 48 !lic on the a b symbol. The e;uation editor now shows themarup %pi simeq .
3te, 58 Delete the MBN teGt and add 3!4!5"at the end of thee;uation. 6e end up with the marup %pi simeq 3!4!5". The resultis shown in Figure %".
#igure $4. #inal result
Custo!i%ations
For!ula editor as a floating window
The formula editor can cover a large part of the 6riter window. To turnthe formula editor into a floating window, do this8
% 5over the mouse over the editor frame, as shown in Figure %%.
2 5old down the !ontroley and double:clic.
$4 OOo3_boo_template
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#igure $$. 5old down the !ontrol e* anddouble0clic on the border of the math editorto turn it into a floating window.
Figure %2shows the result. &ou can doc the floating window again byusing the same steps. 5old down the !ontroley and double:clic the
window frame.
#igure $(. Equation editor as a floating window.
&ow can ' !ake a for!ula bigger?
This is one of the most common ;uestions people as about ==o 3ath.The answer is simple, but not intuitive8
% 4tart the formula editor and choose Format ) Font size.
#igure $3. !hanging the font si6e for a formula.
!ustomi6ations $$
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2 4elect a larger font si0e under7ase si6e(top:most entry, asshown in Figure %.
#igure $&. Edit 7ase si6e 8top9 to mae a formula bigger.The result of this change is illustrated in Figure %
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)uations over !ore than one line
4uppose you want to type an e;uation covering more than one line. For
eGample8 x=3y=1
&our first reaction would be to simply press theEnterey. 5owever, ifyou press theEnterey, though the marup goes to a new line, theresulting e;uation does not. &ou must type the newline commandeGplicitly. This is illustrated in the table below.
Markup Result
' + 3
, + ! x=3y=1
' + 3 -e.li-e
, + ! x=3y=1
&ow do ' add li!its to !y su!*integral?
The sum and int commands can (optionally tae the parametersfromand to. These are used for lower and upper limits respectively. Theseparameters can be used singly or together. +imits for integrals areusually treated as subscripts and superscripts.
Markup Result
s/m 0&$m 1 + ! t$ - a21 k=1
n
ak
i-t 0&$m t$ ' 0t 6t
or
i-t27' 0t 6t
0
x
ft dt or 0
x
f tdt
i-t 0&$m 8e 0 f
s/m t$ i-0i-it, #7)9-*
2n
Note For more details on integrals and sums, see page 22.
#ormula la*out $3
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(rackets with !atrices look ugly+
For bacground, we start with an overview of the matriG command.
Markup Result
mat&i' ) a : b :: ; : 6 * a b
c d
Note?ows are separated by two Us and entries within each row areseparated by one U.
The first problem people have with matrices is that bracets do notscale with the matriG8
Markup Result
mat&i' ) a : b :: ; : 6 * a b
c d
==o 3ath provides scalable bracets. That is, the bracets grow insi0e to match the si0e of their contents. *se the commands left8andright9to mae scalable bracets.
Markup Result
le0t mat&i' ) a : b :: ; : 6 * &ight
a b
c d
"ip *se leftand right;to obtain s;uare bracets.
&ow do ' !ake a derivative?
3aing derivatives essentially comes down to one tric8 Tell OOo it
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Markup Result
)60* $e& )6'* df
dx
)pa&tial 0* $e& )pa&tial ,* f
y
)pa&tial7# 0* $e& )pa&tial t7#* 2 f
t2
&ow do ' align !y e)uations at the e)uals sign?
==o 3ath does not have a command for aligning e;uations on aparticular character, but you can use a matriG to do this, as shown
below.Markup Result
mat&i')
alig-& '(, : )*+)* : alig-l # ::
alig-& ' : )*+)* : alig-l #9,
*
xy = 2x = 2y
The empty braces around O are necessary because O is a binaryoperator and thus needs an eGpression on each side.
&ou can reduce the spacing around O if you change the inter:columnspacing of the matriG8
% 6ith the e;uation editor open, choose Format ) 3,a#ingfromthe menu bar.
#igure $-: !hanging spacing in a matri formula
#ormula la*out $+
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#igure $1. =nserting a cross0reference to an equation number
"ip To insert the e;uation number without parenthesis around it,choose>umberinginstead of,eferenceunder#ormat.
>umbering equations $1
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Math co!!ands $ #eference
,nary * binary operators
Operation Command Display Vsign V% 1
$sign $% 1
V'$ sign V$% 1
$'V sign +1 1
/oolean not neg a a
-ddition V a V b ab
Dot product a cdot b ab
3ultiplication (W a times b ab
3ultiplication (asteris a X b a!b
/oolean Yand a and b a"b
4ubtraction ($ a $ b ab
Division (as a fraction a over b a
b
Division (as an operator a div b a#bDivision (with a slash a ' b a $ b
/oolean Yor a or b a%b
!oncatenation a circ b a &b
$2 OOo3_boo_template
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#elational operators
Operation Command Display
Is e;ual a O b a=b
Is not e;ual a MN b a'2
-pproGimately a approG 2 a(2
Divides a divides b a)b
Does not divide a ndivides b a * b
+ess than a M 2 a+2
reater than a N 2 a,2
4imilar to or e;ual a sime; b ab
Parallel a parallel b a-b=rthogonal to a ortho b a . b
+ess than or e;ual to a leslant b a/b
reater than or e;ual to a geslant b a0b
4imilar to a sim b a1b
!ongruent a e;uiv b a2b
+ess than or e;ual to a MO b ab
reater than or e;ual to a NO b a3b
Proportional a prop b a 4 b
Toward a toward b a b
-rrow left a dlarrow b a 5 b
Double arrow left and right a dlrarrow b a 6 b
-rrow right a drarrow b a 7 b
?ath commands 0 ,eference $
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-et operations
Operation Command Display
Is in a in / a 8B
Is not in a notin / a 9B
=wns - owns b A:b
>mpty set emptyset ;
Intersection - intersection / AB
Zuotient - slash / A $B
-leph aleph ?4ubset - subset / A@B
4ubset or e;ual to - subsete; / AAB
4uperset - supset / ABB
4uperset or e;ual to - supsete; / ACB
)ot subset - nsubset / ADB
)ot subset or e;ual - nsubsete; / AEB
)ot superset - nsupset / AFB
)ot superset or e;ual - nsupsete; / AGB
4et of natural numbers set) H
4et of integers set7 I
4et of rational numbers setZ J
4et of real numbers set? K
4et of compleG numbers set! L
(4 OOo3_boo_template
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Functions
Operation Command Display
>Gponential func eRaQ ea
)atural logarithm ln(a ln a
>Gponential function eGp(a expa
+ogarithm log(a log a
Power aRbQ ab
4ine sin(a sin a
!osine cos(a cosa
Tangent tan(a tan a
!otangent cot(a cot a4;uare root s;rtaQ a
-rcsine arcsin(a arcsin a
-rc cosine arccos(a arccosa
-rctangent arctan(a arctan a
-rc cotangent arccot(a arccot a
nthroot nrootaQbQ ab
5yperbolic sine sinh(a sinh a
5yperbolic cosine cosh(a cosh a
5yperbolic tangent tanh(a tanh a
5yperbolic cotangent coth(a coth a
-bsolute value absaQ )a)
-rc hyperbolic sine arsinh(a arsinh a
-rc hyperbolic cosine arccosh(a arcosh a
-rc hyperbolic tangent arctanh(a artanh a
-rc hyperbolic cotangent arccoth(a arcoth a
Factorial factaQ aM
?ath commands 0 ,eference ($
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.perators
-ll operators can be used with the limit functions (fromJ and toJ.
Operation Command Display
+imit limaQ lim a
4um sumaQ a
Product prodaQ N a
!oproduct coprodaQ O a
*pper and lower boundsshown with integral
int from rS"Q to rStQ a r0
rt
a
Integral intaQ a
Double integral iintaQ Pa
Triple integral iiintaQ Qa
+ower bound shown withsummation symbol
sum fromQb 3
b
!ontour integral lint a Ra
Double curved integral llint a S a
Triple curved integral lllint a Ta*pper bound shown withproduct symbol
prod toQ r N3
r
(( OOo3_boo_template
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Attributes
Operation Command Display
-cute accent acute a Ua
rave accent grave a Va
?everse circumfleG chec a Wa
/reve breve a Xa
!ircle circle a Ya
Lector arrow vec a Za
Tilde tilde a [a
!ircumfleG hat a \a
+ine above bar a ]aDot dot a a
6ide vector arrow widevec abc Zabc
6ide tilde widetilde abc [abc
6ide circumfleG widehat abc \abc
Double dot ddot a _a
+ine over overline abc abc
+ine under underline abc abc
+ine through overstrie abc acb
Triple dot dddot a a
Transparent (useful to get aplaceholder of a given si0e
phantom a
/old font bold a a
Italic font% ital aJ a
?esi0e font si0e %E ;v qv
Following item in sans serif font2 font sans ;v qv
Following item in serif font font serif ;v qv
Following item in fiGed font font fiGed ;v qv
% *n;uoted teGt that is not a command is considered to be a variable. Lariables are, bydefault, italici0ed.
2 There are three custom fonts8 sans serif (without ics, serifs (with ics, and fiGed(non:proportional. To change the actual fonts used for custom fonts and the fontsused for variables (un;uoted teGt, numbers and functions, use Format ) Fonts.
?ath commands 0 ,eference (3
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Operation Command Display
3ae color of following teGt cyan color cyan ;v qv
3ae color of following teGt yellow color yellow;v qv
3ae color of following teGt white color white ;v qv
3ae color of following teGt green color green ;v qv
3ae color of following teGt blue color blue ;v qv
3ae color of following teGt red color red ;v qv
3ae color green returns to defaultcolor blac
color green W ;v Xqv
/race items to change color of morethan one item
color green W ;vQ X qv
For all coloring, the color will apply only to the teGt immediately following thecommand until the neGt space is encountered. In order to have the color apply tomore characters, place the teGt you want in color in curly bracets.
(& OOo3_boo_template
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Miscellaneous
Operation Command Display
Infinity infinity
Partial partial
)abla nabla a
There eGists eGists b
For all forall c
5 bar hbar d
+ambda bar lambdabar e
?eal part re
Imaginary part im f6eierstrass p wp g
+eft arrow leftarrow h
?ight arrow rightarrow
*p arrow uparrow i
Down arrow downarrow j
Dots at bottom dotslow k
Dots at middle dotsaGis l
Dots vertical dotsvert m
Dots diagonal upward dotsup n
Dots diagonal downward dotsdown o
?ath commands 0 ,eference (+
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For!ats
Operation Command Display
+eft superscript a lsupbQ ab
!enter superscript a csupbQ a
b
?ight superscript aRbQ ab
+eft subscript a lsubbQ ab
!enter subscript a csubbQ ab
?ight subscript aSbQ ab
-lign character to left (teGtis aligned center by default
stac 5ello world Ualignl(a Q
"ell! w!rld
a
-lign character to center stac5ello world Ualignc(aQ
"ell! w!rld
a
-lign character to rightstac 5ello world Ualignr(aQ
"ell! w!rld
a
Lertical stac of 2 binomaQbQ a
b
Lertical stac, more than 2 staca U b U 0Qa
b
z
3atriG
matriGa U b UUc U dQ
a b
c d
>;uations aligned at ]O](using ]matriG]
matriGa U ^O^ U alignlbQ UUQ U ^O^ U alignlcV%QQ
a # b
# c
>;uations aligned at ]O](using ]phantom]
stacalignlaQ O b UalignlphantomaQ O cV%QQ
a # b
# c
)ew line asldfHo newline sadfHasldkf$!
sadkf$
4mall gap (grave stuff _stuff st%ff st%ff
+arge gap (tilde stuff`stuff st%ff st%ff
?ath commands 0 ,eference (1
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Characters / Greek
-+P5- A />T- B !5I X D>+T- z >P4I+=) E
>T- " -33- I=T- & 1-PP- ' +-3/D- {
3* ( )* ) =3>- | =3I!?=) * P5I
PI } P4I ?5= + 4I3- ~ T5>T-
*P4I+=) WI 7>T- ,
alpha beta chi delta epsilon
eta gamma iota appa lambda
mu nu omega omicron phi
pi rho sigma tau theta
upsilon varepsilon varphi varpi varrho varsigma vartheta Gi 0eta
Characters / -pecial
and " angle element 8 identical 2
infinite noelement 9 note;ual ' or %
perthousand strictlygreaterthan strictlylessthan tendto
(2 OOo3_boo_template
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'nde0
