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Math Objects:The Equation EditorTitle:Math Objects: The Equation EditorVersion:1.0 First edition: November 2004First Englishedition:November 2004

ContentsOverview..........................................................................................................................................iiCopyright and trademark information.........................................................................................iiFeedback.....................................................................................................................................iiAcknowledgments.......................................................................................................................iiModifications and updates..........................................................................................................iiIntroduction......................................................................................................................................1

Getting started.............................................................................................................................1

Entering a Formula......................................................................................................................2

Complex Formulas...........................................................................................................................3

Brackets are your friends.............................................................................................................3

Sums and integration...................................................................................................................3

Complex layout................................................................................................................................5

Tips and tricks..................................................................................................................................6

Customizing the interface............................................................................................................6

Numbering equations..................................................................................................................6

Math commands - Reference...........................................................................................................8

Unary / binary operators..............................................................................................................8

Relational operators.....................................................................................................................9

Set operations ...........................................................................................................................10

Math Objectsi

OverviewOverviewOpenOffice.org has a component (OOo Math) for mathematical equations. OOo Mathprovides mathematical objects which can be embedded in other OOo documents, or saved ontheir own.Copyright and trademark informationThe contents of this Documentation are subject to the Public Documentation License,Version 1.0 (the "License"); you may only use this Documentation if you comply with theterms of this License. A copy of the License is available at:http://www.openoffice.org/licenses/PDL.rtfThe Original Documentation is Math Objects: The Equation Editor. The Initial Writer(s) ofthe Original Documentation is/are Ian Laurenson © 2004. All Rights Reserved. (Initial Writercontact(s): hillview@paradise.net.nz. The Initial Writer contact(s) is to report errors in thedocumentation. For questions regarding how to use the software, subscribe to the Users MailList and post your question there: http://support.openoffice.org/index.html.)Contributor(s): Daniel Carrera rewrote the explanatory section of the document.Portions created by Daniel Carrera are Copyright © 2004. All Rights Reserved. (Contributorcontact(s): dcarrera@openoffice.org.)All trademarks within this guide belong to legitimate owners.FeedbackPlease direct any comments or suggestions about this document to:authors@user-faq.openoffice.orgAcknowledgmentsThis chapter is based on two documents written by Fred Saalbach. Modifications and updatesVersionDateDescription of Change1.021 November 2004First published editionMath Objectsii

IntroductionIntroductionOpenOffice.org (OOo) has a component for mathematical equations. It is most commonlyused as an equation editor for text documents, but it can also be used with other types ofdocuments or stand-alone. When used inside Writer, the equation is treated as an objectinside the text document.Important note: The equation editor is for writing equations in symbolic form (as in equation 1).If you want to evaluate a numeric value, this is not the chapter you want. See the Calc guide.dfx

dx=lnxtan-1x2 (1) Getting startedTo insert an equation, go to Insert > Object > Formula. The equation editor opens at the bottom of the screen, and the floating Selection toolbox

appears. You will also see a small box (with a gray border) in your document, where theformula will be displayed.Figure 1. Writer document showing Equation Editor , Selection toolbar, and location of resulting equation.Math Objects1

IntroductionThe equation editor uses a markup language to represent formulas. For example, "%beta"creates the Greek character beta (). This markup is designed to read similar to Englishwhenever possible. For example, "a over b" produces a fraction:

a

bEntering a FormulaThere are three main ways of entering a formula:•Type markup in the equation editor.•Right-click on the equation editor and select the symbol from the context menu.•Select a symbol from the Selection toolbox.

The context menu and the Selection toolbox insert the markup corresponding to a symbol.Incidentally, this provides a convenient way to learn the OOoMath markup. When you selecta symbol from the Selection toolbox, it will show up like this in this equation editor:

times And it will display on screen in Writer like this:

×When you are editing in the equation editor, you need to remove the and replace it withthe terms of the equation. For example, "5 times 4" produces

5×4. Below is a short list ofcommon equations and their corresponding markup.DisplayCommandDisplayCommand

a=ba = b%gamma %GAMMA a2a^2ana_n ∫fxdxint f(x) dx∑ansum a_n a ba over b a bstack { a # b } asqrt {a}uvec u x×yx times yx⋅yx cdot yMath Objects2

Complex FormulasComplex FormulasOf course, most people can figure out how to do something simple like a. The problemsappear when you try to write more complex equations. This section explores some generalsituations and suggests solutions.Brackets are your friendsYou may have heard your professor say this. It is true for science, and it is true for OOo.The equation editor knows nothing of order of operation. To make moderately complexformulas, you must use brackets. For example:DisplayCommandx=-b±

b2-4ac

2ax = { -b +- sqrt { b^2 - 4ac } } over { 2a }Tip: Squiggly brackets can be used to collect terms without the bracket appearing in theequation.Sums and integrationThe "sum" and "int" commands can optionally take in "from" and "to" parameters. Theseare used in a way that is meant to resemble how the equation is read in English. Theseparameters can be used singly or together. For example:DisplayCommand

∑n=1 an1 n2sum from { n = 1 } to infinity { a_n + 1 over n^2} ∑a∈A a3sum from { i in A } { a^3 } ∫a b x21 xdxint from a to b { x^2 + 1 over x dx }

reidint from %alpha { r(%theta)e^{i%theta} d %theta }Tip: Though they look the same, the "sum" command is more flexible than "%SIGMA".Tip: Use "infinity" to produce the

∞ symbol.Math Objects3

Complex FormulasMatricesMatrices are done through the matrix command. The basic syntax is:DisplayCommandab

cdmatrix { a # b ## c # d }A single "#" symbol is used to separate entries within a given row. Two "#" symbols areused to separate different rows.One of the first problems people have with matrices is working with brackets. Regularbrackets have a fixed size, which doesn't fit well with matrices (see the table below).OOoMath provides "scalable brackets". These brackets adjust in size ("scale") to fit the sizeof their contents. To obtain scalable brackets, use the left( and right) commands.DisplayCommandType

detab cddet ( matrix { a # b ## c # d } )normaldet ab

cddet left( matrix { a # b ## c # d } right)scalableTip: Use left[ and right] to obtain square brackets.DerivativesTo write a derivative, or a partial derivative, use the "over" command. That is, treat it as if itwere a fraction. For higher-order derivatives, use the ^ symbol, like an exponent.DisplayCommand

dft dt=∂f ∂x dx dt∂f ∂y dy

dt{df(t)} over {dt} = {partial f} over {partial x} {dx } over {dt} + {partial f} over {partial y} {dy } over {dt}Math Objects4

Complex layoutComplex layoutOften, the problem is not in writing the equation as such, but obtaining the desired layout.There are some features that can help:•Adjust alignment with "alignl" (left alignment), "alignr" (right alignment) and"alignc" (centered).•Use matrices for columned layout.•Use white space and several lines to make your equation understandable.•Use ~ or ' to produce white space on the equation.Tip: You can insert white space and additional lines in the markup without affecting the outputof the equation.The following example illustrates most of the above.DisplayCommandSn=1rr2⋯rn

rSn=r⋯rnrn1 1-rSn=1-rn1

Sn=1-rn1

1-rmatrix { S_n #{}={}# alignl 1 + r + r^2 + dotsaxis + r^n ## rS_n #{}={}# alignl r + dotsaxis + r^n + r^{n+1} ##(1-r)S_n #{}={}# alignl 1 - r^{n+1} ## S_n #{}={}# alignl {1 - r^{n+1} } over {1-r}}

In addition to matrices, you can also used the newline command to move to a new line.Notice (below) that the newline command does not have to be on a line of its own.DisplayCommandxy=3

x-y=1x + y = 3 newline x - y = 1Math Objects5

Tips and tricksTips and tricksCustomizing the interfaceThere are a few ways to customize the equation editor's interface to make you moreproductive. Here are some suggestions:•Show/hide the Selection toolbox with View > Selection.

•Turn off AutoUpdate with View >AutoUpdate display to improve speed. You canstill update the formula manually by pressing F9 or through View > Update.

•Turn the editor into a floating window:1)Hover the mouse above the border of the equation editor.2)Hold down the Control key.3)Drag the editor away from the main window.Numbering equationsEquation numbering is possible and simple. Sadly, this feature is deeply hidden. To insert aformula with a number, follow these steps:1)Start a new line.2)Type fn and then press F3.

You will see a numbered formula appear:E=mc2 (2)

Then double-click on the formula to edit it. For example, here is the Riemann Zeta function: z=∑n=1 ∞1 nz (3)

The number in the equation is stored in the form of a field. To refer to an equation by itsnumber (for example, "as shown in Equation (2)"):1)Insert > Cross-reference..

2)Click on the References tab. (See Figure 2.)3)Under Type, select Text.

4)Under Selection, pick the equation number.5)Under Format, choose Reference.

6)Click Insert.

Math Objects6

Tips and tricksDone! If you later add more equations to the paper before the referenced equation, all theequations will automatically renumber and the cross-references will update.Figure 2. Inserting a cross-reference to an equation number.Math Objects7

Math commands - ReferenceMath commands - ReferenceUnary / binary operatorsTable 1. Commands, unary & binaryOperationCommandDisplay+sign+11-sign-1

-1+/- sign+-1

±1-/+ signneg 1

∓1Boolean notneg a

¬aAddition +a + b

abMultiplication dot a cdot b a⋅bMultiplication (X)a times b a×bMultiplication (*)a * b a∗bBoolean anda and b a∧bSubtraction (-)a - b a-bDivision (fraction)a over ba b

Division (operand)a div b

a÷bDivision (slash)a / b a/bBoolean ora or b a∨bConcatenatea circ b a°bMath Objects8

Math commands - ReferenceRelational operatorsTable 2. Commands, relationsOperationCommandDisplayIs equala = ba=bIs not equala <> b

a≠2Approximatelya approx 2 a≈2Dividesa divides b a∣bDoes not dividea ndivides b a2Greater than a > 2 a2Similar to or equala simeq b a≃bParallela parallel b a∥bOrthogonal toa ortho b a⊥bLess than or equal toa leslant b abGreater than or equal to a geslant b abSimilar toa sim b a~bCongruenta equiv b a≡bLess than or equal toa <= b a≥bProportionala prop b a∝bTowarda toward b abArrow left a dlarrow b a⇐bDouble arrow left and righta dlrarrow b a⇔bArrow righta drarrow b a⇒bMath Objects9

Math commands - ReferenceSet operations Table 3. Commands, set operatorsOperationCommandDisplayIs ina in Ba∈BIs not ina notin B

a∉BOwensA owns b

A∋bEmpty set emptyset

∅IntersectionA intersection B

A∩BUnionA union B

A∪BDifference A setminus B

A∖BQuotientA slash B

A/BAlephaleph

ℵSubsetA subset B

A⊂BSubset or equal toA subseteq B

A⊆BSuperset A supset B

A⊃BSuperset or equal toA supseteq B

A⊇BNot subset A nsubset B

A⊄BNot subset or equalA nsubseteq B

A⊈BNot supersetA nsupset B

A⊅BNot Superset or equalA nsupseteq B

A⊉BNatural Numbers Set setN

ℕSet of Integers setZ

Set of complex numberssetC

ℂMath Objects10

Math commands - ReferenceFunctionsTable 4. Commands, functionOperationCommandDisplayExponentialfunc e^{a}eaNatural logarithmln(a)lna

Exponential functionexp(a)

expaLogarithmlog(a) logaPowera^{b}ab

Sinesin(a)

sinaCosinecos(a) cosaTangenttan(a) tanaCotangentcot(a) cotaSquare rootsqrt{a} aArcsinearcsin(a) arcsinaArc cosinearccos(a) arccosaArctangentarctan(a) arctanaArc cotangentarccot(a) arccotanth rootnroot{a}{b} a bHyperbolic sinesinh(a) sinhaHyperbolic cosinecosh(a) coshaHyperbolic tangenttanh(a) tanhaHyperbolic cotangentcoth(a) cothaAbsolute valueabs{a} ∣a∣Arc hyperbolic sinearsinh(a) arsinhaArc hyperbolic cosinearccosh(a) arcoshaArc hyperbolic tangentarctanh(a) artanhaArc hyperbolic cotangentarccoth(a) arcothafactorialfact(a) a!Math Objects11

Math commands - ReferenceOperatorsAll operators can be used with the limit functions ("from" and "to")Table 5. Commands, operatorsOperationCommandDisplayLimitlim(a)limaSumsum(a)

∑aProductprod(a) ∐aLimits from and to (shownwith intigral)int from {r_0} to {r_t} a ∫r0 rt aIntigralint{a} ∫aDouble intigraliint{a} ∬aTripple Intigraliiint{a} ∭aLower limit shown withsummation symbol sum from{3}b ∑3 bCurved intigerallint a ∮aDouble curved intigeralllint a ∯aTripple curved intigerallllint a ∰aUpper limit shown withproduct symbolprod to{3} r rMath Objects12

Math commands - ReferenceAttributesTable 6. AttributesOperationCommandDisplayAcute accent acute aaGrave accentgrave a

aReverse circumflexcheck a aBrevebreve a aCircle circle a aTildetilde a aCircumflex hat a aLine abovebar a aDot dot a

˙aWide vector arrowwidevec abc

abc

Wide tildewidetilde abc

abcWide circumflexwidehat abc abcDouble dot ddot

¨aLine over overline abc

abcLine under underline abc abcLine throughoverstrike acb acbRipple dot dddot a aTransparent (useful to get aplaceholder of a given size)phantom aBold fontbold a aItalic font1ital a aResize fontsize 16 qv qvFollowing item in sans seriffont2font sans qv qvFollowing item in serif fontfont serif qv qvFollowing item in fixed fontfont fixed qv

qv1Unquoted text that isn't a command is considered to be a variable. Variables are, by default, italicized.2There are three custom fonts: sans serif (without kicks), serifs (with kicks), and fixed (non proportional). Tochange the actual fonts used for custom fonts and the fonts used for variables (unquoted text), numbers andfunctions, use: Format > Fonts.

Math Objects13

Math commands - ReferenceOperationCommandDisplayMake color of following textcyancolor cyan qvqvMake color of following textyellowcolor yellow qv

qvMake color of following textgreencolor white qv qvMake color of following textwhitecolor green qv qvMake color of following textbluecolor blue qv qvMake color of following textredcolor red qv qvMake color green returns todefault color blackcolor green X qvXqv Brace items to change colorof more than one itemcolor green {X qv}Xqv

Math Objects14

Math commands - ReferenceOthersTable 7. Commands, othersOperationCommandDisplayInfinity infinity∞Partial partial

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