Copyright This document is Copyright © 2012–2015 by its contributors as listed below. You may distribute it and/or modify it under the terms of either the GNU General Public License (http://www.gnu.org/licenses/gpl.html), version 3 or later, or the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), version 4.0 or later. All trademarks within this guide belong to their legitimate owners.
Contents Copyright..........................................................................................................................................2 Contributors.................................................................................................................................2 Feedback.................................................................................................................................... 2 Acknowledgments.....................................................
Formula library...............................................................................................................................36 Using Math................................................................................................................................36 Using Writer, Calc, Draw, or Impress....................................................................................... 36 Using your formula library.........................................................................
Set operation commands...............................................................................................................70 Functions....................................................................................................................................... 71 Operators....................................................................................................................................... 73 Attributes......................................................................
| Math Guide Version 4.
Math Guide Preface
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Who is this book for? LibreOffice Math is a formula (equation) editor that is an integral part of LibreOffice. Anyone who wants to learn how to insert formulas and equations using Math will find this guide valuable. If you have never used LibreOffice Math before, or you want an introduction to all of the LibreOffice components, you might like to read the LibreOffice Getting Started Guide first.
Paid support and training Alternatively, you can pay for support services. Service contracts can be purchased from a vendor or consulting firm specializing in LibreOffice. What you see may be different LibreOffice runs on Windows, Linux, and Mac OS X operating systems, each of which has several versions and can be customized by users (fonts, colors, themes, window managers). Illustrations The illustrations in this guide were taken from a variety of computers and operating systems.
NOTE Some Linux operating systems, for example Ubuntu, include LibreOffice as part of the installation and may not include the Galaxy icon set. You should be able to download the Galaxy icon set from the software repository for your Linux operating system.
In most cases, you can interact only with the dialog (not the document itself) as long as the dialog remains open. When you close the dialog after use (usually, clicking OK or another button saves your changes and closes the dialog), then you can again work with your document. Some dialogs can be left open as you work, so you can switch back and forth between the dialog and your document. An example of this type is the Find & Replace dialog.
How can I contribute to LibreOffice? You can help with the development and user support of LibreOffice in many ways, and you do not need to be a programmer. To start, check out this webpage: http://www.documentfoundation.org/contribution/ May I distribute the PDF of this book, or print and sell copies? Yes, as long as you meet the requirements of one of the licenses in the copyright statement at the beginning of this book. You do not have to request special permission.
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Math Guide Chapter 1 Creating & Editing Formulas
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Introduction Math is a formula editor module included with LibreOffice that allows you to create or edit formulas (equations) in a symbolic form, within LibreOffice documents or as stand-alone objects; example formulas are shown below. However, if you want to evaluate numeric values using formulas, then refer to the Calc Guide for more information as Math does not carry out any actual calculation.
• From the Start Center, click Math Formula. • From within LibreOffice Math, use the keyboard shortcut Ctrl+N. As you enter the markup language in the Formula Editor, the formula will appear in the Preview window during and after input of the markup language. The Elements Dock to the left of the Preview window and/or the Elements dialog as a floating dialog may also appear, if these have been selected in View on the main menu bar.
When you have completed entering the markup language for your formula, close the Formula Editor by pressing the Esc key or by clicking an area outside the formula in your document. Double-clicking on the formula object in your document will open the Formula Editor again so that you can edit the formula. Formulas are inserted as OLE objects into documents. You can, as with any OLE object, change how the object is placed within your document.
Tip When using the Elements dialog or the Elements Dock, it is recommended to have Tips selected in the LibreOffice Options. This will help you identify the categories and symbols you want to use in your formula. Go to Tools > Options on the main menu bar, then select LibreOffice > General in the Options dialog and select Tips in the Help section. Elements Dock The Elements Dock has the same categories as the Elements dialog and either can easily be used when entering your formula data.
Figure 6: Context menu in Formula Editor Markup language Markup language is entered directly into the Formula Editor. For example, typing the markup language 5 times 4 into the Formula Editor creates the simple formula 5×4 . If you are experienced in using markup language, it can be the quickest way to enter a formula. Table 2 shows some examples of using markup language to enter commands. For a full list of commands that can be used in the Formula Editor, see Appendix A Commands Reference.
• For an italic Greek character, type a percentage % sign followed by the i character, then the English name of the Greek character in lower or UPPER case. For example, typing %iTHETA creates the italic Greek character Θ. Symbols dialog Greek characters can also be entered into a formula using the Symbols dialog. 1) Make sure your cursor is in the correct position in the Formula Editor.
2) Select the first placeholder > before the word times in the Formula Editor and replace it with the character 5. The formula in your document updates automatically. 3) Select the second placeholder > after the word times in the Formula Editor and replace it with the character 4. The formula in your document updates automatically. Tip To move forward from one placeholder to the next placeholder in a formula, press the F4 key.
3) Select the formula element you want to change use one of the following methods: – Click on the formula element in the preview window positioning the cursor at the beginning of the formula element in the Formula Editor, then select the formula element in the Formula Editor. – Double-click on the formula element in the preview window to select the formula element in the Formula Editor.
Example 3 When braces are used in markup language, they are used to define the layout of the formula and are not displayed or printed. If you want to use braces within your formula, you use the commands lbrace and rbrace within the markup language. x over {–x + 1} gives the result x – x+1 Replace the braces using the commands lbrace and rbrace in the markup language.
For example, the unpaired brackets in the formula [ a; b [ are deliberate, but gives the result ¿ a ;b ¿ . To remove the inverted question marks and create unpaired brackets, backslashes are ¿ added. The formula now becomes \ [ a; b \ [ and the result [ a ; b [ shows unpaired brackets without the inverted question marks. Scalable brackets To create unpaired scalable brackets or braces in a formula, the markup commands left, right, and none are used.
It is not possible in Math to create multiple line formulas when a line ends with an equals sign and you want to continue the calculation on a new line without completing the term on the right side of the equals sign. If you require a multiple line formula to have an equals sign at the end of a line without a term after the equals sign, then use either empty quotes “” or empty braces {} or the space characters grave ` or tilde ˜. By default, the alignment of a multiple line formula is center aligned.
Note To write function names with primes, as is normal in school notation, you must first add the symbols to the catalog. See Chapter 4 Customization for more information. Markup language characters as normal characters Characters that are used as controls in markup language cannot be entered directly as normal characters. These characters are: %, {, }, &, |, _, ^ and ". For example, you cannot write 2% = 0.02 in markup language and expect the same characters to appear in your formula.
Formatting commands are not interpreted within text used in formulas. If you want to use formatting commands within formula text, then you must break up the text using double quotes in the Formula Editor.
Figure 9: Font Sizes dialog Default formula font size To change the default font size used for all formulas in Math or another LibreOffice module: 1) Before inserting any formulas in your document, go to Format > Font size on the main menu bar to open the Font Sizes dialog (Figure 9). 2) Select a different font size using the Base size spinner or type a new font size in the Base Size box. 3) Click Default and confirm your changes to the base size font.
Formula fonts Current formula fonts To change the fonts used for the current formula in Math or another LibreOffice module: 1) Click in the markup language in the Formula Editor. 2) Go to Format > Fonts on the main menu bar to open the Fonts dialog (Figure 10). 3) Select a new font for each the various options from the drop-down lists. 4) If the font you want to use does not appear in the drop-down list, click Modify and select the option from the context menu to open a fonts dialog.
• – Variables – selects the fonts for the variables in your formula. For example, in the formula x=SIN(y), x and y are variables and will reflect the assigned font. – Functions – selects the fonts for names and properties of functions. For example, the functions in the formula x=SIN(y) are =SIN( ). – Numbers – selects the fonts for the numbers in a formula. – Text – defines the fonts for the text in a formula.
Current formula spacing To change the spacing used for the current formula in Math or another LibreOffice module: 1) Click in the markup language in the Formula Editor. 2) Go to Format > Spacing on the main menu bar to open the Spacing dialog (Figure 11). 3) Click Category and select one of the options from the drop-down list. The options in the Spacing dialog change according to the category selected. 4) Enter new values for the spacing category and click OK. 5) Check the result in your formula.
• • • • • • Limits – defines the spacing between the sum symbol and the limit conditions. – Upper limit – determines the spacing between the sum symbol and the upper limit. – Lower limit – determines the spacing between the sum symbol and the lower limit. Brackets – defines the spacing between brackets and the content. – Excess size (left/right) – determines the vertical distance between the upper edge of the contents and the upper end of the brackets.
Note Independent of using formula alignment given below, it is possible to align formulas using the commands alignl, alignc and alignr. These commands also work for text elements. Current formula alignment To change the alignment used for the current formula in Math or another LibreOffice module: 1) Click in the markup language in the Formula Editor. 2) Go to Format > Alignment on the main menu bar to open the Alignment dialog (Figure 12).
To change the color of the whole formula, you have to enclose the whole formula within brackets. For example, entering the markup language color red {ABC 5 times 4} gives the result ABC 5×4 . For information on the colors available in Math, see Appendix A Commands Reference. Background color It is not possible to select a background color for formulas in LibreOffice Math. The background color for a formula is by default the same color as the document or frame that the formula has been inserted into.
7) Select from the drop-down list for File type either ODF Formula (.odf) or MathML 1.01 (.mml) as the file type for your formula. 8) Click Save to save your formula and close the Save As dialog. Using your formula library You cannot insert a formula from your library into a document by dragging and dropping using the mouse, nor by using Insert > File on the main menu bar. You must insert a formula from your library into your document as an OLE object.
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Math Guide Chapter 2 Formulas in Writer
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Introduction When a formula is inserted into a document, LibreOffice Writer inserts the formula into a frame and treats the formula as an OLE object. Double-clicking on an inserted formula will open the Formula Editor in LibreOffice Math allowing you to edit the formula. For more information on creating and editing formulas, please refer to Chapter 1 Creating & Editing Formulas. This chapter explains what options you can change for each individual formula within your Writer document.
Cross referencing 1) Click in your document where you want the cross reference to appear. 2) Go to Insert > Cross-reference on the menu bar to open the Fields dialog (Figure 13). 3) Click on the Cross-references tab, then select Text in the Type section. 4) In the Selection section, select the formula number you want to refer to. 5) In the Insert reference to section, select Reference and click Insert. 6) When you have finished creating cross references, click Close to close the Fields dialog.
3) Alternatively, right-click on the selected formula object and select Object from the context menu, or go to Format > Frame/Object on the main menu bar to open the Object dialog (Figure 14). 4) Make sure the Type page is selected and select a new anchoring position from the Anchor section. 5) Click OK to save your changes and close the Object dialog. Note The anchoring options are not available in the Object dialog when you are making changes to the various options available for frame styles.
Figure 15: Object dialog – Wrap page Text mode In large formulas placed within a line of text, the formula elements can often be higher than the text height. Therefore, to make large formulas easier to read, it is recommended to always insert large formulas into a separate paragraph of their own so that it is separated from text.
Note The size of the frame that a formula is placed in when inserted into a document cannot be changed. The frame size for a formula object depends on the setting of the formula font size, see Chapter 1 Creating & Editing Formulas for more information. Backgrounds 1) In your document, select the formula where you want to change the background. 2) Right-click on the formula and select Object from the context menu, or go to Format > Frame/Object on the main menu bar to open the object dialog.
Borders 1) In your document, select the formula where you want to change the borders. 2) Right-click on the formula and select Object from the context menu, or go to Format > Frame/Object on the main menu bar to open the object dialog. 3) Click on the Borders tab and select the options you want to use for your formula borders (Figure 17). 4) Click OK to save your changes and close the Object dialog.
Math Guide Chapter 3 Formulas in Calc, Draw & Impress
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Introduction In Calc, Draw, and Impress, formulas are inserted as OLE objects without any background (area fill) or borders. See Chapter 1 Creating & Editing Formulas for more information on inserting formulas into a LibreOffice module. Each formula object is inserted into a spreadsheet, drawing, or slide as follows: • In Calc, formulas are inserted into a selected cell in a spreadsheet with no style assigned to the formula object.
can be deselected if you so wish. However, this is not recommended as resizing a formula object using the Position and Size dialog could lead to distortion of a formula making it difficult to read. Formulas in charts A chart in a Calc spreadsheet is itself an OLE object, therefore, you cannot use the Formula Editor to create and insert a formula into a chart. To insert a formula into a chart, create the formula first using the Formula Editor and copy the formula to the clipboard.
Math Guide Chapter 4 Customization
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Introduction This chapter explains how you can customize LibreOffice Math to suit the way you create formulas for use in LibreOffice documents. Also, refer to the Getting Started Guide for information on how to customize LibreOffice. Chemical formulas The primary purpose of Math is to create mathematical formulas, but it can also be used to write chemical formulas. However, in chemical formulas, the chemical symbols are normally written in uppercase using non-italic characters.
Figure 19: Elements Dock dialog To return the Commands dialog and Elements Dock dialog back to their default positions: 1) Position the cursor on the frame of the dialog, NOT the title bar at the top of the of the dialog. 2) Hold down the Ctrl key and double-click. Adding keyboard shortcuts You can add keyboard shortcuts to LibreOffice to make creating documents much easier and to match your workflow.
Figure 20: Customize dialog – Keyboard page Keyboard customize options The options for customizing keyboard shortcuts are as follows: • LibreOffice – displays shortcut keys that are common to all LibreOffice modules. • Math, Writer, Calc, Draw, or Impress – displays the keyboard shortcuts for the open and current LibreOffice module. • Shortcut Keys – lists the shortcut keys and the associated commands.
• Load – replaces the shortcut key configuration with one that was previously saved. • Save – saves the current shortcut key configuration, so that you can load it later. • Reset – resets modified values back to the default values. Catalog customization If you regularly use a symbol that is not available in Math, you can add it to the Symbols dialog (Figure 21) by opening the Edit Symbols dialog (Figure 22).
Note There are numerous free fonts available that contain several symbols if you cannot find a symbol to use in the fonts already installed on your computer. For example, the STIX font was developed specially for writing mathematical and technical texts. Also, the DejaVu and Lucida fonts have a wide range of symbols that you can use. Note When LibreOffice is installed on a computer, only those user-defined symbols that actually occur in the document are stored with it.
Moving symbols You can move a symbol from one symbol set to another as follows: 1) In the Old symbol set: drop-down list, select the symbol set where the symbol you want to move is located. 2) Select the symbol name you want move from the Old symbol: drop-down list. The symbol appears in the left preview pane at the bottom of the Edit Symbols dialog (Figure 22). 3) In the Symbol set: drop-down list, select the symbol set that you want to move the symbol to.
• Modify – click this button to replace the name of the symbol shown in the left preview window (the old name is displayed in the Old symbol list) with the new name you have entered in the Symbol list. • Delete – click this button to remove the symbol shown in the left preview window from the current symbol set. There will be confirmation of deletion. Deleting the last remaining symbol of a symbol set also deletes the symbol set.
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Math Guide Chapter 5 Exporting & Importing
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Math ML format In addition to exporting documents as PDFs, as described in the Getting Started Guide, LibreOffice offers the possibility of exporting formulas in the MathML format. This allows you or another person to insert formulas into documents that were created in other software, for example, Microsoft Office or an internet browser. Note Some internet browsers do not fully support the MathML format and your formula may not display correctly.
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Math Guide Appendix A Commands Reference
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Introduction This appendix lists all the operators and commands that are available for use in the Formula Editor when you are creating your formulas. The more common operators and commands can be entered by clicking on the appropriate icon in the Elements Dock. Where there is no icon displayed in the following tables for the Elements Dock, then you have to enter the operator or command into the Formula Editor using markup language.
Example formula Operation Markup language Division (Wideslash) {>} wideslash {>} Division (Counter Wideslash) > widebslash > Concatenate > circ > A∘B Boolean NOT neg > ¬A Boolean AND > and > or > & > A∧B Boolean OR > or > A∨B Backslash > bslash > A ∖B Slash in circle > odivide > A⊘B Small multiply symbol in circle > odot > A⊙B Subtract symbol in circle > ominus > A⊖B Add symbol in circle > oplus > A⊕B Multiply symbol in circle
Example formula Operation Markup language Is less than or equal to > <= > A≤B Is less than or equal to > leslant > A⩽B Is greater than > > > or > gt > A >B Is greater than or equal to > >= > A≥B Is greater than or equal to > geslant > A⩾B Is much less than > << > or > ll > A ≪B Is much greater than > >> > or > gg > A ≫B Is approximately equal > approx > A≈B Is similar to > sim > A∼B Is similar to or equal > simeq > A≃B Is c
Example formula Operation Markup language Succeeds > succ > A≻B Precedes or equal to > preccurlyeq > A≼B Succeeds or equal to > succcurlyeq > A≽B Precedes or equivalent to > precsim > A≾B Succeeds or equivalent to > succsim > A≿B Not precedes > nprec > A⊀B Not succeeds > nsucc > A⊁B Definition > def > A≝B Corresponding symbol image of > transl > A⊷B Corresponding symbol original of > transr > A⊶B Elements Dock Set operation commands T
Operation Markup language Example formula Quotient set (slash) between characters > slash > A/B Subset > subset > A⊂B Subset or equal to > subseteq > A⊆B Superset > supset > A⊃B Superset or equal to > supseteq > A⊇B Not subset > nsubset > A⊄B Not subset or equal to > nsubseteq > A⊈B Not superset > nsupset > A⊅B Not superset or equal to > nsupseteq > A⊉B Empty set emptyset ∅ Aleph (cardinal numbers) aleph ℵ Natural numbers set setN ℕ
Example formula Operation Markup language Square root sqrt{>} √A Nth root nroot{>}{>} A Power >^{>} A Natural exponential function func e^{>} e Natural logarithm ln(>) ln ( A) Exponential function exp(>) exp( A) Logarithm log(>) log( A) Sine sin(>) sin( A) Cosine cos(>) cos ( A) Tangent tan(>) tan( A) Cotangent cot(>) cot ( A) Hyperbolic sine sinh(>) sinh ( A) Hyperbolic cosine cosh(>) cosh ( A) Hyperbolic tangent tanh(>) tanh( A )
Example formula Operation Markup language Inverse or area hyperbolic cosine arcosh(>) arcosh ( A) Inverse or area hyperbolic tangent artanh(>) artanh ( A) Inverse or area hyperbolic cotangent arcoth(>) arcoth ( A) Back epsilon backepsilon ∍ Subscript > sub > AB Elements Dock Operators To access the icons used for entering markup language for operator commands into the Formula Editor, select Operators from the drop-down list at the top of the Elements Dock.
Example formula Operation Markup language Sum superscript top sum to{>} > ∑B Sum sup/sub script sum from{>} to{>} > ∑C A B A Product prod > ∏A Product subscript bottom prod from{>} > ∏B Product superscript top prod to{>} > A A ∏B B Product sup/sub script prod from{>} to{>} > ∏C A Coproduct coprod > ∐A Coproduct subscript bottom coprod from{>} > ∐B Coproduct superscript top coprod to{>} > Coproduct sup/sub script coprod from{>} to{>} <
Operation Markup language Integral subscript bottom int from{>} > Integral superscript top int to{>} > Example formula Elements Dock ∫B A A ∫B B Integral sup/sub script int from{>} to{>} > ∫C A Double integral iint > ∬A Double integral subscript bottom iint from{>} > ∬B Double integral superscript top iint to{>} > Double integral sup/sub script iint from{>} to{>} > A A ∬B B ∬C A Triple integral iiint > ∭A Triple integral subscript bottom iiint
Example formula Operation Markup language Triple integral sup/sub script iiint from{>} to{>} > ∭C Curve integral lint > ∮A Curve integral subscript bottom lint from{>} > ∮B Curve integral superscript top lint to{>} > B A A A ∮B B Curve integral sup/sub script lint from{>} to{>} > ∮C A Double curve integral llint > ∯A Double curve integral subscript bottom llint from{>} > ∯B Double curve integral superscript top llint to{>} > Double curve integral
Example formula Operation Markup language Triple curve integral superscript top lllint to{>} > Triple curve integral sup/sub script lllint from{>} to{>} > Elements Dock A ∰B B ∰C A Note For customized operators, use the command oper followed by your custom operator. 1 For example, entering oper OP from 0 to 1 A will give the formula A OP 0 .
Example formula Operation Markup language Tilde tilde > ~ A Circumflex hat > A^ Reverse circumflex check > Ǎ Large vector arrow widevec {>} ⃗ AB Large tilde widetilde {>} ~ AB Large circumflex widehat {>} ^ AB Line over overline {>} AB Line below underline {>} AB Line through overstrike {>} AB Transparent (blank placeholder to create space) phantom {>} Bold font bold > AB Not bold font nbold > AB Italic font ital > or italic > AB Not ital
Example formula Operation Markup language Color cyan color cyan {>} AB Color magenta color magenta {>} AB Color yellow color yellow {>} AB Color gray color gray {>} AB Color lime color lime {>} AB Color maroon color maroon {>} AB Color navy color navy {>} AB Color olive color olive {>} AB Color purple color purple {>} AB Color silver color silver {>} AB Color teal color teal {>} AB Elements Dock Note The font command changes the font type The first
Example formula Operation Markup language Right round bracket only >\) A) Square brackets [>] [ AB] Left square bracket only \[> [A Right square bracket only >\] A] Double square brackets ldbracket > rdbracket ⟦ AB⟧ Left double square bracket only \ldbracket > ⟦A Right double square bracket only > \rdbracket A⟧ Braces lbrace > rbrace {AB} Left brace only \lbrace > {A Right brace only > \rbrace A} Angle brackets langle > rangle ⟨ AB ⟩ Left angle brack
Example formula Operation Markup language Single lines lline > rline |AB| Left single line only \lline > |A Right single line only > \rline A| Double lines ldline > rdline ‖AB‖ Left double line only \ldline > ‖A Right double line only > \rdline A‖ Scalable round brackets left ( > right ) ( BA ) Scalable left round bracket only left ( > right none ( BA Scalable right round bracket only left none > right ) A B Scalable square brackets left [ > right ] [ ] S
Example formula Operation Markup language Scalable left brace only left lbrace {>} right none { AB Scalable right brace only left none {>} right rbrace A B Scalable angle brackets left langle > right rangle ⟨ ⟩ Scalable left angle bracket only left langle {>} right none ⟨ Scalable right angle bracket only left none {>} right rangle A B Scalable operator brackets left langle > mline > right none ⟨| ⟩ Scalable left operator bracket left langle > mline > right none Scal
Example formula Operation Markup language Scalable single lines left lline > right rline Scalable left single line left lline > right none Scalable right single line left none > right rline Scalable double lines left ldline > right rdline Scalable left double line left ldline > right none Scalable right double line left none > right rdline Scalable top brace {>} overbrace {>} ⏞ ABC Scalable bottom brace {>} underbrace {>} ABC ⏟ Elements Dock | AB | | AB A B| ‖ BA ‖
Example formula Operation Markup language Superscript center >csup{>} 20 Subscript center >csub{>} 20 New line newline 123 CD Small gap ` 123 456 Blank or large gap ~ 123 456 No space (suppresses space between elements) nospace {>} 12+4+5 Align left alignl > ABC D Align center alignc > ABC D Align right alignr > ABC D Vertical stack (2 elements) binom{>}{>} AB 12 Vertical stack (more than 2 elements) stack{> # > # >} AB 12 CD Matrix stack matrix
Others To access the icons used for entering markup language for other commands into the Formula Editor, select Others from the drop-down list at the top of the Elements Dock, or click the Others icon in the Elements dialog.
Example formula Operation Markup language Math axis ellipsis dotsaxis ⋯ Vertical ellipsis dotsvert ⋮ Upward diagonal ellipsis dotsup or dotsdiag ⋰ Downward diagonal ellipsis dotsdown ⋱ Back epsilon backepsilon ∍ Elements Dock Greek characters Greek characters are normally entered into a formula using the Symbols dialog (see Chapter 1 Creating & Editing Formulas for more information).
Table 4: Lowercase Greek characters %alpha α %beta β %gamma γ %delta δ %varepsilon ε %zeta %eta η %theta %iota ι %kappa ζ κ %lambda %mu %nu ν %xi %omicron %pi π %rho ρ %varsigma ξ ς λ ο θ μ %sigma σ %tau τ %upsilon υ %varphi φ %chi χ %psi ψ %omega ω %vartheta %phi ϕ %varpi ϖ %varrho ϱ %epsilon ϑ ϵ Δ Table 5: Uppercase italic Greek characters %iALPHA Α %iBETA Β %iGAMMA Γ %iDELTA %iEPSILON Ε %iZETA Ζ %iETA Η %iTHETA %iKAPPA Κ %iLAMBDA Λ
Note In localized versions of LibreOffice, the names of special characters are also localized. If a document is not localized to the same language, then the names of special characters in the following table may not work correctly. If this happens, you can use the Symbols dialog to select the required special character. When selected in the Symbols dialog, the name of the special character is displayed at the bottom of the Symbols dialog in the correct language.
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