G%Instructions $Quick Instructions нвџџџџџџџШШџџџџџџџџџџџџџџ $Quick InstructionsLUsing Calculon to do a quick plot of a Tsingle function in 2 or more dimensions is*very easy: JT1. Select Work Page (Work tab at the top).aD2. Select and clear the Temporary ": Worksheet with this icon:‚<3. Enter equation editing mode* with this icon: ЃP4. Tap on the worksheet to start the new( equation.  ЦR5. Edit the equation using the pickbox or)B the keyboard and PDA buttons.! ъT6. Select the View Page to see the plotted* function.  VThe most likely cause of dissatisfaction at+Vthis point is that the range of values over+Twhich the function has been plotted is not*\ideal, in which case edit their limits or step.Rsize in the Value Table. The Value Table )Tis available both on the View Page and the*Work Page.  oXTip: If you regularly use Calculon for quick Hplots then disable "Auto-Open First $HWorksheet" and "Load All Packages At$VStartup". Calculon will start up faster and  Pyou will be automatically placed in the (Ptemporary worksheet in equation editing ( mode.ЎenewЎ…eqnoff Program Overviewт'џџџџџџџШШџџџџџџџџџџџџџџ OverviewXCalculon is based around four "pages" which  $Ncan be switched between by means of the'<tabs at the top of the screen.E(Work Page (Work Tab) \This displays and edits the current worksheet..BWorksheets are the means by which!Lequations, text notes and drawings are&Lentered into Calculon. Worksheets are  Rcompletely freeform, equations and other )>content can be placed anywhere.Ј (View Page (View Tab) TThe equations on the current worksheet are*Nprocessed by Calculon to produce one or  Tmore plots in 2, 3 or more dimensions. The*Jplot is viewed on the View Page. The %^calculation is not initiated until the View tab/^is selected. In many cases the calculation will/Pbe instant, but for more complex plots a(\progress bar will indicate the remaining time..XIf the calculations are taking too long they,"can be cancelled.<,Options Page (Ops Tab) LOn this page the colours used for the &Rcurrent plot can be changed. In addition )Lsome general program-wide options can &Xbe set. Both functions are discussed in more,"detail elsewhere. ,Library Page (Lib Tab) TWorksheets in Calculon are arranged into a H"Library" of packages. Each package $Vcorresponds to a file, and can contain many+Vworksheets arranged in heirachical folders.+^In addition there is a special worksheet called/Lthe "Temporary Worksheet" it does not &Vbelong to a package and is never saved (it +Zcan be copied into a package). On the Library-Tpage you can load and unload packages, and*Ncopy and paste worksheets between them.'Worksheets $Editing WorksheetsсqџџџџџџџШШџџџџџџџџџџџџџџ $Editing WorksheetsLThere are four editing modes used when&Xediting worksheets in Calculon. The current  ^editing mode is determined by selecting on of /"these four icons:SV(Note: if this worksheet is "locked" these +Picons will not be visible at the moment)($tText Editing JFor inputting and editing text notes.%$“Draw Mode HFor drawing "scribble"-like sketches$on worksheets.$О*Equation Editing ModeFFor entering and editing equations.#$оMove Mode FFor moving equations and text notes#Faround on the worksheet. Items can #Lalso put cut, copied and pasted, both &<within and between worksheets.&XDepending on which editing mode is selected,,Tvarious other icons will appear across the*Pbottom of the program. Each editing mode(Ris described in detail over the next four)worksheets.  сmoveoff vtextoff Пeqnoff ”drawoff&Editing > Text Mode сщџџџџџџџШШџџџџџџџџџџџџџџ "Text Editing Mode VIn text editing mode you can add text notes+Xto your worksheets (all of these instruction,Rpages are just standard worksheets making)Theavy use of text notes). In text editing *Hmode several formatting icons become$Zavailable, which are specific to text notes. -\You should find that editing text in Calculon % Vis a very similar experience to using other+Xsoftware. Text can be edited, selected, cut,,Rpasted and formatted in the standard way.)&ЇBold<Formats selected text as bold.&Ш Italic@Formats selected text as italic. &щFont Size FClicking on the up and down arrows #Jchanges the font size. Four sizes are%available: >Large Standard Small Very Small  '7Underline 2Underlines selected text. 'XCut&Cuts selected text.'y Paste6Pastes previously cut text.žVNote: there is no "copy" icon. To copy text+Vuse cut and then paste immediately. The cut+\text will be put back where it was, but a copy.Hremains on the pasteboard and can be$"pasted elsewhere.ztextoff Љboldoff8 underoffYcutЩital ы textsize3zpaste&Editing > Draw Modeо№џџџџџџџШШџџџџџџџџџџџџџџ Draw Mode VIn draw mode you can add this kind of thing+&to your worksheets:‹RThere is only one additional option under)draw mode. Џ EraseNEnable this to erase parts of drawings.'PdrawoffБ eraseoff‰PNG  IHDRо№рЃMІIDATxœэнЛrтH@Qfk?Э?йС|˜ƒ 6 жЫ‚! qн:'r`Uмъn=љѕљчѓ=НњРїЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(iЮёўіўъ0>iЕЃ4Wъ>~миš1u;JsяoяП?^§)F№їЋ?Р8ŽƒЅ.з2дЈy{’}j4ЧэыrECЅy{ јїЗїщ›2‰?УPiў­sa Іц‚зšЧЄfdЇ/œ’И!ѓILѓш8|>ЭeˆЗ_ў5Ио.XИѓ ›цaV3ўљЋK ЎызчŸЯW†EюЎ Ї,—/.-OW7ТЈy:ЅЮˆc•ХтТ.—~ќЈyцtйwšЫЕhVЩ№Й–бвєГkщтЪј6iЎ`Ы,Ўннёш0{BћMsн9}тvŽa-Iљі]Ž ?7г§Іљ*ДryЦ›ї]—4їуŠќВыCюЗЏДXхЁsЇ†Yncзi&дyw ƒoњйіžцбнБs•w1d>ФZѓ{ЕЗoыбж–vєєŽЛnїwЙЋ;НWЋЬЄљŸлюњњŸЏПЇ/1u9ƒ §мЗDќъuFdКœGšп˜1e_2^.d§–уjГЯ.ъr Ѓц}ЇWNюїsO жHѓ/?х*Єљ0хmУZ“(i%ЭЉ<Щhcв$JšDэk§кŒ<}Ї{љ˜hќ4ЇќАеФ—ОБ…яŸцсцcZкˆkлЖ4xšЗOПъЗV™b№4з§ЩT?пЛЅ=юЁ/ kѕ;-љжрЃц“мНˆхі8jЎeдч`EИ7ˆ(Ѓ&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&Qв$JšDI“(i%MЂЄI”4‰’&QџџхpПДpIENDЎB`‚.Editing > Equation ModeоаџџџџџџџШШџџџџџШџџџџШШџџ *Equation Editing ModeDCreating and editing equations on "Lworksheets is possible under equation &Vediting mode. To create an equation, select+Pthis mode (using the icon as above) and (6then tap on the worksheet. BDue to the nature of mathematical!Zexpressions, basic editing operations are not-Xalways as simple as they are when applied to,Rtext. A simple "backspace" operation will)Vby necessity behave differently than simply+Nremoving the item behind the caret when'Vapplied in the context of some mathematical+symbols. њF1. To be easy and intuative to use.#  N2. That the edited expression should be'X syntactically "mathematically correct" ,F throughout the editing process.# 9L3. That delete or backspace should not&P remove more than one element at once(N (when there is no selected region).'bTIn general, equation editing works in much*Rthe same way as text editing. There is a )J"caret" which can be moved backwards %Tand forwards. New elements can be inserted*Zat the caret via the "pickbox" or the keypad.-TAlso, parts of equations can be selected, *.cut, copied and pasted.ЁVEquaton editing is probably the single most+Zchallenging aspect in the design of Calculon.$ TUser feedback is essential, and welcomed. *fPThere are a few exceptions however, for (Rexample currently commas can be placed in)Lsyntactically incorrect locations (and&Fsubsequently an error is produced).#ТNThe additional function icons available'Vunder equation editing mode are as follows:+!хCopyJCopies selected region of equation to%pasteboard. !CutFCuts selected region of equation to#pasteboard.  F Paste>Pastes previously cut or copied6equation elements at caret.v GlobalJMake selected variables global or not%8global. See the Help PackageFworksheet on the Global value space#*for more information. Н&Visual Options MenuFOn this menu various visual options#Lrelating to equations in the worksheet&@can be turned on or off. See the Dworksheet titled "Worksheet Visual"4Options" for more details.з\Essentially, equation editing in Calculon has ! Zbeen carefully designed under three criteria:-PIn particular, inserting an element when(Vthere is already a selected region behaves +Vdifferently depending on what is inserted. +PSome types will encompass the selection (T(parenthesis, roots, etc.) whereas others *\will replace it (algebraic values, constants)..Žeqnoff Gpastecut чcopy П viewmenuxglobal&Editing > Move Mode рNџџџџџџџШШџџџџџџџџџџџџџџ Move Mode  JIn move mode text notes and equations%Jcan be moved around on the worksheet.%FItems can be cut, copied and pasted#Rbetween worksheets. In addition there are)Tcouple of options which affect the overall*Nsize of worksheets, and the value space'Jmenu is enabled under move mode (this%Rmenu is used for moving equations between)V"valuespaces" - see elsewhere for details).+WCopyLMakes a copy of the selected item. The&>copy appears immediately on theNworksheet underneath the selected item.'›4Selecting and Moving ItemsTIn move mode tapping on an item selects it*Z(the item will have a dotted line around it).-ZWhen an item is selected, dragging the stylus-Pon it will move it around. Alternatively(Pselected items can be moved by using the((PDA's arrow buttons.ў0Selecting Multiple ItemsRMultiple items can be selected by keeping)Fthe Space button pressed down while#Ttapping on items (on the Sharp Zaurus this*Pis the button in the centre of the arrow(button pad). ”CutPCuts the selected item and puts into the(pasteboard. У PasteJPastes a previously cut item into the%Dworksheet. To make the pasted item"Jappear in a particular place tap the %Nworksheet in that place and then paste.'DOtherwise, the pasted item will be"Rplaced in the centre of the current view.)' Value Space MenuFThis is described on the worksheet #8titled "Using Value Spaces".UTrim WorksheetLThis option tidies up the worksheet by&Jtrimming excess space from the edges.%‡,Add Extra Space At TopLThis icon adds some extra space at the&*top of the worksheet.З2Add Extra Space At BottomPThis icon is available all the time (not(Jjust in move mode) it adds some extra%Jspace at the bottom of the worksheet.%їPTip: When using the PDA arrow buttons to(Lmove items, pressing space (the centre&Rbutton on a Sharp Zaurus) toggles between)Na big jump (5 pixels) and a small jump 'V(1 pixel). This way items can be positioned+8very precisely, if required.Qmoveoff[copy•cutХpaste*vsmenuИ extradown‰extraupXtrim(Exporting WorksheetsпzџџџџџџџШШџџџџџџџџџџџџџџ  (Exporting WorksheetsLOn the Work Page, the export icon (as &Rabove) opens the export window. From this)Nwindow complete worksheets or selected 'Xparts of worksheets can be exported to file.,UTThere are several export formats currently*available: t1) ImageLThe worksheet can be converted into an&Vimage. In this case it will appear exactly +Pas it does in the program, including any(sketches. Л2) Markup LLaTeX and XML are supported. With XML,&Fequations can be included as either#LPresentation MathML or Content MathML.&XSketches are not included in markup exports.,VIn all cases, if there is nothing currently+Rselected on the worksheet then all of the)Vworksheet content is exported. If there are+Xitems selected (i.e. in move mode, appearing,Xwith dotted lines around them) then only the,Tselected items are included in the export.*WHThe export window provides a preview$Lwhich indicates what will be exported.&export0Worksheet Visual Options н-џџџџџџџШШџџџџџџџџџџџџџџ 0Worksheet Visual OptionsHThis worksheet describes the options$Lavailable on the menu under this icon:&UBNote: this menu is only available!> under equation editing mode:їStructure z RIn general, each option toggles on or off)Ta visulisation option for equations on the*Ncurrent worksheet. These options appear'Ras coloured higlights or additions to the)Fequations in worksheet which convey#Padditional information. Some are enabled(Vby default when they are necessary to fully+Lunderstand the current worksheet setup&F(but they can still be turned off).# NThis option elucidates the structure of'Dequations in cases where it may be"Habmiguous. Green brackets are placed$Haround equation elements to show the$Lprecedence of operations, arguments to&.functions and so forth._GlobalsЙ SpacesqXThis options enables highlighting of global ,Xvalues in the worksheet. Globals will appear,Tin bold light blue. Globals and the Global*Hvalue space are explained in a later$worksheet. ЪPThis enables the display of which value (Xspace each equation is in in the worksheet. ,NThe value space number of each equation'Nappears in red brackets after it. Value'Jspaces are the mechanism for plotting%Lmultiple simultaneous plots, they are &@explained in a later worksheet. [< viewmenuЉXeqnoffі bracketsoff^ globalsoffИ spaceoffThe Library сEџџџџџџџШШџџџџџџџџџџџџџџ The Library POn the library page you can manage your (Jworksheets and packages. Most of the %Vfunctions are provided by the icons across +.the bottom of the page.P 0Load and Unload PackagesLThis icon toggles a pane through which&Hyou can select packages to load into$@Calculon. You can also "Unload"  >packages which is equivalent toN"Saving" and "Closing" a file. However,'Nnote "Saving" is a redundant concept in'6Calculon as all changes areDautomatically commited to packages"Jwhen you quit the program. That means%Lall changes are permanent - if unsure, Hcopy a worksheet before editing it. $њNew Worksheet HCreates a new empty worksheet in the$Jcurrently selected package or folder.%vCopyPCopies the currently selected worksheet,(4folder or package onto theN"pasteboard", use Paste to put the copy'2into a folder or package. 4 PastePPastes the previously cut or copied item(Linto the current package or folder (or&Jretrieves a whole package if that was%0what was cut or copied).,New Package ,Creates a new package.SNew Folder *Creates a new folder. …Move UpDMoves the currently selected item ":up one position in the list.  КMove Down DMoves the currently selected item "<down one position in the list.!ю Lock and Unlock@Locking is a simple mechanism to :prevent accidental editing ofLworksheets. If a worksheet is "locked"&Bit can be viewed but not edited. !@Folders and packages can also be Jlocked, which also restricts how they%Lcan altered (i.e. renaming or cutting &Jworksheets is prevented). If you find%<some options are unexpectedly <disabled be sure to check the Dworksheet is not locked or under a"2locked folder or package.Ѓ Rename@Use the rename button to rename @worksheets, folders or packages.  СCutHCuts an item to the "pasteboard", it$Dcan be pasted back later. This can"Balso be used to delete folders or!Fworksheets. Note: only one item can#>on the pastebaord at once - twoLsuccessive "cuts" loses the first item&permenantly! ж>Special Note: Deleting PackagesLPackages cannot be deleted from within&TCalculon. If you "cut" a package and then  "Tquit Calculon, when you run Calculon again  Zthe package will still be available - because-Xthe package file is not deleted. To delete a,Zpackage, delete the file when Calculon is not running.§new/package №lockon …moveup М movedownTfolderzcopyФcut 8pasteSimport.The Temporary WorksheetоЏџџџџџџџШШџџџџџШџџџџШШџџ .The Temporary Worksheet LThe Temporary Worksheet appears at the&^foot of the Library list, titled "<Temporary>"./FThe Temporary Worksheet has several#Vspecial properties that are discussed here.+LIn general its purpose is to provide a&Twork space for quick plots or calculations*Xthat you don't necessarily want to save in a,Rpackage. If all the packages are unloaded)Rfrom the Library, the Temporary Worksheet)Tremains and therefore is the sheet you can*<see and edit on the Work Page.АJNote these points about the Temporary%Worksheet: ЯP1. It cannot be cut or deleted from the ( Library. яX2. It can be copied in the Library, and this,T is the method to use if you decide you*\ want to save it. I.e. select the Temporary.V Worksheet, copy, select the package and+ paste. 8V3. The Temporary Worksheet is automatically+V selected at startup if "Auto-Open First+R Worksheet" is disabled on the Options) Page. tT4. The contents of the Temporary Worksheet*Z are lost when you quit Calculon! Remember Z to copy the worksheet to a package if you-( want to save it.8Turning Equations Into PlotsThe Value TableфєџџџџџџџШШџџџџџџџџџџџџџџXa-441b150.2c-440.2x-220.2y-20200.2$Hy xabcwH c2The Value TableNAt the bottom of the Work Page (and the'RView Page) is a tab marked "Values". ThisTtab displays the "Value Table" which shows*Ninformation about the all the algebraic'@values on the current worksheet. bXThrough the Value Table the roles and limits,Pof each algebraic value on the worksheet(Rcan be set. It is through the Value Table)Vthat you tell Calculon exactly how to turn  Xthe equations on the worksheet into a plot. , Value Roles VA value in an equation can have one of four+Vroles. Consider these equations and have a +0look at the Value Table:h\The Value Table lists all five values a, b, c,&   Rx and y. There is an example of each role  "type amoung them: “axis -  /” Hthis means that the algebraic value $Dis to be used as a location on an "Daxis. In this example x and y are   Jaxes. The locations of points in the %Jplot are therefore determined by the %Fvalues of x and y. If an axis value   Dis not the subject of an equation "@(like x in this example) it also  :behaves like a parameter (seebelow). para - - FThis denotes a value which is to be#<used as a parameter. ParameterDvalues represent intervals between"Fa minimum and maximum (inclusive). #@In this example a is a parameter >which ranges from -4 to 4. Axis>values which are not defined byFequations also act like parameters,#:but in addition they are alsoHinterpreted as positions on an axis.$NIt is by this distinction that Calculon Fsupports plots from both direct and#*parametric equations.Ы user -  ,Ы HThis denotes a "user control" value.$DUser controls have a single value,"<but this value can be adjustedFinteractively on the View Page, and#Jthe plot is recalculated immediately.%FIn this example b is a user control Bwhich can be varied between 1 and!<5. User controls are varied by<means of the sliders under the:Control tab on the View Page.W med - ,W@Refers to an intermediate value. DIntermediate values are defined by"<equations but do not representJlocations on axes. They are typically%Freferred to in other equations that#:do define the axes locations.DIntermediate values can be used to"Fimproves the readability of sets of#Fequations, and speed up calculation#>by calculating values common to<more than one axes definition.FIntermediate values must be defined#<by an equation (c = 2 in this  <example) otherwise an error isproduced. 2Value Range and Step Size0VIn addition to value roles, the Value Table+Xcan be used to set the range (or limits) and,Z"step size" of values. The interpretation of -Nthe range and step size depends on the 'Vvalue role, and in some cases they are not +adjustable: †LRole axis, when not the subject of an  Jequation, and role para are the same: ЅPRange: - defines the interval over which#V the value ranges (inclusive).+У\Step: - defines the size of "steps" the value *\ takes going from the limit minimum.` to the maximum. E.g. limits of -1 to0b 1, step 0.1, produces values -1, -0.9,1^ -0.8, ... 0.9, 1 as "input" to the /* equation.RRole axis when the subject of equation is \slightly different as the value is an "output".not an "input":EPRange: - fixes the limits of the axes on#. the plot.gTStep: - is not applicable (cannot be set).&„2Role user (user control): –VRange: - sets the upper and lower limits of&X the user control (inclusive).,ЖVStep: - fixes the permissable values of the'f user control. E.g. with a range of 1 to3d 4 and a step of 1, the user value will2f take values 1, 2, 3 and 4 only as it is3* adjusted.<Role med (Intermediate value): 0Range: - not applicable.&.Step: - not applicable.=RRange and Step can also be set to Auto in!Vmost cases. This means Calculon will decide+Xon a reasonable setting. This is the default,Vand is often sufficient for quick plots. To+Jspecify the plotted area and optimise%Tcalculation speed, adjusting the range and*0step size is necessary. ZNote that Calculon restricts the role options-Vfor each value to those which are valid for+Zthe value in it current context. For example,-Va value which is the subject of an equation+Rcannot be set to type para (parameter) or (user (user control). ЉRUnderstanding value roles and settings is)Vthe key to exploting the power of Calculon." XReading through this worksheet will probably,Rmake it seem more complicated than it is.)PThe best approach is to study an example(Xwhich is similar to what you want to achieve,Xand use the information here as a reference.,&Simple User Controlн№ПџUџџџџџџШШџџџџџџџџџџџџџџ>a-10100.2x-330.2y-10100.05:sy x3 ax2&Simple User ControlLThis example demonstrates the use of a&Z"user control". The value a in the expression Tbelow is designated type user in the Value TTable. As such its value can be controlled*Zinteractively on the visualisation view using-Bthe slider under the control tab.Multiple Plots ръџџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџmx-440.2y-440.2r-440.2x-440.2y-440.2И0200.2=дy x23"x rИ24y rИ4GrИ4Multiple PlotsXThis worksheet describes how to plot several,:functions on one set of axes.9 NWorksheets in Calculon can contain any  Tnumber of "value spaces". Each value space*Pcorresponds to one plotted "object". An (Xobject can be a point, line or surface. Each,Tvalue space contains one or more equations*Tthat define the object associated with it.*VValue spaces are numbered to identify them,+Xand the space each equation is in appears as,Pa number in brackets after the equation.(ДRAn example should make this clearer, this)Bequation is in value space no. 1,!ю^It defines a very simple function, which is the/Pred line on the plot (see the View Page)(RThese equations are in value space no. 2,)[VSlightly more complex, this is a parametric+Rfunction (theta is the parameter) and the  \result is the second "object" on the plot, the.green spiral. “PNote: if the above equations do not have$Ta red number in square brackets after them*Xthen you need to enable their display - this,Vis explained on "Worksheet Visual Options".+ЬXThe values in the different value spaces are,Tcompletely distinct, even if they have the*Hsame names. Axes variables with same$Rnames determine how the two plots are put)together. PThe number of axes in the whole plot is (Tbased on the total number of distinct axes*Xin all the value spaces. So if, for example,,Pin one value space the axes values x and# Zy are defined, but in a another y and z are,    Zthen the plot will contain 3 axes x, y and z."   ZIn this case the plots might not turn out how-Lyou expect - see the Examples Package.&‚NFinally, have a look at the Value Table'V(Values tab, below) to see how variables in+Ddifferent value spaces are listed."ЏXThere is one complication to the information,Rgiven here, and that is the Global value )Tspace. The Global value space is explained**in a later worksheet.,The Global Value SpaceсQџџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџ[a-340.033x-441y-440.2x-441y-440.29кy ax9ёy  1ax,The Global Value Space PIn addition to the numbered value spaces(Rwhich correspond to objects in the plot, )\there is an additional value space referred to.Vas the "Global Value Space". Values in the +NGlobal space are available to equations'Zacross all other value spaces. Therefore, the-Jglobal space can be used to calculate%\intermediate results which are used by several.Zobjects. Most usefully, a single User Control-Tvalue in the Global space can effect more *@than one object simultaneously. ЊJGlobal values appear in light blue if%Xvisualisation of globals is enabled (see the,Zworksheet titled "Worksheet Visual Options").-VIn the above two equations the a value is a Zglobal user control (check the Value Table to-Xsee how this appears). Adjusting the a value% Vtherefore effect both lines simultaneously.+$Using Value Spaces пОџџџџџџџШШџџџџџџџџџџџџџџ $Using Value SpacesJSo, how do you move equations between%Zvalue spaces? This is achieved via the "Value-DSpace Menu", invoked by this icon:"]TNote, this icon is only available in move *Tmode and when an equation is selected. To *0select move mode tap on: BThe Value Space Menu contains the!$following options:СNewNCreates a new value space and moves the'4selected equation into it.ю CleanLRenumbers the value spaces starting at&Fone. During editing the value space#Hnumbering can become fragmented, for$Pexample "2" and "3" could exist without (Ra "1". This has no real consequences, but)Bthe Clean option tides things up.!O GlobalVMoves the selected equation into the global+Zvalue space. Note that, by necessity, all the-Xvalues in the equation including the subject,Vare individually moved into the gloal space+ also.І Space 1, 2, 3...XMoves the equation into that value space. If,XThere is only "Space 1" listed, the use New.,еRNote that these options will also work if)\multiple equations are selected, in which case.Vall the selected equations are moved to the+*relevant value space.Global Values !JIn addition to moving whole equations%Tbewteen value spaces, individual values in*Vequations can be set to refer to the Global+Tspace. This is achieved by the use of this* icon:~XWhich is available in equation editing mode.,RNote that an equation subject can only be)Vput into the global space if all the values+>that define it are also global.afglobalkˆmoveoffjEvsmenu Plots2D Plot Options нџџџџџџџШШџџџџџШџџџџШШџџ 2D Plot OptionsXThis worksheet describes the function of the,Ticons across the bottom of the screen when*Tviewing a 2D (flat) plot on the View Page.*F Panning Mode LThis is one of two options on 2D plots&Hfor the action which occurs when the$Lstylus is dragged on the plot (or the &FPDA direction buttons are pressed).#:When panning mode is enabled,Pdragging the stylus on the plot moves it(Naround, panning the view over the plot ' area.РZoom mode NThis is the other stylus dragging mode.'JIf this is enabled, dragging up zooms%Rin on the vertical axes, dragging to the)Jright zooms in horizontally. Dragging%Hdown or to the left zooms out on the$ respectiva axis. View Axes HIf enabled, the axes a drawn on the $6plot (if they are in view).M.Horizontal Axes NumbersFIf enabled, scale numbers are drawn#4along the horizontal axis.z*Vertical Axes NumbersFIf enabled, scale numbers are drawn#.along the vertical axisЇNumbers At AxesRThis is toggle with the next option (i.e.)Jone or the other is enabled). In this%Hcase, if this is enabled axes scale $Hnumbers are drawn alongside the axes$ within the plot.ћ$Numbers Along EdgeLIf this is enabled then the axes scale&Jnumbers are drawn at the edge of the %Fplot area irrespective of the axes #locations. {Swap Axes PBy default the axes are arranged so that(Lthe first letter alphabetically is the&Phorizontal axes (this works as expected (Lfor x and y). This icon swaps the axes  around.бReset View NThis puts the view of the plot back to 'Jthe default initial view. This can be%Puseful after zooming or scrolling to get(2back to the overall view.ADraw Grid HThis enables the drawing of a square$Ngrid behind the plot, aligned with the '@axes scale numbers (if present). GmoveoffТzoomoffЉlabelsonaxesoffўlabelsonedgeoff| ylabelsoffP xlabelsoff~ axesswapдreset"axesoffC subaxesoff$3D/nD Plot Options сдџџџџџџџШШџџџџџШџџџџШШџџ $3D/nD Plot OptionsXThis worksheet describes the function of the,Ticons across the bottom of the screen when*Xviewing a a plot of three or more dimensions,"on the View Page.ПPanning Mode JThis is one of three options for the %Laction which occurs when the stylus is&@dragged on the plot (or the PDA Jdirection buttons are pressed). When %Jpanning mode is enabled, dragging the%Hstylus on the plot moves it around, $Hpanning the view over the plot area.$Zoom mode NThis is the third stylus dragging mode.'RIf this is enabled, dragging up or to the)Hright zooms in on the plot. Dragging$<down or to the left zooms out.,View Axes HIf enabled, the axes a drawn on the $6plot (if they are in view).\"View Axes NumbersFIf enabled, scale numbers are drawn#$along all the axes‰Reset View NThis puts the view of the plot back to 'Jthe default initial view. This can be%Puseful after zooming or scrolling to get(2back to the overall view.R Smooth RenderingNIf this is enabled the surface is drawn'Hwith a smooth curved appearance. The$Pother option is flat rendering (below). (Flat RenderingHConversely to smooth rendering, this$Foption draws surfaces as composed a#Pof flat facets. The facet sizes reflect (Rthe actual detail of the calculation. For)Tsmaller facets, reduce the "step size" of *Lparameters (see the earlier worksheet &&"The Value Table").ћCheck Pattern TIf there are surfaces in the plot they can*<be drawn with a "check-board" Jpattern, which in many cases enhances%Dtheir shape. This icon enables and"Ndisables the check pattern. The colours'Lused for the pattern can be set on the&options page. iCheck Size PThis icons reduces or increases the size(Lof squares in the check-board pattern,&Tif it is enabled. Click on the top part of*Pthe icon to increase the check size, on (>the bottom part to decrease it./Rotate Mode NIf this is enabled dragging on the plot'Protates it in horizontal-depth plane or (Pvertical-depth plane. To rotate plots in(Jdimensions higher than three use the %Lsliders under the Rotate tab (see the >later worksheet on this topic).з ShadowJThis enables and disables the drawing%Nof a shadow behind lines or surfaces. A'Lshadow gives various visual cues which&8can enhace the impression of"3-dimensionality.Сmoveoff’zoomoffŒreset.axesoffS smoothoffŽ notsmoothoffћ checkoff] labelsoff1 rotateoffй shadowoffj checksize0Higher Dimensional Plots ‹kџџџџџџџШШџџџџџШџџџџШШџџ—r-440.2w-440.2x-440.2y-440.2z-440.2Б-3.143.1420.2И-3.143.1420.2Р-440.2r2Иmx rБl' yИkTw 2Б2Рn>z rБ 0Higher Dimensional Plots VCalculon can draw points, lines or surfaces #Dwhich are defined in any number of"Vdimensions. Two and three dimensional plots+Xare easy to understand, but plots in four or,Rmore dimensions require some explanation.)XThis worksheet explains the nature of higher,<dimensional plots in Calculon. ~ .Three Dimensional PlotsZFirst, consider three dimensional plots, such-Vas most of the examples in the Introduction+NPackage. These are easy to comprehend -'Zthey represent "objects" which lie in "space"-Tas we normally experience it. The plotted *Lobjects can be rotated around in space&Xexactly as we experience objects in the real, world.ї \However, this is not really true. What you are.Zactually looking at is a flat two dimensional-Himage on the screen of your PDA. The$\reason it is so easy to accept that this image.Rrepresents a three dimensional object is )Rbecause the brain does a very good job of)Ppicking up various "depth cues" from the(Tinfomation it receives. In particular the *Rshading, background shadow and "rotation")Vof the objects convice the brain that it is+Fviewing a three dimensional object.#ŠZIn fact, Calculon does not even display three  Zdimensional objects, it displays a projection# Pof a three dimensional object onto a two(&dimensional screen.Ф0Higher Dimensional PlotsLCalculon behaves exactly the same when Vdrawing a higher dimensional plot. It draws+Na projection of the object onto the two'&dimensional screen. ZThe plotted objects are first projected into -R3-dimensional space, and then shading and)Tshadows are added. Therefore, "depth cues"*Xbased on lighting are not available to infer,Vthe shape of the object in dimensions above+Vthree (and in any case our brains would not+Fknow how to interpret them). Future#Vversions of Calculon may incorporate a full  ^higher dimensional lighting model, if it proves/to be useful. Rotations XRotation of higher dimensional objects gives,Tthe best impression of their structure. To*Nunderstand how rotations are applied to'Zplots it is necessary to briefly consider the-Rnature of rotation in n-dimensinal space. фJIn 3-dimensions we typically think of%L"rotation about an axis" i.e. a wheel &^spinning on its axle. In fact, in general it is/Rmore useful to note that rotation occurs )X"in a plane". I.e. that under rotation every,Rpoint stays within a 2-dimensional plane,)Xand rotates about a point within that plane.,FIn three dimensions, this plane is #Tperpendicular to the axis of rotation. The*Tplane has two dimensions and the axis one,*Vgiving a total of three. In four dimensions+Xthis total must be four, hence the "axis" of,Vrotation is two dimensional - a plane. This+Zseems wierd, but if we continue to hold on to-Xthe idea that rotation occurs within a plane,`then it is quite simple: to define a rotation we0Vsimply define the plane in which it occurs.+PThis view works regardless of the number(.of dimensions involved.оXDragging the stylus horizontally on the View,\Page rotates the plot in the plane defined by .^a horizontal line and an a line projecting into/Xthe screen (depth-wise). Similarly, vertical,Xdragging rotates the plot in a plane defined,Jby the vertical and depth directions.%0 XWith a plot of four or more dimensions, more,Xrotations are available under the Rotate tab"Non the View Page. The first sliders are'Vextensions of the stylus dragging rotations+Hand rotate in the plane defined by a$Rhorizontal line (H) and one of the higher)Xdimensions (D4, D5,... etc.). The second set,Rare a selection of rotations based on the)Nactual plot axes. Note how the two axes'Vwhich define to rotation plane are the only+Ptwo which move in the plot when rotation(*sliders are adjusted.бTThe best way to understand all this is to *Rplay around with rotations on an example.)LThese equations reproduce the 4D Torus&Jexample from the Introdution Package.%Alpha RenderingоџџџџџџџШШџџџџџШџџџџШШџџ Alpha RenderingNFor plots of three or more dimensions, 'LCalculon can use "alpha rendering". In&Neffect, this draws the plot elements as'Lsemi-transparent. In this way obscured&Vfeatures or the structure of complex folded+>surfaces or can be seen better.nPThe alpha level can be set under the tab(Xwith the alpha symbol on the view page. This  \tab is only enabled for plots of three of more.Hdimensions. An alpha level of100% is$Tcompletely opaque (ino transparent effect,*Tas normal). The minimum alpha level is 50%*Pwhich means that objects are drawn as if(Nthey were half-transparent (they appear'Rcomposed of 50% transmitted light and 50%)Xreflected light). The alpha level can be set,Lat anything between 50% to 100% on any&Zplot of three or more dimensions. The current-Palpha setting is remembered by worksheet("between sessions.*XYou will probably notice that the adjusting ,Nthe alpha level to anything below 100% 'Rslows down the responsiveness of rotation)Zslightly. This is because alpha rendering is -Tcomputationally more expensive than fully *Nopaque rendering. This may be addressd '@in a future version of Calculon. *Changing Plot ColoursпюџџџџџџџШШџџџџџџџџџџџџџџ *Changing Plot ColoursVThe colours used in the current plot can be+Jchanged on the Options Page (Ops tab)7 ZUnder "Visualisation Colours" there is a list-Lwhich can be opened up to select which&Titem you wish to change the colour of. The*Xfirst few refer to general features, such as,Fthe background or axes colours. The#Zremainder consist of colours allocated to the-X"objects" in the current plot. Like the plot,Zitself, the list is dynamically created based-Ton the equations on the worksheet. So only*Xitems appropriate to the current plot can be,selected. ЪTLines have one colour allocation only (the*Dcolour of the line). Surfaces have"Tfour - two colours on each side which are *\used for the "check" pattern. All four colours.Vcan be set even if the check pattern is not+$currently enabled.PThere are several controls to select the(Ncolour - a gradianted colour hexagon or'Ppallete of preset colours can be used to(Tselect the colour. A slider can be used to*Xalter the brightness of the selected colour.,c JSurfaces can have one or more colours%Tset to "transparent". This means that that*Xpart of the surface will not be drawn at all,L(as if it did not exist). When used in&Xconjuction with the "check" pattern this can,Rproduce a useful effect where the surface)Tconsists of an semi-open lattice which can*Nbe seen through. The worksheet "Another'PTorus" in the Introduction Package shows(this effect. Exporting Plotsн№џџџџџџџШШџџџџџШџџџџШШџџ  Exporting PlotsLPlots can be exported to various image&Tformats using the icon in the bottom right*8of the View Page (as above).KPThe supported image formats are actually(Tdependent on the underlying Qtopia system,*Tbut typically they include BMP, JPEG, PNG,*FXBM and XPM. PNG is recommended for#best results. ’VThe image is exported exactly as it appears+Non the screen. A scaled down preview in'Lthe export window gives an idea of the&Toverall appeareance of the exported image.*gexportGeneral Optionsн;џџџџџџџШШџџџџџШџџџџШШџџ General OptionsXThere are three general options which can be,Pset on the Options Page (Ops tab). These Roptions affect the overall functioning of)FCalculon and are remembered between sessions. ` 2Auto-Open First WorksheetXIf this is enabled, at startup Calculon will Rautomatically load the first worksheet in)^the Library. If it is disabled, Calculon starts  Lon the clean Temporary Worksheet. This&Xoption is mainly used to display the Welcome,Zworksheet after Calculon is installed for the-\first time. Probably, you will want to disable.it.й 8Load All Packages At Startup`If this is enabled, when Calculon is run all the FCalculon Packages on the system are Tautomatically loaded and available in the *`Library. If it is disabled, Calculon starts only Bwith the Temporary Worksheet, and!Xpackages must be loaded individually via the,JLoad icon. The main downside of auto-%Rloading packages is that it significantly)Xincreases startup time. If you regularly use,VCalculon for quick plots, you will probably #Xwant to disable this options so it starts up,quickly. ˆ HNever Scroll Worksheets Horizontally$ZThis option is enabled by default, and only a-Xvertical scrollbar is presented on the Work ,PPage. The idea is that worksheets should(Ngrow downwards and their content should'Xbe restricted to the screen width. However, ,Zthis is not a limitation and in fact content -Tcan be placed on worksheets vertically and*Thorizontally without limit. Disabling this*Voption will cause a horizontal scrollbar to+Lappear on the Work Page whenever there&Vthe worksheet content is too wide to fit on+the screen.  Performance TipsпsџџџџџџџШШџџџџџШџџџџШШџџ  Performance TipsLCalculon is very fast at what it does, Vespecially considering that it runs on PDAs+Rwith no hardware support for mathematical)Roperations. However, for optimal speed of)Vcalculation and manipulation of plots it is+Bworth bearing in mind these tips:!pT1. Increase the step-size of parameters to*L the maximum you can get away with.&P Larger step size means fewer loci to(X calculate and fewer elements to be drawn, in the plot.ЙH2. Rearrange equations to reduce the$L amount of calculation required. In&T particular, use intermediate values to*R reduce replication between equations.)H The Boy Surface worksheet in the$T Introduction Package demonstrates this* technique.V3. Make sure the alpha level is set to 100%+T on the View Page, if you don't require*L alpha rendering. An alpha level of&T anything other than 100% causes slower*B drawing, and slightly reduces!X responsiveness when rotating or zooming.,,FAQ - Important Points AћџџџџџџџШШџџџџџџџџџџџџџџ ,FAQ - Important PointsRThis worksheet reiterates a few important)Rpoints about Caculon which are mentioned  <elsewhere, but bear repeating:зHCalculon Automatically Saves On ExitJThere is no "Save" option. All loaded%Fpackages which have been edited are#Lautomatically written out to file when&TCalculon closes. If unsure, make copy of a "Vworksheet before editing it. Using "Unload"+Von the Library Page is like a "Save" but is+unnecessary. ENDeleting A Package In Calculon Does Not  Really Delete ItPThe package file is not deleted from the(VPDA so it will be there again when you next+\run Calculon (either automatically loaded, or  "Vavailable to be loaded). To really delete a+ZPackage, delete the file when Calculon is not running. ЩTQ: I dowloaded a Package file from the web'Tand transferred to my PDA via CF/SD Card, *Rnetwork (or some other method). Calculon  Vdoes not recognise the file, and it doesn't+Xlook like a Calculon Package file on the PDA  F(i.e. red box with a shell in it). #TA: This is a common problem and is nothing(Vto do with Calculon. It is a feature of the  Vunderlying Qtopia system on the PDA. Qtopia+Rrequires that documents are identified by)Vmime-type. In order to do this it generates+\an additional description file with the suffix.R".desktop" for every document file on the)Zsystem. In addition, files are placed under a-Zdirectory hierachy which reflects their type,-Ri.e. application/x-calculon for Calculon  ^Packages. The problem is if you transfer a file/`directly even if you put in the right place, the0T.desktop file doesn't exist. This issue is*Pdiscussed in some detail on the Vaagmaer(website:фRhttp://www.vaagmaer.com/calculon/faq.html)Е"A common query...C"Getting More HelpRThe examples in this and the Introduction)XPackage are your best source of information.,VFind one which is close to what you want to+*achieve and study it.ŸVAlmost every icon or control has a tooltip +Vasscociated with it. Tap on the red ? icon $Vat the top right of the screen and then on +*the item of interest.TooltipsŠ ballhelp,Download More PackagesтлџџџџџџџШШџџџџџШџџџџШШџџ ,Download More PackagesHMany of the examples in Introduction$JPackage touch upon topics which could%Pbe expanded on with many more worksheets(Xand examples. And of course, there are also ,Vmany other topics which could make for very+<informative Calculon Packages.  mPAdditional Packages for Calculon will be Havailable for free download from the$"Calculon website: 2www.vaagmaer.com/calculonЈPThere you will be able to get the latest(Jversions of the Introduction and Help%RPackage, and additional packages which we)Rwill release from time to time. The first)Xplanned is the Seashell Package, which will ,Lexpand on the seashell examples in the&VIntroduction Package (if its not available +,yet, it soon will be).&Contribute Packages) ZWe hope that Calculon users will also develop  Tand make available their own Packages. The*Voriginal design philosophy for Calculon was Jthat it should not just be a tool for%Xmathematical visualisation, but a medium for,Feducation. So if you have developed#Lworksheets to demonstrate a particular&Tstrecture or idea, why not share them with*.the Calculon community? Ѓ^If you would like us to distribute your package/Nfrom the Calculon website, email it to:  /Ф*calculon@vaagmaer.comReporting BugsхзџџџџџџџШШџџџџџШџџџџШШџџ Reporting BugsXCalculon is a versatile and powerful program $Hwhich can be configured and used in $Xmany ways. As such, it is impossible to test,Tas thoroughly in development as it will be*\tested "in the field". It is quite likely that.Lsome bugs will surface. Please help us&Tsupport this product by taking the time to*Freport any problems you experience.#‰XThe most vital information required to fix a,Zbug is a method to reproduce it. If possible,-Jplease send a Calculon Package with a Tworksheet which causes or displays the bug*2to calculon@vaagmaer.com.дLMost importantly, please mention whichTversion of Calculon you are using. You can  \find the version number by tapping twice on: #X(at the top right hand corner of the screen),1LIf the bug cannot be encapsulated in a&Jpackage please describe in detail the%Lsequence of operations which cause the&problem.kPEven if neither of the above options are(^possible, it is useful if you can take the time/Fto email us with some idea of what #Dhappened, as we could possubly put"Ptogether a picture from several reports.(ДNOf course, hopefully there won't be any' bugs!bџ ballhelpExamplesFunctions Trigonometricп№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџqx-440.2y-440.2x-440.2y-440.2x-440.2y-440.2!% yx!@ yx!\ yx*Inverse Trigonometricп№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџqx-440.2y-440.2x-440.2y-440.2x-440.2y-440.2")y x1"Fy x1"cy x10Reciprocal Trigonometricп№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџqx-440.2y-440.2x-440.2y-440.2x-440.2y-440.2 yx 2 yxN yx @Inverse Reciprocal Trigonometricп№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџpx-440.2y-440.2x-440.2y-440.2x-44.1y-440.2#y x 1#:y x1#Wy x 1Hyperbolicп№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџqx-440.2y-440.2x-440.2y-440.2x-440.2y-440.2 yx6 yxS yx$Inverse Hyperbolicп№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџux-10100.2y-10100.2x-330.2y-330.2x-330.2y-330.2!y x1@y x1_y x1*Reciprocal Hyperbolicп№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџqx-440.2y-440.2x-440.2y-440.2x-440.2y-440.2** yx *B yx *Z yx :Inverse Reciprocal Hyperbolicп№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџqx-440.2y-440.2x-440.2y-440.2x-440.2y-440.2y x 10y x 1Ky x 1Min and Maxп№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџQx-10100.2y-10150.2x-440.2y-440.2!+yx4 x2!N yx510 x22D GeneralLineп№џџџџџџџШШџџџџџџџџџџџџџџ)x-440.2y-440.2&!y x3 3 x234A simple single line plot.Two Linesњ№џџџџџџџШШџџџГџџџџџџџџџџџГџџџџџџџџџџ_r-440.2x-220.01y-220.2x-220.01y-220.2&`y r2 x2'J r2&€y r2 x2 PTwo lines together making the upper and (Tlower parts of a circle. Note that r (the # bradius) is defined as global, so it is available *in both value spaces.Annulus"№џџџџџџџШШџџџџџГџџџГџџџџRr11.50.5x-220.05z-220.05Б-3.153.150.2!?x rБ!Tz rБ RTwo parameters with two axes results in a)V"surface" on a two dimensional plot, i.e. a+filled-in area. Annulus and Lineп№џџџџџџџШШџџџџџГџџџГџџџџџџџџџџџџџџџџur11.50.5x-220.05y-220.2Б-3.153.150.2x-220.2y-220.2(x rБ?y rБqy x2 BThe annulus in one Value Space...!],The line in another...3D GeneralLine in 3DчHџџџџџџџШШџџџџџџџџџџџџџџ{r-110.05x-110.05y-110.05z-110.05Б-3.153.150.02И-3.153.150.01Gr3 2И4И 12Бvy 2ИŠx rБŸz rБ a<x, y and z are the axes values   \Based on a torus, but there is only really one.Nparameter as everything is derived from' alpha.  Electromagnetism №џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџmx-660.2y-110.2z-110.2x-660.2y-110.2z-110.2wy 2x€wz 2x z0‹ y0PThis demonstates an important principle,(Xthat to define a line in 3-dimensional space,^all the axes must be defined for each plot. If /Tthese two plots were lacking the z = 0 and! Py = 0 statements they would be expanded  'Xout to surfaces (see examples of this in the,8"Undefined Axes 3D" folder). Eggbox№џџџџџџџШШџџџМџџџџџџџГџџџџ:x-660.5y-110.05z-660.5.yxz HThree axes, two of which also act as$parameters, ‰PNG  IHDR№mы]лЎIDATxœэеЁQC@С ƒˆ@"D$‰@RFЪ@RFJI)D "Пˆ@!žŽ УьpwцЭ­–г2РЏЋП>.‹$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@H‚KѕБ›ЯЭ|эчћuŽ‡YЖs:ЮѕћЌзsГ›лЭмэчўeГйЮуqžоцy}ўкеrZЮŸџ†/! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ $! I@HB’€„$ ~:™;ьFїNIENDЎB`‚ Surface and Line п№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџыr-110.05x-110.05y-110.05z-110.05Б-3.153.150.02И-3.153.150.01r-330.2x-330.2y-330.2z-330.2Б-3.153.150.2И-3.153.150.2r3 2Иoy 2ИoCz rБo/x rБ/И 12Б ‡r3Иk yИkЈz rБk”x rБNThese equations define the coiled line:'\F... and these equations define the #"torodial surface: PointsPoints in 2Dп№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџMx-330.2y-330.2x-330.2y-330.2Y' y2( x1YP y1P x2 DTwo points in 2-dimensional space,"Points in 3Dѕ№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџmx-330.2y-330.2z-330.2x-440.2y-440.2z-440.27 y2J z2% x2p6 y2q$ x1rI z1 DTwo points in 3-dimensional space,"GlobalsGlobalsп№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџMx-440.2y-440.2n-440.2n-440.2m yxxeny0.1x}ny0.1XThe global value space can be used to define,Rsub-expressions, the results of which are)Vavailable in all the specific value spaces.+\In this simple example y = sinx is global, and  Pthe two plots are both derived from this(calculation. Global AxesŽ№џџџџџџџШШџџџџџџџџџџџџџџIx-440.2y-440.2n-440.2y-440.2Sž yxR nyZNote that axes values in the global space are-\distinct from those in specific value spaces, .@even if they have the same name. 1\Because of this, the equations below define a .\plane in four dimensions, not three. There are.<two axes in plot labelled "y". [ZThe simplest way to avoid confusion is to not-Xrepeat the use of a symbol in the global and,,specific value spaces."Undefined Axes 2DValue to Lineс№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџ=x-330.2y-330.2x-330.2qy x2rІ x2NAn "undefined axis" is an axis that is '\defined in one value space but not in another..RPlots are expanded out along missing axes)Twhich gives the expected interpretation of*8the mathematical statements.KZIn this example the first value space defines-\axes x and y, but the second refers only to x.   VFor the second plot the y axes is expanded +\to all possible values giving the line of all .&points where x = 2.  (Value to Line [user]№ПџUџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџPa-510.2x-330.2y-10100.05x-330.2-Ry x3 ax2.qxa2 PAnother example of a single defined axis(>being expanded out to a line inX2-dimensional space. This time a global user,Bcontrol a acts on both the plots. &Interval to Surface!№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџLx-330.2y-330.2r120.2x-330.2Jmy x2K… xrZIn this case the second plot defines x as the% Linterval 1<x<2 (via r which is set as   Xparameter in the Value Table). This interval,Xis expanded out along the y axis to give the,Vfilled in area which consists of all points+Bwhere 1<x<2 and y is any value.   4Interval to Surface [user]п№ПџUџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџ_a-520.2x-330.2y-10100.05r120.2x-330.2'6y x3 ax2(Pxar TThe previous example, incorporating a user*Bcontrol which acts on both plots.!:Two Values to Surfaces [user]ѕ№ПџUџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџџГџџџџџџџџџџ‚a-10100.2x-330.2y-10100.05r121x-330.2r10155y-330.2&By x3 ax2'Y xr&n yr DTwo expanded ranges, in the second"Vvalue space y is undefined, whereas in the  *third x is undefined. "Undefined Axes 3D0Line to Surface and Lineп№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџ]x-440.2y-330.2z-330.2x-330.2y-440.2ƒ yxz zx y0TUndefined axes in 3-dimensional plots work*Vin exactly the same way as in 2-dimensional+ plots.1XIn the first value space 3 axes are defined,,Xand the result is a line in 3D space. In the,Zsecond value space the z axis is not defined,-Ztherefore the "line" y = cosx is expanded out  4over z to give a surface.  *Two Lines To Surfaces8№џџџџџџџШШџџџџџџџџџџџџџџџџџџџџџџџџџџMx-330.2y-330.2x-330.2z-330.2>q yx@‡ zx PBetween them, the equations in these two(Zvalue spaces define three axes, so the plots -Vare in 3-dimensions. However, individually +Teach only defines two axes. Each equation *Xwould define a line in 2-dimensional space, ,Zbut as they lie in 3-dimensional space, they -"define surfaces. 4Value To Surface 3D [user]q№џџџџџџџШШџџџџџГџџџГџџџџџџџџџџџџџџџџџџџџ]x-660.3y-330.2z-660.3r-220.2y-330.2ByxzB– yr LThe equation in the first value space &Rrepeats the plot of the previous example )Nnamed "Eggbox". The second value space '\contains a very simple definition y = r, where"  Xr is a user controlled value. As the x and z $  Raxes are undefined, this second equation )Xdefines the plane of all points where y = r.%  PNote how the plane moves up and down the(Jy axis as the value of r is changed.   Error Messages  > Introduction <І№џџџџџџџШШџџџџџџџџџџџџџџ  \The worksheets in this folder describe all the.Terror messages which Calculon can produce. NThese messages appear on the View page,Peither immediately when the View page isVselected, or after the calculation has been+Hperformed. In general, they refer to$Ninconsistencies in the equations on the'Rworksheet, unsupported configurations or )0the calculation results.VEach worksheet describes an error and gives+Nexample equations that produce it. The '\message itself can be seen on the View page. "Error Messages Nothing To Chartп№џџџџџџџШШџџџџџџџџџџџџџџ (TIf there are no equations on the worksheet*Fthen this message will be produced.#Error Messages Nothing To Chart(Incomplete Equationsп№џџџџџџџШШџџџџџџџџџџџџџџ)x-330.2y-330.2I{ yx&RThis message is produced when there is an)Tincomplete entry somewhere in an equation.*RThese are shown by red question marks, as)Rbelow. Simply edit the equation to remove) or replace them.Error Messages:Some Equations Are IncompleteNo Axes DefinedК№џџџџџџџШШџџџџџџџџџџџџџџ)a-440.2y-440.2G‹ya2PЁ a7Error MessagesNo Axes Defined(XCalculon supports plots of two axes or more. $RA plot on one axes would just consist of )Rpoints along a straight line (this can be)Vemulated, see the Examples package). A plot Vwith no axes doesn't exist! If no values in+Vthe equations are defined as type axis then" Pthis is the error that will be produced.(Only One AxisЩ№џџџџџџџШШџџџџџџџџџџџџџџ)x-330.2y-330.29ž yxpž x2Error Messages*Only One Axis Defined# \This occurs when only one value is set to type.Zaxis in the Value Table. Having only one axis )^defines a plot in one dimensional space (i.e. a/Zset of points along a line). This version of -ZCalculon only supports plots of two or more  %`dimensions. However, it is possible to visualise0Va one dimensional plot by adding a "dummy" +Xaxis with a constant value (see the Examples$ Tpackage for an example of this technique).*(Circular Definitionsп№џџџџџџџШШџџџџџџџџџџџџџџ9a-440.2q-440.2s-440.2xqs2[xs 2a˜w aqError MessagesBCircular Definitions in Equations!(\If a value is defined in terms of itself, then.Zthis error is produced. Note, the circularity-Fcould be directly obvious as in the#Lexpression q = q + 2, or only apparent   Jover a series of equations, as below:%*Innappropriate CommasК№џџџџџџџШШџџџџџџџџџџџџџџ9a-440.2x-440.2y-440.2‚ xa2aya3 a2Error Messages<Commas At Inappropriate Places$ VIn this version of Calculon commas are used Vonly to separate the arguments of functions+Xwhich can take multiple arguments. Currently,Nthis includes only the min() and max() Rfunctions. In future versions of Calculon! Tcommas will probably have additional uses.*XBelow, the left equation shows a correct use,Pof commas, whereas the one on the right (2causes the error message.8Results Completely UndefinedК№џџџџџџџШШџџџџџџџџџџџџџџ(x140.2y-440.2UŸ yxError Messages@Results Are Completely Undefined $