%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % WELCOME TO iCAS % % The core of iCAS is based on REDUCE, a powerful CAS system with comparable capabilities % to Maple and Mathematica with a track record spanning over 40 years in academic and research % institutions. iCAS brings all the capabilities of REDUCE and the embedded gnuplot plotting % engine to your iPad. Best of all, iCAS is entirely self-contained and runs natively on your iPad % so no internet connection is required to harness its power. % % This file is written as a short tutorial to walk you through some simple examples to become % familiar with the app and help you get started. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % BASIC USAGE % % Enter the desired command or operation and press return to execute the command or operation. % Try it by tapping to the right of the semicolon on the line below and then tapping return. 6 * 7; % If fancy output is enabled, the results can be viewed in a typeset format by tapping a translucent % button that appears on the upper right hand corner of this view when there is fancy output or % iCAS detects LaTeX content. The output view can be zoomed using the standard pinch gestures. % % Fancy output can be globally enabled with the "Create Fancy Output" option or on a case by case % basis using the fancy switch. If fancy output is enabled and the "Automatically Show" option is % enabled, iCAS will automatically show the rendered fancy output when it is generated. % % Execute the following lines (i.e. place the cursor to the right of the semicolon and tap the return % key) to see the difference between plain and fancy output. df(x^x,x); on fancy; df(x^x,x); % Notice the pseudo-LaTeX output format and the "TeX" translucent button that appeared on the % top right of the window. Tapping the "TeX" button generates a typeset version of the file that % can be optionally emailed as a LaTeX source file for publishing, presentation, and/or sharing with % colleagues. % % Fancy output works best with a line length of 80 or more. iCAS sets the linelength to the optimal % width for plain output when a CAS session is started based on the font style and size settings. % Therefore, we recommend setting the linelength to 80 when using fancy output. iCAS provides a % convenience command called fancy_output that sets the fancy switch and sets the linelength to 80 % characters. Note that turning the fancy switch off does not affect the linelength so you may need % to set the linelength to an appropriate value after using fancy output. The linelength is reset when % a new CAS session is initiated (e.g. by using either the "bye" or "quit" command). % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % KEYBOARD USAGE % % By default, iCAS uses the system keyboard. A user configurable macro keyboard and a % numerical keyboard are also optionally available. The enabled keyboards and the default % keyboard can be configured in the app Settings. The app Settings can be accessed either through the % global Settings app or by tapping the Settings button on the top right corner of the screen. % % To switch between the enabled keyboards, use a horizontal swipe gesture in the text area when a % keyboard is active. % % By default, tapping a button other than the "CLEAR" or "BATCH" buttons on the macro % keyboard causes the active keyboard to automatically switch to the system keyboard to allow % entry of variables, parameters, arguments, etc. This behavior can be enabled/disabled using the % "Auto Hide Macros" setting. % % Tap the clear line below to active the keyboard and swipe from right to left to reveal the macro % keyboard. Now tap the "integral" button. % Now double tap "function" and replace it with some function of x, say x, to keep it quick and % simple. Then execute the line. Unless you've disabled fancy output, iCAS will have output a % pseudo-LaTeX output that you can view by tapping the "TeX" button at the top right. Go ahead % and tap it to see the output in the LaTeX viewer. % % Tapping return on the system keyboard can be configured to automatically switch to the macro % keyboard to enable the entry of other CAS commands. This is controlled by the "Return Shows % Macros" setting. % % To edit the contents of a macro button, tap and hold down the button for 1 second or longer. % % Instances of \n in macros get automatically converted into new lines. This makes it possible to % create macros with text spanning multiple lines. % % Assigning \r to a macro button turns that button into a silent return key. That is, it inserts a % new line character without processing the contents of the line. % % Assigning \b to a macro button turns that button into a backspace/delete key. % % Assigning \c to a macro button turns that button into a clear key. % % Assigning \cb to a macro button turns that button into a clear batch output key. The macro has % no effect if there is no batch output. % % The cursor placement within a macro can be optionally specified by including \^ in the macro where % the cursor should be after the macro is inserted. For example, the macro “(\^)” will cause the % cursor to be placed between the two parentheses. % % The macro buttons can be optionally labelled by including the desired label surrounded by the # % character in the macro text. For example, if a macro contains #LABEL#, the button will display % LABEL in a larger font instead of the actual contents of the macro. % % The following labels (in uppercase) are automatically displayed with the mathematical symbol for % the corresponding CAS operator/constant: DF, E, I, INFINITY, INT, PI, PROD, and SUM. % % The default integral, derivative, pi, and infinity buttons are examples that utilize these features. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % PLOTTING % % iCAS includes a full implementation of gnuplot that can be accessed in CAS mode using the % gnuplot package or directly in plot mode (more on modes later). By default, iCAS loads the % gnuplot package so unless you changed the "Always Load gnuplot" setting, it should already be % loaded. % % By default, iCAS automatically shows newly generated or updated plots. This behavior can be % disabled in the global settings. % % Plots can be magnified using the standard pinch gestures. iCAS supports landscape orientations % in all its views so plots can be viewed in either portrait or landscape orientations. Execute the % line below to see plotting in action and use the pinch gesture to zoom in/out and swipe gestures % to pan around the plot while zoomed in. plot(sin(x)); % Unless specified, iCAS uses the title "iCAS Plot" and the file name "CASPlot" for plot files. The % default plot title can be changed in the global settings and can also be set on a per plot basis. % Execute the below line to see an example. plot(cos(x), title="cos(x)", output="cos(x)"); % Plot files can be accessed by tapping the "folder" button on the right side of the menu bar. Go % ahead and tap the button now. % % The files organizer picker has four wheels. One for text files such as this one, one for plot files, % one for REDUCE inout files, and one for macro keyboard files. Aim the left picker wheel to view the % corresponding files. Files can be deleted, mailed, or viewed/selected with the buttons above the % picker wheels. % % The displayed contents can be emailed, copied, or printed by tapping the "send" button button on % the right side of the bottom toolbar. Text files are emailed using the active font style. The % font style, font size, and colors can be configured using the styles panel revealed by tapping the % "styles" button on the left of the bottom toolbar. The available font styles are "Helvetica", "Times", % and "Courier". Although not the prettiest, Courier can be optimal as it is the closest to a monospace % font on iOS devices. % % Plots can be emailed in SVG format which is a resolution independent format supported by major % major browsers including Safari and FireFox. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % OPERATION MODES % % iCAS supports three operation modes. % % • CAS Mode % • Plot Mode % • Text Editor Mode % % By default, the application's color theme changes to indicate the active mode. This color feedback % behavior can be disabled in the app Settings, if desired. % % In CAS mode (the current mode unless you've changed the mode with the mode controls switch % in the middle of the toolbar), iCAS behaves as a terminal interface to the CAS engine. % % In Plot mode, iCAS behaves as a direct terminal interface to the gnuplot engine. Go ahead and % dismiss the keyboard and tap the "plot" mode button (the button with a graph) to switch to Plot % mode. Then execute each of the following lines in sequence. This is an example straight from the % gnuplot demonstration samples web page. set output "3D Log" set title "3D Log" set samples 30; set isosamples 30 set hidden3d set pm3d set surface set view 50,220 set xrange [-2:2] set yrange [-2:2] splot log(x*x*y*y) % As you can see, iCAS accepts gnuplot commands directly. % % In Text Editor mode, iCAS behaves as a plain text editor. Pressing return does not invoke either % CAS or plot operations. This mode is useful for general-purpose text editing, to create input files % for batch execution (described below), to create/preview LaTeX documents, etc. % % The active file is automatically saved when the application is quit/placed in the background or % when a new file is opened. % % There may be times when you need to abort the active CAS session. To abort a CAS session that is % idle, simply use the REDUCE "bye" or "quit" command. A new session will be automatically % restarted. To abort a CAS session that is busy, tap the "Abort" button that replaces the % "Settings" button while iCAS is busy. Set the mode to CAS mode using the mode buttons and go % ahead and abort the CAS session using the following example that intentionally invokes a very long % for-loop. for i:=0:10000000 do j:=i; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % BATCH OPERATION % % In addition to the interactive operation that we've just used, iCAS supports batch execution of % entire file contents. That is, iCAS can process the entire contents of the active file either in CAS % mode or Plot mode. To do so, use the special "BATCH" macro keyboard button. Unlike % interactive results which are output at the current cursor location, CAS mode batch execution % results are appended to the end of the file surrounded by "%%% Begin Batch Results" and % "%%% End Batch Results" so they can be easily located with a quick search. % % Plot mode results are of course the creation of plot files. Note that plot files are not % automatically shown when they are generated in batch mode. To view batch generated plot % files, please use the files picker. % % Now, this file contains interactive output from the examples that we've run so if you process this % file in batch mode, it will result in errors. Therefore, please try batch execution using one of the % example files. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % FOR MORE INFORMATION % % We hope that you found this tutorial helpful. You'll find more examples for various areas in the % files picker. You will also find more information in the iCAS FAQ at the following URL. % % http://alsoftiphone.com/iCAS/faq % % Last but not least, if you have any questions or feedback, please don't hesitate to contact us at % support@alsoftiphone.com. You can quickly do so by either tapping the "i" button on the bottom % right corner and then tapping the "Feedback" button or by tapping the "Contact Support" button at % the bottom of the app Settings. % % We hope that you will find iCAS a useful companion for your computation needs. % % Best Regards, % AL Software % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%