%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % WELCOME TO i41CX+ CAS % % The core of i41CX+ CAS 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. i41CX+ CAS brings all the capabilities of REDUCE and the embedded gnuplot plotting % engine to your iPad. Best of all, i41CX+ CAS 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 i41CX+ CAS 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 % i41CX+ CAS 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, i41CX+ CAS 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. i41CX+ CAS 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. i41CX+ CAS 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, i41CX+ CAS 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, i41CX+ CAS 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 % % i41CX+ CAS includes a full implementation of gnuplot that can be accessed using the gnuplot % package. By default, i41CX+ CAS loads the gnuplot package so unless you changed the % "Always Load gnuplot" setting, it should already be loaded. % % By default, i41CX+ CAS 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. i41CX+ CAS 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, i41CX+ CAS uses the title "i41CX+ 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 two wheels. One for plot files and one for macro keyboard files. % Aim the left picker wheel to manipulate 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 "share” 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 color scheme can be configured using the corresponding % buttons 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. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % TERMINATING CAS % % 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. To abort a CAS session that is busy, tap % the "Stop" button that replaces the "Done" button while i41CX+ CAS is busy. 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; % To restart a CAS session, use the "CAS" button on the macro keyboard. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % BATCH OPERATION % % In addition to the interactive operation that we've just used, i41CX+ CAS supports batch % execution of entire I41CXED file contents. That is, i41CX+ CAS can process the entire % contents of the active file. To do so, use the special "CAS" macro keyboard button. Unlike % interactive results which are output at the current cursor location, 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. % % 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 disciplines % in the other files. You will also find more information in the CAS section of the i41CX+ FAQ % at the following URL. % % http://alsoftiphone.com/i41CXplus/faq % % Last but not least, if you have any questions or feedback, please don't hesitate to contact us at % support@alsoftiphone.com. % % We hope that you will find i41CX+ CAS a useful companion for your computation needs. % % Best Regards, % AL Software % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%