123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390 |
- %%%%%%%%%%%%%%%%%%%%%%
- % 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 iPhone or iPod
- % touch.
- %
- % Best of all, iCAS is entirely self-contained
- % and runs natively on your iPhone or iPod
- % touch 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 when 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" setting 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.
- %
- % To dismiss the keyboard, tap the center of
- % the top bar where "Welcome" is currently
- % displayed) or tap the "dismiss" keyboard
- % button above the keyboard if the "Arrow
- % Keys" setting is enabled. This restores
- % access to the toolbar butons.
- %
- % 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# in its definition, 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 app 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
- % bottom toolbar. Go ahead and dismiss the
- % keyboard (tap "Welcome" above) 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, emailed, 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 ont 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 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 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
- %
- %%%%%%%%%%%%%%%%%%%%%%
|