Welcome_iPad.red

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%                                                      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.
%
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%                                                           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).
%
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%                                                       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.
%
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%                                                               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.
%
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%                                                       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;

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%                                                       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.
%
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%                                                   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
%
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