5f892713c3 2021-03-03 1: %%%%%%%%%%%%%%%%%%%%%%
5f892713c3 2021-03-03 2: % WELCOME TO iCAS
5f892713c3 2021-03-03 3: %
5f892713c3 2021-03-03 4: % The core of iCAS is based on REDUCE, a
5f892713c3 2021-03-03 5: % powerful CAS system with comparable
5f892713c3 2021-03-03 6: % capabilities to Maple and Mathematica
5f892713c3 2021-03-03 7: % with a track record spanning over 40 years
5f892713c3 2021-03-03 8: % in academic and research institutions.
5f892713c3 2021-03-03 9: % iCAS brings all the capabilities of
5f892713c3 2021-03-03 10: % REDUCE and the embedded gnuplot
5f892713c3 2021-03-03 11: % plotting engine to your iPhone or iPod
5f892713c3 2021-03-03 12: % touch.
5f892713c3 2021-03-03 13: %
5f892713c3 2021-03-03 14: % Best of all, iCAS is entirely self-contained
5f892713c3 2021-03-03 15: % and runs natively on your iPhone or iPod
5f892713c3 2021-03-03 16: % touch so no internet connection is required
5f892713c3 2021-03-03 17: % to harness its power.
5f892713c3 2021-03-03 18: %
5f892713c3 2021-03-03 19: % This file is written as a short tutorial
5f892713c3 2021-03-03 20: % to walk you through some simple examples
5f892713c3 2021-03-03 21: % to become familiar with the app and help
5f892713c3 2021-03-03 22: % you get started.
5f892713c3 2021-03-03 23: %
5f892713c3 2021-03-03 24: %%%%%%%%%%%%%%%%%%%%%%
5f892713c3 2021-03-03 25: % BASIC USAGE
5f892713c3 2021-03-03 26: %
5f892713c3 2021-03-03 27: % Enter the desired command or operation
5f892713c3 2021-03-03 28: % and press return to execute the command or
5f892713c3 2021-03-03 29: % operation. Try it by tapping to the right of
5f892713c3 2021-03-03 30: % the semicolon on the line below and then
5f892713c3 2021-03-03 31: % tapping return.
5f892713c3 2021-03-03 32:
5f892713c3 2021-03-03 33: 6 * 7;
5f892713c3 2021-03-03 34:
5f892713c3 2021-03-03 35: % If fancy output is enabled, the results can be
5f892713c3 2021-03-03 36: % viewed in a typeset format by tapping a
5f892713c3 2021-03-03 37: % translucent button that appears on the upper
5f892713c3 2021-03-03 38: % right hand corner of this view when there is
5f892713c3 2021-03-03 39: % fancy output or when iCAS detects LaTeX
5f892713c3 2021-03-03 40: % content. The output view can be zoomed
5f892713c3 2021-03-03 41: % using the standard pinch gestures.
5f892713c3 2021-03-03 42: %
5f892713c3 2021-03-03 43: % Fancy output can be globally enabled with
5f892713c3 2021-03-03 44: % the "Create Fancy Output" setting or on a
5f892713c3 2021-03-03 45: % case by case basis using the fancy switch.
5f892713c3 2021-03-03 46: % If fancy output is enabled and the
5f892713c3 2021-03-03 47: % "Automatically Show" option is enabled,
5f892713c3 2021-03-03 48: % iCAS will automatically show the rendered
5f892713c3 2021-03-03 49: % fancy output when it is generated.
5f892713c3 2021-03-03 50: %
5f892713c3 2021-03-03 51: % Execute the following lines (i.e. place the
5f892713c3 2021-03-03 52: % cursor to the right of the semicolon and tap
5f892713c3 2021-03-03 53: % the return key) to see the difference
5f892713c3 2021-03-03 54: % between plain and fancy output.
5f892713c3 2021-03-03 55:
5f892713c3 2021-03-03 56: df(x^x,x);
5f892713c3 2021-03-03 57: on fancy;
5f892713c3 2021-03-03 58: df(x^x,x);
5f892713c3 2021-03-03 59:
5f892713c3 2021-03-03 60: % Notice the pseudo-LaTeX output format
5f892713c3 2021-03-03 61: % and the "TeX" translucent button that
5f892713c3 2021-03-03 62: % appeared on the top right of the window.
5f892713c3 2021-03-03 63: % Tapping the "TeX" button generates a
5f892713c3 2021-03-03 64: % typeset version of the file that can be
5f892713c3 2021-03-03 65: % optionally emailed as a LaTeX source file
5f892713c3 2021-03-03 66: % for publishing, presentation, and/or sharing
5f892713c3 2021-03-03 67: % with colleagues.
5f892713c3 2021-03-03 68: %
5f892713c3 2021-03-03 69: % Fancy output works best with a line length
5f892713c3 2021-03-03 70: % of 80 or more. iCAS sets the linelength to
5f892713c3 2021-03-03 71: % the optimal width for plain output when a
5f892713c3 2021-03-03 72: % CAS session is started based on the font
5f892713c3 2021-03-03 73: % style and size settings. Therefore, we
5f892713c3 2021-03-03 74: % recommend setting the linelength to 80
5f892713c3 2021-03-03 75: % when using fancy output. iCAS provides a
5f892713c3 2021-03-03 76: % convenience command called fancy_output
5f892713c3 2021-03-03 77: % that sets the fancy switch and sets the
5f892713c3 2021-03-03 78: % linelength to 80 characters. Note that
5f892713c3 2021-03-03 79: % turning the fancy switch off does not
5f892713c3 2021-03-03 80: % affect the linelength so you may need to
5f892713c3 2021-03-03 81: % set the linelength to an appropriate value
5f892713c3 2021-03-03 82: % after using fancy output. The linelength
5f892713c3 2021-03-03 83: % is reset when a new CAS session is
5f892713c3 2021-03-03 84: % initiated (e.g. by using either the "bye"
5f892713c3 2021-03-03 85: % or "quit" command).
5f892713c3 2021-03-03 86: %
5f892713c3 2021-03-03 87: %%%%%%%%%%%%%%%%%%%%%%
5f892713c3 2021-03-03 88: % KEYBOARD USAGE
5f892713c3 2021-03-03 89: %
5f892713c3 2021-03-03 90: % By default, iCAS uses the system keyboard.
5f892713c3 2021-03-03 91: % A user configurable macro keyboard and a
5f892713c3 2021-03-03 92: % numerical keyboard are also optionally
5f892713c3 2021-03-03 93: % available. The enabled keyboards and the
5f892713c3 2021-03-03 94: % default keyboard can be configured in the
5f892713c3 2021-03-03 95: % app Settings. The app Settings can be
5f892713c3 2021-03-03 96: % accessed either through the global Settings
5f892713c3 2021-03-03 97: % app or by tapping the Settings button on
5f892713c3 2021-03-03 98: % the top right corner of the screen.
5f892713c3 2021-03-03 99: %
5f892713c3 2021-03-03 100: % To switch between the enabled keyboards,
5f892713c3 2021-03-03 101: % use a horizontal swipe gesture in the text
5f892713c3 2021-03-03 102: % area when a keyboard is active.
5f892713c3 2021-03-03 103: %
5f892713c3 2021-03-03 104: % To dismiss the keyboard, tap the center of
5f892713c3 2021-03-03 105: % the top bar where "Welcome" is currently
5f892713c3 2021-03-03 106: % displayed) or tap the "dismiss" keyboard
5f892713c3 2021-03-03 107: % button above the keyboard if the "Arrow
5f892713c3 2021-03-03 108: % Keys" setting is enabled. This restores
5f892713c3 2021-03-03 109: % access to the toolbar butons.
5f892713c3 2021-03-03 110: %
5f892713c3 2021-03-03 111: % By default, tapping a button other than
5f892713c3 2021-03-03 112: % the "CLEAR" or "BATCH" buttons on the
5f892713c3 2021-03-03 113: % macro keyboard causes the active keyboard
5f892713c3 2021-03-03 114: % to automatically switch to the system
5f892713c3 2021-03-03 115: % keyboard to allow entry of variables,
5f892713c3 2021-03-03 116: % parameters, arguments, etc. This behavior
5f892713c3 2021-03-03 117: % can be enabled/disabled using the "Auto
5f892713c3 2021-03-03 118: % Hide Macros" setting.
5f892713c3 2021-03-03 119: %
5f892713c3 2021-03-03 120: % Tap the clear line below to active the
5f892713c3 2021-03-03 121: % keyboard and swipe from right to left to
5f892713c3 2021-03-03 122: % reveal the macro keyboard. Now tap the
5f892713c3 2021-03-03 123: % "integral" button.
5f892713c3 2021-03-03 124:
5f892713c3 2021-03-03 125:
5f892713c3 2021-03-03 126:
5f892713c3 2021-03-03 127: % Now double tap "function" and replace it
5f892713c3 2021-03-03 128: % with some function of x, say x, to keep it
5f892713c3 2021-03-03 129: % quick and simple. Then execute the line.
5f892713c3 2021-03-03 130: % Unless you've disabled fancy output, iCAS
5f892713c3 2021-03-03 131: % will have output a pseudo-LaTeX output
5f892713c3 2021-03-03 132: % that you can view by tapping the "TeX"
5f892713c3 2021-03-03 133: % button at the top right. Go ahead and tap it
5f892713c3 2021-03-03 134: % to see the output in the LaTeX viewer.
5f892713c3 2021-03-03 135: %
5f892713c3 2021-03-03 136: % Tapping return on the system keyboard
5f892713c3 2021-03-03 137: % can be configured to automatically switch
5f892713c3 2021-03-03 138: % to the macro keyboard to enable the entry
5f892713c3 2021-03-03 139: % of other CAS commands. This is controlled
5f892713c3 2021-03-03 140: % by the "Return Shows Macros" setting.
5f892713c3 2021-03-03 141: %
5f892713c3 2021-03-03 142: % To edit the contents of a macro button, tap
5f892713c3 2021-03-03 143: % and hold down the button for 1 second or
5f892713c3 2021-03-03 144: % longer.
5f892713c3 2021-03-03 145: %
5f892713c3 2021-03-03 146: % Instances of \n in macros get automatically
5f892713c3 2021-03-03 147: % converted into new lines. This makes it
5f892713c3 2021-03-03 148: % possible to create macros with text
5f892713c3 2021-03-03 149: % spanning multiple lines.
5f892713c3 2021-03-03 150: %
5f892713c3 2021-03-03 151: % Assigning \r to a macro button turns that
5f892713c3 2021-03-03 152: % button into a silent return key. That is,
5f892713c3 2021-03-03 153: % it inserts a new line character without
5f892713c3 2021-03-03 154: % processing the contents of the line.
5f892713c3 2021-03-03 155: %
5f892713c3 2021-03-03 156: % Assigning \b to a macro button turns that
5f892713c3 2021-03-03 157: % button into a backspace/delete key.
5f892713c3 2021-03-03 158: %
5f892713c3 2021-03-03 159: % Assigning \c to a macro button turns that
5f892713c3 2021-03-03 160: % button into a clear key.
5f892713c3 2021-03-03 161: %
5f892713c3 2021-03-03 162: % Assigning \cb to a macro button turns that
5f892713c3 2021-03-03 163: % button into a clear batch output key. The
5f892713c3 2021-03-03 164: % macro has no effect if there is no batch
5f892713c3 2021-03-03 165: % output.
5f892713c3 2021-03-03 166: %
5f892713c3 2021-03-03 167: % The cursor placement within a macro can be
5f892713c3 2021-03-03 168: % optionally specified by including \^ in
5f892713c3 2021-03-03 169: % the macro where the cursor should be after
5f892713c3 2021-03-03 170: % the macro is inserted. For example, the
5f892713c3 2021-03-03 171: % macro “(\^)” will cause the cursor to be
5f892713c3 2021-03-03 172: % placed between the two parentheses.
5f892713c3 2021-03-03 173: %
5f892713c3 2021-03-03 174: % The macro buttons can be optionally
5f892713c3 2021-03-03 175: % labelled by including the desired label
5f892713c3 2021-03-03 176: % surrounded by the # character in the macro
5f892713c3 2021-03-03 177: % text. For example, if a macro contains
5f892713c3 2021-03-03 178: % #LABEL# in its definition, the button will
5f892713c3 2021-03-03 179: % display LABEL in a larger font instead of
5f892713c3 2021-03-03 180: % the actual contents of the macro.
5f892713c3 2021-03-03 181: %
5f892713c3 2021-03-03 182: % The following labels (in uppercase) are
5f892713c3 2021-03-03 183: % automatically displayed with the
5f892713c3 2021-03-03 184: % mathematical symbol for the corresponding
5f892713c3 2021-03-03 185: % CAS operator/constant: DF, E, I,
5f892713c3 2021-03-03 186: % INFINITY, INT, PI, PROD, and SUM.
5f892713c3 2021-03-03 187: %
5f892713c3 2021-03-03 188: % The default integral, derivative, pi, and
5f892713c3 2021-03-03 189: % infinity buttons are examples that utilize
5f892713c3 2021-03-03 190: % these features.
5f892713c3 2021-03-03 191: %
5f892713c3 2021-03-03 192: %%%%%%%%%%%%%%%%%%%%%%
5f892713c3 2021-03-03 193: % PLOTTING
5f892713c3 2021-03-03 194: %
5f892713c3 2021-03-03 195: % iCAS includes a full implementation of
5f892713c3 2021-03-03 196: % gnuplot that can be accessed in CAS mode
5f892713c3 2021-03-03 197: % using the gnuplot package or directly in
5f892713c3 2021-03-03 198: % plot mode (more on modes later). By
5f892713c3 2021-03-03 199: % default, iCAS loads the gnuplot package so
5f892713c3 2021-03-03 200: % unless you changed the "Always Load
5f892713c3 2021-03-03 201: % gnuplot" setting, it should already be
5f892713c3 2021-03-03 202: % loaded.
5f892713c3 2021-03-03 203: %
5f892713c3 2021-03-03 204: % By default, iCAS automatically shows
5f892713c3 2021-03-03 205: % newly generated or updated plots. This
5f892713c3 2021-03-03 206: % behavior can be disabled in the global
5f892713c3 2021-03-03 207: % settings.
5f892713c3 2021-03-03 208: %
5f892713c3 2021-03-03 209: % Plots can be magnified using the standard
5f892713c3 2021-03-03 210: % pinch gestures. iCAS supports landscape
5f892713c3 2021-03-03 211: % orientations in all its views so plots can be
5f892713c3 2021-03-03 212: % viewed in either portrait or landscape
5f892713c3 2021-03-03 213: % orientations. Execute the line below to
5f892713c3 2021-03-03 214: % see plotting in action and use the pinch
5f892713c3 2021-03-03 215: % gesture to zoom in/out and swipe gestures
5f892713c3 2021-03-03 216: % to pan around the plot while zoomed in.
5f892713c3 2021-03-03 217:
5f892713c3 2021-03-03 218: plot(sin(x));
5f892713c3 2021-03-03 219:
5f892713c3 2021-03-03 220: % Unless specified, iCAS uses the title "iCAS
5f892713c3 2021-03-03 221: % Plot" and the file name "CASPlot" for plot
5f892713c3 2021-03-03 222: % files. The default plot title can be changed
5f892713c3 2021-03-03 223: % in the app Settings and can also be set
5f892713c3 2021-03-03 224: % on a per plot basis. Execute the below line
5f892713c3 2021-03-03 225: % to see an example.
5f892713c3 2021-03-03 226:
5f892713c3 2021-03-03 227: plot(cos(x), title="cos(x)", output="cos(x)");
5f892713c3 2021-03-03 228:
5f892713c3 2021-03-03 229: % Plot files can be accessed by tapping the
5f892713c3 2021-03-03 230: % "folder" button on the right side of the
5f892713c3 2021-03-03 231: % bottom toolbar. Go ahead and dismiss the
5f892713c3 2021-03-03 232: % keyboard (tap "Welcome" above) and tap
5f892713c3 2021-03-03 233: % the button now.
5f892713c3 2021-03-03 234: %
5f892713c3 2021-03-03 235: % The files organizer picker has four wheels.
5f892713c3 2021-03-03 236: % One for text files such as this one, one for
5f892713c3 2021-03-03 237: % plot files, one for REDUCE inout files, and
5f892713c3 2021-03-03 238: % one for macro keyboard files. Aim the left
5f892713c3 2021-03-03 239: % picker wheel to view the corresponding
5f892713c3 2021-03-03 240: % files. Files can be deleted, emailed, or
5f892713c3 2021-03-03 241: % viewed/selected with the buttons above the
5f892713c3 2021-03-03 242: % picker wheels.
5f892713c3 2021-03-03 243: %
5f892713c3 2021-03-03 244: % The displayed contents can be emailed,
5f892713c3 2021-03-03 245: % copied, or printed by tapping the "send"
5f892713c3 2021-03-03 246: % button button on the right side of the bottom
5f892713c3 2021-03-03 247: % toolbar. Text files are emailed using the
5f892713c3 2021-03-03 248: % active font style. The ont style, font size,
5f892713c3 2021-03-03 249: % and colors can be configured using the styles
5f892713c3 2021-03-03 250: % panel revealed by tapping the "styles" button
5f892713c3 2021-03-03 251: % on the left of the bottom toolbar. The
5f892713c3 2021-03-03 252: % available font styles are "Helvetica",
5f892713c3 2021-03-03 253: % "Times", and "Courier". Although not the
5f892713c3 2021-03-03 254: % prettiest, Courier can be optimal as it is
5f892713c3 2021-03-03 255: % the closest to a monospace font on iOS
5f892713c3 2021-03-03 256: % devices.
5f892713c3 2021-03-03 257: %
5f892713c3 2021-03-03 258: % Plots can be emailed in SVG format which
5f892713c3 2021-03-03 259: % is a resolution independent format
5f892713c3 2021-03-03 260: % supported by major browsers including
5f892713c3 2021-03-03 261: % Safari and FireFox.
5f892713c3 2021-03-03 262: %
5f892713c3 2021-03-03 263: %%%%%%%%%%%%%%%%%%%%%%
5f892713c3 2021-03-03 264: % OPERATION MODES
5f892713c3 2021-03-03 265: %
5f892713c3 2021-03-03 266: % iCAS supports three operation modes.
5f892713c3 2021-03-03 267: %
5f892713c3 2021-03-03 268: % • CAS Mode
5f892713c3 2021-03-03 269: % • Plot Mode
5f892713c3 2021-03-03 270: % • Text Editor Mode
5f892713c3 2021-03-03 271: %
5f892713c3 2021-03-03 272: % By default, the application's color theme
5f892713c3 2021-03-03 273: % changes to indicate the active mode. This
5f892713c3 2021-03-03 274: % color feedback behavior can be disabled in
5f892713c3 2021-03-03 275: % the app Settings, if desired.
5f892713c3 2021-03-03 276: %
5f892713c3 2021-03-03 277: % In CAS mode (the current mode unless
5f892713c3 2021-03-03 278: % you've changed the mode with the mode
5f892713c3 2021-03-03 279: % controls switch in the middle of the
5f892713c3 2021-03-03 280: % toolbar), iCAS behaves as a terminal
5f892713c3 2021-03-03 281: % interface to the CAS engine.
5f892713c3 2021-03-03 282: %
5f892713c3 2021-03-03 283: % In Plot mode, iCAS behaves as a direct
5f892713c3 2021-03-03 284: % terminal interface to the gnuplot engine.
5f892713c3 2021-03-03 285: % Go ahead and dismiss the keyboard and tap
5f892713c3 2021-03-03 286: % the "plot" mode button (the button with a
5f892713c3 2021-03-03 287: % graph) to switch to Plot mode. Then
5f892713c3 2021-03-03 288: % execute each of the following lines in
5f892713c3 2021-03-03 289: % sequence. This is an example straight from
5f892713c3 2021-03-03 290: % the gnuplot demonstration samples web
5f892713c3 2021-03-03 291: % page.
5f892713c3 2021-03-03 292:
5f892713c3 2021-03-03 293: set output "3D Log"
5f892713c3 2021-03-03 294: set title "3D Log"
5f892713c3 2021-03-03 295: set samples 30; set isosamples 30
5f892713c3 2021-03-03 296: set hidden3d
5f892713c3 2021-03-03 297: set pm3d
5f892713c3 2021-03-03 298: set surface
5f892713c3 2021-03-03 299: set view 50,220
5f892713c3 2021-03-03 300: set xrange [-2:2]
5f892713c3 2021-03-03 301: set yrange [-2:2]
5f892713c3 2021-03-03 302: splot log(x*x*y*y)
5f892713c3 2021-03-03 303:
5f892713c3 2021-03-03 304: % As you can see, iCAS accepts gnuplot
5f892713c3 2021-03-03 305: % commands directly.
5f892713c3 2021-03-03 306: %
5f892713c3 2021-03-03 307: % In Text Editor mode, iCAS behaves as a
5f892713c3 2021-03-03 308: % plain text editor. Pressing return does not
5f892713c3 2021-03-03 309: % invoke either CAS or plot operations. This
5f892713c3 2021-03-03 310: % mode is useful for general-purpose text
5f892713c3 2021-03-03 311: % editing, to create input files for batch
5f892713c3 2021-03-03 312: % execution (described below), to
5f892713c3 2021-03-03 313: % create/preview LaTeX documents, etc.
5f892713c3 2021-03-03 314: %
5f892713c3 2021-03-03 315: % The active file is automatically saved when
5f892713c3 2021-03-03 316: % the application is quit/placed in the
5f892713c3 2021-03-03 317: % background or when a new file is opened.
5f892713c3 2021-03-03 318: %
5f892713c3 2021-03-03 319: % There may be times when you need to abort
5f892713c3 2021-03-03 320: % the active CAS session. To abort a CAS
5f892713c3 2021-03-03 321: % session that is idle, simply use the
5f892713c3 2021-03-03 322: % REDUCE "bye" or "quit" command. A
5f892713c3 2021-03-03 323: % new session will be automatically restarted.
5f892713c3 2021-03-03 324: % To abort a CAS session that is busy, tap
5f892713c3 2021-03-03 325: % the "Abort" button that replaces the
5f892713c3 2021-03-03 326: % "Settings" button while iCAS is busy. Set
5f892713c3 2021-03-03 327: % the mode to CAS mode using the mode
5f892713c3 2021-03-03 328: % buttons and go ahead and abort the CAS
5f892713c3 2021-03-03 329: % session using the following example that
5f892713c3 2021-03-03 330: % intentionally invokes a very long for-loop.
5f892713c3 2021-03-03 331:
5f892713c3 2021-03-03 332: for i:=0:10000000 do j:=i;
5f892713c3 2021-03-03 333:
5f892713c3 2021-03-03 334: %%%%%%%%%%%%%%%%%%%%%%
5f892713c3 2021-03-03 335: % BATCH OPERATION
5f892713c3 2021-03-03 336: %
5f892713c3 2021-03-03 337: % In addition to the interactive operation
5f892713c3 2021-03-03 338: % that we've just used, iCAS supports batch
5f892713c3 2021-03-03 339: % execution of entire file contents. That
5f892713c3 2021-03-03 340: % is, iCAS can process the entire contents
5f892713c3 2021-03-03 341: % of the active file either in CAS mode or
5f892713c3 2021-03-03 342: % Plot mode. To do so, use the special
5f892713c3 2021-03-03 343: % "BATCH" macro keyboard button. Unlike
5f892713c3 2021-03-03 344: % interactive results which are output at the
5f892713c3 2021-03-03 345: % current cursor location, CAS mode batch
5f892713c3 2021-03-03 346: % execution results are appended to the end
5f892713c3 2021-03-03 347: % of the file surrounded by "%%% Begin Batch
5f892713c3 2021-03-03 348: % Results" and "%%% End Batch Results" so
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