





                                    !Graph 
     
    Overview 
     
    This Risc OS application produces graphs of mathematical functions. It 
    is fully multitasking and obeys Acorns rules for Risc Os applications. 
     
    It can graph cartesian, parametric and polar functions. 
     
    Axes can be manually set or automatically calculated. 
     
    Multiple graphs of any one type can be produced on the same set of 
    axes. 
     
    Zooming of cartesian functions is possible by using the mouse to 
    define the zoom area. This is useful for solving equations. 
     
    The coordinates of the pointer can be displayed for cartesian and 
    parametric graphs. This is useful for identifying the position of 
    features of interest. 
     
    Functions and axes values can be saved to disc.  
     
    The graphs produced can be saved as a draw file for loading into !draw 
    for enhancement and for exporting to D.T.P. applications. 
     
    Functions are checked for errors before plotting. 
     
    Functions can be entered in true algebraic form. 
     
    A large number of inbuilt functions are provided such as hyperbolic 
    trig functions and a factorial function. 
     
    Operation in degrees or radians. 
     
    The displayed graph will be scaled instantly as the display window is 
    resized. This means that the full graph will be displayed irrespective 
    of the window size. 
     
    Help messages are produced if !help is installed. 
     
     














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    Loading 
     
    The application can be loaded in one of two ways. 
     
    1    Insert and mount the disc. Double click on the !graphs icon. This 
         will install the application on the right of the icon bar. 
         Clicking once with select will cause the graph window to be 
         opened. 
     
    2    Insert and mount the disc. Double click on a graph data file. 
         These can be identified by having f(x)= on their icon. 
         This will cause the application to load and the graph file to be 
         loaded. The graph icon will appear on the icon bar. There will be 
         a pause whilst the functions are evaluated. A window will open 
         and the graphs will be displayed. 
     
    A minimum of 200k must be available to load !graph 
     
    Main menu 
     
    The main menu can be popped up at any time by clicking menu whilst 
    over the graphs window. 
     
    The menu has the following options:- 
     
    1    Save data.  
         This allows the functions and axes ranges to be saved to disc. 
     
         Follow the arrow to the right of the menu. A standard Risc Os 
         save window will appear. Enter the file name in the text box or 
         change the existing name. Then either drag the file icon to a 
         directory viewer or, if a full path name exists in the text box 
         click on OK 
     
    2    Save graph 
         This saves the current graph, as displayed in the graph window, 
         as a draw file for loading into other applications such as !Draw 
         and D.T.P.  The size of the graph saved does not depend upon the 
         window size. It may be rescaled within !draw. 
     
         Follow the arrow to the right of the menu. A standard Risc Os 
         save window will appear. Enter the file name in the text box or 
         change the existing name. Then either drag the file icon to a 
         directory viewer or, if a full path name exists in the text box 
         click on OK 
     
         Files saved in this form cannot be loaded back into !graph. 
     
    3    Coordinates 
         When selected this opens a small window which shows the current 
         coordinates of the tip of the pointer in the coordinate system of 
         the the current axes. This is not available with polar graphs and 
         only operates when the pointer is over the graph window. This may 
         be cancelled either by clicking on the close window icon for the 


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         coordinates window or by selecting it again from the menu. 
     
    4    Axes 
         This causes the axes window to be opened, or brought to the top. 
         The axes window contains information about the current values 
         being used for drawing the graph. It is also used to determine if 
         some of the values are to be calculated automatically. A value 
         may be entered by moving to the box containing a value and 
         entering the new value. 
         Shaded values may not be entered since these will be calculated 
         automatically. 
         Clicking on the Auto Yes/No icon switches between the automatic 
         calculation of axes or the manual entering of all ranges. 
         Minimum values should be less than maximum values otherwise. If 
         they are entered the wrong way around they will be swapped. If 
         they are equal they will be adjusted. Values are given to a 
         maximum of six places of decimals.  
         The automatic calculation of axes values means that 
         re-calculation time is somewhat longer. Automatic calculation may 
         give unpredictable results if the function goes to infinity in 
         the graphed region. 
     
    5    Functions 
         This allows the function which is to be graphed to be entered and 
         edited. 
         The long box is used to enter the function (see the section on 
         functions) 
         The plot option can be set to yes or no. It must be set to yes if 
         the graph is to be displayed.  
         Up to six cartesian and three polar and parametric functions can 
         be entered. Each function is numbered. The function displayed can 
         be changed by clicking on the left or right arrow. The box at the 
         top right indicates in which colour the function will be drawn. 
     
    6    Cartesian 
         This selects cartesian functions and axes. Other types are stored 
         internally. Any present cartesian functions are calculated and 
         displayed. 
     
    7    Polar 
         This selects polar functions and axes. Other types are stored 
         internally. Any present polar functions are calculated and 
         displayed. 
     
    8    Parametric 
         This selects parametric functions and axes. Other types are 
         stored internally. Any present parametric functions are 
         calculated and displayed. 
     
    9    Degrees 
         This selects between degrees and radian angular measure. 
         This may be ticked (to indicate degrees are to be used) or 
         unticked (to indicate the use of radians). Select changes the 
         state of the tick. (Default not ticked) 


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    10   Show axes 
         This selects between displaying and not displaying the axes. When 
         ticked the axes will be displayed. (Default is ticked) 
     
    Redrawing the graphs 
     
    Since the redrawing of a graph takes a little while (depending on the 
    complexity of the graph) the display is only recalculated when 
    required. To force re-calculation press select whist over the graph 
    window. The standard hour glass will be displayed whist re-calculation 
    takes place. Any regions of the graph where the function evaluations 
    are not possible (E.G. square roots of negative values) will result in 
    slower computation.  
     
    Loading a file 
     
    With the application loaded a graph data file may be loaded either 
    by:- 
     
    1    Double clicking on the file in a directory viewer. 
    2    Dragging the file and dropping it on the !graph icon on the icon 
         bar. 
     
    In both cases the graph data file will be loaded and the functions 
    recalculated. Any previous functions will be lost. 
     
     
    Functions 
     
    Cartesian functions are entered in terms of the variable x. 
     
    Polar and parametric functions are entered in terms of the variable t. 
     
    Functions can be entered in true algebraic form.  
    For example  
     
         cos 3x sin 2x  
     
    will be evaluated as (cos(3*x)) * (sin(2*x)) 
     
    If in doubt about the order of evaluation add brackets to force 
    correct evaluation order. Functions may be entered in upper or lower 
    case and spaces are not important. 
     
    Help 
     
    By installing the application !help the program will give relevant 
    help depending upon the position of the mouse. 







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    Operators and functions used 
     
    +         Addition 
    -         Subtraction 
    *         Multiplication 
    /         Division 
     
    ^         is used to raise to a power. EG  x^3 for x cubed. 
    DIV       The integer part of the division eg x DIV 5 
    MOD       The remainder part of the division eg x MOD 5 
    INT       The integer part of the following expression. eg INT x 
    SGN       The sign of the expression. -1 for negative, 0 for zero 1 
              for positive. 
    ABS       The absolute value of the following expression eg ABS x 
    PI        The constant 3.14159265 
    RND       A pseudo random number in the range 0 to 1 
    SQR       The square root of the following expression eg SQR x 
    LN        The natural logarithm of the following expression eg LN x 
    LOG       The logarithm to base ten of the following expression. eg 
              LOG x 
    EXP       e raised to the power of the expression. eg EXP x 
     
    FACT      The factorial of the expression in brackets eg FACT6 
     
    COSH      The hyperbolic cosine of the expression. eg COSHx 
    SINH      The hyperbolic sine of the expression. eg SINHx 
    TANH      The hyperbolic tangent of the expression. eg TANHx 
    ARCCOSH   The inverse hyperbolic cosine of the expression. eg ARCCOSHx 
    ARCSINH   The inverse hyperbolic sine of the expression. eg ARCSINHx 
    ARCTANH   The inverse hyperbolic tangent of the expression. eg 
              ARCTANHx 
     
     
    The following take notice of the degree\radian mode selection.  
     
    SIN       The sine of the expression eg SIN x 
    COS       The cosine of the expression eg COS x 
    TAN       The tangent of the expression eg TAN x 
    ASC       The inverse sine (arc sine) of the expression eg ASC x 
    ACS       The inverse cosine (arc cosine) of the expression eg ACS x 
    ATN       The inverse tangent (arc tangent) of the expression eg ATN x 
     
     
    Zooming 
     
    When cartesian axes are being used it is possible to zoom in on an 
    area. Move to the bottom left of the boundary of the region to be 
    zoomed. Press adjust. 
     
    A bounding box will be drawn from where the pointer is to where the 
    pointer was when adjust was clicked. 
     
    Move to the top right of the area so that the bounding box contains 
    the area to be zoomed. Press adjust again. 


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    The graph will now be re-drawn with the new axes range. 
     
     
    Saving as a sprite 
     
    It is usually preferable to export the graph as a draw file, it may be 
    saved as a sprite by using the grab sprite option on !paint and 
    grabbing the graph from the window. 















































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    Note 
     
    The file type 777 has been used for a graph data file.  
     
     
     
     
    A F Lane 
    3 Lansdowne Gardens 
    Hailsham 
    East Sussex 
    BN27 1LQ 
     
    February 1990 
     









































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