File |
Constants |
Compile |
Create in another variable |
Create array of IVPs |
Clear |
Graph |
Parameters |
Font |
Set n-body problem |
Help |
Demo |
File submenus
New |
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Open |
Open ode file |
Load script |
Load script file |
Open to Connect |
Open one of several connected problems |
Open special points and… |
Differentiate 0 times Differentiate 1 time Differentiate 2 times Assume the conv. radius = radius limit |
Save |
Save ode file |
Save as |
Save ode file |
Save script |
Save script file |
Save to clipboard… |
The path to script file The command line with the scrip file |
Load data |
Load the Results file |
Save data |
Save the Results file |
Save as table |
Save the solution in tabulated form |
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Explanation of other main menu items
Constants |
Inserts popular constants into the section Constants |
Compile |
Initiates compilation of the problem |
Create in another variable |
Creates a connected problem in another independent variable selected by the user |
Create array of IVPs |
Creates a new IVP n times larger than the original one for a set of n initial vectors specified in different manners |
Graph |
Opens the Graph window after successful compilation and specification of the desired trajectories |
Parameters |
Allows to specify: · a new order of differentiation other than the default; · another convergence radius limit; · to display this entire summery of all parameters. |
Font |
To change the font for the four edit windows |
Set n-body problem |
To set the Newtonian n-body problem up to 100 bodies |
Help |
To display help files for various topics |
Demo |
To run preloaded script files described in Help/Samples menu |
The four tabbed pages in the Main window
Equation setting |
Debugging |
Integration setting |
Graph setting |
Contains the four edit controls for entering initial value problems |
Tables containing all variable and their derivatives, and the list of AD instructions for the problem |
Contains all the parameters controlling the manner of integration process |
Contains the table of all variables with the tools to specify the desired trajectories for plotting in the Graph window |
Order of differentiation (default 30) |
Main menu/Parameters or |
Convergence radius upper limit (default 10) |
Main menu/Parameters or |
Direction of the integration |
Forward/Backward radio buttons |
Editing equations, initial values, parameters, method for computing the convergence radius, opening the Polynomial Designer, creation of ODEs in another state variables, creation of an array of IVPs |
Equations setting page |
Specifying method of error control and error tolerances, number of elements to be stored, terminal value (if any), blind integration controls (if compiled successfully) |
Integration setting page |
Specifying trajectories for 2D/3D graphing (if compiled successfully) |
Graph setting page |
Inspecting values of the variables and elements (if compiled successfully) |
Debugging page |
Opening graph window (if compiled successfully) |
Main menu/Graph |
Specifying degrees or radians (in expressions for constants or initial values) applied only in the left panes: the Constants and Initial values.
In the right panes only radians are in use disregarding these radio buttons! |
Degrees/Radians radio buttons |
Specifying how large set of variables to use for obtaining heuristic convergence radius: |
Radio buttons: · Main only · Main and auxiliary (default) · Main, auxiliary, and internal
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Quotient k=h/R (default 0.5) |
Corresponding edit control |
Method of the error control |
Radio buttons · Middle step · Back step · No error control |
Specifying relative or absolute error one by one or for a selection of cells |
Radio buttons · One cell edit or · Multi cell selection |
To continue or not integration process even after maximum number of step splits the error tolerance failed |
Go despite error check box |
Setting an absolute and relative error tolerances |
Corresponding columns in the table |
To specify the Result array of elements anew and how many elements to store |
Edit control in Results array and check box buttons: · Main variables only, plus possibly… · Auxiliary variable also |
Make Result array Circular or appendable |
Check box Circular On. If Check box Circular is Off, array Results is appendable via the button Append |
To visualize the window for specifying massive integration for the predefined set of initial vectors |
Check box Massive computation On |
Restart blind integration from initial values |
Restart button |
Specifying how many steps n must be performed for every click of More button |
Edit control in Integrate panel |
Integrate n steps more |
Button More |
Specifying terminal value (if any) |
Edit control to … |
Applying terminal value |
Check button if Termination is On |
Making current values new initial values |
Button ¬ |
Placing current values into the clipboard file for exporting into another initial value problem |
Button ¯ |
Making clipboard file values new initial values |
Button ¬ |
Copy the entire table into the clipboard |
Button Copy to clipboard |
Pasting a column of initial values from external editor or MS excel |
Button Paste IVP |
Specifying curves to graph |
Table "Select functions to graph" |
To generate automatically all curves corresponding to variables having format x, y, x1, y1, x2, y2, … or x1, y1, z1, x2, y2, z2,… - in 3D |
Button {x1, y1}…>> |
Generating the curves according to the selection and switching to the Graph window |
Button Graph |
An attempt to applying previous boundaries and curves to changed equations |
Button Previous |
Specifying 2D or 3D graphing |
Corresponding radio buttons |
Specifying Red/Blue or Blue/Red glasses for 3D graphing |
Click onto the glass icon |
Specifying whether do display Taylor coefficients of derivatives |
Radio buttons · Taylor coefficients · Derivatives |
Copying the entire table into the clipboard (for Excel) |
Button Copy all |
What do display: either the values at the current point, or the selected analytical elements from the available |
Radio buttons · Current values · Analytical elements |
Visualize the Taylor profile chart for a selected function |
Check box Show Taylor profile |
To see the line which caused exception during compilation in the equations at the Equations page |
Button Look |
To display all AD instructions or only differential AD instructions |
Radio buttons · All instructions · Differential instructions |
File |
Main window |
Sizes |
Switch from t to… |
Swap assignment to axes |
Clear |
Field of directions |
Parameters |
Default colors |
Help |
File submenus
Save image |
Saving one image in a selection of different formats |
Save movie sequence |
Saving a sequence of images for creating a movie |
Load script |
Loads scripts like the respective item in the Main Window |
Save script |
Saves scripts like the respective item in the Main Window |
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Prints the image |
Image info |
Displays the technical info about the image |
Explanation of other main menu items
Main window |
Switches focus to the Main Window bringing it in front |
Sizes |
Provides a tool to quickly set the popular sizes of the graph area |
Switch from t to… |
Provides a tool to switch between different independent variables while integration of a set of connected problems. For example, it allows to switch from integration in respect to t into integration in respect to x, y, …. |
Swap assignment to axes |
Swaps assignments of particular variables to axes OX, OY, (OZ) |
Clear |
Clears the graph area without restarting |
Field of directions |
Provides a tool for plotting advance phase portraits or fields of directions for a selected pair (or triplet) of variables |
Parameters |
Allows to specify parameters for… · 3D scene; · Bullet & curve width; · Density of curves; · Tubular plot; · Font for images; · Grid; · Constrains on form size; · Lines and solid body type; · Since which curve # to plot both curves and bullets (while plotting bullets only for curves prior to this #); · Timer type |
Default colors |
Resetting the default colors for curves |
Setting the boundaries along X , Y (and Z) axes (the 3D cage sizes) |
Corresponding edit controls, then Apply button |
Quick specification of the boundaries for a few standard areas and scaling them |
Menu item Size |
Swapping the assignment of the curves to the coordinate axes: X ↔ Y, X ↔ Z, or Y ↔ Z. |
Menu item Swap axes |
Adjusting the boundaries to accommodate the curves after more steps of integration. (The analytic elements must be stored in Results array specified in the (Integration setting page, Main window) |
Adjust button |
Increasing the boundaries proportionally 1.25 times (zooming out) |
Button "Zoom Out" |
Decreasing the boundaries proportionally 1.25 times (zooming in) |
Button "Zoom In" |
Direction of integration Forward or Backward |
The respective radio buttons |
Resetting integration from initial values (not clearing the graph) |
Restart button |
Specifying how many steps n must be performed on More button click |
The edit control under Integrate… |
Integrate n steps more |
Button More (Space bar) |
"Playing" the motion whose elements were stored |
Button Play |
Specifying the play time (sec) |
The edit control above the Play button |
Perform auto integration in a given time intervals (sec) without clicking button More (or Space bar) |
Check box Auto |
Plotting trajectories as 1 pixel thin curves with no bullets |
Check box Curves and Radio button Thin must be checked |
Plotting trajectories as thick curves |
Check box Curves and Radio button Thick must be checked |
Displaying bullets |
Check box Bullets must be checked |
Displaying m×n grid line on graph field |
Check box Grid |
Changing the number of cells in X and Y of the grid |
Parameters/Grid |
Drawing a field of directions for one of curves |
Menu item Field of directions and · Make (by default), or use · Phase portrait designer |
To add a curve corresponding to the initial values at the mouse click by setting these values as the new initial values, restarting, and integrating the given number of steps forward and backward |
The check box in Plotting IVP at mouse click … must be checked. It changes the default mouse action from dragging curves to picking the clicked coordinates as the initial values. |
Calling the Switch board to switch from one independent variable to another |
Main menu item Switch from t to … |
Specifying bullet size (and thick curve width) |
Menu item Parameters/Bullet & curve width |
Specifying curve density as distance between centers of dots on curve in pixels 0.25 to 5 (where 5 corresponds to a dotted line) |
Menu item Parameters/Curve density |
Rotation of non-planar 3D curves |
Slide controls a and b, or the values in the table under menu Paramters/3D scene |
To control whether the rotation center is at the center of the cage or at the point (Xmin, Ymin, Zmin) |
The nameless check box between the a and b handles: The center of the cage is anchored if the check box is checked |
Axonometric view of 3D curves |
Axonometric radio button |
3D stereo anaglyph view |
Stereo radio button |
Visualize 3D cage of the parallelepiped or the Axes |
Cage On check box Axes On check box |
Display curves as tubular graphics |
Tube On check box |
Adjusting parameters of stereo viewing |
The table under menu Parameters/3D scene |