Chapter 3. The Structural Relation Window

The structural relation window is a new feature introduced in GrafEq 2.04. It displays a flow chart (a treelike, structural representation) for a relation. The window can be brought up by selecting Relation #k (Structure) from the Graph menu, or selecting Structural Window from a Relation menu. The structural window is helpful for understanding, and confirming, operator precedence within a relation. Figure 3.1 shows a structural relation window displaying the relation y=sinx:

Figure 3.1: A structural relation window displaying y=sinx

The structural relation window consists of the following elements:

- a title bar,
- a parameter bar,
- a tree structure field, and
- a tree control bar.

The elements of the structural relation window are explained as follows:

Hint: | A structural relation window’s title bar, parameter bar, and its relation description are synchronized with, or equivalent to, their algebraic relation window counterparts. Custom ticks windows have the same setup for title and parameter bars. Therefore, the corresponding manual sections are equivalent.

Title bar
  The title bar displays the graph title and the relation title followed by the “(Structural)” label, which distinguishes it from the title bar of the algebraic relation window. The relation title can be changed using the parameter bar's title edit box. Figure 3.2 shows the title bar:

  Figure 3.2: The title bar of a structural relation window

Parameter bar
  The parameter bar is for customizing the relation title, starting and stopping graphing, modifying the relation colour, and changing the font size used to display elements of the structural representation. Figure 3.3 shows the parameter bar:

  Figure 3.3: The parameter bar of a structural relation window

  The elements, from left to right, are explained as follows:

  Title edit box
    The title edit box is for changing the relation’s title. Custom titles are useful in demonstrations and for print-outs. The default title, “Relation #1”, is easily changed: click on the title edit box to start editing. The new title will replace the old one in all menus, windows, and buttons that show the relation’s title.

  Active checkbox
    As with the Active checkbox in the algebraic window paramenter bar, the structural relation window’s Active checkbox is for starting and stopping relation plotting in open graph view windows. Clicking on the checkbox, or the checkbox name, toggles between the selected and unselected states. Deselecting the checkbox halts graph plotting and hides the relation from all graph views. Selecting the checkbox resumes graph plotting from where it left off and shows the relation in all graph views.

    Hint: | The Active checkbox is greyed out and unavailable if any constraint of the relation is invalid.

  Colour pop-up menu
    The Colour pop-up menu is for changing the colour used for the relation in graph views. This control is useful for optimizing the clarity of graph views. The colour can be changed by clicking on the Colour box to access the pop-up colour menu, and then selecting the desired colour from the menu. For black-and-white graphs, a Pattern pop-up menu replaces the Colour pop-up menu. Colour computers can display black-and-white graphs. For more information, refer to the colour buddy section of the View Buddy Floating Window chapter.

  Font Size pop-up menu
    The Font Size pop-up menu is for changing the font size used in the tree nodes. This control is useful for presentations via an overhead liquid crystal display (LCD) or large screen television. The font size can be changed by clicking on the Font Size pop-up menu to bring up a list of available font sizes, and then selecting a new size from the menu.

  Hint: | The font size of the structural relation window affects the tree structure field, while the font size of the algebraic window affects the constraint fields. However, the title edit box, Active checkbox, and Colour pop-up menu of corresponding structural and algebraic relation windows are identical, and are synchronized. Changes in one will be reflected in the other. Some controls in the structural relation window’s parameter bar do not change the behaviour or the appearance within the structural window itself. The Active checkbox affects the behaviour (graphing) of graph view windows. The Colour pop-up menu affects the appearance (graph colour) of graph view windows.

Tree structure field
  The tree structure field displays a relation using a tree structure. The tree structure is updated as the relation is entered. Figure 3.4 shows the sequence of tree structures displayed as the relation y=sinx is entered:

  Figure 3.4: The sequence of tree structures displayed as y=sinx is entered

Tree control bar
  The tree control bar is for customizing general attributes of the tree structure field, including node colour and tree structure format. Figure 3.5 shows the tree control bar:

  Figure 3.5: The tree control bar of a structural relation window

  The elements, from left to right, are explained as follows:

  Node Colour pop-up menu
    The node Colour pop-up menu is for changing the colour used to display tree nodes in the structural window. This control is useful for optimizing the clarity of the displayed tree structure. The colour can be changed by first clicking on the colour pop-up to bring up the pop-up colour menu, and then selecting the desired colour from the menu.

  Combine Commutative checkbox
    The Combine Commutative option is for combining commutative operations within the tree structure. Clicking on the checkbox toggles between its selected and unselected states.

    Figure 3.6 shows two tree structures for the same relation: The one the left, with the Combine Commutative unselected, shows a full, binary tree structure. The one on the right, with the Combine Commutative selected, shows a flatter tree structure, with commutative operations combined together.

    Binary | n-ary

    Figure 3.6: Alternative tree structure presentations

Conclusion
To conclude this chapter of the manual, following are some additional hints and tips about the structural relation window:

- Each structural relation window describes one relation; the relation can consist of a single constraint, or have multiple constraints. Constraints are linked together using an “and” operation.
- A structural window can be brought up by selecting Relation #n (Structure) from the Graph menu.
- Each structural relation window is associated with an algebraic window, and both describe the same relation. Corresponding structural and algebraic windows are synchronized, so common attributes describing the relation can be changed in either window, and are reflected in both. Common attributes include the relation title, graphing activity, and relation colour. For details about the algebraic window, see the Algebraic Relation Window chapter.
- A relation’s structural window, algebraic window, and easy button floating window can be shown or hidden by selecting or deselecting the appropriate option from a Relation menu. A Relation menu appears only when an algebraic or structural relation window is foremost.

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