Chapter 1. The Algebraic Relation Window

The algebraic relation window is for entering the algebraic specification of a relation. One appears automatically at startup, after the title screen is removed. More can be brought up by selecting New Relation from the Graph menu. Figure 1.1 shows a blank algebraic relation window:

Figure 1.1: A blank algebraic relation window

The algebraic relation window consists of the following elements:

- a title bar,
- a parameter bar, and
- some constraint fields.

In addition, an easy button floating window is available for help in relation entry. Easy buttons are especially useful when entering symbols not readily available from the standard keys on a keyboard, such as p, or any powers. For details, refer to the Easy Button Floating Window chapter.

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

Hint: | An algebraic window’s title bar, parameter bar, and relation constraints are synchronized with, or equivalent to, their structural 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 “(Algebraic)” label, which distinguishes it from the title bar of the structural relation window. Relation title can be changed using the parameter bar's title edit box. Figure 1.2 shows the title bar:

  Figure 1.2: The title bar of an algebraic window

Parameter bar
  The parameter bar is for customizing the relation title, starting and stopping graphing, modifying the graph colour, and changing the font size used to display constraints within the algebraic relation window. Figure 1.3 shows the parameter bar:

  Figure 1.3: The parameter bar of an algebraic 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
    The 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 to display relation constraints in the relation window. This control is useful for presentations via an overhead liquid crystal display (LCD) or a large screen television. The font size can be changed by clicking on the Font Size pop-up menu to bring up a menu of available font sizes, and then selecting the desired size from the menu. All constraints of the current algebraic relation window will be displayed in the selected font size.

  Hint: | Some options in the algebraic relation window’s parameter bar do not change the behaviour or the appearance within the algebraic 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.

Constraint fields
  Constraint fields are for entering relation constraints. The constraints entered are displayed in standard mathematics format, which is desirable when including relations in handouts or documents (by copying relations from GrafEq and pasting them into a word processor). The formatted presentation also gives some visual feedback that constraints are interpreted as intended. Figure 1.4 shows a sample relation with two constraints (in two constraint fields):

  Figure 1.4: An algebraic window with two constraint fields
  While a constraint is being entered or changed,
  - prompts appear at the bottom of the constraint field, and the easy button floating window is available to offer support for the specification process;
  - a blinking cursor is present;
  - the Active checkbox of the algebraic window is unselected, and greyed out unless all constraints of the relation are valid;
  - press the Tab key to move to the next constraint, or to create a new one if there is not a next constraint;
  - press the Tab key while holding down the Shift key to move to the previous constraint, or to create a new one if there is not a previous constraint.

  When functions are entered using multiple characters, the characters are unformatted, and presented in red, until GrafEq recognizes them as a function name: red signifies unrecognized entries. GrafEq can interpret “sin” as the sine function, instead of the product “s×i×n”, only after an argument, such as x, is entered. A good example is the square root function, when entered as “sqrt”: GrafEq will replace the letters with a graphical radical symbol after an argument is started.

  Hint: | If the cursor is positioned away from the end of the relation string during editing, all characters to the right side of the cursor become unformatted. With the default preference settings, unformatted characters are shown in solid red on colour displays, while they are outlined in black (not filled in) on black-and-white displays.

  Tip: | The “Symbol” and “Times” TrueType fonts must be installed in order to produce attractive screen output, unless the font settings have been changed in the preferences.

  Tip: | More information on the format and structure of constraints and the parser is available in the How GrafEq Works chapter.

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

- Each algebraic relation window describes one relation; the relation can be defined using a single constraint or multiple constraints. Additional constraint fields can be brought up by pressing the Tab key from within the algebraic relation window.
- Each graph can have one or more relations. Each relation is described in one algebraic window, and is normally assigned a colour different from that of the other relations. Additional algebraic windows can be opened by selecting New Relation from the Graph menu. Relations from the same graph are plotted on the same views, using the same coordinate system.
- New graphs can be opened by selecting New Graph from the File menu. When a new graph is opened, a new algebraic relation window appears automatically. The default graph title is “Graph #k”, where k is a new sequence number. Different graphs are unrelated; to view multiple relations in the same window, multiple relations are created within one graph.
- Besides the algebraic window, each relation may be presented using a tree structure in a structural relation window. Corresponding algebraic and structural windows are synchronized, so common attributes describing the relation can be changed in either window, and are reflected in both. Examples of common attributes include the relation title, graphing activity, and relation colour.
  The tree structure representation in the structural relation window is a new feature introduced in GrafEq 2.04. For details, see the Structural Relation Window chapter.
- The keystrokes field is a strip beneath the current constraint field. It shows the keystrokes used to produce the formatted relation in the constraint field. Keystroke information is especially useful when the intuitive mathematics symbols and notation have no obvious correspondence with the keys on a keyboard. Figure 1.5 shows a sample keystrokes field with its corresponding constraint field:

  Figure 1.5: An algebraic window with its keystroke field
  Prior to version 2.04, GrafEq always provided this information via the keystroke field. But as of GrafEq 2.04, keystroke information can be revealed within the constraint entry fields by positioning the cursor to the left of the entries. The keystroke field is hidden using the default preferences, although it is still available and remains useful for printing purposes. To display the keystrokes field, change the preferences.
- A relation entry can be completed by selecting the Active box of its algebraic window or by pressing the enter key. When relation entries are completed, the algebraic window will collapse to display just the title bar, parameter bar, and constraint fields - prompts, the blinking cursor, the keystroke field, and the easy button floating window will disappear. The Active checkbox will be selected, but it can be freely deselected and selected without editing any constraints.
- Clicking within any constraint field of a completed algebraic window will return you to the edit mode and remove the relation from any opened graph views.

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