Operations, functions and symbols provided by the easy buttons require certain formats, and take varying number of arguments. Most entries are mathematically intuitive. Relation editing windows also provide hints at the bottom of the window view to prompt for the next step of action.

Algebra Easy Buttons

Power Functions	Inverse Power Functions

Figure A.1: Algebra Easy Buttons

The entities x and y within the easy buttons represent expressions that should be entered after the button-click; and the entity a represents arguments that should be entered prior to the button-click. Each button is explained as follows:

• For the a², and a³ buttons, enter an argument first; then click the button;

• For the 10^x, and e^x buttons, click the button first; then enter the power expression (represented by x). The effects can be observed in the relation visual format, the relation tree structure, and the relation graph.
  For example, to enter “e^33.54”,
  1. click the e^x button;
  2. enter the power expression represented by x, which is “33.54” in this example.
  Hint: Parentheses would be necessary for power terms such as x/y, or 2xy, but not if the power is a single simple term.
  Experiment with GrafEq to see the differences when these power terms are entered with, and without parentheses.

• For the a^x button, enter the argument first; then click the button; then enter the power index expression (represented by x).
  For example, to enter “x²+y³=5^2xy”,
  1. enter “x”;
  2. click the a² button;
  3. enter “+y”;
  4. click the a³ button;
  5. enter “=5”;
  6. click the a^x button; and
  7. enter the expression “(2xy)”.
  Hint: The same parenthesis rules apply to a^x, 10^x, and e^x, which means that parentheses are necessary for power terms such as x/y, or 2xy, but not for single simple terms. Experiment!

• For the square-root, log, and ln buttons, click the button first; then enter an argument, which can be a single simple term or a complex term enclosed in appropriate parenthesis.

• For the cube-root button, click the button first; then enter the argument and finish the term with a closing parenthesis.

• For the xth-rooty button, click the button first; then enter the root index expression (represented by x) follow by a comma; then enter an argument expression (represented by y); and finally finish the term with a closing parenthesis.
  For example, to enter “5th root of 2x+y”,
  1. click the xth-rooty button;
  2. enter the root index expression represented by x, which is “5” in this example,
  3. follow by a comma;
  4. enter the argument expression represented by y, which is “2x+y” in this example,
  5. finish term with a closing parenthesis.

• For the log_xy button, click the button first; then enter an expression for the log base (represented by x); followed by the argument expression (represented by y).
  For example, to enter “log₂x”,
  1. click the log_xy button;
  2. enter the logarithm base represented by x, which is “2” in this example;
  3. enter the argument represented by y, which is “x” in this example.
  Hint: Parentheses are not required if the base and the argument are single simple terms or fractions of single simple terms, such as x, y, x/y, 2, 3, or 2/3. Parentheses are necessary for terms such as x+y, 2xy, or for two consecutive numeric terms that would otherwise be treated as one number. Try it out!!

Arithmetic Easy Buttons

Figure A.2: Arithmetic Easy Buttons

The *, -, and / are all infix binary operators (used in between two arguments), while +, -, ± can be either infix binary, or prefix unary (used in front of one argument, which can be a single term or a complex term enclosed in appropriate parentheses).

Basic Easy Buttons

Figure A.3: Basic Easy Buttons

Factoring Easy Buttons

Figure A.4: Factoring Easy Buttons

• For mod, lcm, gcd, and gamma, click the button, then enter arguments.
  Gamma takes one argument, which can be a single term or a complex term enclosed in appropriate parentheses. Mod takes two arguments while lcm and gcd takes two or more, each separated by a comma, and the last one followed by a closing parenthesis.
• For !, enter an argument first, then click the button. The single argument can be a single term or a complex term enclosed in appropriate parentheses.

Greek Easy Buttons

Set a	Set j	Set s
Set A	Set J	Set S

Figure A.5: Greek Easy Buttons - Lower and Uppercase Characters

Integer Easy Buttons

Figure A.6: Integer Easy Buttons

• For both floor and ceiling operations, click the opening button, then enter the argument, then click the closing button. The single argument can be a single term or a complex term enclosed in appropriate parentheses.
• For round, and trunc, click the button first, then enter an arguments.
  The single argument can be a single term or a complex term enclosed in appropriate parentheses.

Measure Easy Buttons

Figure A.7: Measure Easy Buttons

• For |x|, click the button first, then enter an arguments, which can be a single term or a complex term enclosed in appropriate parentheses, then close by clicking the button again.
• For signum, click the button first, then enter an arguments, which can be a single term or a complex term enclosed in appropriate parentheses.
• For angle, click the button first, then enter an arguments, which can be a single term or a complex term enclosed in appropriate parentheses.

Numbers Easy Buttons

Figure A.8: Numbers Easy Buttons

Numbers can be conveniently entered via the computer keyboard; this easy button set is provided for completeness, and is turned off in preferences settings by factory default.

Order Easy Buttons

Figure A.9: Order Easy Buttons

• Click the ordering buttons first, then enter arguments.
  
• Min and max return the minimum and maximum respectively, of specified arguments, and min_x and max_x return the xth smallest and the xth largest respectively, of specified arguments.
• Min and max each takes two or more arguments, each separated by a comma, and the last one followed by a closing parenthesis.
• For min_x and max_x, enter a positive integer base first, then enter an appropriate number of arguments, each separated by a comma, and the last one followed by a closing parenthesis.
  Hint: The number of argument should be equal to or larger than the value of x.

Relational Easy Buttons

Direct Relations	Negated Relations

Figure A.10: Relational Easy Buttons

All relational symbols are infix binary operators(used between two arguments).

Roman Easy Buttons

Set a	Set j	Set s
Set A	Set J	Set S

Figure A.11: Roman Easy Buttons - Lower and Uppercase Characters

Roman characters can be conveniently entered via the computer keyboard; this easy button set is provided for completeness, and is turned off in preferences settings by factory default.

Set Easy Buttons

Figure A.12: Set Easy Buttons

• For braces, brackets, and parentheses, click the opening button, then enter argument(s), then click the closing button to finish.
• Pairs of braces, brackets, and parentheses can all be used to control precedence.
• Pairs of braces can also be used to enclose set elements (with a comma separating every two successive set elements).
• “If” is used within braces for conditional definition, with one or more sets of a value term followed by if, then the condition. “If” should be preceded a space, and followed by a space. A typical example is y={x if x>0, 0 if x=0, -x if x<0}
• “is member” and “is not member” are for set membership definition.
• “,” is required for separating elements or arguments.

Trig Easy Buttons

Circle Functions	Hyperbola Functions	Square Functions	Diamond Functions
Inverse	Inverse	Inverse	Inverse
Circle Functions	Hyperbola Functions	Square Functions	Diamond Functions
Inverse	Inverse	Inverse	Inverse
Circle Relations	Hyperbola Relations	Square Relations	Diamond Relations

Figure A.13: Trig Easy Buttons

All trig operators are prefix binary, to be used in front of one argument which can be a single simple term or a complex term enclosed in appropriate parenthesis.

To conclude this section of the manual, following are some additional hints and tips about the easy button floating window:

• The display of each group of easy buttons in the floating window can be toggled on or off by clicking the triangular arrow adjacent to the corresponding set name.
• Easy button groups altogether with the respective headings can be hidden from the easy button floating window, across sessions, by unselecting the respective “Available” checkboxes from the File Preferences 's Windows - Algebraic Window - Easy Buttons - Access menu. By factory default, all but Measure, Numbers, and Roman buttons are selected, but a smaller selection may be appropriate for a beginners’ class or a special lesson.
• All functions, operations and symbols may also be entered via the keyboard. The key-combinations for special characters and operators are listed in Appendix E, the Keyboard Shortcuts appendix.