Equation Editor

The Equation Editor is a simple tool that the user can use to customize any transformation to his/her specific needs. Any equation selected in the Specific Function Lists also appears in the Equation Editor, so that a selected equation can be changed in coefficients, exponents, etc.

Top Menu

This windows has its own top menu, although it is a simple one. The top entries are:

Configure

• Configure > Function Lists. This menu brings the preselected functions panel. Double clicking on any function of the panels Transcomplex, 2-Variables, or 1-Variable copy the equations to the Equation Editor.
• Configure > Chalkboards Background > Colors.  This menu brings the Colors palettes so you can change the background of the text boxes where the equations are written. The default color is green.
• Configure > Chalkboards > Font. This menu brings  the Fonts windows. 

Calculator

This menu brings the Calculator. The menu does the same Options > View Calculator

Random Numbers is a simple random numbers generator when using the primitive Rnd(arg).

In addition to the top menu, below the Equation Editor is divided in the following panels:

Equations panel

Whether you use a single-variable function or a two-variables transcomplex function, every graph or surface is always made of two equations. In the case of single variable real functions, one of the equations is always set to 0 (zero). In the case of a two-variables real functions, one of the equations is always set to a single variable, like x or z.

• Allowed variables: letters for variables are the letters x and z. No matter if you have substituted the X-axis with some other label like Ohms, Distance, etc, in the Equation Editor you keep using the letter x for the variable in the axis. Same for the Z-axis. 
• Upper cases are interpreted the same as lowercases. However, you may retain some uppercase letter for better readability. Thus, Sqrt(x) is the same as sqrt(x).
• Fractions: should be written as (1/2), (15/6), etc. No ellipsis for repeating decimals like 0.333....; use the fraction equivalent or round the number.
• Negative signs can be used in front of a variable, like -x^2. If confusion should be arrive when using signs, then use the factor equivalent, like (-1)*x^2.
• Exponents should always be nonnegative integers. For example, x^(-2) should be written as 1/(x^2). Fractional exponents should be expressed as fractions of roots; for example x^(2/3) should be written as (x^2)/(x^3).
• Spaces can be used at will to improve readability. Thus, Abs(x) = Abs( x ).
• Parentheses only are allowed: no square brackets ([ ]), no curly brackets ({ }).
• Math operations: + for addition, - for subtraction, * for multiplication,  / for division, ^ for exponentiation.
• Math constants: Write pi as 3.141593 or rounded, and e as 2.718282 or rounded.
• Function primitives  syntax: follow the built-in syntax or grammar for primitive functions to be incorporated into equations. For example, even when we commonly write the hyperbolic sine of x as sinh(x), the primitive syntax for this is written as Hsin(x), or hsin(x). Another case of possible confusion are the inverses of the trigonometric functions. For example, the inverse of the sin(x) function should be written as ArcSin(x) and not as sin^-1(x). 

Primitives To Be Used (Drag To Above) panel

The Primitives TO Be Used panel works in conjunction with the other panel below of title Primitives.  

Expanded button

A primitive written here by the primitives list below could be have been made of other primitives. For example, the hyperbolic sine is a function mathematically defined as (Exp(arg) - Exp(-arg))/2, however, in the editor is written as Hsin(arg). If the Expanded button is depressed, the user will see the long version of the hyperbolic sine.

Non Expanded button

The user can see the expanded version of a primitive function, however, the Equation Editor accepts only the non expanded version to compute and render graphs.

Primitives List (Select Here)

Primitives are the building blocks of equations. When we state the equation Y = sin (x) * Hcos(z), the primitives are sin(arg) and Hcos(arg). We later substitute the argument arg for a constant, a variable, or another primitive. For example: Y = sin(3.1416 * x) * Hcos(z).

When the user clicks on a function on the Primitives list, this function is immediately copied to the Primitives To Be Used box.

Copying Equations To The Equation Boxes

• Once a primitive is copied to the Primitives To Be Used box, the user can click and drag the equation to the equation boxes.
• Only non-expanded functions can be dragged to the equation boxes.
• Once correctly dragged, the editor warns the user about replacing the argument and the operation involved. The user will see the following error message: Invalid character: ? Two new panels for replacing will open. Click on the appropriate button.
• The user must substitute a variable (x or z) for the parameter arg prior to closing and using the equations for rendering or graphing a function. 

Sort button

This button arranges the primitives list alphabetically to simply the finding of a particular primitive.

 Save New Equations button

Equations edited by the user can be saved for later reference. The saved equations appear in the Favorites panel of the XYZ-Space Sample Functions.

Restore U(x, z), Restore V(x, z) and Restore Both

During an equation editing session, you may want to go back for some particular reason. Use these buttons to accomplish this task.

XYZ-Space Sample Functions

The XYZ-Space Sample functions panel is the place to invoke many predefined function lists like the Transcomplex Functions list, other  real-valued functions, and the Favorites tab, the place where the user stores his/her equations and functions. 

There are 4 useful panels to invoke predefined functions:

Transcomplexs Tab

This is a list of some interesting elementary transcomplex functions like W = Sin(x + iz), W = Cos(x + iz), W = Log(x + iz), etc. For every function in this list the domain is assumed to be complex numbers. When a function in this list is selected two complex parametric equations are copied to the equation editor.

For example, for the transcomplex function W = (x + iz)^2, the parametric equations are: U(x, z) = x^2 - z^2 and V(x, z) = 2xz. The program plots both functions simultaneously resulting in surfaces of unusual shape.

For a short introduction to the Transcomplex Numbers click here.

2-Var Tab

This is a list of functions of two real variables of the type y = f(x, z). For every function in this list, one of the parametric functions, the function V(x,z), is assumed to be the single real variable z. When a function in this list is selected, the resulting surface is a typical figure like those found in math textbooks.

1-Var Tab

This is a list of functions of one real variable of the type y = f(x). For every function in this list the domain is assumed to be the variable z. When a function in this list is selected, one of the parametric functions, the function V(x,z), is assumed to be zero (0). The resulting figure is a line plot.

Favorites Tab

This is a list of the functions that the user have saved in the current or previous sessions.

Since 4DLab always plots with two parametric equations, the Favorites Tab is divided in two windows; the Equation 1 window and the Equation 2 window. Both refer to the same function.

Functions to this list are added via the menu sequence File - Save Equations, or via the button Save New Equations when the user is in the equation editor.

To delete functions in this list, first click the Equation 1 list. Then select the desired function with the right button of the mouse. The warning "Do you want to delete this pair of equations" appear. Confirm with Yes if you want to go ahead with the deletion process, or click No if you want to cancel the delete.

To modify an equation set, select the equation in the Equation 1 window, open the Equation Editor where they were copied, make the adjustments or modifications you wish and save the equations again. Since the program retains the original equations, delete the original function as described above (if you want to only have the latest modification) .