Mathematical Object Forms

In MathScript, each atomic mathematical object has a name and a type. An object name is an alphanumeric sequence, possibly containing underscores, beginning with a letter, and containing no more than 32 characters). These objects may be:

- combined to produce new objects

The results of combination are non-atomic objects. These are called Mathematical Object Forms . For example, sin²+cos² is a form of type function. It can be graphed in the same way that sin, or cos can. Thus graph sin^2+cos^2 would cause the graph of the constant function 1 to be drawn. If x is a variable, then the form sin(x) is a form of type expression. This is not of function type, so graph sin(x) would not work.

- presented in the Display Objects

Vectors may be displayed in Data Window columns, or combined and transformed in those columns as vectors. Or they may be plotted in 2 or 3 dimensional graphics windows.

- read from text fields

The functions: text, textlist, and textstring bring forms into programs from Text Fields. The text function reads the field named in its argument for a mathematical object form. Thus the text must in fact be a meaningful form (and not the Gettysburg Address). Usually a program sets a variable to the result, and works with that. For example,

make u text("input"), or u := text("input") sets the variable u to whatever form appears in the field "input".

If a program wanted to build a function of x using a form of type expression in the variable x that appeared in the field "input" (for example, sin(x^2)+3*x), it might contain the lines

...

let u be text("input");

let f(x) be value u;

...

- transformed in mathematically meaningful ways

For example: equations may be solved, expressions may be differentiated, curves may have coordinate transformations applied to them, and so on.

- compared with one another

Often the comparison is visual, sometimes geometric or algebraic. The richest possibilities of course combine these modes of comparison.

- manipulated by programs

This last is very important. Interactive exploration is powerful, but limited. Often iterative or recursive procedures are needed. For example, they are used in illustrating limits or Fourier Series, or in developing the contours of a strange attractor.