CHAPTER 4

This chapter discusses several functions useful in crystallography. MAC library supplies these functions for other parts of CCL and CPL. When two functions are said equal to each other, an equation is formed. The condition under which the equation is satisfied is called solution of the equation. Solving equations is a common task. MAC library includes a few types of equations. Both function and equation have their geometric representation. It is often easier to think with some geometric objects in mind or to illustrate on paper. Some of these objects are coded in form of classes in MAC library, and wrapped into Python as module cpl.mac.geo. This chapter offers some more tools for crystallographic programming.

**4.1 Generalized Gaussian Function**

This is a generalized Gaussian function defined as below:

_{},

where
*a*, *b*, *c*, *d*, *e*,
and *f* are parameters. *a*
is the center of the function, or the average; *g*(*a*) = *f*.
*b* is the base of the exponential
expression; and b ยก