More flexibility is desired in describing variable indices than

 is available in describing function indices. Variable index sets have

 their possible values defined by a range similar to the function index

 range or by a "list." The variable index range differs from the

 function index range in that its upper and lower limits will be

 permitted to be functions of either the function index value itself or

 the function index range limits. This restriction allows for many

 different arrangements of indexed variables. The equation

 f. = 0 = x. +x -x i=1,2,...10 2-2
 1 i-i" +1
 represented by a tri-diagonal incidence matrix, would have its index

 sets described as:

 i: L = 1 j: L = i-i

 U = 10 U = i+l

 A= 1 A=

 where both the lower and upper limits of the variable index range are

 defined as offsets from the function index value. Other examples of

 variable index ranges are:

 ji: L = L. j2: L ij3: L = L.

 U = U U. U U.
 i 1
 A =1 A = 1 A 1

These; three examples illustrate the other three basic forms of the

variable index range. The first, jil, defines a lower triangular

incidence matrix, the second, j,, defines an upper triangular incidence

matrix, and th third, J3, defines a full incidence mritrix.

 A second means of defining variable indices, the variable index

list, allows even greater flexibility. Suppose we have an indexed

equation of the following form: