f. = x. +x.-x 2-3
 S1i-2 1 1+1
The variable indices for this function cannot be expressed as an index

range depending on the function index. In order to describe the index

relationships in an equation of this type, we use a list. The variable

index list is a list of offsets from the function index value; it has

arbitrary length. The variable index list for equation 2-3 would have

length 3 and would be:

 j: ii-2


 il-


There is some overlap between index lists and ranges. For example,

either a list or a range can be used to describe the tri-diagonal

relationship in equation 2-2. The index list and range provide for a

structural description of a wide range of indexed functions, and in

particular seem to describe any which are likely to occur in modeling

any chemical process.


2.2 Function-Variable Incidence Matrices

 Since the incidence matrix is widely used to display structural

 information about a set of equations, it would be desirable to be able

 to represent a set of indexed equations in an incidence matrix.

 Unfortunately, for a typical problem such as a 20 stage, 4 component

 distillation column the number of rows would be 180 and the number of

 columns would be even greater. Incidence matrices of this size make

 analysis by hand time consuming and error prone. Even computer analysis

 becomes expensive, especially when much larger problems are encountered.