It should be noted that variable index names cannot be assigned

casually. An example will serve to point out a possible pitfall. The

problem occurs when there is more than one variable index. Consider

the following set of equations:

 f. = 0 = x +x. -y +y 2-5
 1112 11-1,i2 1li2 ,1i2 11,i2+1

One might be tempted to assign four variable index names as follows:

 iJl i-1 j2:' il J3: i2 j4: i2

 i- ii+1 12+1

This, however, does not accurately reflect the structure of the

equations 2-5 for f. does not contain the variables y. Variables
 11i2 j2j4
y j2j include yi. i+y. y ,i2. ,y.i+,i2"1, the second and

third of which do not occur in equation f. This error can be
 1112
avoided by several methods. First note that the problem arose from

attempting to define a single set of variable indices for the variable

y. Since this is not possible in this case, this equation could not

be represented as it is in a Function-Variable Incidence Matrix. By

rewriting the variables y as y and z, this shortcoming can be overcome.

It should be noted that this type of problem is unlikely to occur, and

does not occur in any of the several chemical process models examined

in the course of this work.

 The Function-Variable Incidence Matrix then provides the means

for compactly displaying the structure of a wide variety of sets of

indexed equations and variables. Further, with slight modifications,

virtually all sets of indexed equations and variables can be included.

The FVIM will subsequently be shown to be valuable in effecting a speedy

structural analysis of large sets of indexed equations.