these special IDM's are produced by the same method. An IDM for the

function index in question is chosen. The logical "AND" or logical "OR"

of each of the other IDM's (for that function index) and the chosen IDM

is then stored in place of the chosen IDM. By successively operating on

all of the IDM's required, the end result is the logical "AND" or "OR"

of all desired IDM's. The resulting IDM is then available for analysis.

In the case of the logical "AND," if it can be output set assigned, the

result is an output set assignment which can be used for all IDM's

depending on that function index. In the case of the logical "OR," if

an output set can be found to fully precedence order, then the function

index fully precedence orders. When this is the case this function

index should be nested outside those which do not fully precedence

order.

 The output set assignments are made by an algorithm which allows

the incidence matrix elements to have weights and then minimizes (or

maximizes) the sum of the weights of the output elements (Gupta et al.,

1974). In order to fully utilize that capability, weights should be

assigned to the IDM elements. If this is not done an arbitrary output

set is chosen. The weights should be assigned to the elements in a

manner which indicates to the algorithm which are the preferred outputs.

One such possible weighting scheme could be to assign weights to reflect

the non-linearity of an equation in a certain term. For example,

consider the following set of indexed equations:

 f. = 0 = x +2x. 3(lnx -- )+3x 1-4 4-1
 11 1- 11 1 x. il+1
 11
For any value of ii, it would be considerably easier to solve eqn. 4-1

for x. or x.1 than for x This can be reflected in the IDM by
 11-1 11+1 11