If the number of function indices were less than the number of

variable indices for an output selection there could be many more

variables than functions. While an output set assignment would be

possible, determining the output variable index values for a particular

set of function index values would be difficult or impossible. For this

reason it will be required that the output variable type has the same

number of indices as the function type for which it is the output.

 Suppose next that each of the variable indices for an output

variable type does not depend upon a different function index. Then

there must be a function index which does not appear in the output

variable type. The range on this index could be increased until there

are more functions than variables. This would mean that the variable

type could not be the output. Therefore, each of the variable indices

must depend upon a different function index.

 The following restrictions, then, are imposed on the FVIM output

set assignment:

1. A separate variable type must be the output for each function type.

2. The number of indices for an output variable type must be the same as

for the function type for which it is the output.

3. For an output variable type, each variable index must depend upon a

different function index of the function type for which the variable

type is the output.

 An interesting observation about the restrictions imposed on the

output choice is that it is possible to have a set of equations which in

expanded form has an output set assignment, and yet not be able to

assign outputs to the FVIM. As an example, consider the constraint

equation for the sum of the mole fractions in the liquid phase on a