full incidence matrix it is called the "expanded problem."

3.1.7 General Solution Procedure

 Existing algorithms generate a solution procedure for a particular

set of equations. It is the aim of the algorithms here, not only to

treat indexed equation sets, but to generate solution procedures which

are independent of the index limits. A solution procedure which

satisfies this requirement is called a "general solution procedure."

3.1.8 Function Ordering

 There is a natural ordering of function indices. They are either

incremented or decremented in steps of equal size. There is no such

natural ordering for the function types. In fact, the order of the

functions is usually determined from precedence ordering considerations.

The order in which the function types appear in the FVIM is called the

"function ordering." The function ordering can change as the solution

procedure is generated.


3.2 An Example Problem

 Suppose that a solution procedure is desired for this set of

equations:

 f(il,i2) = 0 = f[x(j1,j3),y(jl,ji),z(jl)]
 3-1
 g(il,i2) = 0 = g[x(j2,j4),y(j2,j4),z(j2)]

The decomposed representation of these equations is shown in Fig. 3-Z,

which also defines the indices shown in the equations. To solve these

equations, which may be assumed to be non-linear, a solution procedure

must be specified.

 Suppose the following solution procedure is chosen. Assign x to f

and y to g. Assign the index outputs as shown in the IDM's. Both