A convenient, compact representation of the structure of a set of

indexed equations is afforded by the "Function-Variable Incidence

Matrix" (FVIM). The FVIM is not a true incidence matrix, and because

of that has some unusual properties. A Function-Variable Incidence

Matrix is a matrix whose rows each correspond to a function type and

whose columns each correspond to a variable type. An element a.. of

an FVIM exists if the variable type corresponding to j occurs in the

function type corresponding to i, otherwise the element does not exist.

An element which exists does not assume a value in the conventional

sense. Instead, the element assumes the names of the variable indices

which correspond to that variable type's incidence in the appropriate

function type. As an example consider the following set of equations:

 f = 0 = x +x -y. +y 2-4
 1112 i1-1,i2 1ii2 112 t1-2+1

 g = 0 = x. +y -y
 gil1i 112 i li 2 +1,1i2

The Function-Variable Incidence Matrix would be:

 x y



 g(il,i2) 3?j4 1 324




 it
 __-- I

where I iL-1 J2: il h3" O

 iL i]+!

 J4: i2 Js: i2

 i +2

 In the position corresponding to function type f and variable type x

 is the element jij4. From the definitions of the variable indices we

 can deduce that in function type f we would find variables x. il- 2 or

 more compactly noted, variables x..
 S13 L


I