Eliminate a variable from a set of edit rules
Description
Eliminating a variable amounts to deriving all (nonredundant) linear (in)equations not containing that variable. Geometrically, it can be interpreted as a projection of the solution space (vectors satisfying all equations) along the eliminated variable's axis.
Usage
1 2 
Arguments
A 

b 

neq 
[ 
nleq 
[ 
variable 

H 

h 

eps 

Value
A list
with the folowing components
A
: theA
corresponding to the system with variables eliminated.b
: the constant vector corresponding to the resulting systemneq
: the number of equationsH
: The memory matrix storing how each row was derivedh
: The number of variables eliminated from the original system.
Details
For equalities Gaussian elimination is applied. If inequalities are involved,
FourierMotzkin elimination is used. In principle, FMelimination can
generate a large number of redundant inequations, especially when applied
recursively. Redundancies can be recognized by recording how new inequations
have been derived from the original set. This is stored in the H
matrix
when multiple variables are to be eliminated (Kohler, 1967).
References
D.A. Kohler (1967) Projections of convex polyhedral sets, Operational Research Center Report , ORC 6729, University of California, Berkely.
H.P. Williams (1986) Fourier's method of linear programming and its dual. American Mathematical Monthly 93, pp 681695.
Examples
1 2 3 4 5 6 7 8 9 10 