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.
1 2 
A 

b 

neq 
[ 
nleq 
[ 
variable 

H 

h 

eps 

A list
with the folowing components
A
: the A
corresponding to the system with variables eliminated.
b
: the constant vector corresponding to the resulting system
neq
: the number of equations
H
: The memory matrix storing how each row was derived
h
: The number of variables eliminated from the original system.
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).
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.
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