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Examples of ANLDE systems
Here is an example of a typical ANLDE system:
x1 + x2 = 2*x1 + 3*x3
x3 + x4 = x1 + 2*x2 + x3
If you process it with Process ANLDE system feature in the
menu on the left of this page, then you see its Hilbert basis (minimal
solutions), found by the syntactic algorithm:
h1 = (1,1,0,3) and h2 = (0,3,1,6)
The same result is given by
the slopes algorithm
(M.Filgueiras and A.-P.Tomas);
this is an alternative solver, supported by Web-SynDic.
Thus, any solution of this ANLDE system has the form:
x = a*h1 + b*h2
for nonnegative integer a and b
Using the cost function
x1 + x2 + x3 + x4 -> min
one can solve the optimization problem with this cost function and the
considered ANLDE system as constraints and get one particular solution
of the ANLDE system by standard integer programming methods:
x = (1,1,0,3)
The optimal solution is always equal to an element of
the Hilbert basis.
As ILP solver we use
lp_solve
(M.Berkelaar) - another alternative solver, supported by Web-SynDic.
This solver is based on the well-known technique
of simplex algorithm among with branch-and-bound method.
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