Am 24.01.11 07:47, schrieb tvn:
> hi, just wondering if the Fourier-Motzkin algorithm for eliminating
> variable from a system of linear inequalities is implemented somewhere in
> Sage ?
>
Hi,
it shouldn't be too hard to implement Fourier-Motzkin elemimination
yourself. Here is the definition of a function with projects the
Polyhedron P: (A*x<=b) along the vector c. The Fouier-Motzkin
elimination is just the special case with c = e_j (the unit vector with
Komponent j = 1).
Greetings,
Philipp
def proj_Poly(P,c):
A,b = P
m = A.nrows(); M = range(0,m)
n = A.ncols()
N = [i for i in M if A[i,:]*c < 0]
Z = [i for i in M if A[i,:]*c == 0]
P = [i for i in M if A[i,:]*c > 0]
p = Z + [(i,j) for i in N for j in P]
r = len(p)
D = Matrix(r,n); d = Matrix(r,1)
for i in range(0,r):
if not isinstance(p[i],tuple):
D[i,:] = A[p[i],:]
d[i] = b[p[i]]
else:
(s,t) = p[i]
D[i,:] = (A[t,:]*c)*A[s,:] - (A[s,:]*c)*A[t,:]
d[i] = (A[t,:]*c)*b[s] - (A[s,:]*c)*b[t]
return (D,d)
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