Can someone please tell me why it is impossible to solve the following
system of boolean equations in SAGE:
sage: N=144
sage: P = BooleanPolynomialRing(N,'x',order='lex')
sage: t = []
sage: for i in range(0,N):
t.append(var(P.gen(i)))
sage: print "t",t
t [x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,
x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28,
x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42,
x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56,
x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70,
x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84,
x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98,
x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110,
x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121,
x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132,
x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143]
sage: e = [x20 + x15 + 1, x21 + x15 + 1, x28 + x15, x29 + x15, x63 +
x31 + x15, x63 + x36, x63 + x37, x63 + x39 + 1, x63 + x44 + 1, x63 +
x45 + 1, x63 + x46 + 1, x79 + x47 + 1, x79 + x20 + 1, x79 + x21 + 1,
x79 + x28, x79 + x29, x95 + x79 + x31 + 1, x36 + 1, x37 + 1, x95 +
x39, x44, x45, x95 + x46, x95 + x47 + x111]
sage: e
[x20 + x15 + 1,
x21 + x15 + 1,
x28 + x15,
x29 + x15,
x63 + x31 + x15,
x63 + x36,
x63 + x37,
x63 + x39 + 1,
x63 + x44 + 1,
x63 + x45 + 1,
x63 + x46 + 1,
x79 + x47 + 1,
x79 + x20 + 1,
x79 + x21 + 1,
x79 + x28,
x79 + x29,
x95 + x79 + x31 + 1,
x36 + 1,
x37 + 1,
x95 + x39,
x44,
x45,
x95 + x46,
x95 + x47 + x111]
sage: v = [x20, x21, x28, x29, x15, x63, x31, x36, x37, x39, x44, x45,
x46, x47, x79, x95, x111]
sage: s = solve(e,v)
sage-3.1.2/local/lib/python2.5/site-packages/sage/calculus/
equations.py in solve(f, *args, **kwds)
1431 s = m.solve(variables)
1432 except:
-> 1433 raise ValueError, "Unable to solve %s for %s"%(f,
args)
1434 a = repr(s)
1435 sol_list = string_to_list_of_solutions(a)
ValueError: Unable to solve [x20 + x15 + 1, x21 + x15 + 1, x28 + x15,
x29 + x15, x63 + x31 + x15, x63 + x36, x63 + x37, x63 + x39 + 1, x63 +
x44 + 1, x63 + x45 + 1, x63 + x46 + 1, x79 + x47 + 1, x79 + x20 + 1,
x79 + x21 + 1, x79 + x28, x79 + x29, x95 + x79 + x31 + 1, x36 + 1, x37
+ 1, x95 + x39, x44, x45, x95 + x46, x95 + x47 + x111] for ([x20, x21,
x28, x29, x15, x63, x31, x36, x37, x39, x44, x45, x46, x47, x79, x95,
x111],)
Thanks for your help!
Regards,
vpv
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