from sage.matroids.advanced import setprint
M=Matroid(groundset='abcdef',circuit_closures={1: ['ab'],4: ['abcde'],6: [
'abcdef']})
setprint(M.circuits())
setprint(M.circuit_closures())
M
M.is_valid()The set 'ab' is a circuit closure with rank 1, therefore it must be a parallel pair. This is confirmed by the fact that the only circuit of M is the set 'ab'. The set 'abcdef' is defined as having rank 6 in the construction of the matroid, therefore it is an independent set. This is plainly contradictory; 'ab' and all its supersets are dependent, but 'abcdef' and all subsets are independent. So there is no matroid with the circuit closures and ranks given. Additionally, M can be seen to have rank 5 by the output of the fourth line. Again, this contradicts the construction. But is_valid returns True. Compare with N=matroid(groundset='abcdef',circuits=['ab']) setprint(N.circuits()) setprint(N.circuit_closures()) N.is_valid() The matroid N returns the same set of circuits, but not the same circuit closures. As a matroid can be defined by either its circuits, or its circuit closures with their ranks, this is again a contradiction; at least one of M & N must not actually be a matroid. Running Sage 6.4.1 on 64-bit Arch Linux, kernel version 3.17.3-1-ARCH. Intel Core i5-4670 quad-core processor. Compiled from source. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
