MATH7490 HW2 2017.sagews

M = Matroid(groundset=[1,2,3,4,5,6,7], circuit_closures={1: [[1,4]], 2: [[1,2,4,5], [3,5,7]], 3: [[1,2,4,5,3,7,6]]})

M.is_valid()

True

M.show()

/ext/sage/sage-8.0/local/lib/python2.7/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment. warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')

M2 = M.dual()

M2.circuit_closures()

{2: set([frozenset([3, 6, 7])]), 3: set([frozenset([1, 2, 4, 6]), frozenset([2, 3, 5, 6, 7])]), 4: set([frozenset([1, 2, 3, 4, 5, 6, 7])])}