Complex sentence: Matroid parity can be solved in polynomial time for linear matroids, but is NP-hard for certain compactly-represented matroids, and requires more than a polynomial number of steps in the matroid oracle model.
Split into simpler sentences: Matroid parity can be solved in polynomial time for linear matroids. However, it is NP-hard for certain compactly-represented matroids, and requires more than a polynomial number of steps in the matroid oracle model.