Before revision:  These two results stand in sharp contrast to computing the Tutte polynomial of a k-vertex graph (that is, the Tutte polynomial of a graphic {\em  matroid of dimension k---which is representable in dimension k over the binary field so that every vector has exactly two nonzero coordinates), which is known to be computable in 2^k k^{O(1)} time [Bj\"orklund {\em et al. , FOCS 2008].
After revision:  This is in sharp contrast to computing the Tutte polynomial of a k-vertex graph (that is, the Tutte polynomial of a graphic {\em matroid of dimension k---which is representable in dimension k over the binary field so that every vector has exactly two nonzero coordinates), which is known to be computable in 2^k k^{O(1)} time [Bj\"orklund {\em et al. , FOCS 2008].