  We present a set of generators for the symplectic group which is different
from the well-known set of transvections, from which the chain equivalence for
quadratic forms in characteristic 2 is an immediate result. Based on the chain
equivalences for quadratic forms, both in characteristic 2 and not 2, we
provide chain equivalences for tensor products of quaternion algebras over
fields with no nontrivial 3-fold Pfister forms. The chain equivalence for
biquaternion algebras in characteristic 2 is also obtained in this process,
without any assumption on the base-field.
