Intersecting two classical groups

A new algorithm is presented to compute the algebra of adjoints associated to a pair of forms on a common finite vector space. This algebra is used in several recent and ongoing projects to study central products, intersections of classical groups, and automorphism groups. The implementation of the new algorithms in Magma greatly outperforms its predecessor and hence, in restricted yet important settings, increases the practicality of the various algorithms that use adjoint algebras.