Complex sentence: The terms "covariant" and "contravariant" were introduced by James Joseph Sylvester in 1853 in the context of algebraic invariant theory, where, for instance, a system of simultaneous equations is contravariant in the variables.
Split into simpler sentences: The terms "covariant" and "contravariant" were introduced by James Joseph Sylvester in 1853 in order to study algebraic invariant theory. In this context, for instance, a system of simultaneous equations is contravariant in the variables.