  We present a practical, algebraic method for efficiently calculating the
Yukawa couplings of a large class of heterotic compactifications on Calabi-Yau
three-folds with non-standard embeddings. Our methodology covers all of, though
is not restricted to, the recently classified positive monads over favourable
complete intersection Calabi-Yau three-folds. Since the algorithm is based on
manipulating polynomials it can be easily implemented on a computer. This makes
the automated investigation of Yukawa couplings for large classes of smooth
heterotic compactifications a viable possibility.
