  Studies on time and memory costs of products in geometric algebra have been
limited to cases where multivectors with multiple grades have only non-zero
elements. This allows to design efficient algorithms for a generic purpose;
however, it does not reflect the practical usage of geometric algebra. Indeed,
in applications related to geometry, multivectors are likely to be full
homogeneous, having their non-zero elements over a single grade. In this paper,
we provide a complete computational study on geometric algebra products of two
full homogeneous multivectors, that is, the outer, inner, and geometric
products of two full homogeneous multivectors. We show tight bounds on the
number of the arithmetic operations required for these products. We also show
that algorithms exist that achieve this number of arithmetic operations.
