High-level, user friendly interface that hides the details. (solve a b) should return $X$, from $AX=B$, regardless of whether $A$ is a dense matrix, an $LU$ decomposition, or something else; similarly, $X$ should be a vector/matrix when $B$ is. Users should not need to memorize names like DGESV, especially when CLOS makes it so easy to deal with these things. Also, you don't need to make sure that