Book: generalize input columns to expressions in lookup argument.

Signed-off-by: Daira Hopwood <daira@jacaranda.org>

book/src/concepts/arithmetization.md

@@ -30,8 +30,8 @@ A UPA circuit depends on a ***configuration***:
   another row relative to this one (with wrap-around, i.e. taken modulo $n$). The maximum
   degree of each polynomial is given by the polynomial degree bound.
 
-* A sequence of ***lookup arguments*** defined over tuples of ***input columns*** and
-  ***table columns***.
+* A sequence of ***lookup arguments*** defined over tuples of ***input expressions***
+  (which are multivariate polynomials as above) and ***table columns***.
 
 A UPA circuit also defines:
 

book/src/design/proving-system/lookup.md

@@ -89,6 +89,9 @@ ways:
   - The commitments to the columns of $S$ can be precomputed, then combined cheaply once
     the challenge is known by taking advantage of the homomorphic property of Pedersen
     commitments.
+  - The columns of $A$ can be given as arbitrary polynomial expressions using relative
+    references. These will be substituted into the product column constraint, subject to
+    the maximum degree bound. This potentially saves one or more advice columns.
 - Then, a lookup argument for an arbitrary-width relation can be implemented in terms of a
   subset argument, i.e. to constrain $\mathcal{R}(x, y, ...)$ in each row, consider
   $\mathcal{R}$ as a set of tuples $S$ (using the method of the previous point), and check