transpose codewords only once when proving

[jan-ferdinand]

When evaluating the AIR constraints to compute the quotient codewords, the STARK prover currently treats each table separately. For each table, the table's corresponding trace codewords over the arithmetic domain (see #114) are computed, tansposed, and used as evaluation points on the table's AIR constraints.

Refactor the code such that concatenating all trace codewords and transposing the result can be used for all table's constraints. This probably requires a consistent globally canonical ordering of all tables,¹ globally unique column indices derived from that ordering, and indexing into the transposed codewords using these indices.

Footnotes

1. We probably have that already. To the best of my knowledge, we currently don't rely on its existence. ↩

[jan-ferdinand]

Blocked by #139.