User:Inthar/MV3: Difference between revisions
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# ''S'' can be built by stacking alternating generators, resulting in a circle of the form either g1 g2 ... g1 g2 g1 g3 or g1 g2 ... g1 g2 g3. | # ''S'' can be built by stacking alternating generators, resulting in a circle of the form either g1 g2 ... g1 g2 g1 g3 or g1 g2 ... g1 g2 g3. | ||
# ''S'' is generated by two chains of generators separated by a fixed interval; either both chains are of size ''m'', or one chain has size ''m'' and the second has size ''m-1''. | # ''S'' is generated by two chains of generators separated by a fixed interval; either both chains are of size ''m'', or one chain has size ''m'' and the second has size ''m-1''. | ||
=== Definition: QL === | |||
A scale word ''S'' with ''k'' step sizes X_1, ..., X_k (with a_1 X_1's, ..., and a_k X_k's) is ''quantized-line'' (QL) if S, when viewed as a set of instructions tracing a path in Z^k from the origin, results in a path that is a closest approximation to the line [a_1 : a_2 : ... : a_k] intersecting the origin in R^k. | |||
=== MV3 Theorem 1 === | === MV3 Theorem 1 === | ||