NCCollectOnVariables

A key concept in understanding the NCCollectOnVariables option for NCProcess, which is abbreviated as NCCV, is the notion of a maximal product of knowns within a monic monomial.

Definition 9.2 v v ... v is a maximal product of knowns in v ... v if

1. 1 a b n
2. v is a known for a j b
3. if a > 1, then v is unknown.
4. if b < n, then v is unknown.

NCCollectOnVariables takes as input a polynomial p. On each term of p, NCCollectOnVariables computes a list of maximal products of knowns. NCCollectOnVariables then repeatedly applies NCCollect to transform p into a parenthesized expressions with respect to the maximal products of knowns. NCCollectOnVariables uses the maximal products of knowns with the largest degree before using the maximal products of knowns with lower degrees. For example, if A, B, C, D, E, F and G are knowns and a, b, d, e and h are unknowns, then when NCCollectOnVariables is applied to a b A B C d + D e + F G h A C, it returns first tries to collect with respect to {A B C} and then collect with respect to {F G, A C} and then collect with respect to {D}.