29 Numerics library [numerics]

Define GENERALIZED_­NONCOMMUTATIVE_­SUM(op, a1, ..., aN) as follows:

• (1.1)

  a1 when N is 1, otherwise

• (1.2)

  op(GENERALIZED_­NONCOMMUTATIVE_­SUM(op, a1, ..., aK),
  op(GENERALIZED_­NONCOMMUTATIVE_­SUM(op, aM, ..., aN)) for any K where $1<K+1=M\le N$.

Define GENERALIZED_­SUM(op, a1, ..., aN) as GENERALIZED_­NONCOMMUTATIVE_­SUM(op, b1, ..., bN), where b1, ..., bN may be any permutation of a1, ..., aN.