In mathematics, an addition chain for computing a positive integer n can be given by a sequence of natural numbers v and a sequence of index pairs w such that each term in v is the sum of two previous terms, the indices of those terms being specified by w:
- v =(v0,...,vs), with v0 = 1 and vs = n
- for each 0< i ≤ s holds: vi = vj + vk, with wi=(j,k) and 0 ≤ j,k ≤ i − 1
Often only v is given since it is easy to extract w from v, but sometimes w is not uniquely reconstructible. An introduction is given by Knuth.
Read more about Addition Chain: Examples, Methods For Computing Addition Chains, Chain Length, Brauer Chain, Scholz Conjecture
Famous quotes containing the words addition and/or chain:
“The addition of a helpless, needy infant to a couple’s life limits freedom of movement, changes role expectancies, places physical demands on parents, and restricts spontaneity.”
—Jerrold Lee Shapiro (20th century)
“We are all bound to the throne of the Supreme Being by a flexible chain which restrains without enslaving us. The most wonderful aspect of the universal scheme of things is the action of free beings under divine guidance.”
—Joseph De Maistre (1753–1821)