summatus

Summatus is a term used mainly in mathematical discourse and computer science to denote an operation that combines a collection of numbers into a total or into a sequence of partial totals. The word is derived from Latin summatus, the past participle of summere, meaning "taken together" or "totalized." There is no single formal definition of summatus, and its meaning varies by context.

In common usage, summatus often refers to the cumulative sum operator. Given a finite sequence a1, a2, ..., an, summatus can denote the sequence of partial sums s_k = a1 + ... + a_k for k = 1,...,n, or, more tersely, the final total sum S = sum_{i=1}^n a_i. In data processing and probability contexts, summatus is sometimes used to describe normalization by dividing each component by the total, producing a distribution v_i / sum(v).

In programming and algorithmic discussions, summatus is used as an informal shorthand for reducing a list to a single scalar equal to the sum of its elements, or, less commonly, for computing cumulative sums as a separate step.

Examples: For the list [2, 3, 5], the cumulative sums are [2, 5, 10], and the final total is 10; using summatus normalization on [2,3,5] would produce [2/10, 3/10, 5/10] = [0.2, 0.3, 0.5].

See also: summation, aggregation, normalization, cumulative sum.