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In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
For separate items: the price-of-fairness of max-min fairness is unbounded. For example, suppose Alice has two items with values 1 and e, for some small e>0. George has two items with value e. The capacity is 1. The maximum sum is 1 - when Alice gets the item with value 1 and George gets nothing. But the max-min allocation gives both agents ...
Let A be the sum of the negative values and B the sum of the positive values; the number of different possible sums is at most B-A, so the total runtime is in (()). For example, if all input values are positive and bounded by some constant C , then B is at most N C , so the time required is O ( N 2 C ) {\displaystyle O(N^{2}C)} .
Computers typically use binary arithmetic, but to make the example easier to read, it will be given in decimal. Suppose we are using six-digit decimal floating-point arithmetic, sum has attained the value 10000.0, and the next two values of input[i] are 3.14159 and 2.71828. The exact result is 10005.85987, which rounds to 10005.9.
In the subset sum problem, the goal is to find a subset of S whose sum is a certain target number T given as input (the partition problem is the special case in which T is half the sum of S). In multiway number partitioning , there is an integer parameter k , and the goal is to decide whether S can be partitioned into k subsets of equal sum ...
Pushout (category theory) (also called an amalgamated sum or a cocartesian square, fibered coproduct, or fibered sum), the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domainor pushout, leading to a fibered sum in category theory; QCD sum rules, in quantum field theory; Riemann sum, in calculus
If an element lies in both, there will be two effectively distinct copies of the value in A + B, one from A and one from B. In type theory, a tagged union is called a sum type. Sum types are the dual of product types. Notations vary, but usually the sum type A + B comes with two introduction forms inj 1: A → A + B and inj 2: B → A + B.
{{#if: test string | value if true | value if false}} (selects one of two values based on whether the test string is true or false) {{#ifeq: string 1 | string 2 | value if equal | value if unequal}} (selects one of two values based on whether the two strings are equal—a numerical comparison is done whenever that is possible)