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In computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms, an associative array is a function with finite domain. [1] It supports 'lookup', 'remove', and 'insert ...
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
Common examples are the use of reserved values, where, for example, a function returning a positive number may return -1 to indicate failure, and sentinel values, most often used in tagged pointers. Sometimes, untagged unions are used to perform bit-level conversions between types, called reinterpret casts in C++.
Was one of the big three spreadsheets (the others being Lotus 123 and Excel). EasyOffice EasySpreadsheet – for MS Windows. No longer freeware, this suite aims to be more user friendly than competitors. Framework – for MS Windows. Historical office suite still available and supported. It includes a spreadsheet.
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.
Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.
One of the most common examples of an algebraic data type is the singly linked list. A list type is a sum type with two variants, Nil for an empty list and Cons x xs for the combination of a new element x with a list xs to create a new list. Here is an example of how a singly linked list would be declared in Haskell: