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For example, in the Pascal programming language, the declaration type MyTable = array [1.. 4, 1.. 2] of integer, defines a new array data type called MyTable. The declaration var A: MyTable then defines a variable A of that type, which is an aggregate of eight elements, each being an integer variable identified by two indices.
Examples of reference types are object (the ultimate base class for all other C# classes), System. String (a string of Unicode characters), and System. Array (a base class for all C# arrays). Both type categories are extensible with user-defined types.
Classes are self-describing user-defined reference types. Essentially all types in the .NET Framework are classes, including structs and enums, that are compiler generated classes. Class members are private by default, but can be declared as public to be visible outside of the class or protected to be visible by any descendants of the class.
Arrays can have multiple dimensions, thus it is not uncommon to access an array using multiple indices. For example, a two-dimensional array A with three rows and four columns might provide access to the element at the 2nd row and 4th column by the expression A[1][3] in the case of a zero-based indexing
For example, to perform an element by element sum of two arrays, a and b to produce a third c, it is only necessary to write c = a + b In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine.
Some languages may allow list types to be indexed or sliced like array types, in which case the data type is more accurately described as an array. In type theory and functional programming, abstract lists are usually defined inductively by two operations: nil that yields the empty list, and cons, which adds an item at the beginning of a list. [1]
Matrix multiplication is an example of a 2-rank function, because it operates on 2-dimensional objects (matrices). Collapse operators reduce the dimensionality of an input data array by one or more dimensions. For example, summing over elements collapses the input array by 1 dimension.
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 ...