Массив элементтерін индекспен белгілеу әдісі

Manner of referring to elements of arrays or tensors

index notation, or indicial notation in relativity theory and abstract algebra
In mathematics and computer programming, index notation is used to specify the elements of an array of numbers. The formalism of how indices are used varies according to the subject. In particular, there are different methods for referring to the elements of a list, a vector, or a matrix, depending on whether one is writing a formal mathematical paper for publication, or when one is writing a computer program.

It is frequently helpful in mathematics to refer to the elements of an array using subscripts. The subscripts can be integers or variables. The array takes the form of tensors in general, since these can be treated as multi dimensional arrays. Special (and more familiar) cases are vectors (1d arrays) and matrices (2d arrays). The following is only an introduction to the concept: index notation is used in more detail in mathematics (particularly in the representation and manipulation of tensor operations). See the main article for further details.

The notation allows a clear generalization to multi dimensional arrays of elements: tensors. For example,

representing a set of many equations. In tensor analysis, superscripts are used instead of subscripts to distinguish covariant from contravariant entities, see covariance and contravariance of vectors and raising and lowering indices.

In several programming languages, index notation is a way of addressing elements of an array. This method is used since it is closest to how it is implemented in assembly language whereby the address of the first element is used as a base, and a multiple (the index) of the element size is used to address inside the array. For example, if an array of integers is stored in a region of the computer's memory starting at the memory cell with address 3000 (the base address), and each integer occupies four cells (bytes), then the elements of this array are at memory locations 0x3000, 0x3004, 0x3008, , 0x3000 + 4(n − 1) (note the zero based numbering). In general, the address of the ith element of an array with base address b and element size s is b + is.

In the C programming language, we can write the above as (pointer form) or (array indexing form), which is exactly equivalent because the C standard defines the array indexing form as a transformation to pointer form. Coincidentally, since pointer addition is commutative, this allows for obscure expressions such as which is equivalent to .

In other programming languages such as Pascal, indices may start at 1, so indexing in a block of memory can be changed to fit a start at 1 addressing scheme by a simple linear transformation – in this scheme, the memory location of the ith element with base address b and element size s is b + (i − 1)s.