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In abstract algebra and multilinear algebra, a multilinear form on a vector space over a field is a map: that is separately -linear in each of its arguments. [1] More generally, one can define multilinear forms on a module over a commutative ring.
A class diagram exemplifying the singleton pattern.. In object-oriented programming, the singleton pattern is a software design pattern that restricts the instantiation of a class to a singular instance.
Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...
For example, the factory interface is commonly implemented as a singleton to provide global access for creating flyweights. Generally speaking, the retrieval algorithm begins with a request for a new object via the factory interface. The request is typically forwarded to an appropriate cache based on what kind of object it is. If the request is ...
The interior of a line segment in an at least two-dimensional ambient space is empty, but its relative interior is the line segment without its endpoints. The interior of a disc in an at least three-dimensional ambient space is empty, but its relative interior is the same disc without its circular edge.
Octave programs consist of a list of function calls or a script. The syntax is matrix-based and provides various functions for matrix operations. It supports various data structures and allows object-oriented programming. [26] Its syntax is very similar to MATLAB, and careful programming of a script will allow it to run on both Octave and ...
A set such as {{,,}} is a singleton as it contains a single element (which itself is a set, but not a singleton). A set is a singleton if and only if its cardinality is 1. In von Neumann's set-theoretic construction of the natural numbers, the number 1 is defined as the singleton {}.
A function : is monotone in this topological sense if and only if it is non-increasing or non-decreasing, which is the usual meaning of "monotone function" in real analysis. A function between topological spaces is (sometimes) called a proper map if every fiber is a compact subspace of its domain. However, many authors use other non-equivalent ...