Transcendental functionIn mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically. Examples of transcendental functions include the exponential function, the logarithm, and the trigonometric functions. Formally, an analytic function f (z) of one real or complex variable z is transcendental if it is algebraically independent of that variable.
Quadratic integerIn number theory, quadratic integers are a generalization of the usual integers to quadratic fields. Quadratic integers are algebraic integers of degree two, that is, solutions of equations of the form x2 + bx + c = 0 with b and c (usual) integers. When algebraic integers are considered, the usual integers are often called rational integers. Common examples of quadratic integers are the square roots of rational integers, such as , and the complex number i = , which generates the Gaussian integers.
ML (programming language)ML (Meta Language) is a general-purpose functional programming language. It is known for its use of the polymorphic Hindley–Milner type system, which automatically assigns the types of most expressions without requiring explicit type annotations, and ensures type safety - there is a formal proof that a well-typed ML program does not cause runtime type errors. ML provides pattern matching for function arguments, garbage collection, imperative programming, call-by-value and currying.
Absorbing elementIn mathematics, an absorbing element (or annihilating element) is a special type of element of a set with respect to a binary operation on that set. The result of combining an absorbing element with any element of the set is the absorbing element itself. In semigroup theory, the absorbing element is called a zero element because there is no risk of confusion with other notions of zero, with the notable exception: under additive notation zero may, quite naturally, denote the neutral element of a monoid.
Generic programmingGeneric programming is a style of computer programming in which algorithms are written in terms of data types to-be-specified-later that are then instantiated when needed for specific types provided as parameters. This approach, pioneered by the ML programming language in 1973, permits writing common functions or types that differ only in the set of types on which they operate when used, thus reducing duplicate code. Generics was introduced to the main-stream programming with Ada in 1977 and then with templates in C++ it became part of the repertoire of professional library design.
Inductive reasoningInductive reasoning is a method of reasoning in which a general principle is derived from a body of observations. It consists of making broad generalizations based on specific observations. Inductive reasoning is distinct from deductive reasoning, where the conclusion of a deductive argument is certain given the premises are correct; in contrast, the truth of the conclusion of an inductive argument is probable, based upon the evidence given.
Algebraic integerIn algebraic number theory, an algebraic integer is a complex number which is integral over the integers. That is, an algebraic integer is a complex root of some monic polynomial (a polynomial whose leading coefficient is 1) whose coefficients are integers. The set of all algebraic integers A is closed under addition, subtraction and multiplication and therefore is a commutative subring of the complex numbers. The ring of integers of a number field K, denoted by OK, is the intersection of K and A: it can also be characterised as the maximal order of the field K.
Red–black treeIn computer science, a red–black tree is a specialised binary search tree data structure noted for fast storage and retrieval of ordered information, and a guarantee that operations will complete within a known time. Compared to other self-balancing binary search trees, the nodes in a red-black tree hold an extra bit called "color" representing "red" and "black" which is used when re-organising the tree to ensure that it is always approximately balanced.
Type classIn computer science, a type class is a type system construct that supports ad hoc polymorphism. This is achieved by adding constraints to type variables in parametrically polymorphic types. Such a constraint typically involves a type class T and a type variable a, and means that a can only be instantiated to a type whose members support the overloaded operations associated with T.
First-class functionIn computer science, a programming language is said to have first-class functions if it treats functions as first-class citizens. This means the language supports passing functions as arguments to other functions, returning them as the values from other functions, and assigning them to variables or storing them in data structures. Some programming language theorists require support for anonymous functions (function literals) as well.
B-treeIn computer science, a B-tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. The B-tree generalizes the binary search tree, allowing for nodes with more than two children. Unlike other self-balancing binary search trees, the B-tree is well suited for storage systems that read and write relatively large blocks of data, such as databases and s. B-trees were invented by Rudolf Bayer and Edward M.
Normal extensionIn abstract algebra, a normal extension is an algebraic field extension L/K for which every irreducible polynomial over K which has a root in L, splits into linear factors in L. These are one of the conditions for algebraic extensions to be a Galois extension. Bourbaki calls such an extension a quasi-Galois extension. Let be an algebraic extension (i.e. L is an algebraic extension of K), such that (i.e. L is contained in an algebraic closure of K).
