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wiki_1000_chunk_0 | Regular Hadamard matrices | In mathematics a regular Hadamard matrix is a Hadamard matrix whose row and column sums are all equal. While the order of a Hadamard matrix must be 1, 2, or a multiple of 4, regular Hadamard matrices carry the further restriction that the order be a square number. The excess, denoted E(H), of a Hadamard matrix H of ord... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1001_chunk_0 | Stack (mathematics) | In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Stacks are used to formalise some of the main constructions of descent theory, and to construct fine moduli stacks when fine moduli spaces do not exist. Descent theory is concerned with generalisations of s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1002_chunk_0 | Stack (mathematics) | The intuitive meaning of a stack is that it is a fibred category such that "all possible gluings work". The specification of gluings requires a definition of coverings with regard to which the gluings can be considered. It turns out that the general language for describing these coverings is that of a Grothendieck topo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1003_chunk_0 | Singly and doubly even | In mathematics an even integer, that is, a number that is divisible by 2, is called evenly even or doubly even if it is a multiple of 4, and oddly even or singly even if it is not. The former names are traditional ones, derived from ancient Greek mathematics; the latter have become common in recent decades. These names... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1004_chunk_0 | Narrowing of algebraic value sets | In mathematics an expression represents a single value. A function maps one or more values to one unique value. Inverses of functions are not always well defined as functions. Sometimes extra conditions are required to make an inverse of a function fit the definition of a function. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1005_chunk_0 | Narrowing of algebraic value sets | A variable may only take on a single value in each possible world. The value sets tag each value in the value set with the world to which it belongs. Possible worlds belong to world sets. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1006_chunk_0 | Narrowing of algebraic value sets | A world set is a set of all mutually exclusive worlds. Combining values from different possible worlds is impossible, because that would mean combining mutually exclusive possible worlds. The application of functions to value sets creates combinations of value sets from different worlds. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1007_chunk_0 | Isogonal trajectory | In mathematics an orthogonal trajectory is a curve, which intersects any curve of a given pencil of (planar) curves orthogonally. For example, the orthogonal trajectories of a pencil of concentric circles are the lines through their common center (see diagram). Suitable methods for the determination of orthogonal traje... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1008_chunk_0 | Rectangular mask short-time Fourier transform | In mathematics and Fourier analysis, a rectangular mask short-time Fourier transform (rec-STFT) has the simple form of short-time Fourier transform. Other types of the STFT may require more computation time than the rec-STFT. The rectangular mask function can be defined for some bound (B) over time (t) as w ( t ) = { 1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1009_chunk_0 | Bol loop | In mathematics and abstract algebra, a Bol loop is an algebraic structure generalizing the notion of group. Bol loops are named for the Dutch mathematician Gerrit Bol who introduced them in (Bol 1937). A loop, L, is said to be a left Bol loop if it satisfies the identity a ( b ( a c ) ) = ( a ( b a ) ) c {\displaystyle... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1010_chunk_0 | Boolean domain | In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true. In logic, mathematics and theoretical computer science, a Boolean domain is usually written as {0, 1}, or B . {\displaystyle \mathbb {B} .} The algebraic structure that natural... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1011_chunk_0 | Boolean domain | The initial object in the category of bounded lattices is a Boolean domain. In computer science, a Boolean variable is a variable that takes values in some Boolean domain. Some programming languages feature reserved words or symbols for the elements of the Boolean domain, for example false and true. However, many progr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1012_chunk_0 | Relation algebra | In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation. The motivating example of a relation algebra is the algebra 2 X 2 of all binary relations on a set X, that is, subsets of the cartesian square X2, with R•S interpreted ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1013_chunk_0 | Two-element Boolean algebra | In mathematics and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean domain. The elements of the Boolean domain are 1 and 0 by convention, so that B = {0, 1}. Paul Halmos's name for this algebra "2" has some following in the literatur... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1014_chunk_0 | Vaughan's identity | In mathematics and analytic number theory, Vaughan's identity is an identity found by R. C. Vaughan (1977) that can be used to simplify Vinogradov's work on trigonometric sums. It can be used to estimate summatory functions of the form ∑ n ≤ N f ( n ) Λ ( n ) {\displaystyle \sum _{n\leq N}f(n)\Lambda (n)} where f is so... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1015_chunk_0 | Perturbation theory | In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In per... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1016_chunk_0 | Perturbation theory | Successive terms in the series at higher powers of ε {\displaystyle \varepsilon } usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1017_chunk_0 | Perturbation theory | Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. The field in general remains actively and heavily researched across multiple disciplines. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1018_chunk_0 | Generalized momentum | In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time. Canonical coordinates are used in the Hamiltonian formulation of classical mechanics. A closely related concept also appears in quantum mechani... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1019_chunk_0 | Poisson commutativity | In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. The Poisson bracket also distinguishes a certain class of coordinate transfo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1020_chunk_0 | Poisson commutativity | For instance, it is often possible to choose the Hamiltonian itself H = H ( q , p , t ) {\displaystyle H=H(q,p,t)} as one of the new canonical momentum coordinates. In a more general sense, the Poisson bracket is used to define a Poisson algebra, of which the algebra of functions on a Poisson manifold is a special case... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1021_chunk_0 | Centered hexagonal number | In mathematics and combinatorics, a centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. The following figures illustrate this arrangement for the first four centered hexagonal num... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1022_chunk_0 | Elementary cellular automaton | In mathematics and computability theory, an elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. Ther... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1023_chunk_0 | Delaunay triangulation | In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum of all ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1024_chunk_0 | Gabriel graph | In mathematics and computational geometry, the Gabriel graph of a set S {\displaystyle S} of points in the Euclidean plane expresses one notion of proximity or nearness of those points. Formally, it is the graph G {\displaystyle G} with vertex set S {\displaystyle S} in which any two distinct points p ∈ S {\displaystyl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1025_chunk_0 | Distinct degree factorization | In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1026_chunk_0 | Computational differentiation | In mathematics and computer algebra, automatic differentiation (auto-differentiation, autodiff, or AD), also called algorithmic differentiation, computational differentiation, is a set of techniques to evaluate the partial derivative of a function specified by a computer program. Automatic differentiation exploits the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1027_chunk_0 | Polynomial factorization | In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain. Polynomial factorization is one of the fundamental components of computer... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1028_chunk_0 | Polynomial factorization | But most of the knowledge on this topic is not older than circa 1965 and the first computer algebra systems: When the long-known finite step algorithms were first put on computers, they turned out to be highly inefficient. The fact that almost any uni- or multivariate polynomial of degree up to 100 and with coefficient... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1029_chunk_0 | Binary exponentiation | In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. Some variants are commonly referred to as square-and-multiply algorithms or bin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1030_chunk_0 | Indicial notation | 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 wr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1031_chunk_0 | Precedence rule | In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operators. The rank of an operator is called its precedence, a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1032_chunk_0 | Precedence rule | For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9. When expo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1033_chunk_0 | Fixed-point combinator | In mathematics and computer science in general, a fixed point of a function is a value that is mapped to itself by the function. In combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator): page 26 is a higher-order function fix {\displaystyle {\textsf {fix}}} that returns some fixed po... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1034_chunk_0 | Horner's method | In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and P... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1035_chunk_0 | Recamán's sequence | In mathematics and computer science, Recamán's sequence is a well known sequence defined by a recurrence relation. Because its elements are related to the previous elements in a straightforward way, they are often defined using recursion. It takes its name after its inventor Bernardo Recamán Santos, a Colombian mathema... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1036_chunk_0 | Zeno machine | In mathematics and computer science, Zeno machines (abbreviated ZM, and also called accelerated Turing machine, ATM) are a hypothetical computational model related to Turing machines that are capable of carrying out computations involving a countably infinite number of algorithmic steps. These machines are ruled out in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1037_chunk_0 | Balanced boolean function | In mathematics and computer science, a balanced boolean function is a boolean function whose output yields as many 0s as 1s over its input set. This means that for a uniformly random input string of bits, the probability of getting a 1 is 1/2. Examples of balanced boolean functions are the function that copies the firs... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1038_chunk_0 | Normal form (mathematics) | More generally, for a class of objects on which an equivalence relation is defined, a canonical form consists in the choice of a specific object in each class. For example: Jordan normal form is a canonical form for matrix similarity. The row echelon form is a canonical form, when one considers as equivalent a matrix a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1039_chunk_0 | Normal form (mathematics) | Therefore, in computer algebra, normal form is a weaker notion: A normal form is a representation such that zero is uniquely represented. This allows testing for equality by putting the difference of two objects in normal form. Canonical form can also mean a differential form that is defined in a natural (canonical) wa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1040_chunk_0 | Recursive step | In mathematics and computer science, a class of objects or methods exhibits recursive behavior when it can be defined by two properties: A simple base case (or cases) — a terminating scenario that does not use recursion to produce an answer A recursive step — a set of rules that reduces all successive cases toward the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1041_chunk_0 | Recursive step | By this base case and recursive rule, one can generate the set of all natural numbers. Other recursively defined mathematical objects include factorials, functions (e.g., recurrence relations), sets (e.g., Cantor ternary set), and fractals. There are various more tongue-in-cheek definitions of recursion; see recursive ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1042_chunk_0 | Functional form | In mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following: takes one or more functions as arguments (i.e. a procedural parameter, which is a parameter of a procedure that is itself a procedure), returns a function as its result.All other functions are first... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1043_chunk_0 | Circuit-finding oracle | In mathematics and computer science, a matroid oracle is a subroutine through which an algorithm may access a matroid, an abstract combinatorial structure that can be used to describe the linear dependencies between vectors in a vector space or the spanning trees of a graph, among other applications. The most commonly ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1044_chunk_0 | Primality certificate | In mathematics and computer science, a primality certificate or primality proof is a succinct, formal proof that a number is prime. Primality certificates allow the primality of a number to be rapidly checked without having to run an expensive or unreliable primality test. "Succinct" usually means that the proof should... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1045_chunk_0 | Random tree | In mathematics and computer science, a random tree is a tree or arborescence that is formed by a stochastic process. Types of random trees include: Uniform spanning tree, a spanning tree of a given graph in which each different tree is equally likely to be selected Random minimal spanning tree, spanning trees of a grap... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1046_chunk_0 | Rational series | In mathematics and computer science, a rational series is a generalisation of the concept of formal power series over a ring to the case when the basic algebraic structure is no longer a ring but a semiring, and the indeterminates adjoined are not assumed to commute. They can be regarded as algebraic expressions of a f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1047_chunk_0 | Recursive definition | In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set (Aczel 1977:740ff). Some examples of recursively-definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set. A rec... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1048_chunk_0 | Recursive definition | {\displaystyle {\begin{aligned}&0!=1.\\&(n+1)!=(n+1)\cdot n!.\end{aligned}}} This definition is valid for each natural number n, because the recursion eventually reaches the base case of 0. The definition may also be thought of as giving a procedure for computing the value of the function n!, starting from n = 0 and pr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1049_chunk_0 | Recursive definition | Note that this definition assumes that N {\displaystyle \mathbb {N} } is contained in a larger set (such as the set of real numbers) — in which the operation + is defined. Properties of recursively defined functions and sets can often be proved by an induction principle that follows the recursive definition. For exampl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1050_chunk_0 | Shortest-path tree | In mathematics and computer science, a shortest-path tree rooted at a vertex v of a connected, undirected graph G is a spanning tree T of G, such that the path distance from root v to any other vertex u in T is the shortest path distance from v to u in G. In connected graphs where shortest paths are well-defined (i.e. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1051_chunk_0 | Shortest-path tree | Construct the shortest-path tree using the edges between each node and its parent.The above algorithm guarantees the existence of shortest-path trees. Like minimum spanning trees, shortest-path trees in general are not unique. In graphs for which all edge weights are equal, shortest path trees coincide with breadth-fir... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1052_chunk_0 | Shortest-path tree | In graphs that have negative cycles, the set of shortest simple paths from v to all other vertices do not necessarily form a tree. For simple connected graphs, shortest-path trees can be used to suggest a non-linear relationship between two network centrality measures, closeness and degree. By assuming that the branche... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1053_chunk_0 | Splicing rule | In mathematics and computer science, a splicing rule is a transformation on formal languages which formalises the action of gene splicing in molecular biology. A splicing language is a language generated by iterated application of a splicing rule: the splicing languages form a proper subset of the regular languages. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1054_chunk_0 | Stack-sortable permutation | In mathematics and computer science, a stack-sortable permutation (also called a tree permutation) is a permutation whose elements may be sorted by an algorithm whose internal storage is limited to a single stack data structure. The stack-sortable permutations are exactly the permutations that do not contain the permut... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1055_chunk_0 | String similarity | In mathematics and computer science, a string metric (also known as a string similarity metric or string distance function) is a metric that measures distance ("inverse similarity") between two text strings for approximate string matching or comparison and in fuzzy string searching. A requirement for a string metric (e... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1056_chunk_0 | String similarity | The most widely known string metric is a rudimentary one called the Levenshtein distance (also known as edit distance). It operates between two input strings, returning a number equivalent to the number of substitutions and deletions needed in order to transform one input string into another. Simplistic string metrics ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1057_chunk_0 | Algorithmic problem | In mathematics and computer science, an algorithm ( ) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1058_chunk_0 | Algorithmic problem | Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus".In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1059_chunk_0 | Apply | In mathematics and computer science, apply is a function that applies a function to arguments. It is central to programming languages derived from lambda calculus, such as LISP and Scheme, and also in functional languages. It has a role in the study of the denotational semantics of computer programs, because it is a co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1060_chunk_0 | Apply | Apply is also a continuous function in homotopy theory, and, indeed underpins the entire theory: it allows a homotopy deformation to be viewed as a continuous path in the space of functions. Likewise, valid mutations (refactorings) of computer programs can be seen as those that are "continuous" in the Scott topology. T... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1061_chunk_0 | Computable analysis | In mathematics and computer science, computable analysis is the study of mathematical analysis from the perspective of computability theory. It is concerned with the parts of real analysis and functional analysis that can be carried out in a computable manner. The field is closely related to constructive analysis and n... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1062_chunk_0 | Computable analysis | This might be considered surprising as an integral is (loosely speaking) an infinite sum. While this result could be explained by the fact that every computable function from {\displaystyle \mathbb {} to R {\displaystyle \mathbb {R} } is uniformly continuous, the notable thing is that the modulus of continuity can alw... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1063_chunk_0 | Algorithmic number theory | In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to dio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1064_chunk_0 | 4-connected graph | In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The conne... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1065_chunk_0 | Currying | In mathematics and computer science, currying is the technique of translating the evaluation of a function that takes multiple arguments into evaluating a sequence of functions, each with a single argument. For example, currying a function f {\displaystyle f} that takes three arguments creates a nested unary function g... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1066_chunk_0 | Currying | The currying of a function with more than two arguments can then be defined by induction. Currying is related to, but not the same as, partial application. Currying is useful in both practical and theoretical settings. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1067_chunk_0 | Currying | In functional programming languages, and many others, it provides a way of automatically managing how arguments are passed to functions and exceptions. In theoretical computer science, it provides a way to study functions with multiple arguments in simpler theoretical models which provide only one argument. The most ge... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1068_chunk_0 | Currying | It was introduced by Gottlob Frege, developed by Moses Schönfinkel, and further developed by Haskell Curry.Uncurrying is the dual transformation to currying, and can be seen as a form of defunctionalization. It takes a function f {\displaystyle f} whose return value is another function g {\displaystyle g} , and yields ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1069_chunk_0 | Graph edit distance | In mathematics and computer science, graph edit distance (GED) is a measure of similarity (or dissimilarity) between two graphs. The concept of graph edit distance was first formalized mathematically by Alberto Sanfeliu and King-Sun Fu in 1983. A major application of graph edit distance is in inexact graph matching, su... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1070_chunk_0 | Perfect code | In mathematics and computer science, in the field of coding theory, the Hamming bound is a limit on the parameters of an arbitrary block code: it is also known as the sphere-packing bound or the volume bound from an interpretation in terms of packing balls in the Hamming metric into the space of all possible words. It ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1071_chunk_0 | Mutually recursive | In mathematics and computer science, mutual recursion is a form of recursion where two mathematical or computational objects, such as functions or datatypes, are defined in terms of each other. Mutual recursion is very common in functional programming and in some problem domains, such as recursive descent parsers, wher... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1072_chunk_0 | Addition-chain exponentiation | In mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by a positive integer power that requires a minimal number of multiplications. Using the form of the shortest addition chain, with multiplication instead of addition, computes the desired exponent (instead of multip... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1073_chunk_0 | Addition-chain exponentiation | More generally, addition-chain exponentiation may also refer to exponentiation by non-minimal addition chains constructed by a variety of algorithms (since a shortest addition chain is very difficult to find). The shortest addition-chain algorithm requires no more multiplications than binary exponentiation and usually ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1074_chunk_0 | Addition-chain exponentiation | There are also several methods to approximate a shortest addition chain, and which often require fewer multiplications than binary exponentiation; binary exponentiation itself is a suboptimal addition-chain algorithm. The optimal algorithm choice depends on the context (such as the relative cost of the multiplication a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1075_chunk_0 | BIT predicate | In mathematics and computer science, the BIT predicate, sometimes written BIT ( i , j ) {\displaystyle {\text{BIT}}(i,j)} , is a predicate that tests whether the j {\displaystyle j} th bit of the number i {\displaystyle i} (starting from the least significant digit) is 1, when i {\displaystyle i} is written as a binary... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1076_chunk_0 | Entscheidungsproblem | In mathematics and computer science, the Entscheidungsproblem (German for 'decision problem'; pronounced ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that considers, as input, a statement and answers "yes" or "no" according to whether the statement is universa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1077_chunk_0 | Floor function | In mathematics and computer science, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x).For examp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1078_chunk_0 | Fuzzy concept | Susan Haack comments: "Whereas in classical set theory an object either is or is not a member of a given set, in fuzzy set theory membership is a matter of degree; the degree of membership of an object in a fuzzy set is represented by some real number between 0 and 1, with 0 denoting no membership and 1 full membership... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1079_chunk_0 | Probabilistic finite automata | In mathematics and computer science, the probabilistic automaton (PA) is a generalization of the nondeterministic finite automaton; it includes the probability of a given transition into the transition function, turning it into a transition matrix. Thus, the probabilistic automaton also generalizes the concepts of a Ma... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1080_chunk_0 | Method of conditional probabilities | In mathematics and computer science, the probabilistic method is used to prove the existence of mathematical objects with desired combinatorial properties. The proofs are probabilistic — they work by showing that a random object, chosen from some probability distribution, has the desired properties with positive probab... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1081_chunk_0 | Method of conditional probabilities | That is, the method derandomizes the proof. The basic idea is to replace each random choice in a random experiment by a deterministic choice, so as to keep the conditional probability of failure, given the choices so far, below 1. The method is particularly relevant in the context of randomized rounding (which uses the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1082_chunk_0 | Trace theory | In mathematics and computer science, trace theory aims to provide a concrete mathematical underpinning for the study of concurrent computation and process calculi. The underpinning is provided by an algebraic definition of the free partially commutative monoid or trace monoid, or equivalently, the history monoid, which... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1083_chunk_0 | Fibonacci coding | In mathematics and computing, Fibonacci coding is a universal code which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers. Each code word ends with "11" and contains no other instances of "11" before the end. The Fibonacci code is closely rela... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1084_chunk_0 | Decimal comma | In mathematics and computing, a radix point or radix character is a symbol used in the display of numbers to separate the integer part of the value from its fractional part. In English and many other languages (including many that are written right-to-left), the integer part is at the left of the radix point, and the f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1085_chunk_0 | Decimal comma | It is important to know which notation is being used when working in different software programs. The respective ISO standard defines both the comma and the small dot as decimal markers, but does not explicitly define universal radix marks for bases other than 10. Fractional numbers are rarely displayed in other number... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1086_chunk_0 | Root-finding algorithms | In mathematics and computing, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f, from the real numbers to real numbers or from the complex numbers to the complex numbers, is a number x such that f(x) = 0. As, generally, the zeros of a functi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1087_chunk_0 | Root-finding algorithms | However, most root-finding algorithms do not guarantee that they will find all the roots; in particular, if such an algorithm does not find any root, that does not mean that no root exists. Most numerical root-finding methods use iteration, producing a sequence of numbers that hopefully converges towards the root as it... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1088_chunk_0 | Root-finding algorithms | Since the iteration must be stopped at some point, these methods produce an approximation to the root, not an exact solution. Many methods compute subsequent values by evaluating an auxiliary function on the preceding values. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1089_chunk_0 | Root-finding algorithms | The limit is thus a fixed point of the auxiliary function, which is chosen for having the roots of the original equation as fixed points, and for converging rapidly to these fixed points. The behavior of general root-finding algorithms is studied in numerical analysis. However, for polynomials, root-finding study belon... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1090_chunk_0 | Root-finding algorithms | The efficiency of an algorithm may depend dramatically on the characteristics of the given functions. For example, many algorithms use the derivative of the input function, while others work on every continuous function. In general, numerical algorithms are not guaranteed to find all the roots of a function, so failing... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1091_chunk_0 | Levenberg–Marquardt nonlinear least squares fitting algorithm | In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting. The LMA interpolates between the Gauss–Newton algorithm ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1092_chunk_0 | Levenberg–Marquardt nonlinear least squares fitting algorithm | The LMA is more robust than the GNA, which means that in many cases it finds a solution even if it starts very far off the final minimum. For well-behaved functions and reasonable starting parameters, the LMA tends to be slower than the GNA. LMA can also be viewed as Gauss–Newton using a trust region approach. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1093_chunk_0 | Levenberg–Marquardt nonlinear least squares fitting algorithm | The algorithm was first published in 1944 by Kenneth Levenberg, while working at the Frankford Army Arsenal. It was rediscovered in 1963 by Donald Marquardt, who worked as a statistician at DuPont, and independently by Girard, Wynne and Morrison.The LMA is used in many software applications for solving generic curve-fi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1094_chunk_0 | Hex format | In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1095_chunk_0 | Hex format | For example, an 8-bit byte can have values ranging from 00000000 to 11111111 (0 to 255 decimal) in binary form, which can be conveniently represented as 00 to FF in hexadecimal. In mathematics, a subscript is typically used to specify the base. For example, the decimal value 24,779 would be expressed in hexadecimal as ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1096_chunk_0 | Hex format | In programming, several notations denote hexadecimal numbers, usually involving a prefix. The prefix 0x is used in C, which would denote this value as 0x60CB. Hexadecimal is used in the transfer encoding Base16, in which each byte of the plaintext is broken into two 4-bit values and represented by two hexadecimal digit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1097_chunk_0 | Hex digit | In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1098_chunk_0 | Hex digit | For example, an 8-bit byte can have values ranging from 00000000 to 11111111 (0 to 255 decimal) in binary form, which can be conveniently represented as 00 to FF in hexadecimal. In mathematics, a subscript is typically used to specify the base. For example, the decimal value 30,227 would be expressed in hexadecimal as ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
wiki_1099_chunk_0 | Hex digit | In programming, several notations denote hexadecimal numbers, usually involving a prefix. The prefix 0x is used in C, which would denote this value as 0x7613. Hexadecimal is used in the transfer encoding Base16, in which each byte of the plaintext is broken into two 4-bit values and represented by two hexadecimal digit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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