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Matrix inversion lemma Summary Woodbury_matrix_identity In mathematics (specifically linear algebra), the Woodbury matrix identity, named after Max A. Woodbury, says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix. Alternative nam... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matrix inversion lemma Summary Woodbury_matrix_identity While the identity is primarily used on matrices, it holds in a general ring or in an Ab-category. The Woodbury matrix identity allows cheap computation of inverses and solutions to linear equations. However, little is known about the numerical stability of the fo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Positive operator Summary Positive_operator In mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operator A {\displaystyle A} acting on an inner product space is called positive-semidefinite (or non-negative) if, for every x ∈ Dom ( A ) {\displaystyle x\i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiple integrals Summary Double_integration In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in R 2 {\displaystyle \mathbb {R} ^{2}} (the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Alexander's theorem Summary Alexander's_theorem In mathematics Alexander's theorem states that every knot or link can be represented as a closed braid; that is, a braid in which the corresponding ends of the strings are connected in pairs. The theorem is named after James Waddell Alexander II, who published a proof in ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Alexander's theorem Summary Alexander's_theorem A good construction example is found in Colin Adams's book.However, the correspondence between knots and braids is clearly not one-to-one: a knot may have many braid representations. For example, conjugate braids yield equivalent knots. This leads to a second fundamental ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Antoine's horned sphere Summary Antoine's_horned_sphere In mathematics Antoine's necklace is a topological embedding of the Cantor set in 3-dimensional Euclidean space, whose complement is not simply connected. It also serves as a counterexample to the claim that all Cantor spaces are ambiently homeomorphic to each oth... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Haboush's theorem Summary Haboush's_theorem In mathematics Haboush's theorem, often still referred to as the Mumford conjecture, states that for any semisimple algebraic group G over a field K, and for any linear representation ρ of G on a K-vector space V, given v ≠ 0 in V that is fixed by the action of G, there is a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nef polygon Summary Nef_polygon In mathematics Nef polygons and Nef polyhedra are the sets of polygons and polyhedra which can be obtained from a finite set of halfplanes (halfspaces) by Boolean operations of set intersection and set complement. The objects are named after the Swiss mathematician Walter Nef (1919–2013)... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cauchy–Euler operator Summary Cauchy–Euler_operator In mathematics a Cauchy–Euler operator is a differential operator of the form p ( x ) ⋅ d d x {\displaystyle p(x)\cdot {d \over dx}} for a polynomial p. It is named after Augustin-Louis Cauchy and Leonhard Euler. The simplest example is that in which p(x) = x, which h... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dirac structure Summary Dirac_structure In mathematics a Dirac structure is a geometric construction generalizing both symplectic structures and Poisson structures, and having several applications to mechanics. It is based on the notion of constraint introduced by Paul Dirac and was first introduced by Ted Courant and ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dirac structure Summary Dirac_structure (Similar definitions can be made for vector spaces over other fields.) An alternative (equivalent) definition often used is that D {\displaystyle D} satisfies D = D ⊥ {\displaystyle D=D^{\perp }} , where orthogonality is with respect to the symmetric bilinear form on V × V ∗ {\di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lie coalgebra Summary Lie_coalgebra In mathematics a Lie coalgebra is the dual structure to a Lie algebra. In finite dimensions, these are dual objects: the dual vector space to a Lie algebra naturally has the structure of a Lie coalgebra, and conversely. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Polynomial solutions of P-recursive equations Summary Polynomial_solutions_of_P-recursive_equations In mathematics a P-recursive equation can be solved for polynomial solutions. Sergei A. Abramov in 1989 and Marko Petkovšek in 1992 described an algorithm which finds all polynomial solutions of those recurrence equation... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
P-recursive equation Summary P-recursive_equation In mathematics a P-recursive equation is a linear equation of sequences where the coefficient sequences can be represented as polynomials. P-recursive equations are linear recurrence equations (or linear recurrence relations or linear difference equations) with polynomi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
P-recursive equation Summary P-recursive_equation The sequences which are solutions of these equations are called holonomic, P-recursive or D-finite. From the late 1980s, the first algorithms were developed to find solutions for these equations. Sergei A. Abramov, Marko Petkovšek and Mark van Hoeij described algorithms... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Steinberg symbol Summary Steinberg_symbol In mathematics a Steinberg symbol is a pairing function which generalises the Hilbert symbol and plays a role in the algebraic K-theory of fields. It is named after mathematician Robert Steinberg. For a field F we define a Steinberg symbol (or simply a symbol) to be a function ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Yetter–Drinfeld category Summary Yetter–Drinfeld_category In mathematics a Yetter–Drinfeld category is a special type of braided monoidal category. It consists of modules over a Hopf algebra which satisfy some additional axioms. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cocycle Summary Cocycle In mathematics a cocycle is a closed cochain. Cocycles are used in algebraic topology to express obstructions (for example, to integrating a differential equation on a closed manifold). They are likewise used in group cohomology. In autonomous dynamical systems, cocycles are used to describe par... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Group structure and the axiom of choice Summary Group_structure_and_the_axiom_of_choice In mathematics a group is a set together with a binary operation on the set called multiplication that obeys the group axioms. The axiom of choice is an axiom of ZFC set theory which in one form states that every set can be wellorde... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
System of linear inequalities Summary Linear_inequality In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: < less than > greater than ≤ less than or equal to ≥ greater than or equal to ≠ not equal toA linear inequality loo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Power closed Summary Power_closed In mathematics a p-group G {\displaystyle G} is called power closed if for every section H {\displaystyle H} of G {\displaystyle G} the product of p k {\displaystyle p^{k}} powers is again a p k {\displaystyle p^{k}} th power. Regular p-groups are an example of power closed groups. On ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Partial differential algebraic equation Summary Partial_differential_algebraic_equation In mathematics a partial differential algebraic equation (PDAE) set is an incomplete system of partial differential equations that is closed with a set of algebraic equations. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Polydivisible number Summary Polydivisible_number In mathematics a polydivisible number (or magic number) is a number in a given number base with digits abcde... that has the following properties: Its first digit a is not 0. The number formed by its first two digits ab is a multiple of 2. The number formed by its first... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Primitive abundant number Summary Primitive_abundant_number In mathematics a primitive abundant number is an abundant number whose proper divisors are all deficient numbers.For example, 20 is a primitive abundant number because: The sum of its proper divisors is 1 + 2 + 4 + 5 + 10 = 22, so 20 is an abundant number. The... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Radial basis function Summary Radial_basis_function In mathematics a radial basis function (RBF) is a real-valued function φ {\textstyle \varphi } whose value depends only on the distance between the input and some fixed point, either the origin, so that φ ( x ) = φ ^ ( ‖ x ‖ ) {\textstyle \varphi (\mathbf {x} )={\hat ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Radial basis function Summary Radial_basis_function They are often used as a collection { φ k } k {\displaystyle \{\varphi _{k}\}_{k}} which forms a basis for some function space of interest, hence the name. Sums of radial basis functions are typically used to approximate given functions. This approximation process can... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Regular Hadamard matrices Summary 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 num... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stack (mathematics) Summary Category_fibered_in_groupoids 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 ex... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stack (mathematics) Summary Category_fibered_in_groupoids 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Countably compact space Summary Countable_compactness In mathematics a topological space is called countably compact if every countable open cover has a finite subcover. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Translation surface Summary Translation_surface In mathematics a translation surface is a surface obtained from identifying the sides of a polygon in the Euclidean plane by translations. An equivalent definition is a Riemann surface together with a holomorphic 1-form. These surfaces arise in dynamical systems where the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Eberlein compactum Summary Eberlein_compactum In mathematics an Eberlein compactum, studied by William Frederick Eberlein, is a compact topological space homeomorphic to a subset of a Banach space with the weak topology. Every compact metric space, more generally every one-point compactification of a locally compact me... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Singly and doubly even Summary 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 la... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Narrowing of algebraic value sets Introduction Narrowing_of_algebraic_value_sets > Introduction 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Narrowing of algebraic value sets Introduction Narrowing_of_algebraic_value_sets > Introduction Some Boolean operations, in particular do not have inverses that may be defined as functions. In particular the disjunction "or" has inverses that allow two values. In natural language "or" represents alternate possibilities... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Narrowing of algebraic value sets Introduction Narrowing_of_algebraic_value_sets > Introduction Narrowing is based on value sets that allow multiple values to be packaged and considered as a single value. This allows the inverses of functions to always be considered as functions. To achieve this value sets must record ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Narrowing of algebraic value sets Introduction Narrowing_of_algebraic_value_sets > Introduction 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 |
Narrowing of algebraic value sets Introduction Narrowing_of_algebraic_value_sets > Introduction 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 valu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Narrowing of algebraic value sets Introduction Narrowing_of_algebraic_value_sets > Introduction Narrowing reduces those worlds by eliminating combinations of different worlds from the same world set. Narrowing rules also detect situations where some combinations of worlds are shown to be impossible. No back tracking is... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Isogonal trajectory Summary Orthogonal_trajectories 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). Suitab... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Isogonal trajectory Summary Orthogonal_trajectories Both steps may be difficult or even impossible. In such cases one has to apply numerical methods. Orthogonal trajectories are used in mathematics for example as curved coordinate systems (i.e. elliptic coordinates) or appear in physics as electric fields and their equ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Rectangular mask short-time Fourier transform Summary 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-... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bol loop Summary 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Boolean domain Summary 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} .... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Boolean domain Summary 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 examp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Relation algebra Summary 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
List of group theory topics Summary List_of_group_theory_topics In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as g... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
List of group theory topics Summary List_of_group_theory_topics Various physical systems, such as crystals and the hydrogen atom, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Two-element Boolean algebra Summary 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vaughan's identity Summary Vaughan's_lemma 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 \s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Perturbation theory Summary Perturbation_analysis 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 proble... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Perturbation theory Summary Perturbation_analysis 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Perturbation theory Summary Perturbation_analysis 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generalized momentum Summary Conjugate_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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Poisson commutativity Summary Poisson_brackets 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 dist... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Poisson commutativity Summary Poisson_brackets 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 fu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Centered hexagonal number Summary 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 illustrat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementary cellular automaton Summary 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Delaunay triangulation Summary 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)... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Delaunay triangulation Summary Delaunay_triangulation By considering circumscribed spheres, the notion of Delaunay triangulation extends to three and higher dimensions. Generalizations are possible to metrics other than Euclidean distance. However, in these cases a Delaunay triangulation is not guaranteed to exist or b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gabriel graph Summary 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euler's method Summary Euler's_method In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of or... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Distinct degree factorization Summary Polynomial_factorization_over_finite_fields 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 fi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Computational differentiation Summary Algorithmic_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 specif... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Polynomial factorization Summary 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 fact... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Polynomial factorization Summary 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 multiv... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Binary exponentiation Summary Repeated_squaring 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 refe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Indicial notation Summary Index_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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Precedence rule Summary Standard_mathematical_order_of_operations 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Precedence rule Summary Standard_mathematical_order_of_operations 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Precedence rule Summary Standard_mathematical_order_of_operations Thus 3 + 52 = 28 and 3 × 52 = 75. These conventions exist to avoid notational ambiguity while allowing notation to remain brief. Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses ( ) can be used. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Precedence rule Summary Standard_mathematical_order_of_operations For example, (2 + 3) × 4 = 20 forces addition to precede multiplication, while (3 + 5)2 = 64 forces addition to precede exponentiation. If multiple pairs of parentheses are required in a mathematical expression (such as in the case of nested parentheses)... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Precedence rule Summary Standard_mathematical_order_of_operations These rules are meaningful only when the usual notation (called infix notation) is used. When functional or Polish notation are used for all operations, the order of operations results from the notation itself. Internet memes sometimes present ambiguous ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fixed-point combinator Summary 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 {\di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Horner's method Summary Horner_scheme 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 m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Horner's method Summary Horner_scheme {\displaystyle {\begin{aligned}a_{0}&+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+\cdots +a_{n}x^{n}\\&=a_{0}+x{\bigg (}a_{1}+x{\Big (}a_{2}+x{\big (}a_{3}+\cdots +x(a_{n-1}+x\,a_{n})\cdots {\big )}{\Big )}{\bigg )}.\end{aligned}}} This allows the evaluation of a polynomial of degree n with only ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recamán's sequence Summary 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 invento... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Zeno machine Summary 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 step... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Balanced boolean function Summary 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 bala... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal form (mathematics) Summary Data_normalization In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an object and allows it to be ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal form (mathematics) Summary Data_normalization 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 canoni... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal form (mathematics) Summary Data_normalization In this context, a canonical form is a representation such that every object has a unique representation (with canonicalization being the process through which a representation is put into its canonical form). Thus, the equality of two objects can easily be tested by... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal form (mathematics) Summary Data_normalization 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 differen... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recursive step Formal definitions Recursive_structure > Formal definitions 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 re... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recursive step Formal definitions Recursive_structure > Formal definitions 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. Ther... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Functional form Summary 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
History monoid Summary History_monoid In mathematics and computer science, a history monoid is a way of representing the histories of concurrently running computer processes as a collection of strings, each string representing the individual history of a process. The history monoid provides a set of synchronization pri... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
History monoid Summary History_monoid History monoids were first presented by M.W. Shields.History monoids are isomorphic to trace monoids (free partially commutative monoids) and to the monoid of dependency graphs. As such, they are free objects and are universal. The history monoid is a type of semi-abelian categoric... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Circuit-finding oracle Summary 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Prolongable morphism Summary Prolongable_morphism In mathematics and computer science, a morphic word or substitutive word is an infinite sequence of symbols which is constructed from a particular class of endomorphism of a free monoid. Every automatic sequence is morphic. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pebble game Summary Pebble_game In mathematics and computer science, a pebble game is a type of mathematical game played by placing "pebbles" or "markers" on a directed acyclic graph according to certain rules: A given step of the game consists of either placing a pebble on an empty vertex or removing a pebble from a p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Primality certificate Summary 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Primality certificate Summary Primality_certificate These problems already trivially lie in co-NP. This was the first strong evidence that these problems are not NP-complete, since if they were, it would imply that NP is subset of co-NP, a result widely believed to be false; in fact, this was the first demonstration of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Random tree Summary 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 spannin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Rational series Summary 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recursive definition Summary Inductive_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, Fi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recursive definition Summary Inductive_definition is defined by the rules 0 ! = 1. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recursive definition Summary Inductive_definition ( n + 1 ) ! = ( n + 1 ) ⋅ n ! . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Recursive definition Summary Inductive_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 va... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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