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noun
- (commutative algebra) Clipping of uniformizing parameter.
- (programming, loosely) An actual value given to such a formal parameter.
- A value kept constant during an experiment, equation, calculation, or similar, but varied over other versions of the experiment, equation, calculation, etc.
- (crystallography) The ratio of the three crystallographic axes which determines the position of any plane.
- (sciences) A variable that describes a property or characteristic of some system (material, object, event, etc.) or some aspect thereof.
- (geometry) In the ellipse and hyperbola, a third proportional to any diameter and its conjugate, or in the parabola, to any abscissa and the corresponding ordinate.
- (programming) An input variable of a function definition, that gets an actual value (argument) at execution time.
- A characteristic or feature that distinguishes something from others.
- (crystallography) The fundamental axial ratio for a given species.
- (statistics) Any measured quantity of a statistical population that summarises or describes an aspect of the population.
- (machine learning) A variable of a model that is trained by a machine learning algorithm.
- a constant in the equation of a curve that can be varied to yield a family of similar curves
- any factor that defines a system and determines (or limits) its performance
- a quantity (such as the mean or variance) that characterizes a statistical population and that can be estimated by calculations from sample data
- (computer science) a reference or value that is passed to a function, procedure, subroutine, command, or program
adj
- (commutative algebra, of an ideal) Generated by differences of monomials.
- (algebraic geometry, of a stack) Any of several generalizations of the notion of toric varieties to stacks: the stack quotient of a toric variety by its torus; the stack quotient of a toric variety by a subgroup of its torus.
- (algebraic geometry, of a variety) Containing an algebraic torus as a dense subset, such that the group action of the torus on itself extends to the whole space; or, the embedding map taking the torus into the space. See Toric variety on Wikipedia.Wikipedia
- (geometry, algebra) Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.
- (error correction) A particular topological quantum error correcting code; see Toric code on Wikipedia.Wikipedia
- (geometry, of a manifold, generalizing the case of toric varieties) (Narrowly) A compact smooth toric variety. (Broadly) Quasitoric: a closed, real, even-dimensional smooth manifold equipped with an effective, smooth action by an algebraic torus whose orbits are simple complex polytopes and such that the action is locally the same as a faithful real representation of the group.
noun
- A universal algebra.
- (figurative) A system or process (especially one that is complex or convoluted) that substitutes one thing for another, or uses signs or symbols to represent concepts or ideas.
- An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.
- (countable, set theory, mathematical analysis) A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).
- (uncountable, mathematics, sometimes capitalized) Abstract algebra: A broad field of study in modern mathematics (often mentioned alongside analysis) loosely characterized by its concern for abstraction and symmetry, dealing with the behavior, classification, and application of a large class of objects (called algebraic structures) and the maps between them (called, most generally, morphisms).
- (uncountable, medicine, historical, rare) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
- (uncountable, mathematics) Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.
- the mathematics of generalized arithmetical operations
adj
- (algebra, of an algebraic structure) Having a commutative operation.
- (mathematics, of a binary operation) Such that the order in which the operands are taken does not affect their image under the operation.
- Relating to exchange; interchangeable.
- (mathematics, of a diagram of morphisms) Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.
- (of a binary operation) independent of order; as in e.g.: ‘a x b’ = ‘b x a’
noun
adj
noun
- (universal algebra) Any equivalence relation defined on an algebraic structure which is preserved by operations defined by the structure.
- (mathematics, linear algebra) Matrix similarity by an orthogonal matrix.
- (mathematics, geometry) The quality of being isometric — roughly, the same measure and shape.
- (psychology) A well-adjusted state or condition in which people are not lying to themselves or in denial.
- (mathematics, number theory) A relation between two numbers indicating they give the same remainder when divided by some given number.
- The quality of agreeing or corresponding; being suitable and appropriate.
- the quality of agreeing; being suitable and appropriate
noun
- (algebra) An algebraic structure (Σ,∨,∧,∼,0,1) where ∨ and ∧ are idempotent binary operators, ∼ is a unary involutory operator (called "complement"), and 0 and 1 are nullary operators (i.e., constants), such that (Σ,∨,0) is a commutative monoid, (Σ,∧,1) is a commutative monoid, ∧ and ∨ distribute with respect to each other, and such that combining two complementary elements through one binary operator yields the identity of the other binary operator. (See Boolean algebra (structure)#Axiomatics.)
- (algebra, logic, computing) Specifically, an algebra in which all elements can take only one of two values (typically 0 and 1, or "true" and "false") and are subject to operations based on AND, OR and NOT
- (mathematics) The study of such algebras; Boolean logic, classical logic.
- a system of symbolic logic devised by George Boole; used in computers
noun
- In universal algebra: an equational class; the class of all algebraic structures of a given signature, satisfying a given set of identities.
- A specific variation of something.
- (cybernetics) The total number of distinct states of a system; also, the logarithm to the base 2 of the total number of distinct states of a system.
- A deviation or difference.
- (radio, television, theater) Ellipsis of variety performance or variety show (“a type of entertainment featuring a succession of short, unrelated performances by various artistes such as (depending on the medium) acrobats, comedians, dancers, magicians, singers, etc.”).
- (linguistics) A specific form of a language, neutral to whether that form is an accent, dialect, register, etc., and to its prestige level; an isolect or lect.
- (radio, television, theater) The kind of entertainment given in variety performances or shows; also, the production of, or performance in, variety performances or shows.
- (algebraic geometry) Ellipsis of algebraic variety (“the set of solutions of a given system of polynomial equations over the real or complex numbers; any of certain generalisations of such a set that preserves the geometric intuition implicit in the original definition”).
- (botany, taxonomy) A rank in a taxonomic classification below species and (if present) subspecies, and above form; hence, an organism of that rank.
- A collection or number of different things.
- The quality of being varied; diversity.
- (philately) A stamp, or set of stamps, which has one or more characteristics (such as colour, paper, etc.) differing from other stamps in the same issue, especially if such differences are intentionally introduced.
- (biology, loosely) An animal or plant (or a group of such animals or plants) with characteristics causing it to differ from other animals or plants of the same species; a strain or cultivar.
- (biology) a taxonomic category consisting of members of a species that differ from others of the same species in minor but heritable characteristics
- a category of things distinguished by some common characteristic or quality
- noticeable heterogeneity
- a difference that is usually pleasant
- a collection containing a variety of sorts of things
- a show consisting of a series of short unrelated performances
adj
- (universal algebra, of an algebraic structure) Containing more than one element, and such that the only congruences on the structure are the diagonal relation (the equivalence relation a≡b⟺a=b) and the universal relation (the equivalence relation such that a≡b for all a,b). Equivalently, containing more than one element and having no proper non-trivial quotient algebras.
- (module theory, of a module) Being non-trivial, and having no proper non-trivial submodules (equivalently, no proper non-trivial quotient modules).
- Uncomplicated; lacking complexity; taken by itself, with nothing added.
- Free from duplicity; guileless, innocent, straightforward.
- (botany) Not compound, but possibly lobed.
- Easy; not difficult.
- (now colloquial, euphemistic) Feeble-minded; foolish.
- (zoology) Consisting of a single individual or zooid; not compound.
- (algebra, of a Lie algebra) Being non-abelian and having no proper non-zero ideals. (Note that this is non-equivalent to the usual algebra sense; in particular, the abelian Lie algebra of dimension 1 over any given field is non-trivial and has no proper non-zero ideals, but is by convention not considered simple.)
- (mineralogy) Homogenous.
- (ring theory, of a ring) Being non-zero, and having no proper non-zero two-sided ideals (equivalently, no proper non-trivial quotient rings). For commutative rings, this definition coincides with that of a field.
- Without ornamentation; plain.
- (mathematics, real analysis, measure theory, of a real-valued function) Equal to a finite linear combination of indicator functions on measurable sets.
- (group theory, of a group) Being non-trivial, and having no proper non-trivial normal subgroups (equivalently, no proper non-trivial quotient groups).
- Undistinguished in social condition; of no special rank.
- (category theory, of an object in a category with a terminal object) Being non-isomorphic to the terminal object, and such that its only quotient objects (up to isomorphism) are the terminal object and itself.
- (chemistry, pharmacology) Consisting of one single substance; uncompounded.
- Using steam only once in its cylinders, in contrast to a compound engine, where steam is used more than once in high-pressure and low-pressure cylinders. (of a steam engine)
- exhibiting childlike simplicity and credulity
- (botany) of leaf shapes; of leaves having no divisions or subdivisions
- having few parts; not complex or complicated or involved
- apart from anything else; without additions or modifications
- easy and not involved or complicated
- lacking mental capacity and subtlety
- unornamented
noun
- (weaving) A drawloom.
- (logic) A simple or atomic proposition.
- (pharmacology) A herbal preparation made from one plant, as opposed to something made from more than one plant.
- (Roman Catholicism) A feast which is not a double or a semidouble.
- (weaving) Part of the apparatus for raising the heddles of a drawloom.
- a person lacking intelligence or common sense
- any herbaceous plant having medicinal properties
adj
- (algebra, of an ideal) Having its complement closed under multiplication.
- Early; blooming; being in the first stage.
- First in excellence, quality, or value.
- First in importance, degree, or rank.
- (algebra, of a nonzero module) Such that the annihilator of any nonzero submodule is equal to the annihilator of the whole module.
- First in time, order, or sequence.
- Marked or distinguished by the prime symbol.
- (mathematics, technical) Such that if it divides a product, it divides one of the multiplicands.
- (mathematics, lay) Having exactly two integral factors: itself and unity (1 in the case of integers).
- used of the first or originating agent
- being at the best stage of development
- first in rank or degree
- of or relating to or being an integer that cannot be factored into other integers
- of superior grade
noun
- (Christianity) The religious service appointed to this hour.
- (historical) The first hour of daylight; the first canonical hour.
- The symbol ′ used to indicate feet, minutes, derivation and other measures and mathematical operations.
- (algebra, number theory) A prime element of a mathematical structure, particularly a prime number.
- The most active, thriving, or successful stage or period.
- A feather, from the wing of the cock ostrich, that is of the palest possible shade.
- (psychology) A stimulus which causes priming.
- The chief or best individual or part.
- An inch, as composed of twelve seconds in the duodecimal system.
- (backgammon) A series of consecutive blocks. A prime of six prevents the opponent's pieces from passing.
- (fencing) The first defensive position, with the sword hand held at head height, and the tip of the sword at head height.
- (card games) A four-card hand containing one card of each suit in the game of primero; the opposite of a flush in poker.
- Something which is first in importance or rank: a prime defense company, mortgage lender, etc.
- (film) Contraction of prime lens, a film lens.
- (cycling) An intermediate sprint within a race, usually offering a prize and/or points.
- (music) The first note or tone of a musical scale.
- the period of greatest prosperity or productivity
- a natural number that has exactly two distinct natural number divisors: 1 and itself
- the second canonical hour; about 6 a.m.
- the time of maturity when power and vigor are greatest
verb
- (mathematics) To mark with a prime mark.
- (transitive) To fill or prepare the chamber of a mechanism for its main work.
- To apply priming to (a musket or cannon); to apply a primer to (a metallic cartridge).
- (intransitive, of a steam boiler) To work so that foaming occurs from too violent ebullition, which causes water to become mixed with, and be carried along with, the steam that is formed.
- (intransitive) To serve as priming for the charge of a gun.
- To prepare; to make ready.
- (transitive) To apply a coat of primer paint to.
- fill with priming liquid
- cover with a primer; apply a primer to
- insert a primer into (a gun, mine, or charge) preparatory to detonation or firing
adj
- (algebra, commutative algebra, of a ring element in a ring B relative to a subring A) Being the root of some monic polynomial in A.
- Constituting a whole together with other parts or factors; not omittable or removable.
- (mathematics) Relating to integration (“the process of finding the integral [noun] of a function”).
- (mathematics) Of, pertaining to, or being an integer.
- constituting the undiminished entirety; lacking nothing essential especially not damaged
- of or denoted by an integer
- existing as an essential constituent or characteristic
noun
- (mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.
- (mathematics) A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign.
- (specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
- (mathematics) An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;
- the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)
adj
- (mathematics, multilinear algebra, of a bilinear form) That is alternating and nondegenerate.
- (mathematics, multilinear algebra, of a vector space) That is equipped with an alternating nondegenerate bilinear form.
- (petrology, mineralogy) Of or pertaining to a symplectite; symplectitic.
- (group theory, of a group) Whose characteristic abelian subgroups are cyclic.
- That moves in the same direction as a system of synchronized waves.
- (mathematics) Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form.
- Placed in or among, as if woven together.
noun
adj
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- (geometry) Of or relating to homogeneous coordinates.
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature
noun
adj
adj
- (linear algebra, of a matrix) Which commutes with its conjugate transpose.
- (commutative algebra, of a ring) Such that all of its localizations at prime ideals are integrally closed domains.
- (topology, of a topology or topological space) In which disjoint closed sets can be separated by disjoint neighborhoods.
- (complex analysis, of a family of continuous functions) Which is pre-compact.
- (commutative algebra, of a domain) Integrally closed: equal its own integral closure in its field of fractions.
- (functional analysis, of a Hilbert space operator) Which commutes with its adjoint.
- (probability theory, statistics, of a distribution, random variable, etc.) Which has a very specific bell curve shape; that is or has the qualities of a normal distribution.
- (physics, of a mode in an oscillating system) In which all parts of an object vibrate at the same frequency (a normal mode).
- (rail transport, of points) In the default position, set for the most frequently used route.
- (chemistry) Of, relating to, or being a solution containing one equivalent weight of solute per litre of solution.
- (category theory, of a category) Which contains only normal morphisms.
- (organic chemistry) Describing a straight chain isomer of an aliphatic hydrocarbon, or an aliphatic compound in which a substituent is in the 1- position of such a hydrocarbon.
- (fandom slang, sarcastic, with “about”) Fervently interested in a subject; obsessed.
- (algebraic geometry, of a variety or scheme) Such that the local ring at every point is an integrally closed domain.
- (category theory, of a morphism) Which is the kernel or cokernel of some morphism, respectively.
- (number theory, of a real number) In whose representation in a given base b ≥ 2, for every positive integer n, the bⁿ possible strings of n digits follow a uniform distribution.
- Usual, healthy; not sick or ill or unlike oneself.
- (set theory, of a function from the ordinals to the ordinals) Which is strictly monotonically increasing and continuous with respect to the order topology.
- (algebra, of a field extension of a field K) Which is the splitting field of a family of polynomials in K.
- (algebra, of a subgroup) With cosets which form a group.
- (education, of a school) Teaching teachers how to teach; teaching teachers the norms of education.
- According to norms or rules or to a regular pattern.
- (geometry) Perpendicular to a tangent of a curve or tangent plane of a surface.
- in accordance with scientific laws
- conforming with or constituting a norm or standard or level or type or social norm; not abnormal
- forming a right angle
- being approximately average or within certain limits in e.g. intelligence and development
noun
- (geometry, countable) A line or vector that is perpendicular to another line, surface, or plane.
- (medicine, countable) A person who is healthy, normal, as opposed to one who is morbid.
- (slang, countable) A person who is normal, who fits into mainstream society, as opposed to those who live alternative lifestyles.
- (countable, uncountable) The usual state.
- something regarded as a normative example
noun
- (algebra) Any of certain algebraic objects (ring, field or vector space, etc., whose definition includes a commutative operation called addition) regarded as a group under addition.
- (category theory) Any group object (such as a group functor, group scheme, etc.), whose binary operation is called addition.
- (group theory) Any (often, but not necessarily, abelian) group whose binary operation is called addition.
noun
- (mathematics) homogeneous polynomial
- (mathematics) a function f(x) which has the property that for any c, f(cx)=cf(x).
- (mathematics) the ratio of two homogeneous polynomials, such that the sum of the exponents in a term of the numerator is equal to the sum of the exponents in a term of the denominator.
noun
adj
- (linear algebra, of a function in two variables) Linear (preserving linear combinations) in each variable.
- (complex analysis, physics, engineering) Of or pertaining to a Möbius transformation (type of conformal map representable as the ratio of two linear functions).
- linear with respect to each of two variables or positions
adj
- (linear algebra, of an operator or matrix) For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.
- (module theory, of a module) In which each submodule is a direct summand; equivalently, equal to a direct sum of simple submodules.
- (representation theory, of a linear representation of a group or algebra) Being a direct sum of simple representations (also known as irreducible representations).
- (ring theory, of an algebra or ring) Semisimple as a module over itself; equivalently, such that all (left) modules are semisimple.
- (category theory, most generally, of an abelian category) Containing a collection of simple objects such that all objects in the category are direct sums of these simple objects.
- (Lie theory, of a Lie algebra) Being a direct sum of simple Lie algebras.
- (group theory, of an algebraic group) Being a linear algebraic group whose radical of the identity component is trivial.
- (of a ring, somewhat proscribed) Semiprimitive: having trivial Jacobson radical.
noun
- (commutative algebra, of a module M over a commutative ring R) The set of all prime ideals of R such that the localization of M at the prime is nonzero, denoted operatorname SuppM
- (sometimes attributive) Something which supports.
- An accompaniment in music.
- Evidence.
- (fuzzy set theory) A set whose elements are at least partially included in a given fuzzy set (i.e., whose grade of membership in that fuzzy set is strictly greater than zero).
- (mathematics) in relation to a function, the set of points where the function is not zero; the closure of that set.
- (structural analysis) Horizontal, vertical or rotational support of structures: movable, hinged, fixed.
- An actor playing a subordinate part with a star.
- (computing) Compatibility and functionality for a given product or feature.
- Answers to questions and resolution of problems regarding something sold.
- Financial or other help.
- (gymnastics) Clipping of support position.
- financial resources provided to make some project possible
- any device that bears the weight of another thing
- the act of bearing the weight of or strengthening
- supporting structure that holds up or provides a foundation
- a military operation (often involving new supplies of men and materiel) to strengthen a military force or aid in the performance of its mission
- aiding the cause or policy or interests of
- the activity of providing for or maintaining by supplying with money or necessities
- something providing immaterial assistance to a person or cause or interest
- the financial means whereby one lives
- a musical part (vocal or instrumental) that supports or provides background for other musical parts
- documentary validation
verb
- (transitive) To answer questions and resolve problems regarding something sold.
- (transitive) To serve, as in a customer-oriented position; to give support to.
- (transitive) To provide evidence for; to lend credibility to.
- (transitive) To provide sustenance or maintenance for; to sustain in integrity or livelihood.
- (transitive) To back or favor a cause, party, etc., mentally or with concrete aid:
- (transitive) To help keep from falling.
- (transitive) To play a lesser part in the same production with (a star performer).
- (transitive) To assist or be involved with, but not be responsible for.
- (transitive) To help, particularly financially; to subsidize.
- (transitive, said of electronic devices, programming languages, etc.) To be designed to provide capacity for; to work or be compatible with (a part, accessory, file type, program, algorithm, etc.).
- be the physical support of; carry the weight of
- be a regular customer or client of
- put up with something or somebody unpleasant
- argue or speak in defense of
- support with evidence or authority or make more certain or confirm
- adopt as a belief
- give moral or psychological support, aid, or courage to
- establish or strengthen as with new evidence or facts
- play a subordinate role to (another performer)
- be behind; approve of
- support materially or financially
noun
- (algebra, of a coalgebra over an element g) An element x ∈ C such that μ(x) = x ⊗ g + g ⊗ x, where μ is the comultiplication and g is an element that maps to the multiplicative identity 1 of the base field under the counit (in particular, if C is a bialgebra, g = 1).
- (algebra, lattice theory, of a lattice) An element that is not a positive integer multiple of another element of the lattice.
- (algebra, field theory) An element that generates a simple extension.
- (number theory) Given a modulus n, a number g such that every number coprime to n is congruent (modulo n) to some power of g; equivalently, a generator of the multiplicative field of integers modulo n.
- (group theory, of a free group) An element of a free generating set of a given free group.
- (algebra, field theory, of a finite field) An element that generates the multiplicative group of a given Galois field (finite field).
noun
adj
name
noun
adj
noun
- (algebra, of a monomial) The sum of the exponents of the variables involved in the expression.
- (Christianity) An ecclesiastical rank or position, usually for the sake of ministry, (especially, when plural) holy orders.
- (countable) An association of knights.
- (sciences, engineering, logic) Scale: size or scope.
- (order theory) A partially ordered set.
- (architecture) The disposition of a column and its component parts, and of the entablature resting upon it, in classical architecture; hence (since the column and entablature are the characteristic features of classical architecture) a style or manner of architectural design.
- (countable) Conformity with law or decorum; freedom from disturbance; general tranquillity; public quiet.
- (chemistry) The overall power of the rate law of a chemical reaction, expressed as a polynomial function of concentrations of reactants and products.
- (countable) A request for some product or service; a commission to purchase, sell, or supply goods.
- (uncountable) The state of being well arranged.
- (graph theory, of a graph) The number of vertices in the graph (i.e. the set-theoretic order of the set of vertices of the graph).
- (set theory, of a set or algebraic structure) The number of elements contained within (the given object); formally, the cardinality (of the given object).
- A number of things or persons arranged in a fixed or suitable place, or relative position; a rank; a row; a grade; especially, a rank or class in society; a distinct character, kind, or sort.
- Any group of people with common interests.
- (countable) A command.
- (electronics) A power of polynomial function in an electronic circuit’s block, such as a filter, an amplifier, etc.
- (order theory) The relation with which a partially ordered set is equipped.
- (finance) A written direction to furnish someone with money or property; compare money order, postal order.
- (countable) A position in an arrangement, disposition, or sequence.
- (group theory, of an element g of a group G) The smallest positive natural number n such that (denoting the group operation multiplicatively) gⁿ is the identity element of G, if such an n exists; if no such n exists the element is said to be of infinite order (or sometimes zero order).
- (countable) A decoration, awarded by a government, a dynastic house, or a religious body to an individual, usually for distinguished service to a nation or to humanity.
- (countable, biology, taxonomy) A category in the classification of organisms, ranking below class and above family; a taxon at that rank.
- (cricket) The sequence in which a side’s batsmen bat; the batting order.
- (algebra, of a polynomial in one variable) The order of the leading monomial; (equivalently) the largest power of the variable involved in the given expression.
- (countable) Arrangement, disposition, or sequence.
- (countable) A group of religious adherents, especially monks or nuns, set apart within their religion by adherence to a particular rule or set of principles.
- a request for something to be made, supplied, or served
- established customary state (especially of society)
- logical or comprehensible arrangement of separate elements
- a body of rules followed by an assembly
- a formal association of people with similar interests
- a commercial document used to request someone to supply something in return for payment and providing specifications and quantities
- the act of putting things in a sequential arrangement
- a degree in a continuum of size or quantity
- a condition of regular or proper arrangement
- (often plural) a command given by a superior (e.g., a military or law enforcement officer) that must be obeyed
- a group of person living under a religious rule
- (biology) taxonomic group containing one or more families
- a legally binding command or decision entered on the court record (as if issued by a court or judge)
- (architecture) one of original three styles of Greek architecture distinguished by the type of column and entablature used or a style developed from the original three by the Romans
verb
- (transitive) To set in some sort of order.
- (transitive) To issue a command to; to charge.
- (transitive) To arrange, set in proper order.
- To admit to holy orders; to ordain; to receive into the ranks of the ministry.
- (transitive) To request some product or service; to secure by placing an order.
- give instructions to or direct somebody to do something with authority
- issue commands or orders for
- arrange thoughts, ideas, temporal events
- bring into conformity with rules or principles or usage; impose regulations
- bring order to or into
- make a request for something
- appoint to a clerical posts
- place in a certain order
- assign a rank or rating to
adj
- (commutative algebra, of a finite module over a noetherian local ring) Such that its depth is equal to its Krull dimension.
- (commutative algebra, of a noetherian local ring) Cohen-Macaulay as a module over itself.
- (commutative algebra, of a module M over a noetherian ring) Such that all localizations of M at maximal ideals contained in the support of M are either Cohen-Macaulay or trivial.
- (commutative algebra, of a noetherian ring) Cohen-Macaulay as a module over itself.
noun
adj
- (object-oriented programming) Using or relating to covariance.
- (category theory, of a functor) Which preserves the order of morphism composition: formally, which associates each morphism f:X→Y to a morphism F(f):F(X)→F(Y).
- changing so that interrelations with another variable quantity or set of quantities remain unchanged
noun
- (commutative algebra) Clipping of uniformizing parameter.
- (programming, loosely) An actual value given to such a formal parameter.
- A value kept constant during an experiment, equation, calculation, or similar, but varied over other versions of the experiment, equation, calculation, etc.
- (crystallography) The ratio of the three crystallographic axes which determines the position of any plane.
- (sciences) A variable that describes a property or characteristic of some system (material, object, event, etc.) or some aspect thereof.
- (geometry) In the ellipse and hyperbola, a third proportional to any diameter and its conjugate, or in the parabola, to any abscissa and the corresponding ordinate.
- (programming) An input variable of a function definition, that gets an actual value (argument) at execution time.
- A characteristic or feature that distinguishes something from others.
- (crystallography) The fundamental axial ratio for a given species.
- (statistics) Any measured quantity of a statistical population that summarises or describes an aspect of the population.
- (machine learning) A variable of a model that is trained by a machine learning algorithm.
- a constant in the equation of a curve that can be varied to yield a family of similar curves
- any factor that defines a system and determines (or limits) its performance
- a quantity (such as the mean or variance) that characterizes a statistical population and that can be estimated by calculations from sample data
- (computer science) a reference or value that is passed to a function, procedure, subroutine, command, or program
noun
- A universal algebra.
- (figurative) A system or process (especially one that is complex or convoluted) that substitutes one thing for another, or uses signs or symbols to represent concepts or ideas.
- An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.
- (countable, set theory, mathematical analysis) A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).
- (uncountable, mathematics, sometimes capitalized) Abstract algebra: A broad field of study in modern mathematics (often mentioned alongside analysis) loosely characterized by its concern for abstraction and symmetry, dealing with the behavior, classification, and application of a large class of objects (called algebraic structures) and the maps between them (called, most generally, morphisms).
- (uncountable, medicine, historical, rare) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
- (uncountable, mathematics) Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.
- the mathematics of generalized arithmetical operations
noun
adj
noun
- (universal algebra) Any equivalence relation defined on an algebraic structure which is preserved by operations defined by the structure.
- (mathematics, linear algebra) Matrix similarity by an orthogonal matrix.
- (mathematics, geometry) The quality of being isometric — roughly, the same measure and shape.
- (psychology) A well-adjusted state or condition in which people are not lying to themselves or in denial.
- (mathematics, number theory) A relation between two numbers indicating they give the same remainder when divided by some given number.
- The quality of agreeing or corresponding; being suitable and appropriate.
- the quality of agreeing; being suitable and appropriate
noun
- (algebra) An algebraic structure (Σ,∨,∧,∼,0,1) where ∨ and ∧ are idempotent binary operators, ∼ is a unary involutory operator (called "complement"), and 0 and 1 are nullary operators (i.e., constants), such that (Σ,∨,0) is a commutative monoid, (Σ,∧,1) is a commutative monoid, ∧ and ∨ distribute with respect to each other, and such that combining two complementary elements through one binary operator yields the identity of the other binary operator. (See Boolean algebra (structure)#Axiomatics.)
- (algebra, logic, computing) Specifically, an algebra in which all elements can take only one of two values (typically 0 and 1, or "true" and "false") and are subject to operations based on AND, OR and NOT
- (mathematics) The study of such algebras; Boolean logic, classical logic.
- a system of symbolic logic devised by George Boole; used in computers
noun
- In universal algebra: an equational class; the class of all algebraic structures of a given signature, satisfying a given set of identities.
- A specific variation of something.
- (cybernetics) The total number of distinct states of a system; also, the logarithm to the base 2 of the total number of distinct states of a system.
- A deviation or difference.
- (radio, television, theater) Ellipsis of variety performance or variety show (“a type of entertainment featuring a succession of short, unrelated performances by various artistes such as (depending on the medium) acrobats, comedians, dancers, magicians, singers, etc.”).
- (linguistics) A specific form of a language, neutral to whether that form is an accent, dialect, register, etc., and to its prestige level; an isolect or lect.
- (radio, television, theater) The kind of entertainment given in variety performances or shows; also, the production of, or performance in, variety performances or shows.
- (algebraic geometry) Ellipsis of algebraic variety (“the set of solutions of a given system of polynomial equations over the real or complex numbers; any of certain generalisations of such a set that preserves the geometric intuition implicit in the original definition”).
- (botany, taxonomy) A rank in a taxonomic classification below species and (if present) subspecies, and above form; hence, an organism of that rank.
- A collection or number of different things.
- The quality of being varied; diversity.
- (philately) A stamp, or set of stamps, which has one or more characteristics (such as colour, paper, etc.) differing from other stamps in the same issue, especially if such differences are intentionally introduced.
- (biology, loosely) An animal or plant (or a group of such animals or plants) with characteristics causing it to differ from other animals or plants of the same species; a strain or cultivar.
- (biology) a taxonomic category consisting of members of a species that differ from others of the same species in minor but heritable characteristics
- a category of things distinguished by some common characteristic or quality
- noticeable heterogeneity
- a difference that is usually pleasant
- a collection containing a variety of sorts of things
- a show consisting of a series of short unrelated performances
noun
adj
noun
- (algebra) Any of certain algebraic objects (ring, field or vector space, etc., whose definition includes a commutative operation called addition) regarded as a group under addition.
- (category theory) Any group object (such as a group functor, group scheme, etc.), whose binary operation is called addition.
- (group theory) Any (often, but not necessarily, abelian) group whose binary operation is called addition.
noun
- (mathematics) homogeneous polynomial
- (mathematics) a function f(x) which has the property that for any c, f(cx)=cf(x).
- (mathematics) the ratio of two homogeneous polynomials, such that the sum of the exponents in a term of the numerator is equal to the sum of the exponents in a term of the denominator.
noun
adj
- (linear algebra, of a function in two variables) Linear (preserving linear combinations) in each variable.
- (complex analysis, physics, engineering) Of or pertaining to a Möbius transformation (type of conformal map representable as the ratio of two linear functions).
- linear with respect to each of two variables or positions
noun
- (commutative algebra, of a module M over a commutative ring R) The set of all prime ideals of R such that the localization of M at the prime is nonzero, denoted operatorname SuppM
- (sometimes attributive) Something which supports.
- An accompaniment in music.
- Evidence.
- (fuzzy set theory) A set whose elements are at least partially included in a given fuzzy set (i.e., whose grade of membership in that fuzzy set is strictly greater than zero).
- (mathematics) in relation to a function, the set of points where the function is not zero; the closure of that set.
- (structural analysis) Horizontal, vertical or rotational support of structures: movable, hinged, fixed.
- An actor playing a subordinate part with a star.
- (computing) Compatibility and functionality for a given product or feature.
- Answers to questions and resolution of problems regarding something sold.
- Financial or other help.
- (gymnastics) Clipping of support position.
- financial resources provided to make some project possible
- any device that bears the weight of another thing
- the act of bearing the weight of or strengthening
- supporting structure that holds up or provides a foundation
- a military operation (often involving new supplies of men and materiel) to strengthen a military force or aid in the performance of its mission
- aiding the cause or policy or interests of
- the activity of providing for or maintaining by supplying with money or necessities
- something providing immaterial assistance to a person or cause or interest
- the financial means whereby one lives
- a musical part (vocal or instrumental) that supports or provides background for other musical parts
- documentary validation
verb
- (transitive) To answer questions and resolve problems regarding something sold.
- (transitive) To serve, as in a customer-oriented position; to give support to.
- (transitive) To provide evidence for; to lend credibility to.
- (transitive) To provide sustenance or maintenance for; to sustain in integrity or livelihood.
- (transitive) To back or favor a cause, party, etc., mentally or with concrete aid:
- (transitive) To help keep from falling.
- (transitive) To play a lesser part in the same production with (a star performer).
- (transitive) To assist or be involved with, but not be responsible for.
- (transitive) To help, particularly financially; to subsidize.
- (transitive, said of electronic devices, programming languages, etc.) To be designed to provide capacity for; to work or be compatible with (a part, accessory, file type, program, algorithm, etc.).
- be the physical support of; carry the weight of
- be a regular customer or client of
- put up with something or somebody unpleasant
- argue or speak in defense of
- support with evidence or authority or make more certain or confirm
- adopt as a belief
- give moral or psychological support, aid, or courage to
- establish or strengthen as with new evidence or facts
- play a subordinate role to (another performer)
- be behind; approve of
- support materially or financially
noun
- (algebra, of a coalgebra over an element g) An element x ∈ C such that μ(x) = x ⊗ g + g ⊗ x, where μ is the comultiplication and g is an element that maps to the multiplicative identity 1 of the base field under the counit (in particular, if C is a bialgebra, g = 1).
- (algebra, lattice theory, of a lattice) An element that is not a positive integer multiple of another element of the lattice.
- (algebra, field theory) An element that generates a simple extension.
- (number theory) Given a modulus n, a number g such that every number coprime to n is congruent (modulo n) to some power of g; equivalently, a generator of the multiplicative field of integers modulo n.
- (group theory, of a free group) An element of a free generating set of a given free group.
- (algebra, field theory, of a finite field) An element that generates the multiplicative group of a given Galois field (finite field).
noun
adj
name
noun
adj
noun
- (algebra, of a monomial) The sum of the exponents of the variables involved in the expression.
- (Christianity) An ecclesiastical rank or position, usually for the sake of ministry, (especially, when plural) holy orders.
- (countable) An association of knights.
- (sciences, engineering, logic) Scale: size or scope.
- (order theory) A partially ordered set.
- (architecture) The disposition of a column and its component parts, and of the entablature resting upon it, in classical architecture; hence (since the column and entablature are the characteristic features of classical architecture) a style or manner of architectural design.
- (countable) Conformity with law or decorum; freedom from disturbance; general tranquillity; public quiet.
- (chemistry) The overall power of the rate law of a chemical reaction, expressed as a polynomial function of concentrations of reactants and products.
- (countable) A request for some product or service; a commission to purchase, sell, or supply goods.
- (uncountable) The state of being well arranged.
- (graph theory, of a graph) The number of vertices in the graph (i.e. the set-theoretic order of the set of vertices of the graph).
- (set theory, of a set or algebraic structure) The number of elements contained within (the given object); formally, the cardinality (of the given object).
- A number of things or persons arranged in a fixed or suitable place, or relative position; a rank; a row; a grade; especially, a rank or class in society; a distinct character, kind, or sort.
- Any group of people with common interests.
- (countable) A command.
- (electronics) A power of polynomial function in an electronic circuit’s block, such as a filter, an amplifier, etc.
- (order theory) The relation with which a partially ordered set is equipped.
- (finance) A written direction to furnish someone with money or property; compare money order, postal order.
- (countable) A position in an arrangement, disposition, or sequence.
- (group theory, of an element g of a group G) The smallest positive natural number n such that (denoting the group operation multiplicatively) gⁿ is the identity element of G, if such an n exists; if no such n exists the element is said to be of infinite order (or sometimes zero order).
- (countable) A decoration, awarded by a government, a dynastic house, or a religious body to an individual, usually for distinguished service to a nation or to humanity.
- (countable, biology, taxonomy) A category in the classification of organisms, ranking below class and above family; a taxon at that rank.
- (cricket) The sequence in which a side’s batsmen bat; the batting order.
- (algebra, of a polynomial in one variable) The order of the leading monomial; (equivalently) the largest power of the variable involved in the given expression.
- (countable) Arrangement, disposition, or sequence.
- (countable) A group of religious adherents, especially monks or nuns, set apart within their religion by adherence to a particular rule or set of principles.
- a request for something to be made, supplied, or served
- established customary state (especially of society)
- logical or comprehensible arrangement of separate elements
- a body of rules followed by an assembly
- a formal association of people with similar interests
- a commercial document used to request someone to supply something in return for payment and providing specifications and quantities
- the act of putting things in a sequential arrangement
- a degree in a continuum of size or quantity
- a condition of regular or proper arrangement
- (often plural) a command given by a superior (e.g., a military or law enforcement officer) that must be obeyed
- a group of person living under a religious rule
- (biology) taxonomic group containing one or more families
- a legally binding command or decision entered on the court record (as if issued by a court or judge)
- (architecture) one of original three styles of Greek architecture distinguished by the type of column and entablature used or a style developed from the original three by the Romans
verb
- (transitive) To set in some sort of order.
- (transitive) To issue a command to; to charge.
- (transitive) To arrange, set in proper order.
- To admit to holy orders; to ordain; to receive into the ranks of the ministry.
- (transitive) To request some product or service; to secure by placing an order.
- give instructions to or direct somebody to do something with authority
- issue commands or orders for
- arrange thoughts, ideas, temporal events
- bring into conformity with rules or principles or usage; impose regulations
- bring order to or into
- make a request for something
- appoint to a clerical posts
- place in a certain order
- assign a rank or rating to
noun
adj
- (object-oriented programming) Using or relating to covariance.
- (category theory, of a functor) Which preserves the order of morphism composition: formally, which associates each morphism f:X→Y to a morphism F(f):F(X)→F(Y).
- changing so that interrelations with another variable quantity or set of quantities remain unchanged
Nessuna parola corrispondente trovata. Prova una descrizione più ampia.
adj
- (commutative algebra, of an ideal) Generated by differences of monomials.
- (algebraic geometry, of a stack) Any of several generalizations of the notion of toric varieties to stacks: the stack quotient of a toric variety by its torus; the stack quotient of a toric variety by a subgroup of its torus.
- (algebraic geometry, of a variety) Containing an algebraic torus as a dense subset, such that the group action of the torus on itself extends to the whole space; or, the embedding map taking the torus into the space. See Toric variety on Wikipedia.Wikipedia
- (geometry, algebra) Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.
- (error correction) A particular topological quantum error correcting code; see Toric code on Wikipedia.Wikipedia
- (geometry, of a manifold, generalizing the case of toric varieties) (Narrowly) A compact smooth toric variety. (Broadly) Quasitoric: a closed, real, even-dimensional smooth manifold equipped with an effective, smooth action by an algebraic torus whose orbits are simple complex polytopes and such that the action is locally the same as a faithful real representation of the group.
adj
- (algebra, of an algebraic structure) Having a commutative operation.
- (mathematics, of a binary operation) Such that the order in which the operands are taken does not affect their image under the operation.
- Relating to exchange; interchangeable.
- (mathematics, of a diagram of morphisms) Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.
- (of a binary operation) independent of order; as in e.g.: ‘a x b’ = ‘b x a’
adj
- (universal algebra, of an algebraic structure) Containing more than one element, and such that the only congruences on the structure are the diagonal relation (the equivalence relation a≡b⟺a=b) and the universal relation (the equivalence relation such that a≡b for all a,b). Equivalently, containing more than one element and having no proper non-trivial quotient algebras.
- (module theory, of a module) Being non-trivial, and having no proper non-trivial submodules (equivalently, no proper non-trivial quotient modules).
- Uncomplicated; lacking complexity; taken by itself, with nothing added.
- Free from duplicity; guileless, innocent, straightforward.
- (botany) Not compound, but possibly lobed.
- Easy; not difficult.
- (now colloquial, euphemistic) Feeble-minded; foolish.
- (zoology) Consisting of a single individual or zooid; not compound.
- (algebra, of a Lie algebra) Being non-abelian and having no proper non-zero ideals. (Note that this is non-equivalent to the usual algebra sense; in particular, the abelian Lie algebra of dimension 1 over any given field is non-trivial and has no proper non-zero ideals, but is by convention not considered simple.)
- (mineralogy) Homogenous.
- (ring theory, of a ring) Being non-zero, and having no proper non-zero two-sided ideals (equivalently, no proper non-trivial quotient rings). For commutative rings, this definition coincides with that of a field.
- Without ornamentation; plain.
- (mathematics, real analysis, measure theory, of a real-valued function) Equal to a finite linear combination of indicator functions on measurable sets.
- (group theory, of a group) Being non-trivial, and having no proper non-trivial normal subgroups (equivalently, no proper non-trivial quotient groups).
- Undistinguished in social condition; of no special rank.
- (category theory, of an object in a category with a terminal object) Being non-isomorphic to the terminal object, and such that its only quotient objects (up to isomorphism) are the terminal object and itself.
- (chemistry, pharmacology) Consisting of one single substance; uncompounded.
- Using steam only once in its cylinders, in contrast to a compound engine, where steam is used more than once in high-pressure and low-pressure cylinders. (of a steam engine)
- exhibiting childlike simplicity and credulity
- (botany) of leaf shapes; of leaves having no divisions or subdivisions
- having few parts; not complex or complicated or involved
- apart from anything else; without additions or modifications
- easy and not involved or complicated
- lacking mental capacity and subtlety
- unornamented
noun
- (weaving) A drawloom.
- (logic) A simple or atomic proposition.
- (pharmacology) A herbal preparation made from one plant, as opposed to something made from more than one plant.
- (Roman Catholicism) A feast which is not a double or a semidouble.
- (weaving) Part of the apparatus for raising the heddles of a drawloom.
- a person lacking intelligence or common sense
- any herbaceous plant having medicinal properties
adj
- (algebra, of an ideal) Having its complement closed under multiplication.
- Early; blooming; being in the first stage.
- First in excellence, quality, or value.
- First in importance, degree, or rank.
- (algebra, of a nonzero module) Such that the annihilator of any nonzero submodule is equal to the annihilator of the whole module.
- First in time, order, or sequence.
- Marked or distinguished by the prime symbol.
- (mathematics, technical) Such that if it divides a product, it divides one of the multiplicands.
- (mathematics, lay) Having exactly two integral factors: itself and unity (1 in the case of integers).
- used of the first or originating agent
- being at the best stage of development
- first in rank or degree
- of or relating to or being an integer that cannot be factored into other integers
- of superior grade
noun
- (Christianity) The religious service appointed to this hour.
- (historical) The first hour of daylight; the first canonical hour.
- The symbol ′ used to indicate feet, minutes, derivation and other measures and mathematical operations.
- (algebra, number theory) A prime element of a mathematical structure, particularly a prime number.
- The most active, thriving, or successful stage or period.
- A feather, from the wing of the cock ostrich, that is of the palest possible shade.
- (psychology) A stimulus which causes priming.
- The chief or best individual or part.
- An inch, as composed of twelve seconds in the duodecimal system.
- (backgammon) A series of consecutive blocks. A prime of six prevents the opponent's pieces from passing.
- (fencing) The first defensive position, with the sword hand held at head height, and the tip of the sword at head height.
- (card games) A four-card hand containing one card of each suit in the game of primero; the opposite of a flush in poker.
- Something which is first in importance or rank: a prime defense company, mortgage lender, etc.
- (film) Contraction of prime lens, a film lens.
- (cycling) An intermediate sprint within a race, usually offering a prize and/or points.
- (music) The first note or tone of a musical scale.
- the period of greatest prosperity or productivity
- a natural number that has exactly two distinct natural number divisors: 1 and itself
- the second canonical hour; about 6 a.m.
- the time of maturity when power and vigor are greatest
verb
- (mathematics) To mark with a prime mark.
- (transitive) To fill or prepare the chamber of a mechanism for its main work.
- To apply priming to (a musket or cannon); to apply a primer to (a metallic cartridge).
- (intransitive, of a steam boiler) To work so that foaming occurs from too violent ebullition, which causes water to become mixed with, and be carried along with, the steam that is formed.
- (intransitive) To serve as priming for the charge of a gun.
- To prepare; to make ready.
- (transitive) To apply a coat of primer paint to.
- fill with priming liquid
- cover with a primer; apply a primer to
- insert a primer into (a gun, mine, or charge) preparatory to detonation or firing
adj
- (algebra, commutative algebra, of a ring element in a ring B relative to a subring A) Being the root of some monic polynomial in A.
- Constituting a whole together with other parts or factors; not omittable or removable.
- (mathematics) Relating to integration (“the process of finding the integral [noun] of a function”).
- (mathematics) Of, pertaining to, or being an integer.
- constituting the undiminished entirety; lacking nothing essential especially not damaged
- of or denoted by an integer
- existing as an essential constituent or characteristic
noun
- (mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.
- (mathematics) A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign.
- (specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
- (mathematics) An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;
- the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)
adj
- (mathematics, multilinear algebra, of a bilinear form) That is alternating and nondegenerate.
- (mathematics, multilinear algebra, of a vector space) That is equipped with an alternating nondegenerate bilinear form.
- (petrology, mineralogy) Of or pertaining to a symplectite; symplectitic.
- (group theory, of a group) Whose characteristic abelian subgroups are cyclic.
- That moves in the same direction as a system of synchronized waves.
- (mathematics) Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form.
- Placed in or among, as if woven together.
noun
adj
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- (geometry) Of or relating to homogeneous coordinates.
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature
adj
- (linear algebra, of a matrix) Which commutes with its conjugate transpose.
- (commutative algebra, of a ring) Such that all of its localizations at prime ideals are integrally closed domains.
- (topology, of a topology or topological space) In which disjoint closed sets can be separated by disjoint neighborhoods.
- (complex analysis, of a family of continuous functions) Which is pre-compact.
- (commutative algebra, of a domain) Integrally closed: equal its own integral closure in its field of fractions.
- (functional analysis, of a Hilbert space operator) Which commutes with its adjoint.
- (probability theory, statistics, of a distribution, random variable, etc.) Which has a very specific bell curve shape; that is or has the qualities of a normal distribution.
- (physics, of a mode in an oscillating system) In which all parts of an object vibrate at the same frequency (a normal mode).
- (rail transport, of points) In the default position, set for the most frequently used route.
- (chemistry) Of, relating to, or being a solution containing one equivalent weight of solute per litre of solution.
- (category theory, of a category) Which contains only normal morphisms.
- (organic chemistry) Describing a straight chain isomer of an aliphatic hydrocarbon, or an aliphatic compound in which a substituent is in the 1- position of such a hydrocarbon.
- (fandom slang, sarcastic, with “about”) Fervently interested in a subject; obsessed.
- (algebraic geometry, of a variety or scheme) Such that the local ring at every point is an integrally closed domain.
- (category theory, of a morphism) Which is the kernel or cokernel of some morphism, respectively.
- (number theory, of a real number) In whose representation in a given base b ≥ 2, for every positive integer n, the bⁿ possible strings of n digits follow a uniform distribution.
- Usual, healthy; not sick or ill or unlike oneself.
- (set theory, of a function from the ordinals to the ordinals) Which is strictly monotonically increasing and continuous with respect to the order topology.
- (algebra, of a field extension of a field K) Which is the splitting field of a family of polynomials in K.
- (algebra, of a subgroup) With cosets which form a group.
- (education, of a school) Teaching teachers how to teach; teaching teachers the norms of education.
- According to norms or rules or to a regular pattern.
- (geometry) Perpendicular to a tangent of a curve or tangent plane of a surface.
- in accordance with scientific laws
- conforming with or constituting a norm or standard or level or type or social norm; not abnormal
- forming a right angle
- being approximately average or within certain limits in e.g. intelligence and development
noun
- (geometry, countable) A line or vector that is perpendicular to another line, surface, or plane.
- (medicine, countable) A person who is healthy, normal, as opposed to one who is morbid.
- (slang, countable) A person who is normal, who fits into mainstream society, as opposed to those who live alternative lifestyles.
- (countable, uncountable) The usual state.
- something regarded as a normative example
adj
- (linear algebra, of an operator or matrix) For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.
- (module theory, of a module) In which each submodule is a direct summand; equivalently, equal to a direct sum of simple submodules.
- (representation theory, of a linear representation of a group or algebra) Being a direct sum of simple representations (also known as irreducible representations).
- (ring theory, of an algebra or ring) Semisimple as a module over itself; equivalently, such that all (left) modules are semisimple.
- (category theory, most generally, of an abelian category) Containing a collection of simple objects such that all objects in the category are direct sums of these simple objects.
- (Lie theory, of a Lie algebra) Being a direct sum of simple Lie algebras.
- (group theory, of an algebraic group) Being a linear algebraic group whose radical of the identity component is trivial.
- (of a ring, somewhat proscribed) Semiprimitive: having trivial Jacobson radical.
adj
- (commutative algebra, of a finite module over a noetherian local ring) Such that its depth is equal to its Krull dimension.
- (commutative algebra, of a noetherian local ring) Cohen-Macaulay as a module over itself.
- (commutative algebra, of a module M over a noetherian ring) Such that all localizations of M at maximal ideals contained in the support of M are either Cohen-Macaulay or trivial.
- (commutative algebra, of a noetherian ring) Cohen-Macaulay as a module over itself.