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noun
- (algebraic geometry) A morphism between algebraic varieties.
- (graph theory) A symmetric tessellation of a closed surface; a decomposition of a two-dimensional manifold into topological disks such that every flag (incident vertex-edge-face triple) can be transformed into any other flag by a symmetry (i.e., an automorphism) of the decomposition.
adj
noun
- (multivariable calculus) The Jacobian matrix of a function of several variables.
- (calculus, of a univariate differentiable function f(x)) A function giving the change in the linear approximation of f at a point x over a small interval Δx or operatorname d!x, the function being called the differential of f and denoted operatorname d!f(x,Δx), operatorname d!f(x), or simply operatorname d!f.
- Any of several generalizations of this concept to functions of several variables or to higher orders: the partial differential, total differential, Gateaux differential, etc.
- One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.
- The differential gear in an automobile, etc.
- A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.
- (differential geometry, of a smooth map ϕ between smooth manifolds) The pushforward or total derivative of ϕ: a linear map from the tangent space at a point x in ϕ's domain to the tangent space at ϕ(x) which is, in a technical sense, the best linear approximation of ϕ at x; denoted operatorname d!ϕₓ.
- (mathematics) Any of several generalizations of the concept(s) above: e.g. the Kähler differential in the setting of schemes, the quadratic differential in the theory of Riemann surfaces, etc.
- (calculus) A quantity representing an infinitesimal change in a variable, now only used as a heuristic aid except in nonstandard analysis but considered rigorous until the 20th century; a fluxion in Newtonian calculus, now usually written in Leibniz's notation as operatorname d!x.
- A qualitative or quantitative difference between similar or comparable things.
- a quality that differentiates between similar things
- a bevel gear that permits rotation of two shafts at different speeds; used on the rear axle of automobiles to allow wheels to rotate at different speeds on curves
- the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
noun
- (mathematics) An element of the umbral calculus.
- The fully shaded inner region of a shadow cast by an opaque object.
- (astronomy) The area on the earth or moon experiencing the total phase of an eclipse.
- One of genus Umbrina of drums (family Sciaenidae).
- (astronomy) The central region of a sunspot.
- (chiefly literary) A shadow.
- One of the family Umbridae of mudminnows.
- a region of complete shadow resulting from total obstruction of light
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
- 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”).
- (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.
- (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
adj
- (mathematics, algebra) Whose coefficients are complex numbers; defined over the field of complex numbers.
- Made up of multiple parts; composite; not simple.
- (geometry) A curve, polygon or other figure that crosses or intersects itself.
- (mathematics, mathematical analysis, of a function) Whose range is a subset of the complex numbers.
- Not simple, easy, or straightforward; complicated.
- (mathematics, of a number) Having the form a + bi, where a and b are real numbers and i is (by definition) the imaginary square root of −1.
- difficult to analyze or understand
- complicated in structure; consisting of interconnected parts
noun
- (psychology) A group of emotionally charged ideas or mental factors, unconsciously associated by the individual with a particular subject, arising from repressed instincts, fears, or desires and often resulting in mental abnormality.
- (taxonomy) A group of closely related species, often distinguished only with difficulty by traditional morphological methods.
- (linguistics) A multimorphemic word, one with several parts, one with affixes.
- A collection of buildings with a common purpose, such as a university or military base.
- An organized cluster of thunderstorms.
- (chemistry) A structure consisting of a central atom or molecule weakly connected to surrounding atoms or molecules, as for example coordination compounds in inorganic chemistry and protein complexes in biochemistry.
- (mathematics) A complex number.
- A fixed mental tendency or obsession.
- A cluster of wildfires burning in the same vicinity.
- An assemblage of related things; a collection.
- A network of interconnected systems.
- a conceptual whole made up of complicated and related parts
- a compound described in terms of the central atom to which other atoms are bound or coordinated
- a whole structure (as a building) made up of interconnected or related structures
- (psychoanalysis) a combination of emotions and impulses that have been rejected from awareness but still influence a person's behavior
verb
adj
- (mathematical analysis) Being defined in terms of objects of differential calculus such as derivatives.
- Of, or relating to division into elements or principles.
- (mathematics, of a function) Being able to be locally represented by convergent power series around every point of the domain.
- (mathematics) Of, or relating to algebra or a similar method of analysis.
- (logic, of a proposition) that follows necessarily by definition; tautologous.
- Of, or relating to any form of analysis, or to analytics.
- (linguistics) Of a language, having a grammar principally dependent on the arrangement of uninflected function words within sentences to indicate meaning.
- Having the ability to analyse.
- using or skilled in using analysis (i.e., separating a whole — intellectual or substantial — into its elemental parts or basic principles)
- using or subjected to a methodology using algebra and calculus
- expressing a grammatical category by using two or more words rather than inflection
- of a proposition that is necessarily true independent of fact or experience
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
adj
- (algebraic geometry) Of a function between varieties: acting as a morphism on an open subset of its domain.
- (algebraic geometry) Of a point on an algebraic variety over a field: whose coordinates belong to the field in question (in contrast to those points of the variety which are only defined over the algebraic closure of the base field).
- Logically sound; not self-contradictory or otherwise absurd.
- (of a person or personal characteristics) Healthy or balanced intellectually; exhibiting reasonableness.
- (arithmetic) Of a number, capable of being expressed as the ratio of two integers.
- (algebraic geometry) Of a variety: (informally) geometrically simple almost everywhere; (formally) birationally equivalent to projective space
- Capable of reasoning.
- (algebra) Of an algebraic expression in indeterminates, or more generally a function: capable of being expressed as the ratio of two polynomials.
- of or associated with or requiring the use of the mind
- having its source in or being guided by the intellect (as distinguished from experience or emotion)
- capable of being expressed as a quotient of integers
- consistent with or based on or using reason
noun
noun
- (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”).
- 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.
- (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.
- In universal algebra: an equational class; the class of all algebraic structures of a given signature, satisfying a given set of identities.
- 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
- (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, multilinear algebra, of a vector space) That is equipped with an alternating nondegenerate bilinear form.
- (mathematics, multilinear algebra, of a bilinear form) That is alternating and nondegenerate.
- (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
- (mathematics) The variable in terms of which an expression is defined.
- By faulty generalisation from a clause's grammatical subject often being coinstantiated with one: an actor or agent; one who takes action.
- A particular area of study.
- A citizen in a monarchy.
- (grammar) The noun, pronoun or noun phrase about whom the statement is made. In active clauses with verbs denoting an action, the subject is the actor. In clauses in the passive voice the subject is the target of the action.
- The main topic of a paper, work of art, discussion, field of study, etc.
- A human, animal, or an inanimate object that is being examined, treated, analysed, etc; especially, one being studied in a scientific experiment, such as a clinical trial.
- (music) The main theme or melody, especially in a fugue.
- (logic) That of which something is stated.
- A person ruled over by another, especially a monarch or state authority.
- (philosophy) A being that has subjective experiences, subjective consciousness, or a relationship with another entity.
- some situation or event that is thought about
- the subject matter of a conversation or discussion
- (logic) the first term of a proposition
- a person who owes allegiance to that nation
- (grammar) one of the two main constituents of a sentence; the grammatical constituent about which something is predicated
- something (a person or object or scene) selected by an artist or photographer for graphic representation
- a branch of knowledge
- a person who is subjected to experimental or other observational procedures; someone who is an object of investigation
adj
- Conditional upon something; used with to.
- Likely to be affected by or to experience something; liable.
- Placed under the power of another; owing allegiance to a particular sovereign or state.
- Placed or situated under; lying below, or in a lower situation.
- likely to be affected by something
- being under the power or sovereignty of another or others
- possibly accepting or permitting
verb
- (transitive, construed with to) To cause (someone or something) to undergo a particular experience, especially one that is unpleasant or unwanted.
- (transitive) To make subordinate or subservient; to subdue or enslave; to subjugate.
- make subservient; force to submit or subdue
- cause to experience or suffer or make liable or vulnerable to
- make accountable for
noun
- (mathematics, differential geometry) A subset of the tangent bundle of a manifold that satisfies certain properties; used to construct the notions of integrability and foliation of a manifold.
- The result of distributing; arrangement.
- (rhetoric) A rhetorical technique in which a subject is divided into multiple cases based on some property or properties, and each case is addressed individually.
- (economics) The apportionment of income or wealth in a population.
- An apportionment by law (of funds, property).
- The total number of something sold or delivered to the clients.
- (logic) The resolution of a whole into its parts.
- (printing, historical) The process of sorting the types and placing them in their proper boxes in the cases.
- (finance) The process or result of the sale of securities, especially their placement among investors with long-term investment strategies.
- An act of distributing or state of being distributed.
- The frequency of occurrence or extent of existence.
- (card games) The way in which a player's hand is divided in suits, or in which a particular suit is divided between the players.
- (steam engines) The steps or operations by which steam is supplied to and withdrawn from the cylinder at each stroke of the piston: admission, suppression or cutting off, release or exhaust, and compression of exhaust steam prior to the next admission.
- (business, marketing) The process by which goods get to final consumers over a geographical market, including storing, selling, shipping and advertising.
- Anything distributed; portion; share.
- (software) A set of bundled software components.
- (mathematics, statistics) A probability distribution; the set of relative likelihoods that a variable will have a value in a given interval.
- the act of distributing or spreading or apportioning
- (statistics) an arrangement of values of a variable showing their observed or theoretical frequency of occurrence
- the commercial activity of transporting and selling goods from a producer to a consumer
- the spatial or geographic property of being scattered about over a range, area, or volume
adj
- (calculus, not comparable) Having a derivative, said of a function whose domain and codomain are manifolds.
- (comparable, of multiple items) able to be differentiated; distinguishable, as for example by differing appearance or measurable characteristics.
- possessing a differential coefficient or derivative
- capable of being perceived as different
noun
- (vector calculus) Divergence; a kind of differential operator.
- (UK, Eton College, school slang) A division; a lesson.
- (UK, Ireland, slang) A foolish person; an idiot.
- (military) A division.
- Alternative form of daeva.
- (UK, Winchester College) division; a subject with multidisciplinary scope.
- (UK, Ireland, uncountable, slang) Divinity, as a school subject.
- (web design) A section of a web page, or the div element that represents it in HTML code.
- (mathematics, computing) A function, implemented in many programming languages, that returns the result of a division of two integers.
verb
adj
- Of, or relating to, algebra.
- of or relating to algebra
- (algebra, of a field) Whose every element is a root of some polynomial whose coefficients are rational.
- (chess, of notation) Describing squares by file (referred to in intrinsic order rather than by the piece starting on that file) and rank, both with reference to a fixed point rather than a player-dependent perspective.
- (algebra, number theory, of a number) Which is a root of some polynomial whose coefficients are rational.
- (mathematics, of an expression, equation, or function) Containing only numbers, letters, and arithmetic operators.
adj
- (mathematics) Synonym of multiperfect.
- (graph theory) Being or relating to a certain type of graph that complies with a theorem ("pluperfect graph theorem") discovered by D. R. Fulkerson in 1970, satisfying even more constraints than a perfect graph.
- More than perfect, utterly perfect, ideal.
- (informal) Used as an intensifier in various interjections.
- (grammar) Pertaining to action completed before another action or event in the past, past perfect.
- more than perfect
noun
noun
- (algebraic geometry) A morphism between algebraic varieties.
- (graph theory) A symmetric tessellation of a closed surface; a decomposition of a two-dimensional manifold into topological disks such that every flag (incident vertex-edge-face triple) can be transformed into any other flag by a symmetry (i.e., an automorphism) of the decomposition.
noun
- (mathematics) An element of the umbral calculus.
- The fully shaded inner region of a shadow cast by an opaque object.
- (astronomy) The area on the earth or moon experiencing the total phase of an eclipse.
- One of genus Umbrina of drums (family Sciaenidae).
- (astronomy) The central region of a sunspot.
- (chiefly literary) A shadow.
- One of the family Umbridae of mudminnows.
- a region of complete shadow resulting from total obstruction of light
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
- 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”).
- (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.
- (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
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
- (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”).
- 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.
- (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.
- In universal algebra: an equational class; the class of all algebraic structures of a given signature, satisfying a given set of identities.
- 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
- (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, multilinear algebra, of a vector space) That is equipped with an alternating nondegenerate bilinear form.
- (mathematics, multilinear algebra, of a bilinear form) That is alternating and nondegenerate.
- (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
- (mathematics) The variable in terms of which an expression is defined.
- By faulty generalisation from a clause's grammatical subject often being coinstantiated with one: an actor or agent; one who takes action.
- A particular area of study.
- A citizen in a monarchy.
- (grammar) The noun, pronoun or noun phrase about whom the statement is made. In active clauses with verbs denoting an action, the subject is the actor. In clauses in the passive voice the subject is the target of the action.
- The main topic of a paper, work of art, discussion, field of study, etc.
- A human, animal, or an inanimate object that is being examined, treated, analysed, etc; especially, one being studied in a scientific experiment, such as a clinical trial.
- (music) The main theme or melody, especially in a fugue.
- (logic) That of which something is stated.
- A person ruled over by another, especially a monarch or state authority.
- (philosophy) A being that has subjective experiences, subjective consciousness, or a relationship with another entity.
- some situation or event that is thought about
- the subject matter of a conversation or discussion
- (logic) the first term of a proposition
- a person who owes allegiance to that nation
- (grammar) one of the two main constituents of a sentence; the grammatical constituent about which something is predicated
- something (a person or object or scene) selected by an artist or photographer for graphic representation
- a branch of knowledge
- a person who is subjected to experimental or other observational procedures; someone who is an object of investigation
adj
- Conditional upon something; used with to.
- Likely to be affected by or to experience something; liable.
- Placed under the power of another; owing allegiance to a particular sovereign or state.
- Placed or situated under; lying below, or in a lower situation.
- likely to be affected by something
- being under the power or sovereignty of another or others
- possibly accepting or permitting
verb
- (transitive, construed with to) To cause (someone or something) to undergo a particular experience, especially one that is unpleasant or unwanted.
- (transitive) To make subordinate or subservient; to subdue or enslave; to subjugate.
- make subservient; force to submit or subdue
- cause to experience or suffer or make liable or vulnerable to
- make accountable for
noun
- (mathematics, differential geometry) A subset of the tangent bundle of a manifold that satisfies certain properties; used to construct the notions of integrability and foliation of a manifold.
- The result of distributing; arrangement.
- (rhetoric) A rhetorical technique in which a subject is divided into multiple cases based on some property or properties, and each case is addressed individually.
- (economics) The apportionment of income or wealth in a population.
- An apportionment by law (of funds, property).
- The total number of something sold or delivered to the clients.
- (logic) The resolution of a whole into its parts.
- (printing, historical) The process of sorting the types and placing them in their proper boxes in the cases.
- (finance) The process or result of the sale of securities, especially their placement among investors with long-term investment strategies.
- An act of distributing or state of being distributed.
- The frequency of occurrence or extent of existence.
- (card games) The way in which a player's hand is divided in suits, or in which a particular suit is divided between the players.
- (steam engines) The steps or operations by which steam is supplied to and withdrawn from the cylinder at each stroke of the piston: admission, suppression or cutting off, release or exhaust, and compression of exhaust steam prior to the next admission.
- (business, marketing) The process by which goods get to final consumers over a geographical market, including storing, selling, shipping and advertising.
- Anything distributed; portion; share.
- (software) A set of bundled software components.
- (mathematics, statistics) A probability distribution; the set of relative likelihoods that a variable will have a value in a given interval.
- the act of distributing or spreading or apportioning
- (statistics) an arrangement of values of a variable showing their observed or theoretical frequency of occurrence
- the commercial activity of transporting and selling goods from a producer to a consumer
- the spatial or geographic property of being scattered about over a range, area, or volume
noun
- (vector calculus) Divergence; a kind of differential operator.
- (UK, Eton College, school slang) A division; a lesson.
- (UK, Ireland, slang) A foolish person; an idiot.
- (military) A division.
- Alternative form of daeva.
- (UK, Winchester College) division; a subject with multidisciplinary scope.
- (UK, Ireland, uncountable, slang) Divinity, as a school subject.
- (web design) A section of a web page, or the div element that represents it in HTML code.
- (mathematics, computing) A function, implemented in many programming languages, that returns the result of a division of two integers.
verb
adj
noun
- (multivariable calculus) The Jacobian matrix of a function of several variables.
- (calculus, of a univariate differentiable function f(x)) A function giving the change in the linear approximation of f at a point x over a small interval Δx or operatorname d!x, the function being called the differential of f and denoted operatorname d!f(x,Δx), operatorname d!f(x), or simply operatorname d!f.
- Any of several generalizations of this concept to functions of several variables or to higher orders: the partial differential, total differential, Gateaux differential, etc.
- One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.
- The differential gear in an automobile, etc.
- A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.
- (differential geometry, of a smooth map ϕ between smooth manifolds) The pushforward or total derivative of ϕ: a linear map from the tangent space at a point x in ϕ's domain to the tangent space at ϕ(x) which is, in a technical sense, the best linear approximation of ϕ at x; denoted operatorname d!ϕₓ.
- (mathematics) Any of several generalizations of the concept(s) above: e.g. the Kähler differential in the setting of schemes, the quadratic differential in the theory of Riemann surfaces, etc.
- (calculus) A quantity representing an infinitesimal change in a variable, now only used as a heuristic aid except in nonstandard analysis but considered rigorous until the 20th century; a fluxion in Newtonian calculus, now usually written in Leibniz's notation as operatorname d!x.
- A qualitative or quantitative difference between similar or comparable things.
- a quality that differentiates between similar things
- a bevel gear that permits rotation of two shafts at different speeds; used on the rear axle of automobiles to allow wheels to rotate at different speeds on curves
- the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
adj
- (mathematics, algebra) Whose coefficients are complex numbers; defined over the field of complex numbers.
- Made up of multiple parts; composite; not simple.
- (geometry) A curve, polygon or other figure that crosses or intersects itself.
- (mathematics, mathematical analysis, of a function) Whose range is a subset of the complex numbers.
- Not simple, easy, or straightforward; complicated.
- (mathematics, of a number) Having the form a + bi, where a and b are real numbers and i is (by definition) the imaginary square root of −1.
- difficult to analyze or understand
- complicated in structure; consisting of interconnected parts
noun
- (psychology) A group of emotionally charged ideas or mental factors, unconsciously associated by the individual with a particular subject, arising from repressed instincts, fears, or desires and often resulting in mental abnormality.
- (taxonomy) A group of closely related species, often distinguished only with difficulty by traditional morphological methods.
- (linguistics) A multimorphemic word, one with several parts, one with affixes.
- A collection of buildings with a common purpose, such as a university or military base.
- An organized cluster of thunderstorms.
- (chemistry) A structure consisting of a central atom or molecule weakly connected to surrounding atoms or molecules, as for example coordination compounds in inorganic chemistry and protein complexes in biochemistry.
- (mathematics) A complex number.
- A fixed mental tendency or obsession.
- A cluster of wildfires burning in the same vicinity.
- An assemblage of related things; a collection.
- A network of interconnected systems.
- a conceptual whole made up of complicated and related parts
- a compound described in terms of the central atom to which other atoms are bound or coordinated
- a whole structure (as a building) made up of interconnected or related structures
- (psychoanalysis) a combination of emotions and impulses that have been rejected from awareness but still influence a person's behavior
verb
adj
- (mathematical analysis) Being defined in terms of objects of differential calculus such as derivatives.
- Of, or relating to division into elements or principles.
- (mathematics, of a function) Being able to be locally represented by convergent power series around every point of the domain.
- (mathematics) Of, or relating to algebra or a similar method of analysis.
- (logic, of a proposition) that follows necessarily by definition; tautologous.
- Of, or relating to any form of analysis, or to analytics.
- (linguistics) Of a language, having a grammar principally dependent on the arrangement of uninflected function words within sentences to indicate meaning.
- Having the ability to analyse.
- using or skilled in using analysis (i.e., separating a whole — intellectual or substantial — into its elemental parts or basic principles)
- using or subjected to a methodology using algebra and calculus
- expressing a grammatical category by using two or more words rather than inflection
- of a proposition that is necessarily true independent of fact or experience
adj
- (algebraic geometry) Of a function between varieties: acting as a morphism on an open subset of its domain.
- (algebraic geometry) Of a point on an algebraic variety over a field: whose coordinates belong to the field in question (in contrast to those points of the variety which are only defined over the algebraic closure of the base field).
- Logically sound; not self-contradictory or otherwise absurd.
- (of a person or personal characteristics) Healthy or balanced intellectually; exhibiting reasonableness.
- (arithmetic) Of a number, capable of being expressed as the ratio of two integers.
- (algebraic geometry) Of a variety: (informally) geometrically simple almost everywhere; (formally) birationally equivalent to projective space
- Capable of reasoning.
- (algebra) Of an algebraic expression in indeterminates, or more generally a function: capable of being expressed as the ratio of two polynomials.
- of or associated with or requiring the use of the mind
- having its source in or being guided by the intellect (as distinguished from experience or emotion)
- capable of being expressed as a quotient of integers
- consistent with or based on or using reason
noun
adj
- (calculus, not comparable) Having a derivative, said of a function whose domain and codomain are manifolds.
- (comparable, of multiple items) able to be differentiated; distinguishable, as for example by differing appearance or measurable characteristics.
- possessing a differential coefficient or derivative
- capable of being perceived as different
adj
- Of, or relating to, algebra.
- of or relating to algebra
- (algebra, of a field) Whose every element is a root of some polynomial whose coefficients are rational.
- (chess, of notation) Describing squares by file (referred to in intrinsic order rather than by the piece starting on that file) and rank, both with reference to a fixed point rather than a player-dependent perspective.
- (algebra, number theory, of a number) Which is a root of some polynomial whose coefficients are rational.
- (mathematics, of an expression, equation, or function) Containing only numbers, letters, and arithmetic operators.
adj
- (mathematics) Synonym of multiperfect.
- (graph theory) Being or relating to a certain type of graph that complies with a theorem ("pluperfect graph theorem") discovered by D. R. Fulkerson in 1970, satisfying even more constraints than a perfect graph.
- More than perfect, utterly perfect, ideal.
- (informal) Used as an intensifier in various interjections.
- (grammar) Pertaining to action completed before another action or event in the past, past perfect.
- more than perfect