Parole in English per 'The quality of being algebraic.'
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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.
noun
adj
name
name
- (algebraic geometry) Initialism of Éléments de géométrie algébrique.
- (military, US) Initialism of Eagle, Globe, and Anchor.
- (computer graphics) Initialism of enhanced graphics adapter, an obsolete computer display standard between CGA and VGA, offering sixteen colours on screen from a palette of sixty-four.
adj
- (mathematics) Of, or relating to algebra or a similar method of analysis.
- using or subjected to a methodology using algebra and calculus
- Of, or relating to division into elements or principles.
- (mathematical analysis) Being defined in terms of objects of differential calculus such as derivatives.
- (mathematics, of a function) Being able to be locally represented by convergent power series around every point of the domain.
- (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)
- 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
- (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
- (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
- (mathematics, of an algebra) That contains an identity element.
- (mathematics, linear algebra, mathematical analysis, of a matrix or operator) Whose inverse is equal to its adjoint.
- Having the quality of oneness.
- (government, of a system of government or administration) That concentrates power in a single body, rather than sharing it with more local bodies.
- characterized by or constituting a form of government in which power is held by one central authority
- of or pertaining to or involving the use of units
- relating to or characterized by or aiming toward unity
- having the indivisible character of a unit
noun
noun
- (algebra) A quantity that remains at a fixed value throughout a given discussion or operation.
- That which is permanent or invariable.
- (sciences) Any property of an experiment, determined numerically, that does not change under given circumstances.
- (computing) An identifier that is bound to an invariant value; a fixed value given a name to aid in readability of source code.
- a quantity that does not vary
- a number representing a quantity assumed to have a fixed value in a specified mathematical context
adj
- Consistently recurring over time; persistent.
- (computing, complexity theory) Bounded above by a constant.
- Firm; solid; not fluid.
- Unchanged through time or space; permanent.
- Steady in purpose, action, feeling, etc.
- unvarying in nature
- uninterrupted in time and indefinitely long continuing
- steadfast in purpose or devotion or affection
adj
noun
- (taxonomy) A taxonomic designation (such as of a subspecies) consisting of more than two terms.
- (linguistics, Sinology) A type of term consisting of multiple parts.
- (algebra, strict sense) An expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power, such as a_nxⁿ+a_n-1xⁿ⁻¹+...+a_0x⁰.
- a mathematical function that is the sum of a number of terms
noun
- Used other than figuratively or idiomatically: see algebraic, analysis.; the use of techniques from algebra (especially elementary algebra) to analyse and solve problems.
- (algebraic geometry, algebraic topology) The study of systems of linear partial differential equations, using techniques from sheaf theory and complex analysis to examine functions and certain generalisations of functions (such as hyperfunctions and microfunctions).
noun
- (commutative algebra, of an ideal) Height.
- (astronomy) The angular distance of a heavenly body above our Earth's horizon.
- (geometry) The line perpendicularly connecting a figure’s vertex, especially a triangle’s apex, to the side opposite to the vertex.
- Highest point or degree.
- The absolute height of a location, usually measured from sea level.
- (geometry) The length of such a line; the distance measured perpendicularly from a figure's vertex to the side opposite to the vertex.
- Height of rank or excellence; superiority.
- A vertical distance.
- elevation especially above sea level or above the earth's surface
- angular distance above the horizon (especially of a celestial object)
- the perpendicular distance from the base of a geometric figure to the opposite vertex (or side if parallel)
noun
- (algebra) A polynomial with two terms.
- (taxonomy) A scientific name at the rank of species, with two terms: a generic name and a specific name.
- (algebra) A quantity expressed as the sum or difference of two terms.
- (mathematics) a quantity expressed as a sum or difference of two terms; a polynomial with two terms
adj
noun
- (algebraic geometry) Alternative form of valence.
- (uncountable, by extension) The capacity of something to combine with other things, as for example the capability of a vaccine as measured by the number of pathogen serotypes that it can counteract.
- (countable, chemistry) Alternative form of valence (“the combining capacity of an atom, functional group, or radical determined by the number of atoms of hydrogen with which it will unite, or the number of electrons that it will gain, lose, or share when it combines with other atoms, etc.”).
- (countable, linguistics) Alternative form of valence (“the number of arguments that a verb can have, including its subject, ranging from zero to three or, less commonly, four”).
- (countable, graph theory) The number of edges connected to a vertex in a graph.
- (uncountable) Importance, significance.
- (chemistry) a property of atoms or radicals; their combining power given in terms of the number of hydrogen atoms (or the equivalent)
- the phenomenon of forming chemical bonds
- (biology) a relative capacity to unite or react or interact as with antigens or a biological substrate
noun
adj
- (Lie theory, of an element x of a Lie algebra L) Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
- (of an algebra over a commutative ring) Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.
- (Lie theory, of a Lie algebra) Such that the lower central series terminates.
- (ring theory, of an ideal I) Such that there exists a natural number k with Iᵏ = 0.
- (semigroup theory, of a semigroup with zero) Containing only nilpotent elements.
- (mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0.
- (group theory, of a group) Admitting a central series of finite length.
- equal to zero when raised to a certain power
noun
adj
- (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
- (number theory, of an integer) Unable to be factored into smaller integers; prime.
- (group theory, of a representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.
- Not able to be brought to a simpler or reduced form.
- (algebra, of an element of a ring) Whose only divisors are units and associates.
- (mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x² + 1).
- (algebraic geometry, of an algebraic variety) Inexpressible as the union of two proper algebraic subvarieties.
- (number theory, of a fraction) Whose numerator and denominator share no common factor greater than 1.
- Not able to be reduced or lessened.
- incapable of being made smaller or simpler
noun
- (mathematics) The set of all things considered.
- A whole world, in the sense of perspective or social setting.
- (literature, films) A collection of stories with characters and settings that typically share a continuity but are less interrelated than those of sequels or prequels.
- Everything under consideration.
- (pantheism) A deity who is equivalent to the sum of everything that exists in the cosmos.
- The sum of everything that exists in the cosmos.
- An entity similar to our universe; one component of a larger entity known as the multiverse.
- An imaginary collection of worlds; the general imaginary world within which a work of fiction takes place, broader than its immediate setting.
- (statistics, psychometrics) The set of all admissible observations.
- (marketing, economics) A sample taken from the population.
- everything that exists anywhere
- everything stated or assumed in a given discussion
- (statistics) the entire aggregation of items from which samples can be drawn
name
adj
- (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.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (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
name
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
- (algebra) A quantity that remains at a fixed value throughout a given discussion or operation.
- That which is permanent or invariable.
- (sciences) Any property of an experiment, determined numerically, that does not change under given circumstances.
- (computing) An identifier that is bound to an invariant value; a fixed value given a name to aid in readability of source code.
- a quantity that does not vary
- a number representing a quantity assumed to have a fixed value in a specified mathematical context
adj
- Consistently recurring over time; persistent.
- (computing, complexity theory) Bounded above by a constant.
- Firm; solid; not fluid.
- Unchanged through time or space; permanent.
- Steady in purpose, action, feeling, etc.
- unvarying in nature
- uninterrupted in time and indefinitely long continuing
- steadfast in purpose or devotion or affection
noun
- Used other than figuratively or idiomatically: see algebraic, analysis.; the use of techniques from algebra (especially elementary algebra) to analyse and solve problems.
- (algebraic geometry, algebraic topology) The study of systems of linear partial differential equations, using techniques from sheaf theory and complex analysis to examine functions and certain generalisations of functions (such as hyperfunctions and microfunctions).
noun
- (commutative algebra, of an ideal) Height.
- (astronomy) The angular distance of a heavenly body above our Earth's horizon.
- (geometry) The line perpendicularly connecting a figure’s vertex, especially a triangle’s apex, to the side opposite to the vertex.
- Highest point or degree.
- The absolute height of a location, usually measured from sea level.
- (geometry) The length of such a line; the distance measured perpendicularly from a figure's vertex to the side opposite to the vertex.
- Height of rank or excellence; superiority.
- A vertical distance.
- elevation especially above sea level or above the earth's surface
- angular distance above the horizon (especially of a celestial object)
- the perpendicular distance from the base of a geometric figure to the opposite vertex (or side if parallel)
noun
- (algebra) A polynomial with two terms.
- (taxonomy) A scientific name at the rank of species, with two terms: a generic name and a specific name.
- (algebra) A quantity expressed as the sum or difference of two terms.
- (mathematics) a quantity expressed as a sum or difference of two terms; a polynomial with two terms
adj
noun
- (algebraic geometry) Alternative form of valence.
- (uncountable, by extension) The capacity of something to combine with other things, as for example the capability of a vaccine as measured by the number of pathogen serotypes that it can counteract.
- (countable, chemistry) Alternative form of valence (“the combining capacity of an atom, functional group, or radical determined by the number of atoms of hydrogen with which it will unite, or the number of electrons that it will gain, lose, or share when it combines with other atoms, etc.”).
- (countable, linguistics) Alternative form of valence (“the number of arguments that a verb can have, including its subject, ranging from zero to three or, less commonly, four”).
- (countable, graph theory) The number of edges connected to a vertex in a graph.
- (uncountable) Importance, significance.
- (chemistry) a property of atoms or radicals; their combining power given in terms of the number of hydrogen atoms (or the equivalent)
- the phenomenon of forming chemical bonds
- (biology) a relative capacity to unite or react or interact as with antigens or a biological substrate
noun
adj
- (Lie theory, of an element x of a Lie algebra L) Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
- (of an algebra over a commutative ring) Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.
- (Lie theory, of a Lie algebra) Such that the lower central series terminates.
- (ring theory, of an ideal I) Such that there exists a natural number k with Iᵏ = 0.
- (semigroup theory, of a semigroup with zero) Containing only nilpotent elements.
- (mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0.
- (group theory, of a group) Admitting a central series of finite length.
- equal to zero when raised to a certain power
noun
adj
- (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
- (number theory, of an integer) Unable to be factored into smaller integers; prime.
- (group theory, of a representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.
- Not able to be brought to a simpler or reduced form.
- (algebra, of an element of a ring) Whose only divisors are units and associates.
- (mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x² + 1).
- (algebraic geometry, of an algebraic variety) Inexpressible as the union of two proper algebraic subvarieties.
- (number theory, of a fraction) Whose numerator and denominator share no common factor greater than 1.
- Not able to be reduced or lessened.
- incapable of being made smaller or simpler
noun
- (mathematics) The set of all things considered.
- A whole world, in the sense of perspective or social setting.
- (literature, films) A collection of stories with characters and settings that typically share a continuity but are less interrelated than those of sequels or prequels.
- Everything under consideration.
- (pantheism) A deity who is equivalent to the sum of everything that exists in the cosmos.
- The sum of everything that exists in the cosmos.
- An entity similar to our universe; one component of a larger entity known as the multiverse.
- An imaginary collection of worlds; the general imaginary world within which a work of fiction takes place, broader than its immediate setting.
- (statistics, psychometrics) The set of all admissible observations.
- (marketing, economics) A sample taken from the population.
- everything that exists anywhere
- everything stated or assumed in a given discussion
- (statistics) the entire aggregation of items from which samples can be drawn
name
Nessuna parola corrispondente trovata. Prova una descrizione più ampia.
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) Of, or relating to algebra or a similar method of analysis.
- using or subjected to a methodology using algebra and calculus
- Of, or relating to division into elements or principles.
- (mathematical analysis) Being defined in terms of objects of differential calculus such as derivatives.
- (mathematics, of a function) Being able to be locally represented by convergent power series around every point of the domain.
- (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)
- 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
- (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
- (mathematics, of an algebra) That contains an identity element.
- (mathematics, linear algebra, mathematical analysis, of a matrix or operator) Whose inverse is equal to its adjoint.
- Having the quality of oneness.
- (government, of a system of government or administration) That concentrates power in a single body, rather than sharing it with more local bodies.
- characterized by or constituting a form of government in which power is held by one central authority
- of or pertaining to or involving the use of units
- relating to or characterized by or aiming toward unity
- having the indivisible character of a unit
noun
adj
noun
- (taxonomy) A taxonomic designation (such as of a subspecies) consisting of more than two terms.
- (linguistics, Sinology) A type of term consisting of multiple parts.
- (algebra, strict sense) An expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power, such as a_nxⁿ+a_n-1xⁿ⁻¹+...+a_0x⁰.
- a mathematical function that is the sum of a number of terms
adj
- (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.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (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