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adj
noun
- a mathematical function that is the sum of a number of terms
- (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.
noun
adj
- (mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x² + 1).
- (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.
- (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
- any distinct quantity contained in a polynomial
- a limited period of time
- one of the substantive phrases in a logical proposition
- the end of gestation or point at which birth is imminent
- a word or expression used for some particular thing
- (usually plural) a statement of what is required as part of an agreement
- (architecture) a statue or a human bust or an animal carved out of the top of a square pillar; originally used as a boundary marker in ancient Rome
- A chronological limitation or restriction, a limited timespan.
- (astrology) An essential dignity in which unequal segments of every astrological sign have internal rulerships which affect the power and integrity of each planet in a natal chart.
- Part of a year, especially one of the divisions of an academic year.
- (mathematics) Any value (variable or constant) or expression separated from another term by a space or an appropriate character, in an overall expression or table.
- Specifically, the conditions in a legal contract that specify the price and also how and when payment must be made.
- A word or phrase (e.g., noun phrase, verb phrase, open compound), especially one from a specialised area of knowledge; a name for a concept.
- (of a patent) The maximum period during which the patent can be maintained into force.
- (logic) The subject or the predicate of a proposition; one of the three component parts of a syllogism, each one of which is used twice.
- Certain days on which rent is paid.
- Any of the binding conditions or promises in a legal contract.
- (computing, informal) A computer program that emulates a physical terminal.
- (nautical) A piece of carved work placed under each end of the taffrail.
- One whose employment has been terminated
- That which limits the extent of anything; limit, extremity, bound, boundary, terminus.
- (art) A statue of the upper body, sometimes without the arms, ending in a pillar or pedestal.
- The time during which legal courts are open.
- With respect to a pregnancy, the usual duration of gestation for the given species (for example, nine months in humans); (metonymic) the end of this duration: the timepoint at which birth usually happens (for example, in humans, approximately 40 weeks from conception), defining the due date.
- Duration of officeholding, or its limit; period in office of fixed length.
- Relations among people.
verb
adj
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.
adj
- (of a polynomial) Having degree one; that is, being of the form a_1x_1+a_2x_2+⋯+a_nx_n+b, where each x_i is a variable. See also Linear polynomials on Wikipedia.Wikipedia
- (of a polynomial equation) Involving only linear polynomials. See also Linear equation on Wikipedia.Wikipedia
- (botany, of leaves) Long and narrow, with nearly parallel sides.
- (media, of video and audio) Delivered or delivering on a fixed schedule, as opposed to on-demand.
- (of a function between vector spaces) An additive, homogeneous mapping; that is, a function f:V→W is linear if it distributes over vector addition (f( mathbf v+ mathbf w)=f( mathbf v)+f( mathbf w)) and respects scalar multiplication (f(c mathbf v)=cf( mathbf v)). If V and W are vector spaces over a field K, f may also be called a K-linear map. See also linear map on Wikipedia.Wikipedia
- Of or relating to lines.
- (physics) A type of length measurement involving only one spatial dimension (as opposed to area or volume).
- Made, or designed to be used, in a step-by-step, sequential manner.
- Having the form of a line; straight or roughly straight; following a direct course.
- (of a function over a module) A module homomorphism; that is, a group homomorphism that commutes with scalar multiplication. See also Module homomorphism on Wikipedia.Wikipedia
- measured lengthwise
- of or in or along or relating to a line; involving or having a single dimension
- (of a leaf shape) long and narrow
- of a circuit or device having an output that is proportional to the input
- designating or involving an equation whose terms are of the first degree
noun
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
verb
- resolve (a polynomial) into factors
- (mathematics, transitive) To create a list of the factors of.
- (mathematics, transitive) To divide an expression into a list of items that, when multiplied together, will produce the original quantity.
- (US, transitive) To warn not to pay or give up goods.
- (US, transitive) To attach the effects of a debtor in the hands of a third party.
adj
- (mathematics, of a polynomial) Able to be factored into polynomials of lower degree, as x²-1.
- (mathematics, of an integer) Able to be factored into smaller integers; composite.
- Capable of being reduced.
- (topology, of a manifold) Containing a sphere of codimension 1 that is not the boundary of a ball.
- capable of being reduced
adj
noun
- A foursome.
- (mathematics) A set of points with all the combinatorial properties of a quadric (a quadric being the set of points of PG(n, q) whose coordinates satisfy a quadratic equation).
- (grammar) A grammatical number referring to four (or more) things.
- (rhetoric) A set of four phrases, separated by pauses when speaking or commas when writing.
adj
- Of a polynomial, being equivalent to the polynomial with reversed and additively inverted coefficients: ∑ᵢ₌₀ⁿa_ixⁱ is antipalindromic iff ∑ᵢ₌₀ⁿa_ixⁱ=∑ᵢ₌₀ⁿ-a_n-ixⁱ⟺a_i=-a_n-i.
- Of a natural number, with respect to base b, being equivalent to the natural number whose digits are reversed and subtracted from b-1: ∑ᵢ₌₀ⁿa_ibⁱ is antipalindromic iff ∑ᵢ₌₀ⁿa_ibⁱ=∑ᵢ₌₀ⁿ(b-1-a_n-i)bⁱ⟺a_i=b-1-a_n-i.
adj
- (mathematics) Of a polynomial expression, involving only the zeroth, second, and fourth powers of a variable, as x⁴ + 3x² + 2. Sometimes extended to any expression involving the biquadrate or fourth power (but no higher powers), as x⁴ − 4x³ + 3x² − x + 1.
- involving the fourth and no higher power of a quantity or degree
noun
noun
adj
verb
- (algebra, transitive and intransitive, acts on a polynomial) To factor into linear factors.
- (transitive, intransitive, slang) To leave.
- (sports, especially baseball) For both teams involved in a doubleheader to win one game each and lose another.
- (intransitive, of a couple) To separate.
- (of an object which expresses the relationship between algebraic structures, particularly a short exact sequence) To contain an object which may be so expressed.
- (transitive) To share; to divide.
- To be broken; to be dashed to pieces.
- (ambitransitive) To (cause to) break up; to throw into discord.
- (intransitive, of something solid, particularly wood) To break along the grain fully or partly along a more or less straight line.
- (intransitive) To burst out laughing.
- (transitive, ergative, of something solid) To divide fully or partly along a more or less straight line.
- (intransitive, politics) To vote for candidates of opposite parties.
- (generally, of an algebraic structure) To be expressable as a direct sum of sub-modules, -algebras, etc.
- come open suddenly and violently, as if from internal pressure
- discontinue an association or relation; go different ways
- go one's own way; move apart
- separate or cut with a tool, such as a sharp instrument
- separate into parts or portions
adj
- (stock exchange, historical, of quotations) Given in sixteenths rather than eighths.
- (London stock exchange) Designating ordinary stock that has been divided into preferred ordinary and deferred ordinary.
- Divided.
- (algebra, of a short exact sequence) Having the middle object (group, module, etc.) equal to the direct sum of the others.
- (of coffee) Comprising half decaffeinated and half caffeinated espresso.
- (stock exchange, of an order, sale, etc.) Divided so as to be done or executed part at one time or price and part at another time or price.
- (especially of wood) cut or ripped longitudinally with the grain
- having been divided; having the unity destroyed
noun
- A crack or longitudinal fissure.
- A dessert or confection resembling a banana split.
- (bowling) A result of a first throw that leaves two or more pins standing with one or more pins between them knocked down.
- (baseball, slang) A split-finger fastball.
- A bottle of wine containing 37.5 centiliters, half the volume of a standard 75-centiliter bottle; a demi.
- (bodybuilding) A workout routine as seen by its distribution of muscle groups or the extent and manner they are targeted in a microcycle.
- A breach or separation, as in a political party; a division.
- A unit of measure used for champagne or other spirits: 18.75 centiliters or one quarter of a standard 75-centiliter bottle. Commercially comparable to ¹⁄₂₀ (US) gallon, which is ¹⁄₂ of a fifth.
- (gymnastics, cheerleading, dance, usually in the phrase "to do the splits") A maneuver of spreading or sliding the feet apart until the legs are flat on the floor 180 degrees apart, either sideways to the body or with one leg in front and one behind, thus lowering the body completely to the floor in an upright position.
- (systematics) The division of a single taxon into two or more taxa; as opposed to a lump.
- A piece that is split off, or made thin, by splitting; a splinter; a fragment.
- (construction) A tear resulting from tensile stresses.
- (music) A recording containing songs by multiple artists; a split single or split album.
- (gambling) A division of a stake happening when two cards of the kind on which the stake is laid are dealt in the same turn.
- A split shot or split stroke.
- (athletics, speedrunning) The elapsed time at specific intermediate points in a race or speedrun.
- (leather manufacture) One of the sections of a skin made by dividing it into two or more thicknesses.
- a promised or claimed share of loot or money
- a dessert of sliced fruit and ice cream covered with whipped cream and cherries and nuts
- (tenpin bowling) a divided formation of pins left standing after the first bowl
- a lengthwise crack in wood
- a bottle containing half the usual amount
- the act of rending or ripping or splitting something
- extending the legs at right angles to the trunk (one in front and the other in back)
- an increase in the number of outstanding shares of a corporation without changing the shareholders' equity
- an opening made forcibly as by pulling apart
- division of a group into opposing factions
adj
- (algebra) Of an algebraic expression in indeterminates, or more generally a function: capable of being expressed as the ratio of two polynomials.
- (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.
- (algebraic geometry) Of a function between varieties: acting as a morphism on an open subset of its domain.
- 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
adj
noun
- (linear algebra) The polynomial produced from a given square matrix by first subtracting the appropriate identity matrix multiplied by an indeterminant and then calculating the determinant.
- (mathematics) A polynomial P(r) corresponding to a homogeneous, linear, ordinary differential equation P(D) y = 0 where D is a differential operator (with respect to a variable t, if y is a function of t).
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
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
- (mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x² + 1).
- (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.
- (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
- any distinct quantity contained in a polynomial
- a limited period of time
- one of the substantive phrases in a logical proposition
- the end of gestation or point at which birth is imminent
- a word or expression used for some particular thing
- (usually plural) a statement of what is required as part of an agreement
- (architecture) a statue or a human bust or an animal carved out of the top of a square pillar; originally used as a boundary marker in ancient Rome
- A chronological limitation or restriction, a limited timespan.
- (astrology) An essential dignity in which unequal segments of every astrological sign have internal rulerships which affect the power and integrity of each planet in a natal chart.
- Part of a year, especially one of the divisions of an academic year.
- (mathematics) Any value (variable or constant) or expression separated from another term by a space or an appropriate character, in an overall expression or table.
- Specifically, the conditions in a legal contract that specify the price and also how and when payment must be made.
- A word or phrase (e.g., noun phrase, verb phrase, open compound), especially one from a specialised area of knowledge; a name for a concept.
- (of a patent) The maximum period during which the patent can be maintained into force.
- (logic) The subject or the predicate of a proposition; one of the three component parts of a syllogism, each one of which is used twice.
- Certain days on which rent is paid.
- Any of the binding conditions or promises in a legal contract.
- (computing, informal) A computer program that emulates a physical terminal.
- (nautical) A piece of carved work placed under each end of the taffrail.
- One whose employment has been terminated
- That which limits the extent of anything; limit, extremity, bound, boundary, terminus.
- (art) A statue of the upper body, sometimes without the arms, ending in a pillar or pedestal.
- The time during which legal courts are open.
- With respect to a pregnancy, the usual duration of gestation for the given species (for example, nine months in humans); (metonymic) the end of this duration: the timepoint at which birth usually happens (for example, in humans, approximately 40 weeks from conception), defining the due date.
- Duration of officeholding, or its limit; period in office of fixed length.
- Relations among people.
verb
adj
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
- (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
adj
noun
adj
noun
- (linear algebra) The polynomial produced from a given square matrix by first subtracting the appropriate identity matrix multiplied by an indeterminant and then calculating the determinant.
- (mathematics) A polynomial P(r) corresponding to a homogeneous, linear, ordinary differential equation P(D) y = 0 where D is a differential operator (with respect to a variable t, if y is a function of t).
adj
- (mathematics) Of a polynomial expression, involving only the zeroth, second, and fourth powers of a variable, as x⁴ + 3x² + 2. Sometimes extended to any expression involving the biquadrate or fourth power (but no higher powers), as x⁴ − 4x³ + 3x² − x + 1.
- involving the fourth and no higher power of a quantity or degree
noun
verb
- resolve (a polynomial) into factors
- (mathematics, transitive) To create a list of the factors of.
- (mathematics, transitive) To divide an expression into a list of items that, when multiplied together, will produce the original quantity.
- (US, transitive) To warn not to pay or give up goods.
- (US, transitive) To attach the effects of a debtor in the hands of a third party.
verb
- (algebra, transitive and intransitive, acts on a polynomial) To factor into linear factors.
- (transitive, intransitive, slang) To leave.
- (sports, especially baseball) For both teams involved in a doubleheader to win one game each and lose another.
- (intransitive, of a couple) To separate.
- (of an object which expresses the relationship between algebraic structures, particularly a short exact sequence) To contain an object which may be so expressed.
- (transitive) To share; to divide.
- To be broken; to be dashed to pieces.
- (ambitransitive) To (cause to) break up; to throw into discord.
- (intransitive, of something solid, particularly wood) To break along the grain fully or partly along a more or less straight line.
- (intransitive) To burst out laughing.
- (transitive, ergative, of something solid) To divide fully or partly along a more or less straight line.
- (intransitive, politics) To vote for candidates of opposite parties.
- (generally, of an algebraic structure) To be expressable as a direct sum of sub-modules, -algebras, etc.
- come open suddenly and violently, as if from internal pressure
- discontinue an association or relation; go different ways
- go one's own way; move apart
- separate or cut with a tool, such as a sharp instrument
- separate into parts or portions
adj
- (stock exchange, historical, of quotations) Given in sixteenths rather than eighths.
- (London stock exchange) Designating ordinary stock that has been divided into preferred ordinary and deferred ordinary.
- Divided.
- (algebra, of a short exact sequence) Having the middle object (group, module, etc.) equal to the direct sum of the others.
- (of coffee) Comprising half decaffeinated and half caffeinated espresso.
- (stock exchange, of an order, sale, etc.) Divided so as to be done or executed part at one time or price and part at another time or price.
- (especially of wood) cut or ripped longitudinally with the grain
- having been divided; having the unity destroyed
noun
- A crack or longitudinal fissure.
- A dessert or confection resembling a banana split.
- (bowling) A result of a first throw that leaves two or more pins standing with one or more pins between them knocked down.
- (baseball, slang) A split-finger fastball.
- A bottle of wine containing 37.5 centiliters, half the volume of a standard 75-centiliter bottle; a demi.
- (bodybuilding) A workout routine as seen by its distribution of muscle groups or the extent and manner they are targeted in a microcycle.
- A breach or separation, as in a political party; a division.
- A unit of measure used for champagne or other spirits: 18.75 centiliters or one quarter of a standard 75-centiliter bottle. Commercially comparable to ¹⁄₂₀ (US) gallon, which is ¹⁄₂ of a fifth.
- (gymnastics, cheerleading, dance, usually in the phrase "to do the splits") A maneuver of spreading or sliding the feet apart until the legs are flat on the floor 180 degrees apart, either sideways to the body or with one leg in front and one behind, thus lowering the body completely to the floor in an upright position.
- (systematics) The division of a single taxon into two or more taxa; as opposed to a lump.
- A piece that is split off, or made thin, by splitting; a splinter; a fragment.
- (construction) A tear resulting from tensile stresses.
- (music) A recording containing songs by multiple artists; a split single or split album.
- (gambling) A division of a stake happening when two cards of the kind on which the stake is laid are dealt in the same turn.
- A split shot or split stroke.
- (athletics, speedrunning) The elapsed time at specific intermediate points in a race or speedrun.
- (leather manufacture) One of the sections of a skin made by dividing it into two or more thicknesses.
- a promised or claimed share of loot or money
- a dessert of sliced fruit and ice cream covered with whipped cream and cherries and nuts
- (tenpin bowling) a divided formation of pins left standing after the first bowl
- a lengthwise crack in wood
- a bottle containing half the usual amount
- the act of rending or ripping or splitting something
- extending the legs at right angles to the trunk (one in front and the other in back)
- an increase in the number of outstanding shares of a corporation without changing the shareholders' equity
- an opening made forcibly as by pulling apart
- division of a group into opposing factions
adj
noun
- a mathematical function that is the sum of a number of terms
- (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.
adj
- (of a polynomial) Having degree one; that is, being of the form a_1x_1+a_2x_2+⋯+a_nx_n+b, where each x_i is a variable. See also Linear polynomials on Wikipedia.Wikipedia
- (of a polynomial equation) Involving only linear polynomials. See also Linear equation on Wikipedia.Wikipedia
- (botany, of leaves) Long and narrow, with nearly parallel sides.
- (media, of video and audio) Delivered or delivering on a fixed schedule, as opposed to on-demand.
- (of a function between vector spaces) An additive, homogeneous mapping; that is, a function f:V→W is linear if it distributes over vector addition (f( mathbf v+ mathbf w)=f( mathbf v)+f( mathbf w)) and respects scalar multiplication (f(c mathbf v)=cf( mathbf v)). If V and W are vector spaces over a field K, f may also be called a K-linear map. See also linear map on Wikipedia.Wikipedia
- Of or relating to lines.
- (physics) A type of length measurement involving only one spatial dimension (as opposed to area or volume).
- Made, or designed to be used, in a step-by-step, sequential manner.
- Having the form of a line; straight or roughly straight; following a direct course.
- (of a function over a module) A module homomorphism; that is, a group homomorphism that commutes with scalar multiplication. See also Module homomorphism on Wikipedia.Wikipedia
- measured lengthwise
- of or in or along or relating to a line; involving or having a single dimension
- (of a leaf shape) long and narrow
- of a circuit or device having an output that is proportional to the input
- designating or involving an equation whose terms are of the first degree
noun
noun
adj
- (mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x² + 1).
- (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.
- (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
adj
- (mathematics, of a polynomial) Able to be factored into polynomials of lower degree, as x²-1.
- (mathematics, of an integer) Able to be factored into smaller integers; composite.
- Capable of being reduced.
- (topology, of a manifold) Containing a sphere of codimension 1 that is not the boundary of a ball.
- capable of being reduced
adj
noun
- A foursome.
- (mathematics) A set of points with all the combinatorial properties of a quadric (a quadric being the set of points of PG(n, q) whose coordinates satisfy a quadratic equation).
- (grammar) A grammatical number referring to four (or more) things.
- (rhetoric) A set of four phrases, separated by pauses when speaking or commas when writing.
adj
- Of a polynomial, being equivalent to the polynomial with reversed and additively inverted coefficients: ∑ᵢ₌₀ⁿa_ixⁱ is antipalindromic iff ∑ᵢ₌₀ⁿa_ixⁱ=∑ᵢ₌₀ⁿ-a_n-ixⁱ⟺a_i=-a_n-i.
- Of a natural number, with respect to base b, being equivalent to the natural number whose digits are reversed and subtracted from b-1: ∑ᵢ₌₀ⁿa_ibⁱ is antipalindromic iff ∑ᵢ₌₀ⁿa_ibⁱ=∑ᵢ₌₀ⁿ(b-1-a_n-i)bⁱ⟺a_i=b-1-a_n-i.
adj
- (mathematics) Of a polynomial expression, involving only the zeroth, second, and fourth powers of a variable, as x⁴ + 3x² + 2. Sometimes extended to any expression involving the biquadrate or fourth power (but no higher powers), as x⁴ − 4x³ + 3x² − x + 1.
- involving the fourth and no higher power of a quantity or degree
noun
adj
- (algebra) Of an algebraic expression in indeterminates, or more generally a function: capable of being expressed as the ratio of two polynomials.
- (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.
- (algebraic geometry) Of a function between varieties: acting as a morphism on an open subset of its domain.
- 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
- (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
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