algebraicadj.

Brit.

/ˌaldʒᵻˈbreɪɪk/, U.S.

/ˌældʒəˈbreɪɪk/

Forms: 1600s algebriaque, 1600s algebraique, 1600s–1700s algebraick, 1600s– algebraic.

Origin: Of multiple origins. Partly formed within English, by derivation. Partly a borrowing from French. Etymons: algebra n., -ic suffix; French algébraïque.

Etymology: Partly < algebra n. + -ic suffix, and partly < Middle French †algébraïque (1585) < post-classical Latin algebraicus (1545 or earlier). Compare French algébrique (1740). Compare also German algebraisch (1600 as algebreisch ). Compare earlier algebraical adj.

1. Of or relating to algebra; characteristic of algebra, occurring in or involving algebra; (esp. of a sum) taken with consideration of the sign (plus or minus) of each term.

ΘΚΠ

the world > relative properties > number > algebra > [adjective]

cossic1557

algebraical1571

cossical1571

algebraic1653

1653 J. Webster Academiarum Examen 24 Who can be ignorant of the..compendious use of all sorts of Symbolisms, that have but any insight into Algebraick Arithmetick?

1684 London Gaz. mdcccclxxxv/4 Algebraick Arithmetick, made easie for the commonest capacity.

1702 J. Harris New Short Treat. Algebra 16 The general way of Division of Compound Quantities is like the ordinary way..; Respect being had to the Rules of Algebraic Addition, Subtraction and Multiplication.

1732 G. Berkeley Alciphron II. vii. xvii. 169 The Algebraic Mark, which denotes the Root of a negative Square, hath its Use in Logistic Operations.

1772 B. Franklin Let. 19 Sept. in Papers (1975) XIX. 300 Tho' the Weight of Reasons cannot be taken with the Precision of Algebraic Quantities, yet when each is considered..and the whole lies before me, I think I can judge better.

1827 O. Gregory Hutton's Course Math. (ed. 9) I. 182 Algebraic Fractions have the same names and rules of operation, as numeral fractions in common arithmetic.

1858 O. W. Holmes Autocrat of Breakfast-table xi. 299 These expressions come to be the algebraic symbols of minds which have grown too weak or indolent to discriminate.

1883 Analyst 10 97 This does not impair the generality in any case, every polynomial being reducible to this form by dividing it through by the algebraic sum of its coefficients.

1910 Encycl. Brit. I. 619/1 These works possess considerable originality, and contain many new improvements in algebraic notation.

1943 G. Greene Ministry of Fear iii. i. 168 One could almost put it into algebraic terms.

1995 Amer. Scientist Mar. 168/2 Rayleigh solved this paradox by considering the superposition (algebraic addition) of a large number of sound waves.

2010 Daily Tel. 11 Nov. 34/6 Hilton also made important contributions to the field of algebraic topology, a branch of mathematics which uses tools from abstract algebra to study topological spaces.

2. Mathematics.

a. Designating an expression involving only the operations of addition, multiplication, raising to a power (squaring, cubing, etc.), and their inverses acting on terms involving constants and variables; spec. (a) designating an equation in which a polynomial in a single variable is equated to zero; (b) designating a function of one variable which is the root of a polynomial in another variable whose coefficients are themselves polynomials with rational coefficients in the first variable. Also: relating to or involving such an expression. Cf. transcendental adj. 4.

ΘΚΠ

the world > relative properties > number > algebra > [adjective] > relating to expressions > relating to equations

algebraic1657

lateral1670

explicable1706

unreduced1762

homogeneous1815

resolvent1860

Pellian1862

equational1864

canonizant1879

variational1879

unilateral1884

non-dimensional1904

open1937

inhomogeneous1943

stiff1952

1657 J. Rowland tr. J. Johnstone Hist. Constancy of Nature 87 To find out the value of Algebraic Æquations_[L. Æquationum algebraicarum] of all things, if it be rationall: and if it be not, yet to expresse it next unto that in Numbers absolute.

1704 J. Harris Lexicon Technicum I. (at cited word) Exponential curves are such as partake both of the nature of Algebraick and Transcendent ones.

1738 Chambers' Cycl. (ed. 2) I. facing sig. 2Hhh Most authors, after Des Cartes, call algebraic curves, geometrical ones.

1819 G. Peacock View Fluxional & Differential Calculus 23 Where the fluent or integral is expressed by an algebraic function.

1871 P. G. Tait & W. J. Steele Treat. Dynamics of Particle (ed. 3) i. 26 When e = 1, the corrected integral..is 2(x + a/4) = y²/2a − a log y/a. This is the only case in which we do not obtain an algebraic curve.

1891 Amer. Jrnl. Math. 13 110 An algebraic function satisfying an algebraic equation whose coefficients are rational functions with integral coefficients of some indeterminate quantities.

1972 C. S. Ogilvy Tomorrow's Math (ed. 2) viii. 153 The famous equation connecting π and e, e^πi = −1, is not algebraic.

2007 I. Stewart Why Beauty is Truth iv. 54 Tartaglia was not the first to find an algebraic solution to a cubic equation.

b. Of a number: that can be expressed as a root of a polynomial in one variable with coefficients that are whole numbers.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > [adjective] > prime > other

commona1398

unarithmetical1671

algebraic1912

square-free1960

insensitive1968

1893 Proc. London Math. Soc. 24 327 (heading) On the algebraical integers derived from an irreducible cubic equation.]

1912 Trans. Amer. Math. Soc. 13 293 While the field R (α,…, α_n) defined by the algebraic numbers α₁,…,α_nis identical with a field R(u) defined by a single algebraic number u, a similar theorem does not hold for finite algebras.

1937 A. A. Albert Mod. Higher Algebra xii. 288 Let us apply this to a field  = ℜ(ξ) which is algebraic of degree n over the field ℜ of all rational numbers. We call the quantities of  algebraic numbers and say that  is an algebraic number field.

1982 Sci. Amer. Dec. 130/2 For example, √2, i (the imaginary square root of −1) and (−1 + i√3)/2 are all algebraic integers because they are roots of the algebraic equations x² − 2 = 0, x² + 1 = 0 and x³ − 1 = 0.

2006 A. Ash & R. Gross Fearless Symmetry viii. 91 If you take a polynomial whose coefficients are arbitrary algebraic numbers, then it too can be factored completely into a constant c times the product of factors of the form (x − a), where c and the a's are still algebraic numbers.

3. Chess. Designating a system for recording moves in which each square on the board is uniquely identified by coordinates indicating its file and rank, the files on the board being standardly denominated a to h and the ranks 1 to 8. Chiefly in algebraic notation. Cf. descriptive adj. 5.Now the only system of notation officially recognized in the laws of the game.

ΚΠ

1853 Brit. Chess Rev. 1 135 In writing and printing annotations,..this system has the advantage over the algebraic form recently introduced.

1860 H. Staunton Chess Praxis 65 Where the Algebraic method has been adopted in practice, it seems to be preferred to any other... It is very desirable that English makers should attach a numbered and lettered margin to their Boards.

1913 H. J. R. Murray Hist. Chess ii. iii. 469 A literal or algebraic notation was also used in Europe in the mediaeval period. Like the descriptive notation, its use would appear to have been borrowed from Muslim players... The files are named a, b, to h.

1968 New Statesman 5 Jan. 23/3 Commendably..the authors [of a book on chess] have adopted the algebraic notation in preference to the clumsy and space-wasting ‘descriptive’ method.

1987 PC Mag. 21 July 548/4 Laptop Chess has two major flaws. First, there is no way to display captured pieces, though you can display or print a game record in algebraic notation.

2002 P. Wolff Compl. Idiot's Guide to Chess 336 If you ever get confused about some aspect of algebraic notation..refer to the tear-out card where I boil it down to the essentials.

Compounds

algebraic geometer n. an expert or specialist in algebraic geometry.

ΚΠ

1851 Cambr. & Dublin Math. Jrnl. 6 245 The permanence in space of the surface, under transformation of coordinates, concerns the algebraic geometer, not the geometrical algebraist.

1933 Isis 20 166 One of the reasons for the small number of workers on differential geometry in those days was..the great attraction exercised by the great algebraic geometers, Steiner, Möbius, Plücker, Chasles, Poncelet, and others.

2010 S.-T. Yan & S. Nadis Shape Inner Space xiii. 300 His proof, rooted in a highly technical, analytical approach, did not provide an explanation in the form that algebraic geometers were looking for.

algebraic geometry n. (originally) the branch of mathematics dealing with geometrical concepts by algebraic means (= analytical geometry n. at analytical adj. Compounds); (in later use chiefly) a branch of algebra concerned with solutions of algebraic equations studied in terms of geometrical concepts.

ΘΚΠ

the world > relative properties > number > geometry > [noun] > branches of

planimetrya1393

conic?a1560

helicosophy1570

stereometry1570

spheric1660

planometry1669

mensuration1704

polygonometry1791

analytical geometry1802

isoperimetry1811

analytic geometry1817

algebraic geometry1821

coordinate geometry1837

non-Euclidean geometry1872

differential geometry1877

pangeometry1878

projective geometry1878

metageometry1890

Riemann geometry1895

variable geometry1957

1821 Cambr. Probl. Index p. vii Algebraic geometry.

1823 D. Lardner Syst. Algebraic Geom. I. p. viii The title ‘Algebraic Geometry’ has been preferred to either of the titles ‘Analytic Geometry’ or ‘the Application of Algebra to Geometry’, because the one is equivocal and the other circumlocutory.

1894 N.E.D. at Degree sb. 13 In algebraic geometry, the degree of a curve or surface is that of the equation expressing it.

1928 V. Snyder et al. Sel. Topics Algebraic Geom. Pref. 3 The purpose of this report is to give a brief..survey of..certain topics in algebraic geometry.

1984 A. Baker Conc. Introd. Theory of Numbers iv. 33 The study of higher congruences..leads to the concept of p-adic numbers and to deep theories in the realm of algebraic geometry.

2006 P. Woit Not even Wrong x. 142 In simplest terms, algebraic geometry is the study of solutions to sets of polynomial equations.

algebraic topology n. a branch of mathematics which studies topological spaces using the tools of abstract algebra.

ΚΠ

1935 S. Lefschetz in Proc. National Acad. Sci. U.S.A. 21 220 This theory may be said to include the parts of algebraic topology related to local connectedness and retracts and to leave out the rest.

1963 D. Bushaw Elem. Gen. Topol. i. 7 Shortly after Fundamenta began to appear, heightened interest in algebraic topology..led to a sharpening of this tool.

2004 Sci. Amer. (U.K. ed.) July 73/3 Poincaré largely created the branch of mathematics called algebraic topology.

algebraic variety n. Mathematics (originally) the set of solutions of a system of polynomial equations; (in later use) any of several generalizations of this to a more abstract context, esp. that developed by French mathematician Alexander Grothendieck (1928–2014).

ΚΠ

1916 Ann. Math. 17 197 Let V_r be an r-dimensional irreducible algebraic variety immersed in an (r + k) space.

1953 Amer. Jrnl. Math. 75 595 At this point we have to distinguish between the notion of an algebraic variety in the classical sense..and that of an abstract variety in the sense of Weil.

2000 M. Hindry & J. H. Silverman Diophantine Geom. a ix. 158 The smoothness of the algebraic variety X can be expressed by the nonvanishing of certain minors..of certain matrices with entries in K.

This entry has been updated (OED Third Edition, September 2012; most recently modified version published online June 2022).

单词	algebraic
释义	algebraicadj. Brit. /ˌaldʒᵻˈbreɪɪk/, U.S. /ˌældʒəˈbreɪɪk/ Forms: 1600s algebriaque, 1600s algebraique, 1600s–1700s algebraick, 1600s– algebraic. Origin: Of multiple origins. Partly formed within English, by derivation. Partly a borrowing from French. Etymons: algebra n., -ic suffix; French algébraïque. Etymology: Partly < algebra n. + -ic suffix, and partly < Middle French †algébraïque (1585) < post-classical Latin algebraicus (1545 or earlier). Compare French algébrique (1740). Compare also German algebraisch (1600 as algebreisch ). Compare earlier algebraical adj. 1. Of or relating to algebra; characteristic of algebra, occurring in or involving algebra; (esp. of a sum) taken with consideration of the sign (plus or minus) of each term. ΘΚΠ the world > relative properties > number > algebra > [adjective] cossic1557 algebraical1571 cossical1571 algebraic1653 1653 J. Webster Academiarum Examen 24 Who can be ignorant of the..compendious use of all sorts of Symbolisms, that have but any insight into Algebraick Arithmetick? 1684 London Gaz. mdcccclxxxv/4 Algebraick Arithmetick, made easie for the commonest capacity. 1702 J. Harris New Short Treat. Algebra 16 The general way of Division of Compound Quantities is like the ordinary way..; Respect being had to the Rules of Algebraic Addition, Subtraction and Multiplication. 1732 G. Berkeley Alciphron II. vii. xvii. 169 The Algebraic Mark, which denotes the Root of a negative Square, hath its Use in Logistic Operations. 1772 B. Franklin Let. 19 Sept. in Papers (1975) XIX. 300 Tho' the Weight of Reasons cannot be taken with the Precision of Algebraic Quantities, yet when each is considered..and the whole lies before me, I think I can judge better. 1827 O. Gregory Hutton's Course Math. (ed. 9) I. 182 Algebraic Fractions have the same names and rules of operation, as numeral fractions in common arithmetic. 1858 O. W. Holmes Autocrat of Breakfast-table xi. 299 These expressions come to be the algebraic symbols of minds which have grown too weak or indolent to discriminate. 1883 Analyst 10 97 This does not impair the generality in any case, every polynomial being reducible to this form by dividing it through by the algebraic sum of its coefficients. 1910 Encycl. Brit. I. 619/1 These works possess considerable originality, and contain many new improvements in algebraic notation. 1943 G. Greene Ministry of Fear iii. i. 168 One could almost put it into algebraic terms. 1995 Amer. Scientist Mar. 168/2 Rayleigh solved this paradox by considering the superposition (algebraic addition) of a large number of sound waves. 2010 Daily Tel. 11 Nov. 34/6 Hilton also made important contributions to the field of algebraic topology, a branch of mathematics which uses tools from abstract algebra to study topological spaces. 2. Mathematics. a. Designating an expression involving only the operations of addition, multiplication, raising to a power (squaring, cubing, etc.), and their inverses acting on terms involving constants and variables; spec. (a) designating an equation in which a polynomial in a single variable is equated to zero; (b) designating a function of one variable which is the root of a polynomial in another variable whose coefficients are themselves polynomials with rational coefficients in the first variable. Also: relating to or involving such an expression. Cf. transcendental adj. 4. ΘΚΠ the world > relative properties > number > algebra > [adjective] > relating to expressions > relating to equations algebraic1657 lateral1670 explicable1706 unreduced1762 homogeneous1815 resolvent1860 Pellian1862 equational1864 canonizant1879 variational1879 unilateral1884 non-dimensional1904 open1937 inhomogeneous1943 stiff1952 1657 J. Rowland tr. J. Johnstone Hist. Constancy of Nature 87 To find out the value of Algebraic Æquations_[L. Æquationum algebraicarum] of all things, if it be rationall: and if it be not, yet to expresse it next unto that in Numbers absolute. 1704 J. Harris Lexicon Technicum I. (at cited word) Exponential curves are such as partake both of the nature of Algebraick and Transcendent ones. 1738 Chambers' Cycl. (ed. 2) I. facing sig. 2Hhh Most authors, after Des Cartes, call algebraic curves, geometrical ones. 1819 G. Peacock View Fluxional & Differential Calculus 23 Where the fluent or integral is expressed by an algebraic function. 1871 P. G. Tait & W. J. Steele Treat. Dynamics of Particle (ed. 3) i. 26 When e = 1, the corrected integral..is 2(x + a/4) = y²/2a − a log y/a. This is the only case in which we do not obtain an algebraic curve. 1891 Amer. Jrnl. Math. 13 110 An algebraic function satisfying an algebraic equation whose coefficients are rational functions with integral coefficients of some indeterminate quantities. 1972 C. S. Ogilvy Tomorrow's Math (ed. 2) viii. 153 The famous equation connecting π and e, e^πi = −1, is not algebraic. 2007 I. Stewart Why Beauty is Truth iv. 54 Tartaglia was not the first to find an algebraic solution to a cubic equation. b. Of a number: that can be expressed as a root of a polynomial in one variable with coefficients that are whole numbers. ΘΚΠ the world > relative properties > number > mathematical number or quantity > [adjective] > prime > other commona1398 unarithmetical1671 algebraic1912 square-free1960 insensitive1968 1893 Proc. London Math. Soc. 24 327 (heading) On the algebraical integers derived from an irreducible cubic equation.] 1912 Trans. Amer. Math. Soc. 13 293 While the field R (α,…, α_n) defined by the algebraic numbers α₁,…,α_nis identical with a field R(u) defined by a single algebraic number u, a similar theorem does not hold for finite algebras. 1937 A. A. Albert Mod. Higher Algebra xii. 288 Let us apply this to a field  = ℜ(ξ) which is algebraic of degree n over the field ℜ of all rational numbers. We call the quantities of  algebraic numbers and say that  is an algebraic number field. 1982 Sci. Amer. Dec. 130/2 For example, √2, i (the imaginary square root of −1) and (−1 + i√3)/2 are all algebraic integers because they are roots of the algebraic equations x² − 2 = 0, x² + 1 = 0 and x³ − 1 = 0. 2006 A. Ash & R. Gross Fearless Symmetry viii. 91 If you take a polynomial whose coefficients are arbitrary algebraic numbers, then it too can be factored completely into a constant c times the product of factors of the form (x − a), where c and the a's are still algebraic numbers. 3. Chess. Designating a system for recording moves in which each square on the board is uniquely identified by coordinates indicating its file and rank, the files on the board being standardly denominated a to h and the ranks 1 to 8. Chiefly in algebraic notation. Cf. descriptive adj. 5.Now the only system of notation officially recognized in the laws of the game. ΚΠ 1853 Brit. Chess Rev. 1 135 In writing and printing annotations,..this system has the advantage over the algebraic form recently introduced. 1860 H. Staunton Chess Praxis 65 Where the Algebraic method has been adopted in practice, it seems to be preferred to any other... It is very desirable that English makers should attach a numbered and lettered margin to their Boards. 1913 H. J. R. Murray Hist. Chess ii. iii. 469 A literal or algebraic notation was also used in Europe in the mediaeval period. Like the descriptive notation, its use would appear to have been borrowed from Muslim players... The files are named a, b, to h. 1968 New Statesman 5 Jan. 23/3 Commendably..the authors [of a book on chess] have adopted the algebraic notation in preference to the clumsy and space-wasting ‘descriptive’ method. 1987 PC Mag. 21 July 548/4 Laptop Chess has two major flaws. First, there is no way to display captured pieces, though you can display or print a game record in algebraic notation. 2002 P. Wolff Compl. Idiot's Guide to Chess 336 If you ever get confused about some aspect of algebraic notation..refer to the tear-out card where I boil it down to the essentials. Compounds algebraic geometer n. an expert or specialist in algebraic geometry. ΚΠ 1851 Cambr. & Dublin Math. Jrnl. 6 245 The permanence in space of the surface, under transformation of coordinates, concerns the algebraic geometer, not the geometrical algebraist. 1933 Isis 20 166 One of the reasons for the small number of workers on differential geometry in those days was..the great attraction exercised by the great algebraic geometers, Steiner, Möbius, Plücker, Chasles, Poncelet, and others. 2010 S.-T. Yan & S. Nadis Shape Inner Space xiii. 300 His proof, rooted in a highly technical, analytical approach, did not provide an explanation in the form that algebraic geometers were looking for. algebraic geometry n. (originally) the branch of mathematics dealing with geometrical concepts by algebraic means (= analytical geometry n. at analytical adj. Compounds); (in later use chiefly) a branch of algebra concerned with solutions of algebraic equations studied in terms of geometrical concepts. ΘΚΠ the world > relative properties > number > geometry > [noun] > branches of planimetrya1393 conic?a1560 helicosophy1570 stereometry1570 spheric1660 planometry1669 mensuration1704 polygonometry1791 analytical geometry1802 isoperimetry1811 analytic geometry1817 algebraic geometry1821 coordinate geometry1837 non-Euclidean geometry1872 differential geometry1877 pangeometry1878 projective geometry1878 metageometry1890 Riemann geometry1895 variable geometry1957 1821 Cambr. Probl. Index p. vii Algebraic geometry. 1823 D. Lardner Syst. Algebraic Geom. I. p. viii The title ‘Algebraic Geometry’ has been preferred to either of the titles ‘Analytic Geometry’ or ‘the Application of Algebra to Geometry’, because the one is equivocal and the other circumlocutory. 1894 N.E.D. at Degree sb. 13 In algebraic geometry, the degree of a curve or surface is that of the equation expressing it. 1928 V. Snyder et al. Sel. Topics Algebraic Geom. Pref. 3 The purpose of this report is to give a brief..survey of..certain topics in algebraic geometry. 1984 A. Baker Conc. Introd. Theory of Numbers iv. 33 The study of higher congruences..leads to the concept of p-adic numbers and to deep theories in the realm of algebraic geometry. 2006 P. Woit Not even Wrong x. 142 In simplest terms, algebraic geometry is the study of solutions to sets of polynomial equations. algebraic topology n. a branch of mathematics which studies topological spaces using the tools of abstract algebra. ΚΠ 1935 S. Lefschetz in Proc. National Acad. Sci. U.S.A. 21 220 This theory may be said to include the parts of algebraic topology related to local connectedness and retracts and to leave out the rest. 1963 D. Bushaw Elem. Gen. Topol. i. 7 Shortly after Fundamenta began to appear, heightened interest in algebraic topology..led to a sharpening of this tool. 2004 Sci. Amer. (U.K. ed.) July 73/3 Poincaré largely created the branch of mathematics called algebraic topology. algebraic variety n. Mathematics (originally) the set of solutions of a system of polynomial equations; (in later use) any of several generalizations of this to a more abstract context, esp. that developed by French mathematician Alexander Grothendieck (1928–2014). ΚΠ 1916 Ann. Math. 17 197 Let V_r be an r-dimensional irreducible algebraic variety immersed in an (r + k) space. 1953 Amer. Jrnl. Math. 75 595 At this point we have to distinguish between the notion of an algebraic variety in the classical sense..and that of an abstract variety in the sense of Weil. 2000 M. Hindry & J. H. Silverman Diophantine Geom. a ix. 158 The smoothness of the algebraic variety X can be expressed by the nonvanishing of certain minors..of certain matrices with entries in K. This entry has been updated (OED Third Edition, September 2012; most recently modified version published online June 2022). < adj.1653
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