polynomialn.adj.

Brit.

/ˌpɒlɪˈnəʊmɪəl/, U.S.

/ˌpɑliˈnoʊmiəl/,

/ˌpɑləˈnoʊmiəl/

Origin: Formed within English, by compounding. Etymons: poly- comb. form, -nomial comb. form.

Etymology: < poly- comb. form + -nomial comb. form. In sense A. 1 after binomial n.; compare multinomial adj., multinomial n. With sense A. 2 compare trinomial n. 2.

A. n.

1. Mathematics. Originally: an expression consisting of many terms, a multinomial. Now: spec. a sum of one or more terms each consisting of a constant multiplied by one or more variables raised to a positive (or non-negative) integral power (e.g. x⁴ − 3x²y + 7).

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > consisting of specific number of terms

binomial1557

binomy1571

trinomy1571

quadrinomial1673

multinomiala1690

polynomiala1690

trinomiala1690

monomial1706

nomial1717

monome1736

infinitinomial1763

polynome1828

mononomial1844

quantic1854

form1859

Jacobi polynomial1882

Jacobi's function1882

ternariant1882

triquaternion1902

term1957

arity1968

a1690 S. Jeake Λογιστικηλογία (1696) 273 Those knit together by both Signs are called..by some Multinomials, or Polynomials, that is, many named.

1753 Chambers's Cycl. Suppl. (at cited word) To raise a polynomial to any given power, may be done by Sir Isaac Newton's binomial theorem.

c1865 J. Wylde Circle of Sci. I. 481/1 We conclude that the polynomial is not a square.

1906 Athenæum 19 May 613/3 The Expansion of Polynomials in Series of Functions.

1941 G. Birkhoff & S. MacLane Surv. Mod. Algebra iv. 88 The polynomial x² + 1..cannot be factored into polynomials with rational coefficients.

1966 J. V. Robison Mod. Algebra & Trig. v. 109 To factor a polynomial, we express the polynomial as a product of other polynomials, called factors of the given polynomial.

1991 New Scientist 5 Oct. 44/1 The Alexander polynomial for the trefoil knot is x² − x + 1, and for the figure-eight knot in Figure 1 it is x² − 3x + 1.

2. Taxonomy. A Latin name consisting of several (usually more than two) terms, as the pre-Linnaean name of a species (chiefly historical), or the modern name of a subspecies or variety. Cf. binomial adj. 2.

ΘΚΠ

the world > life > biology > taxonomy > [adjective] > of names consisting of number of terms

polynomial1885

the mind > language > naming > name or appellation > [noun] > scientific or technical name > with many terms

polyonym1884

polynomial1885

1885 Nature 5 Mar. 413/1 Trinomials—that is, the usage of three names, of which the last is that of the sub-species—are in great favour... Quadrinomials and Polynomials must necessarily follow.

1951 G. H. M. Lawrence Taxon. Vascular Plants ix. 194 Before the middle of the eighteenth century the names of plants commonly were polynomials.

1993 Ann. Missouri Bot. Garden 80 888/1 Specimen 809.1..is presumably the basis for Browne's polynomial and for Linnaeus's epithet.

B. adj.

1. Mathematics. Of an expression: consisting of many terms; spec. of the nature of a polynomial. Also: relating to or involving a polynomial or polynomials; designating an extension of the binomial theorem for determining the expansion of any power of a polynomial expression. Cf. binomial adj. 1, multinomial adj.

ΘΚΠ

the mind > language > naming > [adjective] > having many names

multinominousa1631

parti named1634

multinominal1656

polyonymous1678

polynomial1704

heteronymous1734

polynome1830

plurinominal1881

poecilonymic1889

polyonymic1889

polynomic1898

the world > relative properties > number > algebra > [adjective] > relating to expressions > involving specific number of terms

binomial1570

multinomial1608

quadrinomial1673

solinomial1690

polynomial1704

trinomial1704

infinitinomial1706

monomial1801

tetranomial1817

unipartite1819

monome1829

mononomial1861

polynomic1868

tripartite1869

multinominal1940

1704 J. Harris Lexicon Technicum I Polynomial, or Multinomial Roots, in Mathematicks, are such as are composed of many Nomes, Parts or Members; as, a + b + d + c.

1840 Penny Cycl. XVIII. 360/2 The polynomial theorem means the theorem by which a polynomial expression is raised to its several powers.

1953 A. D. Booth & K. H. V. Booth Automatic Digital Calculators xvi. 189 The first n terms of this series will give the best nth degree polynomial approximation to the given function.

1972 M. Kline Math. Thought xiii. 270 In L'Invention nouvelle, Albert Girard inferred and stated that an nth-degree polynomial equation has n roots if one counts the impossible roots, that is, the complex roots, and if one takes into account the repeated roots.

1990 Glasgow Math. Jrnl. 32 371 Prime rings came into prominence when Posner characterized prime rings satisfying a polynomial identity.

2. Consisting of or characterized by many names or terms; (Taxonomy, of a Latin name) consisting of several (esp. more than two) terms. Cf. binomial adj. 2. Now rare.

ΚΠ

1890 Cent. Dict. Polynomial, 1. containing many names or terms; 2. in zoöl. and bot., specifically, noting a method of nomenclature in which the technical names of species are not confined to two terms.

1894 Bull. Torrey Bot. Club 21 175 The short, descriptive phrase ‘Beureria petalis coriaceis oblongis, calycis foliolis reflexis’..is a polynomial specific name rather than a generic definition.

1945 Rhodora 47 274 Binomial nomenclature was not intended by Linnaeus to supersede the polynomial specific name.

1964 Huntia 1 34 He makes the essential distinction between the old Aristotelian polynomial phrase-names and the new trivial names.

Compounds

polynomial time n. Computing an amount of time expressible as a polynomial in terms of the ‘size’ of a given problem whose solution is required. Frequently attributive, esp. with reference to algorithms which can be executed in polynomial time. Cf. exponential time n. at exponential adj. and n. Compounds.

ΘΚΠ

the world > relative properties > number > mathematics > [adjective] > relating to mathematical enquiry

canonical1738

independenta1739

algorithmic1799

irreflexive1890

uninterpreted1898

consistent1928

polynomial time1972

the world > relative properties > number > algebra > [noun] > expression > consisting of specific number of terms > expressing amount of time

polynomial time1972

1972 R. M. Karp in R. E. Miller & J. W. Thatcher Complexity of Computer Computations 88 The class of languages recognizable by string recognition algorithms which operate in polynomial time is also invariant under a wide range of changes in the class of algorithms.

1982 C. H. Papadimitriou & K. Steiglitz Combinatorial Optimization viii. 166 Exponential algorithms..are quickly abandoned once a polynomial-time algorithm for the same problem is discovered.

1997 Computer Music Jrnl. Summer 37/1 NP-complete problems (NP stands for nondeterministic polynomial time)..can be solved in polynomial time by nondeterministic algorithms.

Derivatives

polyˈnomialism n. Taxonomy (now rare) a polynomial system of nomenclature, as used in the Latin naming of species, subspecies, etc.

ΚΠ

1890 Cent. Dict. Polynomialism, polynomial nomenclature; the method or practice of using polynomials.

1902 Science 26 Dec. 1036/2 Micheli, whose only crime was polynomialism.

1912 Bull. Torrey Bot. Club 39 427 That revived polynomialism..which proceeds unmindful that a name is not a classification.

polyˈnomialist n. Taxonomy (now rare) a person who deploys polynomialism.

ΚΠ

1890 Cent. Dict. Polynomialist, in zoöl. and bot., one who uses polynomials, or a polynomial system of nomenclature.

1902 Bot. Gaz. 33 227 Genera established by polynomialists should be interpreted by their first successor using their generic names.

polyˈnomially adv. with respect to a polynomial or polynomials; spec. in polynomial time.

ΚΠ

1928 Philos. Trans. (Royal Soc.) A. 227 210 Homogeneous polynomials in μ, α_lη^λt., Β₁e^−λt, α₂. Β₂ with coefficients which involve t polynomially and γe^νt through positive and negative powers.

1999 Nature 8 July 133/2 When the underlying computational task exhibits a continuous (‘second order’) phase transition, resource requirements grow only polynomially with problem size.

This entry has been updated (OED Third Edition, September 2006; most recently modified version published online March 2022).

单词	polynomial
释义	polynomialn.adj. Brit. /ˌpɒlɪˈnəʊmɪəl/, U.S. /ˌpɑliˈnoʊmiəl/, /ˌpɑləˈnoʊmiəl/ Origin: Formed within English, by compounding. Etymons: poly- comb. form, -nomial comb. form. Etymology: < poly- comb. form + -nomial comb. form. In sense A. 1 after binomial n.; compare multinomial adj., multinomial n. With sense A. 2 compare trinomial n. 2. A. n. 1. Mathematics. Originally: an expression consisting of many terms, a multinomial. Now: spec. a sum of one or more terms each consisting of a constant multiplied by one or more variables raised to a positive (or non-negative) integral power (e.g. x⁴ − 3x²y + 7). ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > consisting of specific number of terms binomial1557 binomy1571 trinomy1571 quadrinomial1673 multinomiala1690 polynomiala1690 trinomiala1690 monomial1706 nomial1717 monome1736 infinitinomial1763 polynome1828 mononomial1844 quantic1854 form1859 Jacobi polynomial1882 Jacobi's function1882 ternariant1882 triquaternion1902 term1957 arity1968 a1690 S. Jeake Λογιστικηλογία (1696) 273 Those knit together by both Signs are called..by some Multinomials, or Polynomials, that is, many named. 1753 Chambers's Cycl. Suppl. (at cited word) To raise a polynomial to any given power, may be done by Sir Isaac Newton's binomial theorem. c1865 J. Wylde Circle of Sci. I. 481/1 We conclude that the polynomial is not a square. 1906 Athenæum 19 May 613/3 The Expansion of Polynomials in Series of Functions. 1941 G. Birkhoff & S. MacLane Surv. Mod. Algebra iv. 88 The polynomial x² + 1..cannot be factored into polynomials with rational coefficients. 1966 J. V. Robison Mod. Algebra & Trig. v. 109 To factor a polynomial, we express the polynomial as a product of other polynomials, called factors of the given polynomial. 1991 New Scientist 5 Oct. 44/1 The Alexander polynomial for the trefoil knot is x² − x + 1, and for the figure-eight knot in Figure 1 it is x² − 3x + 1. 2. Taxonomy. A Latin name consisting of several (usually more than two) terms, as the pre-Linnaean name of a species (chiefly historical), or the modern name of a subspecies or variety. Cf. binomial adj. 2. ΘΚΠ the world > life > biology > taxonomy > [adjective] > of names consisting of number of terms polynomial1885 the mind > language > naming > name or appellation > [noun] > scientific or technical name > with many terms polyonym1884 polynomial1885 1885 Nature 5 Mar. 413/1 Trinomials—that is, the usage of three names, of which the last is that of the sub-species—are in great favour... Quadrinomials and Polynomials must necessarily follow. 1951 G. H. M. Lawrence Taxon. Vascular Plants ix. 194 Before the middle of the eighteenth century the names of plants commonly were polynomials. 1993 Ann. Missouri Bot. Garden 80 888/1 Specimen 809.1..is presumably the basis for Browne's polynomial and for Linnaeus's epithet. B. adj. 1. Mathematics. Of an expression: consisting of many terms; spec. of the nature of a polynomial. Also: relating to or involving a polynomial or polynomials; designating an extension of the binomial theorem for determining the expansion of any power of a polynomial expression. Cf. binomial adj. 1, multinomial adj. ΘΚΠ the mind > language > naming > [adjective] > having many names multinominousa1631 parti named1634 multinominal1656 polyonymous1678 polynomial1704 heteronymous1734 polynome1830 plurinominal1881 poecilonymic1889 polyonymic1889 polynomic1898 the world > relative properties > number > algebra > [adjective] > relating to expressions > involving specific number of terms binomial1570 multinomial1608 quadrinomial1673 solinomial1690 polynomial1704 trinomial1704 infinitinomial1706 monomial1801 tetranomial1817 unipartite1819 monome1829 mononomial1861 polynomic1868 tripartite1869 multinominal1940 1704 J. Harris Lexicon Technicum I Polynomial, or Multinomial Roots, in Mathematicks, are such as are composed of many Nomes, Parts or Members; as, a + b + d + c. 1840 Penny Cycl. XVIII. 360/2 The polynomial theorem means the theorem by which a polynomial expression is raised to its several powers. 1953 A. D. Booth & K. H. V. Booth Automatic Digital Calculators xvi. 189 The first n terms of this series will give the best nth degree polynomial approximation to the given function. 1972 M. Kline Math. Thought xiii. 270 In L'Invention nouvelle, Albert Girard inferred and stated that an nth-degree polynomial equation has n roots if one counts the impossible roots, that is, the complex roots, and if one takes into account the repeated roots. 1990 Glasgow Math. Jrnl. 32 371 Prime rings came into prominence when Posner characterized prime rings satisfying a polynomial identity. 2. Consisting of or characterized by many names or terms; (Taxonomy, of a Latin name) consisting of several (esp. more than two) terms. Cf. binomial adj. 2. Now rare. ΚΠ 1890 Cent. Dict. Polynomial, 1. containing many names or terms; 2. in zoöl. and bot., specifically, noting a method of nomenclature in which the technical names of species are not confined to two terms. 1894 Bull. Torrey Bot. Club 21 175 The short, descriptive phrase ‘Beureria petalis coriaceis oblongis, calycis foliolis reflexis’..is a polynomial specific name rather than a generic definition. 1945 Rhodora 47 274 Binomial nomenclature was not intended by Linnaeus to supersede the polynomial specific name. 1964 Huntia 1 34 He makes the essential distinction between the old Aristotelian polynomial phrase-names and the new trivial names. Compounds polynomial time n. Computing an amount of time expressible as a polynomial in terms of the ‘size’ of a given problem whose solution is required. Frequently attributive, esp. with reference to algorithms which can be executed in polynomial time. Cf. exponential time n. at exponential adj. and n. Compounds. ΘΚΠ the world > relative properties > number > mathematics > [adjective] > relating to mathematical enquiry canonical1738 independenta1739 algorithmic1799 irreflexive1890 uninterpreted1898 consistent1928 polynomial time1972 the world > relative properties > number > algebra > [noun] > expression > consisting of specific number of terms > expressing amount of time polynomial time1972 1972 R. M. Karp in R. E. Miller & J. W. Thatcher Complexity of Computer Computations 88 The class of languages recognizable by string recognition algorithms which operate in polynomial time is also invariant under a wide range of changes in the class of algorithms. 1982 C. H. Papadimitriou & K. Steiglitz Combinatorial Optimization viii. 166 Exponential algorithms..are quickly abandoned once a polynomial-time algorithm for the same problem is discovered. 1997 Computer Music Jrnl. Summer 37/1 NP-complete problems (NP stands for nondeterministic polynomial time)..can be solved in polynomial time by nondeterministic algorithms. Derivatives polyˈnomialism n. Taxonomy (now rare) a polynomial system of nomenclature, as used in the Latin naming of species, subspecies, etc. ΚΠ 1890 Cent. Dict. Polynomialism, polynomial nomenclature; the method or practice of using polynomials. 1902 Science 26 Dec. 1036/2 Micheli, whose only crime was polynomialism. 1912 Bull. Torrey Bot. Club 39 427 That revived polynomialism..which proceeds unmindful that a name is not a classification. polyˈnomialist n. Taxonomy (now rare) a person who deploys polynomialism. ΚΠ 1890 Cent. Dict. Polynomialist, in zoöl. and bot., one who uses polynomials, or a polynomial system of nomenclature. 1902 Bot. Gaz. 33 227 Genera established by polynomialists should be interpreted by their first successor using their generic names. polyˈnomially adv. with respect to a polynomial or polynomials; spec. in polynomial time. ΚΠ 1928 Philos. Trans. (Royal Soc.) A. 227 210 Homogeneous polynomials in μ, α_lη^λt., Β₁e^−λt, α₂. Β₂ with coefficients which involve t polynomially and γe^νt through positive and negative powers. 1999 Nature 8 July 133/2 When the underlying computational task exhibits a continuous (‘second order’) phase transition, resource requirements grow only polynomially with problem size. This entry has been updated (OED Third Edition, September 2006; most recently modified version published online March 2022). < n.adj.a1690
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