polynomialn.adj.
/ˌpɒlɪˈnəʊmɪəl/, U.S. /ˌpɑliˈnoʊmiəl/, /ˌpɑləˈnoʊmiəl/ 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, αlηλt., Β1e−λt, α2. Β2 with coefficients which involve t polynomially and γeνt 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).
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n.adj.a1690