polynomial

See also: polynômial

English

Etymology

From poly- +‎ -nomial, from νομός (nomós, “portion, part”), by analogy with binomial.

Pronunciation

• (UK) IPA^(key): /ˌpɒlɪˈnəʊmɪəl/

• Audio (Southern England):

  (file)

• (US) IPA^(key): /ˌpɑliˈnoʊmiəl/

Noun

polynomial (plural polynomials)

1. (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 $a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{0}x^{0}$.
   • 1999, William Dunham, Euler: The Master of Us All, Mathematical Association of America, published 1999, page 116:

     Unfortunately, an analogous attack on the octic polynomial becomes exceedingly complicated.

   • 2016, Grigoriy Blekherman, Daniel Plaumann, Rainer Sinn, Cynthia Vinzant, “Low-Rank Sum-of-Squares Representations on Varieties of Minimal Degree”, in arXiv‎^[1]:

     Our upper bound is the best possible, and it implies the existence of low-rank factorizations of positive semidefinite bivariate matrix polynomials and representations of biforms as sums of few squares.

2. (taxonomy) A taxonomic designation (such as of a subspecies) consisting of more than two terms.
3. (linguistics, Sinology) A type of term consisting of multiple parts. This term needs a definition. Please help out and add a definition, then remove the text {{rfdef}}.
   • 2023, Martina Jemelková, “On the Nature of Zero-Meaning Sinograms: Typology and Thematic Classification”, in Studia Orientalia Slovaca‎^[2], volume 22, number 2:

     Alternatively, there are polynomials denoting stages of the day: tónglóng 曈昽 “<fml.> light at daybreak”; or meteorological phenomena, such as wùsōng 雾凇 “(soft) rime”, àidài 叆叇 “<fml.> (of clouds) dense”.

   • 2025, Martina Jemelková, “Chinese Binomes: A Graphical or Phonological Construct?”, in Acta Linguistica Asiatica‎^[3], volume 15, number 2, →DOI:

     The same corpus is used as in the analysis of the thematic scope of polynomials, except that in this case only 720 binomes will be considered.

Hyponyms

• binomial
• homogeneous polynomial
• monomial
• trinomial
• quadrinomial
• quantic

Holonyms

• rational function

Translations

algebraic expression

• Afrikaans: polinoom (af)
• Armenian: բազմանդամ (hy) (bazmandam)
• Azerbaijani: çoxhədli
• Bulgarian: полином m (polinom), многочлен m (mnogočlen)
• Burmese: ကိန်းစုတန်း (my) (kin:cu.tan:)
• Catalan: polinomi m
• Chinese:

  Mandarin: 多項式 / 多项式 (zh) (duōxiàngshì)

• Czech: polynom m
• Danish: polynomium n
• Dutch: polynoom (nl) n or m, veelterm m
• Estonian: polünoom
• Finnish: polynomi (fi)
• French: polynôme (fr) m
• Galician: polinomio m
• German: Polynom (de) n
• Greek: πολυώνυμο (el) n (polyónymo)
• Hindi: बहुपद (bahupad)
• Hungarian: polinom (hu)
• Icelandic: margliða f
• Italian: polinomio (it) m
• Japanese: 多項式 (ja) (たこうしき, takōshiki), 整式 (ja) (seishiki)
• Khmer: ពហុធា (km) (pea’hu’tʰie)
• Korean: 다항식 (ko) (dahangsik)
• Malayalam: ബഹുപദം (bahupadaṁ)
• Maori: pūrau
• Norwegian: polynom (no) n
• Polish: wielomian (pl) m
• Portuguese:

  Brazilian: polinômio (pt) m

  European: polinómio (pt) m

• Romanian: polinom (ro) n
• Russian: многочле́н (ru) m (mnogočlén), полино́м (ru) m (polinóm)
• Spanish: polinomio (es) m
• Swedish: polynom (sv) n
• Tagalog: damikay
• Thai: พหุนาม (pá-hù-naam)
• Turkish: polinom (tr)
• Vietnamese: đa thức (vi)

taxonomic designation

• French: polynôme (fr) m

Adjective

polynomial (not comparable)

1. (algebra) Able to be described or limited by a polynomial.
2. (taxonomy) Of a polynomial name or entity.

Translations

in algebra

• Afrikaans: polinomies
• Catalan: polinomial
• Czech: polynomický
• Finnish: polynominen
• French: polynomial (fr)
• German: polynomisch
• Greek: πολυωνυμικός (el) (polyonymikós)
• Hungarian: polinomiális (hu)
• Italian: polinomiale (it)
• Polish: wielomianowy m
• Portuguese: polinomial
• Romanian: polinomial (ro), polinomic
• Russian: многочле́нный (ru) (mnogočlénnyj), полиномиа́льный (ru) (polinomiálʹnyj)
• Spanish: polinomial, polinómico
• Swedish: polynomiell (sv)
• Thai: พหุนาม (pá-hù-naam)
• Turkish: polinom (tr)
• Vietnamese: đa thức (vi)

in taxonomy

• French: polynominal m, polynominale f, polynomial (fr) m, polynomiale (fr) f

Derived terms

• Abel polynomial
• Alexander-Conway polynomial
• Alexander polynomial
• all-one polynomial
• Bell polynomial
• Bernoulli polynomial
• Bernstein basis polynomial
• Boas-Buck polynomial
• characteristic polynomial
• complementary nondeterministic polynomial
• Conway-Alexander polynomial
• Conway polynomial
• cyclotomic polynomial
• Dickson polynomial
• eigenpolynomial
• elementary symmetric polynomial
• Fibonacci polynomial
• Hermite polynomial
• homogenous polynomial
• hyperbolic polynomial
• Jacobi polynomial
• Jones polynomial
• Kazhdan-Lusztig polynomial
• Lagrange polynomial
• Laguerre polynomial
• Laurent polynomial
• Legendre polynomial
• Lucas polynomial
• Macdonald polynomial
• Maclaurin polynomial
• minimal polynomial
• Mittag-Leffler polynomial
• Narumi polynomial
• nonpolynomial
• nonuniform polynomial time
• Pidduck polynomial
• polynomial algebra
• polynomial basis
• polynomial complexity
• polynomial equation
• polynomial form
• polynomial function
• polynomial interpolation
• polynomialism
• polynomialist
• polynomiality
• polynomially
• polynomial reduction
• polynomial ring
• polynomial sequence
• polynomial time
• polynomial time-reduction
• polynomial-time reduction
• polynomiography
• posynomial
• primitive polynomial
• pseudopolynomial
• pseudo-polynomial time
• quasipolynomial
• rook polynomial
• separable polynomial
• subpolynomial
• superpolynomial
• symmetric polynomial
• Taylor polynomial
• Taylor's polynomial
• Touchard polynomial
• ultrapolynomial
• Zhegalkin polynomial

See also

• Appendix:English polynomial degrees

French

Pronunciation

• Audio (France (Toulouse)):

  (file)

• Audio (France (Vosges)):

  (file)

Adjective

polynomial (feminine polynomiale, masculine plural polynomiaux, feminine plural polynomiales)

1. polynomial

Related terms

• polynôme