different between polynomial vs quantic

English

Etymology

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

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 ${\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{0}x^{0}}$.
2. (taxonomy) A taxonomic designation (such as of a subspecies) consisting of more than two terms.

Hyponyms

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

Holonyms

• rational function

Derived terms

Translations

Adjective

polynomial (not comparable)

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

Translations

See also

• Appendix:English polynomial degrees

French

Adjective

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

1. polynomial

Related terms

• polynôme

English

Etymology

From Latin quantus (“how much”).

Noun

quantic (plural quantics)

1. (mathematics) A homogeneous polynomial in two or more variables.
   • 1858, Arthur Cayley, A Fourth Memoir on Quantics, 1859, Philosophical Transactions of the Royal Society of London, Volume 148, page 421,

     When the two quantics are the first derived functions of the same quantic of any odd order, the lineo-linear invariant does not vanish, but it is not an invariant of the single quantic.

   • 1859, George Salmon, Modern Higher Algebra, page 52,

     74. The discriminant of a binary quantic, or the eliminant of a system of binary quantics, is an invariant.

     We can see a priori that this must be the case, for if a given quantic has a square factor, it will have a square factor still when it is linearly transformed; or if a system of quantics have a common factor, they will still have a common factor when the equations are transformed.

   • 1895, Edwin Bailey Elliott, An Introduction to the Algebra of Quantics, 2011, Facsimile Edition.

References

• quantic in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.