different between quantic vs quintic

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.

English

Etymology

From Latin quintus (“fifth”) +? -ic (“of pertaining to”).

Adjective

quintic (not comparable)

1. (mathematics) Of or relating to the fifth degree, such as a quintic polynomial which has the form ax⁵+bx⁴+cx³+dx²+ex+f (containing a term with the independent variable raised to the fifth power).

Noun

quintic (plural quintics)

1. (mathematics) a quintic polynomial: ax⁵+bx⁴+cx³+dx²+ex+f

Derived terms

• quintic equation
• quintic function