# Trinomial

## Definitions

• Webster's Revised Unabridged Dictionary
• n Trinomial (Math) A quantity consisting of three terms, connected by the sign + or -; as, x + y + z, or ax + 2b - c2 .
• Trinomial (Math) Consisting of three terms; of or pertaining to trinomials; as, a trinomial root.
• Trinomial (Nat. Hist) Consisting of, or involving the use of, three terms; as, a trinomial systematic name specifying the genus, species, and variety.
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Century Dictionary and Cyclopedia
• trinomial In zoology and botany:
• trinomial Consisting of three terms, as the technical name of a subspecies; trionymal: thus, the name Certhia familiaris americana is trinomial. See binomial, polynomial.
• trinomial Using or admitting trinomial or trionymal names in certain cases: as, the trinomial system of nomenclature. Also trinominal.
• trinomial In algebra, consisting of three terms connected by either of the signs + and—: thus, a + b + c, or x—2 xy + y is a trinomial quantity.
• n trinomial A technical name consisting of three words, of which the first is the name of the genus, the second that of the species, and the third that of a geographical race, subspecies, or variety; a trionym. The use of trinomials, formerly interdicted and supposed to be contrary to the canons of nomenclature, has of late become common, especially among American naturalists. (See trinomialism.) A name of three terms the second of which is a generic name in parenthesis (see subgenus) does not constitute a trinomial, and no proper trinomial admits any mark of punctuation, or any word or abbreviation, between its three terms. Thus: Quercus coccinea var. tinctoria is not a pure trinomial.
• n trinomial In algebra, a trinomial expression. See I., 2.
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Chambers's Twentieth Century Dictionary
• adj Trinomial trī-nō′mi-al (math.) consisting of three names or terms connected by the sign plus or minus
• n Trinomial a trinomial quantity
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## Etymology

Webster's Revised Unabridged Dictionary
Pref. tri-, + -nomial, as in binomial,: cf. F. trinôme,

## Usage

### In literature:

It deals with "lumpers" and "splitters," and a possible trinomial nomenclature.
"More Letters of Charles Darwin" by Charles Darwin
The use of the trinomial here is arbitrary.
"The Amphibians and Reptiles of Michoacán, México" by William E. Duellman
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### In science:

When searching for irreducible trinomials of degree r , we can assume that s ≤ r/2, since xr + xs + 1 is irreducible iff the reciprocal polynomial xr + xr−s + 1 is irreducible.
The great trinomial hunt
Over al l trinomials xr + xs + 1 of degree r over GF(2), the probability πd that a trinomial has no non-trivial factor of degree ≤ d is at most c/d, where c is an absolute constant and 1 < d ≤ r/ ln r .
The great trinomial hunt
An upper bound of r on d would probably be incorrect, since it would imply at most c irreducible trinomials of degree r , but we expect this number to be unbounded.
The great trinomial hunt
If the trinomials that have factors of degree less than log2 (r) are excluded by sieving, then by Assumption 1 we are left with O(r/ log r) trinomials to test.
The great trinomial hunt
They found one primitive trinomial; however they missed the trinomial x859433 + x170340 + 1, because of a bug in their sieving routine.
The great trinomial hunt
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