Sentence examples for prime degree from inspiring English sources
We therefore introduce a different method to take advantage of symmetries even in the prime degree extension case.
In the prime degree extension case, V cannot be a subfield, hence the symmetric variables σ j are not restricted to V.
Summary At this point, we have proved that if an escaping set of a Hénon map with prime degree d is biholomorphic to another escaping set, then necessarily the other Hénon map has degree d as well.
In addition, we use Burnside's characterization of transitive groups of prime degree to characterize the structure of vertex-transitive self-complementary k-hypergraphs which have prime order p in the case where k="2ℓ or k="2ℓ+1 and p≡1(mod2ℓ+1), and we present an algorithm to generate all of these structures.
As Andrew McGettigan writes in The Great University Gamble: "Sub-prime degrees, like sub-prime mortgages, are sold to communities relatively unfamiliar with the product".
This idea already provided practical improvements in several previous works for composite-degree extension fields, but its application to prime-degree extension fields has been more challenging.
In this paper, we focus on Diem's version of index calculus for ECDLP over a binary field of prime extension degree n [3,7,15].
While symmetries had also been exploited in similar ECDLP algorithms for curves defined over finite fields with composite extension degrees, our method is the first one in the case of extension fields with prime extension degrees, which is the most interesting case for applications.
It is difficult, according to those who work closely with Downing Street, to overestimate Hill's closeness to and influence over the prime minister – a degree of access matched only by Nick Timothy, with whom she shares the role of chief of staff at Number 10.
Furthermore, the requirement that (C k)) is infinite can often be replaced by the much weaker requirement that (bigcup _{ell } C ell )), where (ell ) runs through a family of finite extensions of (k) of degree prime to (n), is infinite.
Since ([Delta _1] = [mathcal D _1 otimes _mathcal{K } mathcal L ^{(1)}_2]) is ramified at (w), the ramification index (e tilde{w} vert w)) is (> 1) (cf. [34, Theorem 3.4]; note that being of degree prime to (mathrm{char} k), the division algebra (Delta _1) is "inertially split").
