Splitting field (section The field Ki [X]/(f(X)))
in F2; hence f(x) is irreducible in F2[x]. Put r = x + (f(x)) in F2[x]/(f(x)) so F2(r ) is a field and x3 + x + 1 = (x + r)(x2 + ax + b) in F2(r )[x]....
17 KB (2,876 words) - 13:21, 24 October 2024
→ Y and f2: X → Y, define the function O(f1, f2): X → Y by (O(f1, f2))(x) = o(f1(x), f2(x)) for all x ∈ X. Commonly, o and O are denoted by the same symbol...
6 KB (778 words) - 16:54, 24 June 2024
function f : R2 → R2, with (x, y) ↦ (f1(x, y), f2(x, y)), given by f ( [ x y ] ) = [ f 1 ( x , y ) f 2 ( x , y ) ] = [ x 2 y 5 x + sin y ] . {\displaystyle...
26 KB (3,699 words) - 11:26, 3 November 2024
matrix of F2 at v is positive definite. Here the Hessian of F2 at v is the symmetric bilinear form g v ( X , Y ) := 1 2 ∂ 2 ∂ s ∂ t [ F ( v + s X + t Y )...
14 KB (1,942 words) - 10:32, 12 July 2024
years past. An extreme example of this trend would be the Pentax DA 40mm F2.8 XS, released in 2012 and measuring only 9.14 millimetres (0.360 in) long...
16 KB (814 words) - 04:19, 19 August 2024
The Nikon F2 is a professional-level, interchangeable lens, 35 mm film, single-lens reflex (SLR) camera. It was manufactured by the Japanese optics company...
33 KB (4,460 words) - 14:48, 11 August 2024
The Northrop M2-F2 was a heavyweight lifting body based on studies at NASA's Ames and Langley research centers and built by the Northrop Corporation in...
11 KB (859 words) - 04:16, 4 November 2024
The Dassault Mirage F2 was a French prototype two-seat ground attack/fighter aircraft, which was designed to serve as a test bed for the SNECMA TF306 turbofan...
5 KB (356 words) - 17:33, 27 April 2024
continuous and the alternative is restricted to a shift in location, i.e., F1(x) = F2(x + δ), we can interpret a significant Mann–Whitney U test as showing a...
44 KB (5,765 words) - 10:53, 2 November 2024
Not every unital associative algebra over F2 is a Boolean ring: consider for instance the polynomial ring F2[X]. The quotient ring R / I of any Boolean...
12 KB (1,419 words) - 02:48, 30 June 2024