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A primitive polynomial must have a non-zero constant term, for otherwise it will be divisible by x. Over GF(2), x + 1 is a primitive polynomial and all other primitive polynomials have an odd number of terms, since any polynomial mod 2 with an even number of terms is divisible by x + 1 (it has 1 as a root).
Primitive data types, such as Booleans, fixed-size integers, floating-point values, and characters, are value types. Objects, in the sense of object-oriented programming, belong to reference types. Assigning to a variable of reference type simply copies the reference, whereas assigning to a variable of value type copies the value.
Given a prime number q and prime power q m with positive integers m and d such that d ≤ q m − 1, a primitive narrow-sense BCH code over the finite field (or Galois field) GF(q) with code length n = q m − 1 and distance at least d is constructed by the following method. Let α be a primitive element of GF(q m).
In computer science, primitive data types are a set of basic data types from which all other data types are constructed. [1] Specifically it often refers to the limited set of data representations in use by a particular processor , which all compiled programs must use.
In complex analysis, a branch of mathematics, the antiderivative, or primitive, of a complex-valued function g is a function whose complex derivative is g.More precisely, given an open set in the complex plane and a function :, the antiderivative of is a function : that satisfies =.
The primitive recursive functions are a subset of the total recursive functions, which are a subset of the partial recursive functions. For example, the Ackermann function can be proven to be total recursive, and to be non-primitive. Primitive or "basic" functions: Constant functions C k n: For each natural number n and every k
For n = 1, the cyclotomic polynomial is Φ 1 (x) = x − 1 Therefore, the only primitive first root of unity is 1, which is a non-primitive n th root of unity for every n > 1. As Φ 2 (x) = x + 1, the only primitive second (square) root of unity is −1, which is also a non-primitive n th root of unity for every even n > 2.
In fact, for any = (,) in , the Frobenius endomorphism shows that the element lies in F, so α is a root of () = [], and α cannot be a primitive element (of degree p 2 over F), but instead F(α) is a non-trivial intermediate field.