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That is, for any field F that is itself finite or that is the closure of a finite field, if a polynomial P from F n to itself is injective then it is bijective. If F is a finite field, then F n is finite. In this case the theorem is true for trivial reasons having nothing to do with the representation of the function as a polynomial: any ...
Advanced Placement. Advanced Placement ( AP) Precalculus (also known as AP Precalc) is an Advanced Placement precalculus course and examination, offered by the College Board, in development since 2021 [ 1] and announced in May 2022. [ 2] The course debuted in the fall of 2023, with the first exam session taking place in May 2024.
Unit testing, a.k.a. component or module testing, is a form of software testing by which isolated source code is tested to validate expected behavior. [ 1 ] Unit testing describes tests that are run at the unit-level to contrast testing at the integration or system level.
Software testing. Software testing is the act of checking whether software satisfies expectations. Software testing can provide objective, independent information about the quality of software and the risk of its failure to a user or sponsor. [ 1 ] Software testing can determine the correctness of software for specific scenarios, but cannot ...
The greatest common divisor polynomial g(x) of two polynomials a(x) and b(x) is defined as the product of their shared irreducible polynomials, which can be identified using the Euclidean algorithm. [128] The basic procedure is similar to that for integers.
A pseudorandom number generator ( PRNG ), also known as a deterministic random bit generator ( DRBG ), [ 1] is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value ...
Valuation (algebra) In algebra (in particular in algebraic geometry or algebraic number theory ), a valuation is a function on a field that provides a measure of the size or multiplicity of elements of the field. It generalizes to commutative algebra the notion of size inherent in consideration of the degree of a pole or multiplicity of a zero ...
Formally, a modulus of continuity is any increasing real-extended valued function ω : [0, ∞] → [0, ∞], vanishing at 0 and continuous at 0, that is. Moduli of continuity are mainly used to give a quantitative account both of the continuity at a point, and of the uniform continuity, for functions between metric spaces, according to the ...
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