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In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign. The term is also used from the opposite perspective (branches coming together) as when a covering map degenerates at a point of a space, with some collapsing of the fibers of the mapping.
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
In mathematics, the ramification theory of valuations studies the set of extensions of a valuation v of a field K to an extension L of K. It is a generalization of the ramification theory of Dedekind domains. [1] [2] The structure of the set of extensions is known better when L/K is Galois.
The following procedure (Neukirch, p. 47) solves this problem in many cases. The strategy is to select an integer θ in O L so that L is generated over K by θ (such a θ is guaranteed to exist by the primitive element theorem), and then to examine the minimal polynomial H(X) of θ over K; it is a monic polynomial with coefficients in O K.
Windows Calculator, since Windows 98, uses arbitrary precision for basic operations (addition, subtraction, multiplication, division) and 32 digits of precision for advanced operations (square root, transcendental functions). SmartXML, a free programming language with integrated development environment (IDE) for mathematical calculations ...
The tame ramification part ε is defined in terms of the reduction type: ε=0 for good reduction, ε=1 for multiplicative reduction and ε=2 for additive reduction. The wild ramification term δ is zero unless p divides 2 or 3, and in the latter cases it is defined in terms of the wild ramification of the extensions of K by the division points ...
In modular arithmetic, Barrett reduction is an algorithm designed to optimize the calculation of [1] without needing a fast division algorithm.It replaces divisions with multiplications, and can be used when is constant and <.
for some integer k. This integer is called the ramification index of P. Usually the ramification index is one. But if the ramification index is not equal to one, then P is by definition a ramification point, and Q is a branch point. If Y is just the Riemann sphere, and Q is in the finite part of Y, then there is no need to select special ...