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For example, the problem of deciding whether a graph G contains H as a minor, where H is fixed, can be solved in a running time of O(n 2), [25] where n is the number of vertices in G. However, the big O notation hides a constant that depends superexponentially on H .
In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry. [1]
The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, [5] as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.
5 Analytic number theory: additive problems. 6 Algebraic number theory. 7 Quadratic forms. 8 L-functions. 9 Diophantine equations. ... This is a list of topics in ...
To determine if a number is a power of two, conceptually we may repeatedly do integer divide by two until the number won't divide by 2 evenly; if the only factor left is 1, the original number was a power of 2. Using bit and logical operators, there is a simple expression which will return true (1) or false (0):
The problem is known to undergo a "phase transition"; being likely for some sets and unlikely for others. If m is the number of bits needed to express any number in the set and n is the size of the set then / < tends to have many solutions and / > tends to have few or no solutions. As n and m get larger, the probability of a perfect partition ...
OpenCV is a huge image and video processing library designed to work with many languages such as python, C/C++, Java, and more. It is the foundation for many of the applications you know that deal ...
Some subjects generally considered to be part of analytic number theory, for example, sieve theory, [note 9] are better covered by the second rather than the first definition: some of sieve theory, for instance, uses little analysis, [note 10] yet it does belong to analytic number theory. The following are examples of problems in analytic ...