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The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
The problem that we are trying to solve is: given an odd composite number, find its integer factors. To achieve this, Shor's algorithm consists of two parts: A classical reduction of the factoring problem to the problem of order-finding.
Protein folding problem: Is it possible to predict the secondary, tertiary and quaternary structure of a polypeptide sequence based solely on the sequence and environmental information? Inverse protein-folding problem: Is it possible to design a polypeptide sequence which will adopt a given structure under certain environmental conditions?
The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches of mathematics.Due to the applicability of the concept in other topics of mathematics and sciences like computer science there has been a resurgence of interest in finite fields and this is partly due to important applications in coding theory and cryptography.
Although this method finishes in polynomial time, it is not used in practice because the lattice has high dimension and huge entries, which makes the computation slow. The exponential complexity in the Zassenhaus algorithm comes from a combinatorial problem: how to select the right subsets of f 1 ( x ) , … , f r ( x ) {\displaystyle f_{1}(x ...
“For some reason, it all seems like it’s compartmentalized,” she said. “And sports shouldn’t be that. It should be the best sportsperson out there.
There are Nobel Prizes for different categories, though not every prize is awarded each year. In fact, one category has only been handed out 55 times.
A decision problem is a computational problem where the answer for every instance is either yes or no. An example of a decision problem is primality testing: "Given a positive integer n, determine if n is prime." A decision problem is typically represented as the set of all instances for which the answer is yes. For example, primality testing ...
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