Euclid algorithm in a sentence
1) The computational efficiency of Euclid's algorithm has been studied thoroughly.
algorithm collocations
2) An example that uses Euclid's algorithm appears below.
3) This is exploited in the binary version of Euclid's algorithm .
Euclid algorithm example sentences
4) The simple form of Euclid's algorithm uses only subtraction and comparison.5) For comparison, Euclid's original subtraction-based algorithm can be much slower.
6) Continued fraction factorization uses continued fractions, which are determined using Euclid's algorithm .
7) Euclid's algorithm can also be used to solve multiple linear Diophantine equations.
8) For comparison, the efficiency of alternatives to Euclid's algorithm may be determined.
9) They were able to factor 0.2% of the keys using only Euclid's algorithm .
10) E3: "s" and "r": The nut of Euclid's algorithm .
11) Euclid's algorithm is widely used in practice, especially for small numbers, due to its simplicity.
12) As for the integers, Euclidean division allows us to define Euclid's algorithm for computing GCDs.
13) For example , Euclid's algorithm to find the highest common factor of two numbers: Claim 1.
14) This not only proves that Euclid's algorithm computes GCDs, but also proves that GCDs exist.
15) Leopold Kronecker has shown that this version requires the least number of steps of any version of Euclid's algorithm .
example sentences with Euclid algorithm
16) For this reason, methods have been designed to modify Euclid's algorithm for working only with polynomials over the integers.17) For univariate polynomials over the rational numbers one may think that Euclid's algorithm is a convenient method for computing the GCD.
18) These algorithms proceed by a recursion on the number of variables to reduce the problem to a variant of Euclid's algorithm .
19) Euclid's algorithm can be applied to real numbers, as described by Euclid in Book 10 of his "Elements".
20) Using Euclid's algorithm , d can be computed quite easily from phi and e . But it is still hard to get d without knowing phi , which depends on the factorization of n .
21) Surprisingly, the classical Euclid's algorithm turned out to be inefficient for polynomials over infinite fields, and thus new algorithms needed to be developed.
22) Another difference with Euclid's algorithm is that it uses the quotient, denoted "quo", of the Euclidean division instead of the remainder.
23) In the important case of univariate polynomials over a field the polynomial GCD may be computed, like for the integer GCD, by Euclid's algorithm using long division.
24) Book 7 deals strictly with elementary number theory: divisibility, prime numbers, Euclid's algorithm for finding the greatest common divisor, least common multiple.
25) Generalizations of Euclid's algorithm with these basic features have been applied to other mathematical structures, such as tangles and transfinite ordinal numbers.
26) This result suffices to show that the number of steps in Euclid's algorithm can never be more than five times the number of its digits (base 10).
27) Since these numbers "h""i" are the multiplicative inverses of the "M""i", they may be found using Euclid's algorithm as described in the previous subsection.
28) Bézout's identity is essential to many applications of Euclid's algorithm , such as demonstrating the unique factorization of numbers into prime factors.
How to use Euclid algorithm in a sentence
29) The integers "s" and "t" can be calculated from the quotients "q"0, "q"1, etc. by reversing the order of equations in Euclid's algorithm .These examples have been automatically selected and may contain sensitive content that does not reflect the opinions or policies of our website. Please inform us about the inappropriate sentences:nalcakar at gmail.com
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