operative algorithm - translation to russian
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operative algorithm - translation to russian

ALGORITHM USED IN ARITHMETIC
Tonelli algorithm; Tonelli's algorithm; Shanks-Tonelli algorithm; Shanks–Tonelli algorithm; Tonelli-Shanks algorithm; Shanks algorithm

operative algorithm      

математика

рабочий алгоритм

operative algorithm      
рабочий алгоритм
algorithm         
  • Alan Turing's statue at [[Bletchley Park]]
  • The example-diagram of Euclid's algorithm from T.L. Heath (1908), with more detail added. Euclid does not go beyond a third measuring and gives no numerical examples. Nicomachus gives the example of 49 and 21: "I subtract the less from the greater; 28 is left; then again I subtract from this the same 21 (for this is possible); 7 is left; I subtract this from 21, 14 is left; from which I again subtract 7 (for this is possible); 7 is left, but 7 cannot be subtracted from 7." Heath comments that "The last phrase is curious, but the meaning of it is obvious enough, as also the meaning of the phrase about ending 'at one and the same number'."(Heath 1908:300).
  • "Inelegant" is a translation of Knuth's version of the algorithm with a subtraction-based remainder-loop replacing his use of division (or a "modulus" instruction). Derived from Knuth 1973:2–4. Depending on the two numbers "Inelegant" may compute the g.c.d. in fewer steps than "Elegant".
  • 1=IF test THEN GOTO step xxx}}, shown as diamond), the unconditional GOTO (rectangle), various assignment operators (rectangle), and HALT (rectangle). Nesting of these structures inside assignment-blocks results in complex diagrams (cf. Tausworthe 1977:100, 114).
  • A graphical expression of Euclid's algorithm to find the greatest common divisor for 1599 and 650
<syntaxhighlight lang="text" highlight="1,5">
 1599 = 650×2 + 299
 650 = 299×2 + 52
 299 = 52×5 + 39
 52 = 39×1 + 13
 39 = 13×3 + 0</syntaxhighlight>
SEQUENCE OF INSTRUCTIONS TO PERFORM A TASK
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algorithm noun math. алгоритм algorithm validation - проверка правильности алгоритма

Definition

Euclidean Algorithm

Wikipedia

Tonelli–Shanks algorithm

The Tonelli–Shanks algorithm (referred to by Shanks as the RESSOL algorithm) is used in modular arithmetic to solve for r in a congruence of the form r2n (mod p), where p is a prime: that is, to find a square root of n modulo p.

Tonelli–Shanks cannot be used for composite moduli: finding square roots modulo composite numbers is a computational problem equivalent to integer factorization.

An equivalent, but slightly more redundant version of this algorithm was developed by Alberto Tonelli in 1891. The version discussed here was developed independently by Daniel Shanks in 1973, who explained:

My tardiness in learning of these historical references was because I had lent Volume 1 of Dickson's History to a friend and it was never returned.

According to Dickson, Tonelli's algorithm can take square roots of x modulo prime powers pλ apart from primes.

What is the Russian for operative algorithm? Translation of &#39operative algorithm&#39 to Russian