Euclid
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(Named after the Greek geometer, fl ca 300 BC.) A Pascal descendant for development of verifiable system software. No goto, no side effects, no global assignments, no functional arguments, no nested procedures, no floats, no enumeration types. Pointers are treated as indices of special arrays called collections. To prevent aliasing, Euclid forbids any overlap in the list of actual parameters of a procedure. Each procedure gives an imports list, and the compiler determines the identifiers that are implicitly imported. Iterators.
Ottawa Euclid is a variant. ["Report on the Programming Language Euclid", B.W. Lampson et al, SIGPLAN Notices 12(2):1-79, Feb 1977].Last updated: 1998-11-23
Euclidean Algorithm
Euclid's AlgorithmEuclidean norm
The most common norm, calculated by summing the squares of all coordinates and taking the square root. This is the essence of Pythagoras's theorem. In the infinite-dimensional case, the sum is infinite or is replaced with an integral when the number of dimensions is uncountable.
Last updated: 2004-02-15
Euclid's Algorithm
(Or "Euclidean Algorithm") An algorithm for finding the greatest common divisor (GCD) of two numbers. It relies on the identity
gcd(a, b) = gcd(a-b, b)To find the GCD of two numbers by this algorithm, repeatedly replace the larger by subtracting the smaller from it until the two numbers are equal. E.g. 132, 168 -> 132, 36 -> 96, 36 -> 60, 36 -> 24, 36 -> 24, 12 -> 12, 12 so the GCD of 132 and 168 is 12. This algorithm requires only subtraction and comparison operations but can take a number of steps proportional to the difference between the initial numbers (e.g. gcd(1, 1001) will take 1000 steps).
Last updated: 1997-06-30
Nearby terms:
ETSI ♦ ETX ♦ Euclid ♦ Euclidean Algorithm ♦ Euclidean norm ♦ Euclid's Algorithm
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