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The Euclidean algorithm, also called Euclid's algorithm, is an algorithm for finding the greatest common divisor of two numbers a and b. The algorithm can also be defined for ...

The term Euclidean refers to everything that can historically or logically be referred to Euclid's monumental treatise The Thirteen Books of the Elements, written around the ...

An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at some point. ...

A ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...

The first practical algorithm for determining if there exist integers a_i for given real numbers x_i such that a_1x_1+a_2x_2+...+a_nx_n=0, or else establish bounds within ...

A method for finding solutions u and v to a linear congruence au+bv=d by constructing a matrix formed by adjoining a vector containing a and b with a unit matrix, M=[a 1 0; b ...

A more common way to describe a Euclidean ring.

The two-dimensional Euclidean space denoted R^2.

A metric topology induced by the Euclidean metric. In the Euclidean topology of the n-dimensional space R^n, the open sets are the unions of n-balls. On the real line this ...

A Euclidean motion of R^n is an affine transformation whose linear part is an orthogonal transformation.