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A binary operation ∗ on the set S is associative when this diagram commutes.That is, when the two paths from S×S×S to S compose to the same function from S×S×S to S. ...
In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center of A.This is thus an algebraic structure with an addition, a multiplication, and a scalar multiplication (the multiplication by the image of the ring homomorphism of an element of K).
In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.
In algebra, a number that is the multiplier of a variable or expression (e.g., the 3 in ) is called a coefficient. The result of a multiplication is called a product . When one factor is an integer, the product is a multiple of the other or of the product of the others.
The basic principle of Karatsuba's algorithm is divide-and-conquer, using a formula that allows one to compute the product of two large numbers and using three multiplications of smaller numbers, each with about half as many digits as or , plus some additions and digit shifts.
In computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection.
There are also corresponding left and right Peirce decompositions. The left Peirce decomposition of A is the direct sum of eA and (1 − e)A and the right decomposition of A is the direct sum of Ae and A(1 − e). In those simple cases, 1 − e is also idempotent and is orthogonal to e (that is, e(1 − e) = (1 − e)e = 0), and the sum of 1 ...
In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix.