In mathematics, factorization (also factorisation in British English) or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x ¿ 4 factors as (x ¿ 2)(x + 2). In all cases, a product of simpler objects is obtained.
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Factorization of polynomials
In mathematics and computer algebra, polynomial factorization refers to factoring a polynomial into irreducible polynomials over a given field.
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Algebraic extension
In abstract algebra, a field extension L/K is called algebraic if every element of L is algebraic over K, i.e. if every element of L is a root of some non-zero polynomial with coefficients in K. Field extensions that are not algebraic, i.e. which contain transcendental elements, are called transcendental.
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Divisibility rule
A divisibility rule is a shorthand way of discovering whether a given number is divisible by a fixed divisor without performing the division, usually by examining its digits. Although there are divisibility tests for numbers in any radix, and they are all different, this article presents rules and examples only for decimal numbers.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q, which stands for quotient. The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over.
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Prime number
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2 and 3 in addition to 1 and 6.
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Reduce (computer algebra system)
Reduce is a general-purpose computer algebra system geared towards applications in physics. The development of the Reduce computer algebra system was started in the 1960s by Anthony C. Hearn. Since then, many scientists from all over the world have contributed to its development under his direction. Reduce is written entirely in its own LISP dialect called Standard LISP, expressed in an Algol-like syntax called RLISP. The latter is used as a basis for Reduce's user-level language.
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