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In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator p and a non-zero denominator q. [1] For example, is a rational number, as is every integer (e.g., ). The set of all rational numbers, also referred to as " the rationals ", [2] the field of rationals [3 ...
Rational function. In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K.
Perfect number. In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.
All integers are rational, but there are rational numbers that are not integers, such as −2/9. Real numbers (): Numbers that correspond to points along a line. They can be positive, negative, or zero. All rational numbers are real, but the converse is not true.
Rational root theorem. In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational solutions of a polynomial equation with integer coefficients and . Solutions of the equation are also called roots or zeros of the polynomial on the left side.
Problem statement. In the rational reconstruction problem, one is given as input a value . That is, is an integer with the property that . The rational number is unknown, and the goal of the problem is to recover it from the given information. In order for the problem to be solvable, it is necessary to assume that the modulus is sufficiently ...
Julia provides rational numbers with the rational operator, //. For example, 6 // 9 == 2 // 3 && typeof (-4 // 9) == Rational {Int64}. Haskell provides a Rational type, which is really an alias for Ratio Integer (Ratio being a polymorphic type implementing rational numbers for any Integral type of numerators and denominators). The fraction is ...
Let G 2 denote the subgroup of G generated by the point 0 + 1i. G 2 is a cyclic subgroup of order 4. For a prime p of form 4k + 1, let G p denote the subgroup of elements with denominator p n where n is a non-negative integer. G p is an infinite cyclic group, and the point (a 2 − b 2)/p + (2ab/p)i is a generator of G p.