Search results
Results from the WOW.Com Content Network
In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations. Dyadic rationals also ...
In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
Python: the built-in int (3.x) / long (2.x) integer type is of arbitrary precision. The Decimal class in the standard library module decimal has user definable precision and limited mathematical operations (exponentiation, square root, etc. but no trigonometric functions). The Fraction class in the module fractions implements rational numbers ...
Every polynomial with rational coefficients, may be factorized, in a unique way, as the product of a rational number and a polynomial with integer coefficients, which is primitive (that is, the greatest common divisor of the coefficients is 1), and has a positive leading coefficient (coefficient of the term of the highest degree). For example:
Zermelo–Fraenkel set theory with the axiom of choice guarantees the existence of a basis of this vector space: there exists a set B of real numbers such that every real number can be written uniquely as a finite linear combination of elements of this set, using rational coefficients only, and such that no element of B is a rational linear ...
The rational function has a zero at =. Just as the Taylor polynomial of degree d has d + 1 coefficients that depend on the function f, the Padé approximation also has d + 1 coefficients dependent on f and its derivatives. More precisely, in any Padé approximant, the degrees of the numerator and denominator polynomials have to add to the order ...
The essential idea is that we use a set , which is the set of all rational numbers whose squares are less than 2, to "represent" number , and further, by defining properly arithmetic operators over these sets (addition, subtraction, multiplication, and division), these sets (together with these arithmetic operations) form the familiar real numbers.
Julia provides rational numbers with the rational operator, //. For example, 6 // 9 == 2 // 3 && typeof (-4 // 9) == Rational {Int64}. [2] 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 ...