domain. Similarly, the rational fractions with coefficients in a field form the field of fractions of polynomials with coefficient in that field. Considering the rational fractions with real coefficients, radical expressions representing numbers, such as are also rational fractions, as are a transcendental numbers such as since all of and are real numbers, and thus considered as coefficients. These same numbers, however, are not rational fractions with integer coefficients. The term partial fraction is used when decomposing rational fractions into sums of simpler fractions. For example, the rational fraction can be decomposed as the sum of two fractions: This is useful for the computation of antiderivatives of rational functions (see partial fraction decomposition for more). Radical expressions A fraction may also contain radicals in the numerator or the denominator. If the denominator contains radicals, it can be helpful to rationalize it (compare Simplified form of a radical expression), especially if further operations, such as adding or comparing that fraction to another, are to be carried out. It is also more convenient if division is to be done manually. When the denominator is a monomial square root, it can be rationalized by multiplying both the top and the bottom of the fraction by the denominator: The process of rationalization of binomial denominators involves multiplying the top and the bottom of a fraction by the conjugate of the denominator so that the denominator becomes a rational number. For example: Even if this process results in the numerator being irrational, like in the examples above, the process may still facilitate subsequent manipulations by reducing the number of irrationals one has to work with in the denominator. Typographical variations In computer displays and typography, simple fractions are sometimes printed as a single character, e.g. ½ (one half). See the article on Number Forms for information on doing this in Unicode. Scientific publishing distinguishes four ways to set fractions, together with guidelines on use: Special fractions: fractions that are presented as a single character with a slanted bar, with roughly the same height and width as other characters in the text. Generally used for simple fractions, such as: ½, ⅓, ⅔, ¼, and ¾. Since the numerals are smaller, legibility can be an issue, especially for small-sized fonts. These are not used in modern mathematical notation, but in other contexts. Case fractions: similar to special fractions, these are rendered as a single typographical character, but