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| has gloss | eng: In mathematics, a Gaussian rational number is a complex number of the form p + qi, where p and q are both rational numbers. The set of all Gaussian rationals forms the Gaussian rational field, denoted Q(i), obtained by adjoining the imaginary number i to the field of rationals. It thus provides an example of an algebraic number field, which is both a quadratic field and a cyclotomic field (since i is a 4th root of unity). Like all quadratic fields it is a Galois extension of Q with Galois group cyclic of order two, in this case generated by complex conjugation, and is thus an abelian extension of Q, with conductor 4. |
| lexicalization | eng: Gaussian rational |
| instance of | e/Cyclotomic field |
| Meaning | |
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| French | |
| has gloss | fra: En mathématiques, un rationnel de Gauss est un nombre complexe dont les parties réelle et imaginaire sont des nombres rationnels. Lensemble des rationnels de Gauss, muni de laddition et de la multiplication usuelles des nombres complexes, est un corps, généralement noté \mathbbQ}(i). |
| lexicalization | fra: Rationnel de gauss |
| Italian | |
| has gloss | ita: In matematica, un razionale gaussiano è un numero nella forma a+ib, dove a e b sono numeri razionali e i è lunità immaginaria. Linsieme di tutti i razionali gaussiani è un campo, denotato con \mathbbQ}(i). |
| lexicalization | ita: Razionale gaussiano |
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