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Ring of periods : ウィキペディア英語版 | Ring of periods
In mathematics, a period is a number that can be expressed as an integral of an algebraic function over an algebraic domain. Sums and products of periods remain periods, so the periods form a ring. gave a survey of periods and introduced some conjectures about them. ==Definition== A real number is called a period if it is the difference of volumes of regions of Euclidean space given by polynomial inequalities with rational coefficients. More generally a complex number is called a period if its real and imaginary parts are periods. The values of absolutely convergent integrals of rational functions with algebraic coefficients, over domains in given by polynomial inequalities with algebraic coefficients are also periods, since integrals and irrational algebraic numbers are expressible in terms of areas of suitable domains.
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