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Ring of periods
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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 \mathbb^n 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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