Titlebook: Computing the Continuous Discretely; Integer-point Enumer Matthias Beck,Sinai Robins Textbook 20071st edition Springer-Verlag New York 2007

异常

Function STITLE function WTITLE,the proportion of space that the cone к occupies. In slightly different words, if we pick a point х ∊ ℝ. “at random,” then the probability that х ∊ к is precisely the solid angle at the apex of к. Yet another view of solid angles is that they are in fact volumes of spherical polytopes: the region of

多骨

escalate

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https://doi.org/10.1007/3-540-15202-4Fourier theory using rational functions and their partial fraction decomposition. We then define the Fourier transform and the convolution of finite Fourier series, and show how one can use these ideas to prove identities on trigonometric functions, as well as find connections to the classical Dedekind sums.

Hiatus

Function STITLE function WTITLE,is precisely the solid angle at the apex of к. Yet another view of solid angles is that they are in fact volumes of spherical polytopes: the region of intersection of a cone with a sphere. There is a theory here that parallels the Ehrhart theory of Chapters 3 and 4, but which has some genuinely new ideas.

Euthyroid

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Dedekind Sums, the Building Blocks of Lattice-point Enumerationongoing effort to extend these ideas to higher dimensions, but there is much room for improvement. In this chapter we focus on the computational-complexity issues that arise when we try to compute Dedekind sums explicitely.

Cumulus

Counting Lattice Points in Polytopes:The Ehrhart TheoryGiven the profusion of examples that gave rise to the polynomial behavior of the integer-point counting function .(.) for special polytopes ., we now ask whether there is a general structure theorem. As the ideas unfold, the reader is invited to look back at Chapters 1 and 2 as appetizers and indeed as special cases of the theorems developed below.