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1: Viewing DLMF Interactive 3D Graphics

… ►Note that some VRML/X3D browsers are not capable of handling the complex files necessary for our visualizations. …

2: 27.18 Methods of Computation: Primes

… ►The ECPP (Elliptic Curve Primality Proving) algorithm handles primes with over 20,000 digits. …

3: 21.7 Riemann Surfaces

… ►Removing the singularities of this curve gives rise to a two-dimensional connected manifold with a complex-analytic structure, that is, a Riemann surface. All compact Riemann surfaces can be obtained this way. ►Since a Riemann surface

\Gamma

is a two-dimensional manifold that is orientable (owing to its analytic structure), its only topological invariant is its genus

g

(the number of handles in the surface). On this surface, we choose

2g

cycles (that is, closed oriented curves, each with at most a finite number of singular points)

a_{j}

b_{j}

j=1,2,\dots,g

, such that their intersection indices satisfy …

4: 2.4 Contour Integrals

… ►Cases in which

p^{\prime}(t_{0})\neq 0

are usually handled by deforming the integration path in such a way that the minimum of

\Re\left(zp(t)\right)

is attained at a saddle point or at an endpoint. …

5: 2.7 Differential Equations

… ►The exceptional case

f_{0}^{2}=4g_{0}

is handled by Fabry’s transformation: …