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The canonical decomposition allows SnapPea to tell two cusped hyperbolic 3-manifolds apart by turning the problem of recognition into a combinatorial question, i.e. checking if the two manifolds have combinatorially equivalent canonical decompositions. SnapPea is also able to check if two
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noted a method for describing the geometric shape of each hyperbolic tetrahedron by a complex number and a set of nonlinear equations of complex variables whose solution would give a complete hyperbolic metric on the 3-manifold. These equations consist of
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The local minimality of the triangulation is meant to increase the likelihood that such a solution exists, since heuristically one might expect such a triangulation to be "straightened" without causing degenerations or overlapping of tetrahedra.
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SnapPea is usually able to compute the canonical decomposition of a cusped hyperbolic 3-manifold from a given ideal triangulation. If not, then it randomly retriangulates and tries again. This has never been known to fail.
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The recognition algorithm allow SnapPea to tell two hyperbolic knots or links apart. Weeks, et al., were also able to compile different censuses of hyperbolic 3-manifolds by using the algorithm to cull lists of duplicates.
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extension modules which allow the kernel to be used in a Python program or in the interpreter. They also provide a graphical user interface written in Python which runs under most
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source code is extensively commented by
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Once a suitable ideal triangulation is found, SnapPea can try to find a hyperbolic structure. In his
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on the cusps to obtain more hyperbolic 3-manifolds. SnapPea does this by taking any given slopes which determine certain
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From this description of the hyperbolic structure on a link complement, SnapPea can then perform
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420:"Adware or APT – SnapPea Downloader - An Android Malware that implements 12 different exploits"
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to create cusped hyperbolic 3-manifolds and then using the canonical decomposition as before.
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SnapPea has several databases of hyperbolic 3-manifolds available for systematic study.
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At the core of SnapPea are two main algorithms. The first attempts to find a minimal
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to search for solutions. If no solution exists, then this is reported to the user.
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395:"Android 'Gooligan' Hackers Just Scored The Biggest Ever Theft Of Google Accounts"
58:. It is not to be confused with the unrelated android malware with the same name.
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The following people are credited in SnapPea 2.5.3's list of acknowledgments:
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Additionally, from the canonical decomposition, SnapPea is able to:
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Convex hulls and isometries of cusped hyperbolic $ 3$ -manifolds.
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and collaborators have extended the SnapPea kernel and written
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orbifolds where the orbifold locus contains trivalent vertices
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446:"How to Manage Your Android Device from Windows with SnapPea"
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hyperbolic 3-manifolds are isometric by drilling out short
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SnapPea inputs data in a variety of formats. Given a
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hyperbolic manifolds with totally geodesic boundary
27:complement. A fundamental parallelogram is drawn.
370:Weeks, Jeffrey R., SnapPea C source code, (1999)
226:. SnapPea uses an iterative method utilizing
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383:Topology Appl. 52 (1993), no. 2, 127—149.
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525:Damian Heard's extension, allows :
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166:The SnapPeaKernel is released under
484:"SnapPy — SnapPy 2.1 documentation"
471:ReadMe file for the SnapPea kernel
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348:incorporates aspects of SnapPea.
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519:Culler and Dunfield's extension
61:The latest version is 3.0d3.
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566:Free software programmed in C
224:cusp (completeness) equations
77:(see external links below).
50:. The primary developer is
198:Minimal ideal triangulation
186:. The second computes the
44:low-dimensional topologists
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280:Compute the symmetry group
571:Free mathematics software
174:Algorithms and functions
277:Compute the Ford domain
249:Canonical decomposition
239:hyperbolic Dehn filling
188:canonical decomposition
556:Computational topology
473:, accessed 2013-09-06.
393:Fox-Brewster, Thomas.
352:Computational topology
301:This section is empty.
243:Dehn filling equations
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285:Computable invariants
192:hyperbolic 3-manifold
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16:Mathematical software
379:Weeks, Jeffrey R.,
180:ideal triangulation
561:Numerical software
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452:. 4 February 2013
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170:2+ as is SnapPy.
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75:operating systems
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551:3-manifolds
312:August 2021
182:of a given
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82:Colin Adams
63:Marc Culler
545:Categories
490:2014-03-12
399:forbes.com
358:References
134:Lee Mosher
98:Dave Gabai
264:geodesics
150:Alan Reid
122:Al Marden
340:See also
324:Censuses
215:Thurston
46:, study
511:SnapPea
168:GNU GPL
32:SnapPea
517:SnapPy
456:21 May
430:21 May
404:21 May
346:Regina
260:closed
152:, and
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