\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [2][-]{subsection.1.1}{About this manual}{section.1}% 2
\BOOKMARK [2][-]{subsection.1.2}{Bertini\137real product description}{section.1}% 3
\BOOKMARK [2][-]{subsection.1.3}{Where Bertini\137real can be found}{section.1}% 4
\BOOKMARK [2][-]{subsection.1.4}{Who is developing Bertini\137real?}{section.1}% 5
\BOOKMARK [2][-]{subsection.1.5}{Contact}{section.1}% 6
\BOOKMARK [2][-]{subsection.1.6}{Acknowledgements}{section.1}% 7
\BOOKMARK [1][-]{section.2}{Quick Summary}{}% 8
\BOOKMARK [1][-]{section.3}{Input Files}{}% 9
\BOOKMARK [2][-]{subsection.3.1}{On Bertini input syntax}{section.3}% 10
\BOOKMARK [1][-]{section.4}{Preliminary: running Bertini}{}% 11
\BOOKMARK [2][-]{subsection.4.1}{Numerical Irreducible Decomposition}{section.4}% 12
\BOOKMARK [2][-]{subsection.4.2}{Necessary Bertini output files for Bertini\137real}{section.4}% 13
\BOOKMARK [1][-]{section.5}{Running Bertini\137real}{}% 14
\BOOKMARK [2][-]{subsection.5.1}{Files Needed for Input}{section.5}% 15
\BOOKMARK [2][-]{subsection.5.2}{Command prompt, options}{section.5}% 16
\BOOKMARK [2][-]{subsection.5.3}{Parallelism}{section.5}% 17
\BOOKMARK [2][-]{subsection.5.4}{Projections and spheres of interest}{section.5}% 18
\BOOKMARK [3][-]{subsubsection.5.4.1}{The user-defined projection, pi}{subsection.5.4}% 19
\BOOKMARK [3][-]{subsubsection.5.4.2}{The sphere of interest, sphere}{subsection.5.4}% 20
\BOOKMARK [1][-]{section.6}{Running Sampler}{}% 21
\BOOKMARK [2][-]{subsection.6.1}{Curves}{section.6}% 22
\BOOKMARK [3][-]{subsubsection.6.1.1}{Running Sampler \(Using an Example\)}{subsection.6.1}% 23
\BOOKMARK [3][-]{subsubsection.6.1.2}{Available curve sampling algorithms}{subsection.6.1}% 24
\BOOKMARK [2][-]{subsection.6.2}{Surfaces}{section.6}% 25
\BOOKMARK [3][-]{subsubsection.6.2.1}{Running sampler on a surface \(Using an Example\)}{subsection.6.2}% 26
\BOOKMARK [3][-]{subsubsection.6.2.2}{Available surface sampling algorithms}{subsection.6.2}% 27
\BOOKMARK [3][-]{subsubsection.6.2.3}{Known issues with surface sampler}{subsection.6.2}% 28
\BOOKMARK [1][-]{section.7}{Visualization}{}% 29
\BOOKMARK [2][-]{subsection.7.1}{Visualizing in Matlab}{section.7}% 30
\BOOKMARK [3][-]{subsubsection.7.1.1}{Matlab visualization options}{subsection.7.1}% 31
\BOOKMARK [2][-]{subsection.7.2}{Visualizing in Python}{section.7}% 32
\BOOKMARK [2][-]{subsection.7.3}{3D Printing}{section.7}% 33
\BOOKMARK [1][-]{section.8}{Troubleshooting}{}% 34
\BOOKMARK [2][-]{subsection.8.1}{Helpful help}{section.8}% 35
\BOOKMARK [3][-]{subsubsection.8.1.1}{Compilation fails, with an error due to send calls for MPI}{subsection.8.1}% 36
\BOOKMARK [3][-]{subsubsection.8.1.2}{had a critical failure}{subsection.8.1}% 37
\BOOKMARK [3][-]{subsubsection.8.1.3}{sh: matlab: command not found}{subsection.8.1}% 38
\BOOKMARK [3][-]{subsubsection.8.1.4}{Calling Bertini\137real from within Matlab}{subsection.8.1}% 39
\BOOKMARK [1][-]{section.9}{Examples}{}% 40
\BOOKMARK [2][-]{subsection.9.1}{Curves}{section.9}% 41
\BOOKMARK [3][-]{subsubsection.9.1.1}{Circle}{subsection.9.1}% 42
\BOOKMARK [3][-]{subsubsection.9.1.2}{Astroid}{subsection.9.1}% 43
\BOOKMARK [2][-]{subsection.9.2}{Surfaces}{section.9}% 44
\BOOKMARK [3][-]{subsubsection.9.2.1}{Solitude}{subsection.9.2}% 45
\BOOKMARK [3][-]{subsubsection.9.2.2}{Plane}{subsection.9.2}% 46
\BOOKMARK [1][-]{appendix.A}{The Decomposition Algorithms}{}% 47
\BOOKMARK [2][-]{subsection.A.1}{Decomposing curves}{appendix.A}% 48
\BOOKMARK [3][-]{subsubsection.A.1.1}{Critical points}{subsection.A.1}% 49
\BOOKMARK [3][-]{subsubsection.A.1.2}{Intersect with bounding object}{subsection.A.1}% 50
\BOOKMARK [3][-]{subsubsection.A.1.3}{Slice}{subsection.A.1}% 51
\BOOKMARK [3][-]{subsubsection.A.1.4}{Connect the dots}{subsection.A.1}% 52
\BOOKMARK [3][-]{subsubsection.A.1.5}{Merge [optional]}{subsection.A.1}% 53
\BOOKMARK [3][-]{subsubsection.A.1.6}{Sample [optional]}{subsection.A.1}% 54
\BOOKMARK [2][-]{subsection.A.2}{Decomposing surfaces}{appendix.A}% 55
\BOOKMARK [3][-]{subsubsection.A.2.1}{Critical curves}{subsection.A.2}% 56
\BOOKMARK [3][-]{subsubsection.A.2.2}{Bounding curve}{subsection.A.2}% 57
\BOOKMARK [3][-]{subsubsection.A.2.3}{Slice}{subsection.A.2}% 58
\BOOKMARK [3][-]{subsubsection.A.2.4}{Connect the dots}{subsection.A.2}% 59
\BOOKMARK [3][-]{subsubsection.A.2.5}{Merge [optional]}{subsection.A.2}% 60
\BOOKMARK [3][-]{subsubsection.A.2.6}{Sample [optional]}{subsection.A.2}% 61
\BOOKMARK [1][-]{appendix.B}{Install}{}% 62
\BOOKMARK [2][-]{subsection.B.1}{Dependencies}{appendix.B}% 63
\BOOKMARK [3][-]{subsubsection.B.1.1}{Symbolic engine}{subsection.B.1}% 64
\BOOKMARK [2][-]{subsection.B.2}{Instructions for GNU/Linux}{appendix.B}% 65
\BOOKMARK [2][-]{subsection.B.3}{Instructions for OSX}{appendix.B}% 66
\BOOKMARK [3][-]{subsubsection.B.3.1}{Preliminary Work}{subsection.B.3}% 67
\BOOKMARK [3][-]{subsubsection.B.3.2}{Installation}{subsection.B.3}% 68
\BOOKMARK [2][-]{subsection.B.4}{Instructions for Windows}{appendix.B}% 69
\BOOKMARK [3][-]{subsubsection.B.4.1}{Install Cygwin}{subsection.B.4}% 70
\BOOKMARK [3][-]{subsubsection.B.4.2}{Selecting packages for Cygwin}{subsection.B.4}% 71
\BOOKMARK [3][-]{subsubsection.B.4.3}{Initializing Paths}{subsection.B.4}% 72
\BOOKMARK [3][-]{subsubsection.B.4.4}{Organizing Cygwin}{subsection.B.4}% 73
\BOOKMARK [3][-]{subsubsection.B.4.5}{Installing Dependencies}{subsection.B.4}% 74
\BOOKMARK [3][-]{subsubsection.B.4.6}{Linking Cygwin Environment Paths}{subsection.B.4}% 75
\BOOKMARK [3][-]{subsubsection.B.4.7}{Building and Installing Packages}{subsection.B.4}% 76
\BOOKMARK [3][-]{subsubsection.B.4.8}{Installing Bertini and Bertini\137real}{subsection.B.4}% 77
\BOOKMARK [3][-]{subsubsection.B.4.9}{Setting up MATLAB}{subsection.B.4}% 78
\BOOKMARK [2][-]{subsection.B.5}{Testrun \205 the Cayley Cubic}{appendix.B}% 79
\BOOKMARK [1][-]{appendix.C}{Output Files}{}% 80
\BOOKMARK [2][-]{subsection.C.1}{Regardless of dimension}{appendix.C}% 81
\BOOKMARK [3][-]{subsubsection.C.1.1}{output/decomp}{subsection.C.1}% 82
\BOOKMARK [3][-]{subsubsection.C.1.2}{output/run\137metadata}{subsection.C.1}% 83
\BOOKMARK [3][-]{subsubsection.C.1.3}{output/V.vertex}{subsection.C.1}% 84
\BOOKMARK [3][-]{subsubsection.C.1.4}{output/vertex\137types}{subsection.C.1}% 85
\BOOKMARK [3][-]{subsubsection.C.1.5}{output/witness\137set}{subsection.C.1}% 86
\BOOKMARK [3][-]{subsubsection.C.1.6}{/Dir\137Name}{subsection.C.1}% 87
\BOOKMARK [2][-]{subsection.C.2}{Curve files}{appendix.C}% 88
\BOOKMARK [3][-]{subsubsection.C.2.1}{output/curve.cnums}{subsection.C.2}% 89
\BOOKMARK [3][-]{subsubsection.C.2.2}{output/E.edge}{subsection.C.2}% 90
\BOOKMARK [3][-]{subsubsection.C.2.3}{output/samp.curvesamp}{subsection.C.2}% 91
\BOOKMARK [2][-]{subsection.C.3}{Surface files}{appendix.C}% 92
\BOOKMARK [3][-]{subsubsection.C.3.1}{F.faces}{subsection.C.3}% 93
\BOOKMARK [3][-]{subsubsection.C.3.2}{S.surf}{subsection.C.3}% 94
\BOOKMARK [3][-]{subsubsection.C.3.3}{output/samp.surfsamp}{subsection.C.3}% 95
\BOOKMARK [1][-]{section*.64}{Glossary}{}% 96
