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| workshop1109 [2011/09/13 06:35] – [polymake Workshop at UC Berkeley] joswig | workshop1109 [2011/09/14 16:03] – started solutions section joswig |
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| ====== polymake Workshop at UC Berkeley ====== | ====== polymake Workshop at UC Berkeley ====== |
| |
| This is going to take place September 13, 2011, 13:00-18:00 (939 Evans Hall). Everybody welcome. Please bring a laptop, preferably with polymake [[download:start|pre-installed]]. Standard installations available for Ubuntu 11.04, MacOS X 10.6 (and a last minute experimental version for 10.7; thanks to [[http://www.mathematik.tu-darmstadt.de/~paffenholz/|Andreas]]). If you only have a Windows laptop (with a reasonably modern CPU) you can bring it along with an empty USB stick (with at least 2GB capacity): last minute Ubuntu 11.04 live system with polymake available (thanks to [[http://www.uni-frankfurt.de/fb/fb12/mathematik/dm/personen/lorenz/index.html|Benjamin]]). | This is going to take place September 13, 2011, 13:00-18:00 (939 Evans Hall). Everybody welcome. |
| | |
| | Please bring a laptop, preferably with polymake [[download:start|pre-installed]]. Standard installations available for Ubuntu 11.04, MacOS X 10.6 (and a last minute experimental version for 10.7; thanks to [[http://www.mathematik.tu-darmstadt.de/~paffenholz/|Andreas]]). If you only have a Windows laptop (with a reasonably modern CPU) you can bring it along with an empty USB stick (with at least 2GB capacity): last minute Ubuntu 11.04 live system with polymake available (thanks to [[http://www.uni-frankfurt.de/fb/fb12/mathematik/dm/personen/lorenz/index.html|Benjamin]]). |
| |
| The event will start out with a short introduction to the system, and afterwards attendees are invited to explore the system via a set of exercises. | The event will start out with a short introduction to the system, and afterwards attendees are invited to explore the system via a set of exercises. |
| print $rp2->HOMOLOGY; | print $rp2->HOMOLOGY; |
| fan::normal_fan(load("snub-dodecahedron.poly"))->VISUAL; | fan::normal_fan(load("snub-dodecahedron.poly"))->VISUAL; |
| | </code> |
| | |
| | ===== Solutions to Selected Exercises ===== |
| | |
| | ==== 10. Smooth fan in R^3 with 10 rays ==== |
| | |
| | <code> |
| | $c=cube(3); |
| | $cc=new Polytope(INEQUALITIES=>($c->FACETS/(new Matrix<Rational>([[2,-1,-1,-1],[2,-1,1,1],[2,1,-1,1],[2,1,1,-1]])))); |
| | print $cc->N_FACETS, ", ", $cc->SMOOTH; |
| | $cc->VISUAL; |
| | $f=fan::normal_fan($cc); |
| | $f->VISUAL; |
| </code> | </code> |