user_guide:tutorials:apps_topaz

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tutorial:apps_topaz [2017/06/20 10:00] – formatting oroehriguser_guide:apps_topaz [2019/01/25 09:27] – ↷ Page moved from tutorial:apps_topaz to user_guide:apps_topaz oroehrig
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 ===== Introduction to topaz ===== ===== Introduction to topaz =====
 +
 +**This tutorial is also available as a {{ :tutorial:apps_topaz.ipynb |jupyter notebook}} for polymake 3.1.**
  
 This tutorial tries to give the user a first idea about the features of the ''topaz'' application of ''polymake''. We take a look at a variety of small examples. This tutorial tries to give the user a first idea about the features of the ''topaz'' application of ''polymake''. We take a look at a variety of small examples.
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 The first entry of each pair denotes the face, the second is the rank. The ''{-1}''-node is a dummy representing the whole complex. the ''{}''-node is the empty face. If you want to look at a pretty graph representation, try the visualization: The first entry of each pair denotes the face, the second is the rank. The ''{-1}''-node is a dummy representing the whole complex. the ''{}''-node is the empty face. If you want to look at a pretty graph representation, try the visualization:
 <code> <code>
-$s->VISUAL_FACE_LATTICE;+topaz > $s->VISUAL_FACE_LATTICE;
 </code> </code>
  
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 <code> <code>
 topaz > $bs = simplex(3)->BOUNDARY; topaz > $bs = simplex(3)->BOUNDARY;
- 
 topaz > print $bs->SPHERE; topaz > print $bs->SPHERE;
 1 1
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 <code> <code>
 topaz > $c = polytope::cube(3); topaz > $c = polytope::cube(3);
- 
 topaz > $tc = $c->TRIANGULATION; topaz > $tc = $c->TRIANGULATION;
- 
 topaz > print $tc->FACETS; topaz > print $tc->FACETS;
 {0 1 2 4} {0 1 2 4}
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 <code> <code>
 topaz > $b = ball(3); topaz > $b = ball(3);
- 
 topaz > # print a dense representation of the sparse matrix topaz > # print a dense representation of the sparse matrix
 topaz > print dense( $b->COORDINATES ); topaz > print dense( $b->COORDINATES );
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 <code> <code>
 topaz > $a = new Array<Set<Int>>(1); $a->[0] = $bs->FACETS->[4]; topaz > $a = new Array<Set<Int>>(1); $a->[0] = $bs->FACETS->[4];
- 
 topaz > $bs->VISUAL->FACES($a, FacetColor => 'pink'); topaz > $bs->VISUAL->FACES($a, FacetColor => 'pink');
 </code> </code>
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 <code> <code>
 topaz > $k =  klein_bottle(); topaz > $k =  klein_bottle();
- 
 topaz > graphviz($k->VISUAL_FACE_LATTICE->MORSE_MATCHING->FACES($k->MORSE_MATCHING->CRITICAL_FACES)); topaz > graphviz($k->VISUAL_FACE_LATTICE->MORSE_MATCHING->FACES($k->MORSE_MATCHING->CRITICAL_FACES));
 </code> </code>
  • user_guide/tutorials/apps_topaz.txt
  • Last modified: 2019/02/11 23:09
  • by 127.0.0.1