user_guide:tutorials:apps_topaz

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
Last revisionBoth sides next revision
user_guide:apps_topaz [2019/01/25 09:27] – ↷ Page moved from tutorial:apps_topaz to user_guide:apps_topaz oroehriguser_guide:tutorials:apps_topaz [2019/01/25 09:38] – ↷ Page moved from user_guide:apps_topaz to user_guide:tutorials:apps_topaz oroehrig
Line 1: Line 1:
 ===== 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 is also available as a {{ user_guide: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.
Line 24: Line 24:
 topaz > $s = new SimplicialComplex(INPUT_FACES=>[[0],[0,1],[1,2,3]]); topaz > $s = new SimplicialComplex(INPUT_FACES=>[[0],[0,1],[1,2,3]]);
 </code> </code>
-{{ :tutorial:small_complex.png?400|}}+{{ user_guide:small_complex.png?400|}}
 As you can see, redundancies are allowed -- [0] is not a facet of the complex, and thus not necessary for encoding $s. You can compute the inclusion maximal faces like this: As you can see, redundancies are allowed -- [0] is not a facet of the complex, and thus not necessary for encoding $s. You can compute the inclusion maximal faces like this:
 <code> <code>
Line 39: Line 39:
 For more information on visualizing simplicial complex, see the section below. For more information on visualizing simplicial complex, see the section below.
  
-{{:tutorial:face_lattice.png?200 |}}''polymake'' can compute the Hasse diagram of a simplicial complex (watch out, this gets really large for large complexes!). To print all the faces of the complex together with their rank in the face lattice, do this:+{{user_guide:face_lattice.png?200 |}}''polymake'' can compute the Hasse diagram of a simplicial complex (watch out, this gets really large for large complexes!). To print all the faces of the complex together with their rank in the face lattice, do this:
 <code> <code>
 topaz >print $s->HASSE_DIAGRAM->DECORATION; topaz >print $s->HASSE_DIAGRAM->DECORATION;
Line 134: Line 134:
 topaz > help 'objects/SimplicialComplex/methods/Visualization/VISUAL'; topaz > help 'objects/SimplicialComplex/methods/Visualization/VISUAL';
 </code> </code>
-{{ :tutorial:ball_triang.png?300|}}+{{ user_guide:ball_triang.png?300|}}
 for a list of available options and this [[visual_tutorial|tutorial]] for a general intro to visualization in polymake. for a list of available options and this [[visual_tutorial|tutorial]] for a general intro to visualization in polymake.
  
Line 143: Line 143:
 You should give the ''explode'' feature of jReality a try -- it gives a good (and pretty!) overview of the object. You can find it in the left slot of the jReality interface. You should give the ''explode'' feature of jReality a try -- it gives a good (and pretty!) overview of the object. You can find it in the left slot of the jReality interface.
  
-{{:tutorial:ball_triang_pink.png?250 |}} ''topaz'' may also visualize distinguished subcomplexes or just sets of faces with different decorations (colors, styles, etc.). For example, to highlight the fourth facet of ''$bs'' in pink, do this:+{{user_guide:ball_triang_pink.png?250 |}} ''topaz'' may also visualize distinguished subcomplexes or just sets of faces with different decorations (colors, styles, etc.). For example, to highlight the fourth facet of ''$bs'' in pink, do this:
 <code> <code>
 topaz > $a = new Array<Set<Int>>(1); $a->[0] = $bs->FACETS->[4]; topaz > $a = new Array<Set<Int>>(1); $a->[0] = $bs->FACETS->[4];
Line 154: Line 154:
 topaz > graphviz($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>
-{{ :tutorial:kb_mm_faces.gif?400|}}+{{ user_guide:kb_mm_faces.gif?400|}}
 Here the matching of faces is denoted by reversed red arrows and the critical faces are marked red. Check that the graph remains acyclic. Here the matching of faces is denoted by reversed red arrows and the critical faces are marked red. Check that the graph remains acyclic.
  
Line 163: Line 163:
 shows the primal and dual graph of the polytope together with an edge between a primal and a dual node iff the primal node represents a vertex of the corresponding facet of the dual node. shows the primal and dual graph of the polytope together with an edge between a primal and a dual node iff the primal node represents a vertex of the corresponding facet of the dual node.
  
-{{ :tutorial:cube_graph.png?600 |}}+{{ user_guide:cube_graph.png?600 |}}
  
 Visualization of the ''HASSE_DIAGRAM'' is possible via ''VISUAL_FACE_LATTICE''. It renders the graph in a .pdf file. You can even pipe the tikz code to whatever location using the ''tikz'' client: Visualization of the ''HASSE_DIAGRAM'' is possible via ''VISUAL_FACE_LATTICE''. It renders the graph in a .pdf file. You can even pipe the tikz code to whatever location using the ''tikz'' client:
  • user_guide/tutorials/apps_topaz.txt
  • Last modified: 2019/02/11 23:09
  • by 127.0.0.1