Problem with zonotope visualization

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camilo
Posts: 11
Joined: 23 May 2013, 16:11

Problem with zonotope visualization

Postby camilo » 23 May 2013, 16:21

Hi. This forum is great.

I'm having a problem visualizing a zonotope with jReality, which I define as follows:

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polytope > $zm= new Matrix<Rational>([[0,1,-1,0,0,1,0,-1,0],[0,1,-1,0,0,0,1,0,-1],[0,0,0,1,-1,1,0,-1,0],[0,0,0,1,-1,0,1,0,-1]]) polytope > $zv=zonotope($zm) polytope > print $zv; 1 2 -2 2 -2 2 2 -2 -2 1 0 0 2 -2 0 2 0 -2 1 0 0 2 -2 2 0 -2 0 1 -2 2 2 -2 0 0 0 0 1 2 -2 0 0 0 2 0 -2 1 0 0 0 0 -2 2 2 -2 1 0 0 0 0 0 0 0 0 1 -2 2 0 0 -2 0 2 0 1 2 -2 0 0 2 0 -2 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 2 -2 -2 2 1 -2 2 0 0 0 -2 0 2 1 2 -2 -2 2 0 0 0 0 1 0 0 -2 2 -2 0 2 0 1 0 0 -2 2 0 -2 0 2 1 -2 2 -2 2 -2 -2 2 2 polytope > print $z->VERTICES; polymake: used package cddlib Implementation of the double description method of Motzkin et al. Copyright by Komei Fukuda. http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html 1 2 -2 2 -2 2 2 -2 -2 1 0 0 2 -2 0 2 0 -2 1 0 0 2 -2 2 0 -2 0 1 -2 2 2 -2 0 0 0 0 1 2 -2 0 0 0 2 0 -2 1 0 0 0 0 -2 2 2 -2 1 -2 2 0 0 -2 0 2 0 1 2 -2 0 0 2 0 -2 0 1 0 0 0 0 2 -2 -2 2 1 -2 2 0 0 0 -2 0 2 1 2 -2 -2 2 0 0 0 0 1 0 0 -2 2 -2 0 2 0 1 0 0 -2 2 0 -2 0 2 1 -2 2 -2 2 -2 -2 2 2
This gives a 3-d polytope and every seems to work fine, but when i do $z->VISUAL; it responds

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polymake: ERROR: could not provide all required input properties at input line 1.
Am I doing something wrong? (I tested VISUAL with the usual examples and it worked properly). Thanks in advance!!

herr
Developer
Posts: 40
Joined: 30 Dec 2010, 13:15

Re: Problem with zonotope visualization

Postby herr » 23 May 2013, 17:28

You can only visualize polytopes with AMBIENT_DIM <= 3 (or 4, if you like Schlegel diagrams). The AMBIENT_DIM of your polytope is

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polytope > print $zv->AMBIENT_DIM; 8

You could project your 3-dim polytope to 3-space via

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polytope > $zv_proj = projection_full($zv); polytope > print $zv_proj->AMBIENT_DIM; 3
However, you should be careful with the interpretation of the visualized polytope $zv_proj. Different projection maps may lead to different (unexpected) images.


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