- 03 Apr 2024, 11:35
- Forum: Helpdesk
- Topic: "ERROR: Cannot draw zero cycle at ... "
- Replies:
**4** - Views:
**227**

Sorry, the correct homogenization of your example is the following. $quadric = toTropicalPolynomial("max(2*x,1+x+y,2+2*y,1+y+z,2*z,4+2*w)"); $TQuadric = new Hypersurface<Max>(POLYNOMIAL=>$quadric); $TQuadric->VISUAL; My previous explanation is valid: the input needs to be homogeneous, i.e....

- 24 Mar 2024, 12:15
- Forum: Helpdesk
- Topic: "ERROR: Cannot draw zero cycle at ... "
- Replies:
**4** - Views:
**227**

polymake uses homogeneous polynomials throughout. Please replace the first line of your code by
See this tutorial and these jupyter notebooks for more examples.

Code: Select all

```
$quadric = toTropicalPolynomial("max(2*x,w+x+y,2*w+2*y,w+y+z,2*z,4*w)");
```

- 18 Oct 2023, 15:53
- Forum: Helpdesk
- Topic: Recognizing the topology of surfaces
- Replies:
**8** - Views:
**13083**

Could you please upload your `$my_dual_sub` and `$my_signs`? One way would be to save the `$S_0` object and share the resulting JSON.

I can't promise, but maybe we can do a bit more here.

I can't promise, but maybe we can do a bit more here.

- 23 Aug 2023, 11:27
- Forum: General Discussion
- Topic: constructing the bisectors of angles in polyhedra
- Replies:
**3** - Views:
**12795**

I still don't understand. Let's postpone this. Concerning your tertatoid, I think I know a way, modulo some experimenting. Here are the steps. (1) Construct the regular tetrahedron as the convex hull of every other vertex of the cube [-1,1]^3. Call this polytope T. (2) From each edge of T construct ...

- 22 Aug 2023, 12:50
- Forum: General Discussion
- Topic: constructing the bisectors of angles in polyhedra
- Replies:
**3** - Views:
**12795**

What is the "perpendicular bisector" of an edge? Do you mean the affine hyperplane which is perpendicular to a given edge, passing through the midpoint of that edge? Your "tetartoid" is given without coordinates, and from the description given on that web page I cannot deduce how...

- 26 Mar 2023, 19:17
- Forum: Helpdesk
- Topic: Fourier-Motzkin Elimination and the projection method
- Replies:
**7** - Views:
**10587**

Of course, we will fix those errors in polymake. However, your specific computation can be rescued as follows: polytope > $C = new Cone(INEQUALITIES =>[[1,0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,00,0,0,0],[0,0,0,0,1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,...

- 30 Jan 2023, 15:34
- Forum: Helpdesk
- Topic: Computational Complexity of VERTICES_IN_FACETS
- Replies:
**3** - Views:
**8507**

OK, so for fixed dimension d, assuming the resulting polytope to be simplicial (with prob 1) is indeed crucial for the algorithms to run in linear time? This is not what I said. Note that in the expression O(mnd) the parameter m (number of facets) depends on n (number of vertices/input points). Rou...

- 03 Jan 2023, 16:57
- Forum: Helpdesk
- Topic: Computational Complexity of VERTICES_IN_FACETS
- Replies:
**3** - Views:
**8507**

Indeed, polymake employs a convex hull computation to compute the vertex-facet incidences from input points. Most algorithms/implementations produce FACETS and VERTICES_IN_FACETS together. If this is not the case there is a second step to compute scalar products between each row of VERTICES and each...

- 03 Jan 2023, 16:32
- Forum: Helpdesk
- Topic: Computational Complexity of VERTICES_IN_FACETS
- Replies:
**3** - Views:
**8507**

Here is a question that I received: I was wondering what computational complexity I can expect from VERTICES_IN_FACETS for m vertices on the d sphere. Does it rely on a convex hull algorithm? If yes, on which? As I am using this wonderfully practicable function as a non-specialist in convex geometry...

- 23 Sep 2022, 18:19
- Forum: General Discussion
- Topic: How to define Newton polytopes of a list of polynomials and compute the vertices, rays?
- Replies:
**3** - Views:
**13419**

A google search for "polymake" and "newton polytope" reveals:

https://polymake.org/doku.php/user_guid ... s_tutorial

https://polymake.org/doku.php/user_guid ... s_tutorial

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