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2016-11-29 17:47:24 -0500 commented question plotting 3d polytope in R^4

I tried different projection directions, and always the plot seems to have the same non-convexity issues. I guess there is something wrong with these projections.

2016-11-29 17:45:53 -0500 commented answer plotting 3d polytope in R^4

The documentation of affine_hull should be more specific telling what is the output polyhedron, and in which sense it is the same as the original one. As I see, in this example it is a projection to the first 3 coordinates, but it is not similar to the original one, but only affinely equivalent.

2016-11-23 14:27:10 -0500 asked a question plotting 3d polytope in R^4

I'm trying to plot the following polytope on the cloud:

P=Polyhedron(vertices=[[0, 1, 0, 4] , [0, 1, 1, 3] , [3, 1, 1, 0] , [3, 1, 0, 1] , [0, 3, 0, 2] , [0, 3, 1, 1] , [1, 0, 0, 4] , [1, 0, 1, 3] , [3, 0, 1, 1] , [3, 0, 0, 2] , [1, 3, 1, 0] , [1, 3, 0, 1]])
P.plot()

This is a polytope living in R^4, but in fact the sum of the coordinates of each vertex is 5, so it is a 3D polytope. In some cases, sage gives me a nice 3D view of how the polytope looks like, but in this case it gives me something that doesn't even looks convex, so it is not the right projection. I would like to know what is going on and try to solve this issue, so I appreciate ideas on how to correct this, and where to look at on the code.

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2016-09-15 18:04:32 -0500 asked a question chromatic polynomial of empty graph

I know it is kind of silly, but the computation of the chromatic polynomial of the empty graph loops forever.

graphs.EmptyGraph().chromatic_polynomial()

(no question here... just a comment. I guess it is easy to correct, since it is supposed to be 1)

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2014-12-01 12:06:51 -0500 commented answer plot Polyhedron from cloud

Indeed it works now, and is very fast, but still the results are not as good as with jmol. There I was using the thickness option to plot lines and edges and I get 3d objects that are thick cylinders, but here is not as pretty. Also I don't understand the shadows of the colors of the facets of the icosahedron. Anyway thanks a lot!

2014-12-01 11:45:16 -0500 commented answer interactive drawing and tikz

thanks! they are even implementing some sort of python capabilities now... Great!

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2014-10-29 11:57:17 -0500 asked a question plot Polyhedron from cloud

I'm trying to plot some 3d stuff from the cloud. I tried:

icosahedron()

and worked perfectly, but then I tried

v=[(0,0,0),(0,1,0),(0,2,1),(1,0,0),(1,2,3),(2,1,1)]
Polyhedron(vertices=v).plot()

and I only get a single bullet, no error message, no image, no nothing... What is going on?

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2013-04-08 06:31:48 -0500 asked a question music in sage

hi! I would like to see some music features support in sage so that it is possible to easily do some math and music experiments from sage. Do you know a good package that could be added for that purpose? It would be great to have this kind of features from default in a sage instalation, like playing with frequencies and waves to produce nice sounds. Feel free to give here more ideas to that.

2012-09-17 13:29:09 -0500 asked a question interactive drawing and tikz

I would like to see something like this in sage:

-A graphic object that works similar to tikz and the result can be exported almost directly to tikz code.

-It also uses nodes that can be rendered in an interactive window so that all mathematical constructions are updated as you move the nodes, as in some geometry interactive software (like cabri or geometer sketchpad).

What could be a good way to get there? Which alternatives for rendering software might help?

2011-06-26 01:28:17 -0500 commented answer How do I get sage to honor my PYTHONPATH environmental variable?

I'm also interested in this, but unfortunately I don't understand much of what is here written. Is it possible to explain this again for a computer newbie? (I'm trying to do this with ubuntu)

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2011-05-11 23:54:34 -0500 answered a question why remove_face uses alexander duality?

try this:

T=SimplicialComplex(10,[[0,1,2,3,4,5,6],[1,2,3,4,5,6,7],[0,1,2,4,5,6,7],[0,1,2,3,5,6,7],[0,1,2,3,4,5,7],[0,1,2,3,4,7,8],[0,1,2,3,4,6,8],[0,1,2,4,6,7,8],[0,1,2,3,6,7,8],[0,1,3,4,5,7,8],[0,1,3,4,5,6,8],[0,1,4,5,6,7,8],[1,3,4,5,7,8,9],[1,3,4,5,6,8,9],[0,3,4,5,6,8,9],[0,3,4,5,6,9,10],[0,2,3,4,5,6,10],[0,4,5,6,8,9,10],[0,3,4,5,8,9,10],[0,3,4,6,8,9,10],[0,2,4,5,6,7,10],[0,2,3,4,5,7,10],[2,3,4,5,6,7,10],[0,2,3,4,6,8,10],[0,4,5,6,7,8,10],[0,3,4,5,7,8,10],[0,2,4,6,7,8,10],[0,2,3,4,7,8,10],[1,3,4,5,6,7,10]])

FACE=Simplex([1,2,5])

remove_face(T,FACE)
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2011-05-03 06:56:34 -0500 answered a question why remove_face uses alexander duality?

This is the code I got. I'm still novice with python stuff...

def remove_face(SC,FACE):
    """Remove the Simplex FACE from the SimplicialComplex SC, by taking
    the facets of SC not containing FACE, union with
    link(FACE)*boundary(face)."""
    ffboundary=SimplicialComplex(FACE,FACE.faces()) # boundary
    link=SC.link(FACE)#link
    a=ffboundary.join(link,rename_vertices=False)#join
    b=Set([elem for elem in SC.facets() if FACE.is_face(elem)==False])
    c=a.facets().union(b)
    SC2=SimplicialComplex(SC.vertices(),c)
    return SC2

There is a minor problem now in case that FACE is not a face of SC. Maybe an error can be added, but I think the algorithm is right, and the problem is in the way the link is computed.

The problem is that the link of a simplex not being a face in the complex is not the simplicial complex {()} (the irrelevant complex), but simply {} (the void complex). The link definition doesn't include the empty set in this case, so the answer is tecnically wrong.

If the link is void, the join would be void, and no faces are added or removed... Besides, if the link makes this difference, it can be used as a test for a simplex being a face (since {} is supposed to be false).

I tested the examples to compare results with sage documentation (here FACE must be a Simplex), but with real examples (a bit bigger), I didn't manage to wait for sage, while my algorithm was about a second... Regards!

2011-04-27 05:56:04 -0500 asked a question why remove_face uses alexander duality?

The method for simplicial complexes remove_face is very slow for not to say that never ends. The documentation describes the used algorithm, but it seems pretty unefficient. I think it is easier simply to remove the facets containing the face to delete F, and for each facet add the faces not containing F. That is the join of the boundary of F and the complement of F (the link). Why to use such elaborate algorithm?

2011-03-29 05:42:06 -0500 answered a question h_vectors of simplicial complexes

I also noticed that there where no h_vectors in the old documentation... However I messed everything up with the upgrade and now nothing is working (I didn't check before the right way to do it and try to reinstall everything from the begining). This is the situation now: when I run ./sage I get a long message telling at the end:

 ImportError: libgfortran.so.3: cannot open shared object file: No such file or directory
Error importing ipy_profile_sage - perhaps you should run %upgrade?
WARNING: Loading of ipy_profile_sage failed.

then after running %upgrade I get the following

sage: %upgrade
> /home/emerson/sage-4.6.2/local/bin/python "/home/emerson/sage-4.6.2/local/lib/python2.6/site-packages/IPython/upgrade_dir.py" "/home/emerson/sage-4.6.2/local/lib/python2.6/site-packages/IPython/UserConfig" "/home/emerson/.sage/ipython"
/home/emerson/.sage/ipython/__init__.py: Unedited, installing new version
/home/emerson/.sage/ipython/ipy_user_conf.py: Unedited, installing new version

and then

sage: 1+1
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)

/home/emerson/sage-4.6.2/local/bin/<ipython console> in <module>()

NameError: name 'Integer' is not defined

I hope you can tell me what to do now...

2011-03-29 04:51:42 -0500 marked best answer h_vectors of simplicial complexes

Could you edit your message to include a cut-and-paste of exactly what you did and what error message it returned? It seems to work for me just like in the examples, but I'm running Sage 4.6.2 and don't know about earlier versions:

sage: X = SimplicialComplex(3, [[0,1], [1,2], [2,3], [3,0]])
sage: X
Simplicial complex with vertex set (0, 1, 2, 3) and facets {(1, 2), (2, 3), (0, 3), (0, 1)}
sage: X.h_vector()
[1, 2, 1]
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2011-03-25 01:13:33 -0500 commented answer h_vectors of simplicial complexes

I have a 4.6.1 version of sage, but is installed somewhere else, so I cannot send you the precise error message. I think I should try an update... Thanks!

2011-03-25 00:44:51 -0500 asked a question h_vectors of simplicial complexes

In the documentation for finite simplicial complexes it was described the function h_vector, but when I tried to use it, sage told me that there was not such a property for simplicial complexes. Where can it be the problem?