Numerical work with sagemath 2

In my  first post about using sagemaths looked at fixed size simplicial complex, this week I have been exploring using varying size simplicial complexes – growing from a single tetrahedron to over over twenty.

sage: r = [(random(),random(),random()) for _ in range(4)]
sage: for i in range(20):
… r = r+[(random(),random(),random()) for _ in range(1)]
… PointConfiguration(r).triangulate().plot(axis=false)

I would ultimately like the growth to be constrained to satisfy  causal constraints at each stage.

simplex growth 1

Animated gif of output from tachyon viewer of sagemath code

I have also been looking at using pachner flips to generate all possible triangulations of a pointset but I haven’t converted the results to a graphical format as yet.

sage: r = [(random(),random(),random()) for _ in range(20)]
sage: points = PointConfiguration(r)
sage: triang = points.triangulate()
sage: triang.plot(axes=False)
sage: p= points.bistellar_flips()
sage: print p

Results are in text form – over 240 pages –  at the moment, so I’m working on code to process file graphically as results are generated:

pachner move output v1

                                          Sample output of pachner move sagemath code –                                                  note that sagemaths calls pachner moves bistellar flips

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s