Module: sage.geometry.polytope
Polytopes
This module provides access to polymake, which 'has been developed since 1997 in the Discrete Geometry group at the Institute of Mathematics of Technische Universitat Berlin. Since 2004 the development is shared with Fachbereich Mathematik, Technische Universitat Darmstadt. The system offers access to a wide variety of algorithms and packages within a common framework. polymake is flexible and continuously expanding. The software supplies C++ and perl interfaces which make it highly adaptable to individual needs.'
NOTE: If you have trouble with this module do
sage: !polymake --reconfigure # not tested at the command line.
Author Log:
Class: Polymake
Functions: associahedron,
birkhoff,
cell24,
convex_hull,
cube,
from_data,
rand01,
reconfigure
self) |
sage: polymake.cell24() # optional: needs polymake The 24-cell
self, [points=[]]) |
sage: R.<x,y,z> = PolynomialRing(QQ,3) sage: f = x^3 + y^3 + z^3 + x*y*z sage: e = f.exponents() sage: a = [[1] + list(v) for v in e] sage: a [[1, 3, 0, 0], [1, 0, 3, 0], [1, 1, 1, 1], [1, 0, 0, 3]] sage: n = polymake.convex_hull(a) # optional: needs polymake sage: n # optional Convex hull of points [[1, 0, 0, 3], [1, 0, 3, 0], [1, 1, 1, 1], [1, 3, 0, 0]] sage: n.facets() # optional [(0, 1, 0, 0), (3, -1, -1, 0), (0, 0, 1, 0)] sage: n.is_simple() # optional True sage: n.graph() # optional 'GRAPH {1 2} {0 2} {0 1}
'
self) |
Reconfigure polymake.
Remember to run polymake.reconfigure() as soon as you have changed the customization file and/or installed missing software!
Special Functions: __repr__,
_Polymake__make
Class: Polytope
sage: P = polymake.convex_hull([[1,0,0,0], [1,0,0,1], [1,0,1,0], [1,0,1,1], [1,1,0,0], [1,1,0,1], [1,1,1,0], [1,1,1,1]]) # optional: needs polymake
NOTE: If you have trouble with this module do
sage: !polymake --reconfigure # not tested at the command line.
self, datafile, desc) |
Functions: cmd,
data,
facets,
graph,
is_simple,
n_facets,
vertices,
visual,
write
self) |
sage: P = polymake.convex_hull([[1,0,0,0], [1,0,0,1], [1,0,1,0], [1,0,1,1], [1,1,0,0], [1,1,0,1], [1,1,1,0], [1,1,1,1]]) # optional: needs polymake sage: P.facets() # optional [(0, 0, 0, 1), (0, 1, 0, 0), (0, 0, 1, 0), (1, 0, 0, -1), (1, 0, -1, 0), (1, -1, 0, 0)]
self) |
Return True if this polytope is simple.
A polytope is simple if the degree of each vertex equals the dimension of the polytope.
sage: P = polymake.convex_hull([[1,0,0,0], [1,0,0,1], [1,0,1,0], [1,0,1,1], [1,1,0,0], [1,1,0,1], [1,1,1,0], [1,1,1,1]]) # optional: needs polymake sage: P.is_simple() # optional True
Author: Edwin O'Shea (2006-05-02): Definition of simple.
self) |
sage: P = polymake.convex_hull([[1,0,0,0], [1,0,0,1], [1,0,1,0], [1,0,1,1], [1,1,0,0], [1,1,0,1], [1,1,1,0], [1,1,1,1]]) # optional: needs polymake sage: P.n_facets() # optional 6
self) |
sage: P = polymake.convex_hull([[1,0,0,0], [1,0,0,1], [1,0,1,0], [1,0,1,1], [1,1,0,0], [1,1,0,1], [1,1,1,0], [1,1,1,1]]) # optional: needs polymake sage: P.vertices() # optional [(1, 0, 0, 0), (1, 0, 0, 1), (1, 0, 1, 0), (1, 0, 1, 1), (1, 1, 0, 0), (1, 1, 0, 1), (1, 1, 1, 0), (1, 1, 1, 1)]
Special Functions: __add__,
__init__,
_repr_
self, other) |
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