ppl_utils

ppl_utils#

Some extra ppl utilities

ppl is a library to deal with rational polytopes. pplpy is a thin Python wrapper. This file provides some helper functions to use it.

surface_dynamics.misc.ppl_utils.ppl_check_non_negative_cone(C)#

Check whether the input cone C is a subcone of the positive cone

EXAMPLES:

sage: from surface_dynamics.misc.ppl_utils import ppl_check_non_negative_cone  # optional: pplpy
sage: import ppl    # optional: pplpy

sage: gs = ppl.Generator_System()     # optional: pplpy
sage: gs.insert(ppl.point())          # optional: pplpy
sage: gs.insert(ppl.ray(ppl.Variable(0) + ppl.Variable(2)))  # optional: pplpy
sage: ppl_check_non_negative_cone(ppl.C_Polyhedron(gs))  # optional: pplpy

sage: gs.insert(ppl.ray(-ppl.Variable(0) - ppl.Variable(2)))  # optional: pplpy
sage: ppl_check_non_negative_cone(ppl.C_Polyhedron(gs))  # optional: pplpy
Traceback (most recent call last):
...
ValueError: C must be a subcone of the non-negative cone

sage: gs = ppl.Generator_System()  # optional: pplpy
sage: gs.insert(ppl.point(ppl.Variable(2)))  # optional: pplpy
sage: ppl_check_non_negative_cone(ppl.C_Polyhedron(gs))  # optional: pplpy
Traceback (most recent call last):
...
ValueError: the cone does not contain zero
sage: gs.insert(ppl.point())  # optional: pplpy
sage: ppl_check_non_negative_cone(ppl.C_Polyhedron(gs))  # optional: pplpy
Traceback (most recent call last):
...
ValueError: should have only zero as vertices
surface_dynamics.misc.ppl_utils.ppl_cone(rays)#

Convert the list rays into a ppl cone

EXAMPLES:

sage: from surface_dynamics.misc.ppl_utils import ppl_cone  # optional: pplpy
sage: C = ppl_cone([(0,1,2),(1,1,1),(1,0,1)])   # optional: pplpy
sage: C.minimized_generators()   # optional: pplpy
Generator_System {point(0/1, 0/1, 0/1), ray(0, 1, 2), ray(1, 0, 1), ray(1, 1, 1)}
surface_dynamics.misc.ppl_utils.ppl_convert(P)#

Convert a Sage polyhedron to a ppl polyhedron

EXAMPLES:

sage: from surface_dynamics.misc.ppl_utils import ppl_convert  # optional: pplpy
sage: P = ppl_convert(Polyhedron(vertices=[(0,1,0),(1,0,1)], rays=[(0,0,1),[3,2,1]]))  # optional: pplpy
sage: P.minimized_generators()  # optional: pplpy
Generator_System {ray(0, 0, 1), point(0/1, 1/1, 0/1), point(1/1, 0/1, 1/1), ray(3, 2, 1)}
surface_dynamics.misc.ppl_utils.ppl_positive_cone(n)#

Return the positive cone in R^n

EXAMPLES:

sage: from surface_dynamics.misc.ppl_utils import ppl_positive_cone  # optional: pplpy
sage: C = ppl_positive_cone(3)  # optional: pplpy
sage: C.minimized_generators()  # optional: pplpy
Generator_System {point(0/1, 0/1, 0/1), ray(0, 0, 1), ray(0, 1, 0), ray(1, 0, 0)}
surface_dynamics.misc.ppl_utils.ppl_zero_point(n)#

Return the origin in R^n

EXAMPLES:

sage: from surface_dynamics.misc.ppl_utils import ppl_zero_point  # optional: pplpy
sage: ppl_zero_point(3)   # optional: pplpy
point(0/1, 0/1, 0/1)
sage: ppl_zero_point(5)   # optional: pplpy
point(0/1, 0/1, 0/1, 0/1, 0/1)
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