The PPL (Parma Polyhedra Library) backend for polyhedral computations#

class sage.geometry.polyhedron.backend_ppl.Polyhedron_QQ_ppl(parent, Vrep, Hrep, ppl_polyhedron=None, mutable=False, **kwds)#

Bases: sage.geometry.polyhedron.backend_ppl.Polyhedron_ppl, sage.geometry.polyhedron.base_QQ.Polyhedron_QQ

Polyhedra over \(\QQ\) with ppl

INPUT:

  • Vrep – a list [vertices, rays, lines] or None.

  • Hrep – a list [ieqs, eqns] or None.

EXAMPLES:

sage: p = Polyhedron(vertices=[(0,0),(1,0),(0,1)], rays=[(1,1)], lines=[],
....:                backend='ppl', base_ring=QQ)
sage: TestSuite(p).run()
class sage.geometry.polyhedron.backend_ppl.Polyhedron_ZZ_ppl(parent, Vrep, Hrep, ppl_polyhedron=None, mutable=False, **kwds)#

Bases: sage.geometry.polyhedron.backend_ppl.Polyhedron_ppl, sage.geometry.polyhedron.base_ZZ.Polyhedron_ZZ

Polyhedra over \(\ZZ\) with ppl

INPUT:

  • Vrep – a list [vertices, rays, lines] or None.

  • Hrep – a list [ieqs, eqns] or None.

EXAMPLES:

sage: p = Polyhedron(vertices=[(0,0),(1,0),(0,1)], rays=[(1,1)], lines=[],
....:                backend='ppl', base_ring=ZZ)
sage: TestSuite(p).run()
class sage.geometry.polyhedron.backend_ppl.Polyhedron_ppl(parent, Vrep, Hrep, ppl_polyhedron=None, mutable=False, **kwds)#

Bases: sage.geometry.polyhedron.base_mutable.Polyhedron_mutable

Polyhedra with ppl

INPUT:

  • Vrep – a list [vertices, rays, lines] or None.

  • Hrep – a list [ieqs, eqns] or None.

EXAMPLES:

sage: p = Polyhedron(vertices=[(0,0),(1,0),(0,1)], rays=[(1,1)], lines=[], backend='ppl')
sage: TestSuite(p).run()
Hrepresentation(index=None)#

Return the objects of the H-representation. Each entry is either an inequality or a equation.

INPUT:

  • index – either an integer or None

OUTPUT:

The optional argument is an index running from 0 to self.n_Hrepresentation()-1. If present, the H-representation object at the given index will be returned. Without an argument, returns the list of all H-representation objects.

EXAMPLES:

sage: p = polytopes.hypercube(3)
sage: p.Hrepresentation(0)
An inequality (-1, 0, 0) x + 1 >= 0
sage: p.Hrepresentation(0) == p.Hrepresentation()[0]
True

sage: P = p.parent()
sage: p = P._element_constructor_(p, mutable=True)
sage: p.Hrepresentation(0)
An inequality (0, 0, -1) x + 1 >= 0
sage: p._clear_cache()
sage: p.Hrepresentation(0)
An inequality (0, 0, -1) x + 1 >= 0
sage: TestSuite(p).run()
Vrepresentation(index=None)#

Return the objects of the V-representation. Each entry is either a vertex, a ray, or a line.

See sage.geometry.polyhedron.constructor for a definition of vertex/ray/line.

INPUT:

  • index – either an integer or None

OUTPUT:

The optional argument is an index running from 0 to self.n_Vrepresentation()-1. If present, the V-representation object at the given index will be returned. Without an argument, returns the list of all V-representation objects.

EXAMPLES:

sage: p = polytopes.cube()
sage: p.Vrepresentation(0)
A vertex at (1, -1, -1)

sage: P = p.parent()
sage: p = P._element_constructor_(p, mutable=True)
sage: p.Vrepresentation(0)
A vertex at (-1, -1, -1)
sage: p._clear_cache()
sage: p.Vrepresentation(0)
A vertex at (-1, -1, -1)
sage: TestSuite(p).run()
set_immutable()#

Make this polyhedron immutable. This operation cannot be undone.

EXAMPLES:

sage: p = Polyhedron([[1, 1]], mutable=True)
sage: p.is_mutable()
True
sage: hasattr(p, "_Vrepresentation")
False
sage: p.set_immutable()
sage: hasattr(p, "_Vrepresentation")
True