Coverage for local/lib/python2.7/site-packages/sage/geometry/polyhedron/lattice_euclidean_group_element.py : 100%

""" 

Lattice Euclidean Group Elements 

The classes here are used to return particular isomorphisms of 

:class:`PPL lattice 

polytopes<sage.geometry.polyhedron.ppl_lattice_polytope.LatticePolytope_PPL_class>`. 

""" 

######################################################################## 

# Copyright (C) 2012 Volker Braun <vbraun.name@gmail.com> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# 

# http://www.gnu.org/licenses/ 

######################################################################## 

from sage.structure.sage_object import SageObject 

from sage.rings.integer_ring import ZZ 

from sage.modules.all import vector 

from sage.matrix.constructor import matrix 

######################################################################## 

class LatticePolytopeError(Exception): 

""" 

Base class for errors from lattice polytopes 

""" 

pass 

######################################################################## 

class LatticePolytopesNotIsomorphicError(LatticePolytopeError): 

""" 

Raised when two lattice polytopes are not isomorphic. 

""" 

pass 

######################################################################## 

class LatticePolytopeNoEmbeddingError(LatticePolytopeError): 

""" 

Raised when no embedding of the desired kind can be found. 

""" 

pass 

######################################################################## 

class LatticeEuclideanGroupElement(SageObject): 

def __init__(self, A, b): 

""" 

An element of the lattice Euclidean group. 

Note that this is just intended as a container for results from 

LatticePolytope_PPL. There is no group-theoretic functionality to 

speak of. 

EXAMPLES:: 

sage: from sage.geometry.polyhedron.ppl_lattice_polytope import LatticePolytope_PPL, C_Polyhedron 

sage: from sage.geometry.polyhedron.lattice_euclidean_group_element import LatticeEuclideanGroupElement 

sage: M = LatticeEuclideanGroupElement([[1,2],[2,3],[-1,2]], [1,2,3]) 

sage: M 

The map A*x+b with A= 

[ 1 2] 

[ 2 3] 

[-1 2] 

b = 

(1, 2, 3) 

sage: M._A 

[ 1 2] 

[ 2 3] 

[-1 2] 

sage: M._b 

(1, 2, 3) 

sage: M(vector([0,0])) 

(1, 2, 3) 

sage: M(LatticePolytope_PPL((0,0),(1,0),(0,1))) 

A 2-dimensional lattice polytope in ZZ^3 with 3 vertices 

sage: _.vertices() 

((1, 2, 3), (2, 4, 2), (3, 5, 5)) 

""" 

self._A = matrix(ZZ, A) 

self._b = vector(ZZ, b) 

assert self._A.nrows() == self._b.degree() 

def __call__(self, x): 

""" 

Return the image of ``x`` 

INPUT: 

- ``x`` -- a vector or lattice polytope. 

EXAMPLES:: 

sage: from sage.geometry.polyhedron.ppl_lattice_polytope import LatticePolytope_PPL, C_Polyhedron 

sage: from sage.geometry.polyhedron.lattice_euclidean_group_element import LatticeEuclideanGroupElement 

sage: M = LatticeEuclideanGroupElement([[1,2],[2,3],[-1,2]], [1,2,3]) 

sage: M(vector(ZZ, [11,13])) 

(38, 63, 18) 

sage: M(LatticePolytope_PPL((0,0),(1,0),(0,1))) 

A 2-dimensional lattice polytope in ZZ^3 with 3 vertices 

""" 

from sage.geometry.polyhedron.ppl_lattice_polytope import ( 

LatticePolytope_PPL, LatticePolytope_PPL_class) 

if isinstance(x, LatticePolytope_PPL_class): 

if x.is_empty(): 

from sage.libs.ppl import C_Polyhedron 

return LatticePolytope_PPL(C_Polyhedron(self._b.degree(), 

'empty')) 

return LatticePolytope_PPL(*[self(v) for v in x.vertices()]) 

pass 

v = self._A*x+self._b 

v.set_immutable() 

return v 

def _repr_(self): 

r""" 

Return a string representation 

EXAMPLES:: 

sage: from sage.geometry.polyhedron.lattice_euclidean_group_element import LatticeEuclideanGroupElement 

sage: M = LatticeEuclideanGroupElement([[1,2],[2,3],[-1,2]], [1,2,3]) 

sage: M._repr_() 

'The map A*x+b with A=\n[ 1 2]\n[ 2 3]\n[-1 2]\nb = \n(1, 2, 3)' 

""" 

s = 'The map A*x+b with A=\n'+str(self._A) 

s += '\nb = \n'+str(self._b) 

return s 

def domain_dim(self): 

""" 

Return the dimension of the domain lattice 

EXAMPLES:: 

sage: from sage.geometry.polyhedron.lattice_euclidean_group_element import LatticeEuclideanGroupElement 

sage: M = LatticeEuclideanGroupElement([[1,2],[2,3],[-1,2]], [1,2,3]) 

sage: M 

The map A*x+b with A= 

[ 1 2] 

[ 2 3] 

[-1 2] 

b = 

(1, 2, 3) 

sage: M.domain_dim() 

2 

""" 

return self._A.ncols() 

def codomain_dim(self): 

""" 

Return the dimension of the codomain lattice 

EXAMPLES:: 

sage: from sage.geometry.polyhedron.lattice_euclidean_group_element import LatticeEuclideanGroupElement 

sage: M = LatticeEuclideanGroupElement([[1,2],[2,3],[-1,2]], [1,2,3]) 

sage: M 

The map A*x+b with A= 

[ 1 2] 

[ 2 3] 

[-1 2] 

b = 

(1, 2, 3) 

sage: M.codomain_dim() 

3 

Note that this is not the same as the rank. In fact, the 

codomain dimension depends only on the matrix shape, and not 

on the rank of the linear mapping:: 

sage: zero_map = LatticeEuclideanGroupElement([[0,0],[0,0],[0,0]], [0,0,0]) 

sage: zero_map.codomain_dim() 

3 

""" 

return self._A.nrows()