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sagemath
GitHub Repository: sagemath/sagelib
 Path: blob/master/sage/geometry/polyhedron/cdd_file_format.py
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"""

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Generate cdd ``.ext`` / ``.ine`` file format

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"""

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

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#       Copyright (C) 2008 Marshall Hampton <[email protected]>

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#       Copyright (C) 2011 Volker Braun <[email protected]>

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#

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

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#

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#                  http://www.gnu.org/licenses/

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

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from misc import _set_to_None_if_empty, _common_length_of, _to_space_separated_string

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

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def cdd_Vrepresentation(cdd_type, vertices, rays, lines):

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    r"""

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    Return a string containing the V-representation in cddlib's ext format.

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    NOTE:

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    If there is no vertex given, then the origin will be implicitly

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    added. You cannot write the empty V-representation (which cdd

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    would refuse to process).

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    EXAMPLES::

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        sage: from sage.geometry.polyhedron.cdd_file_format import cdd_Vrepresentation

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        sage: print cdd_Vrepresentation('rational', [[0,0]], [[1,0]], [[0,1]])

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        V-representation

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        linearity 1 1

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        begin

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          3 3 rational

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          0 0 1

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          0 1 0

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          1 0 0

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        end

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    """

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    vertices = _set_to_None_if_empty(vertices)

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    rays     = _set_to_None_if_empty(rays)

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    lines    = _set_to_None_if_empty(lines)

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    num, ambient_dim = _common_length_of(vertices, rays, lines)

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    # cdd implicitly assumes that the origin is a vertex if none is given

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    if vertices==None:

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        vertices = [[0]*ambient_dim]

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        num += 1

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    s = 'V-representation\n'

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    if lines!=None:

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        n = len(lines)

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        s += "linearity " + repr(n) + ' '

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        s += _to_space_separated_string(range(1,n+1)) + '\n'

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    s += 'begin\n'

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    s += ' ' + repr(num) + ' ' + repr(ambient_dim+1) + ' ' + cdd_type + '\n'

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    if lines!=None:

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        for l in lines:

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            s += ' 0 ' + _to_space_separated_string(l) + '\n'

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    if rays!=None:

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        for r in rays:

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            s += ' 0 ' + _to_space_separated_string(r) + '\n'

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    if vertices!=None:

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        for v in vertices:

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            s += ' 1 ' + _to_space_separated_string(v) + '\n'

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    s += 'end\n'

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    return s

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

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def cdd_Hrepresentation(cdd_type, ieqs, eqns):

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    r"""

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    Return a string containing the H-representation in cddlib's ine format.

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    EXAMPLES::

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        sage: from sage.geometry.polyhedron.cdd_file_format import cdd_Hrepresentation

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        sage: cdd_Hrepresentation('rational', None, [[0,1]])

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        'H-representation\nlinearity 1 1\nbegin\n 1 2 rational\n 0 1\nend\n'

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    """

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    ieqs = _set_to_None_if_empty(ieqs)

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    eqns  = _set_to_None_if_empty(eqns)

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    num, ambient_dim = _common_length_of(ieqs, eqns)

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    ambient_dim -= 1

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    s = 'H-representation\n'

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    if eqns!=None:

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        assert len(eqns)>0

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        n = len(eqns)

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        s += "linearity " + repr(n) + ' '

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        s += _to_space_separated_string(range(1,n+1)) + '\n'

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    s += 'begin\n'

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    s += ' ' + repr(num) + ' ' + repr(ambient_dim+1) + ' ' + cdd_type + '\n'

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    if eqns!=None:

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        for e in eqns:

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            s += ' ' + _to_space_separated_string(e) + '\n'

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    if ieqs!=None:

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        for i in ieqs:

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            s += ' ' + _to_space_separated_string(i) + '\n'

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    s += 'end\n'

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    return s

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