Python DiGraph.add_edges方法代码示例

# 需要导入模块: from sage.graphs.all import DiGraph [as 别名]
# 或者: from sage.graphs.all.DiGraph import add_edges [as 别名]
def _is_valid_digraph_edge_set( edges, frozen=0 ):
    """
    Returns True if the input data is the edge set of a digraph for a quiver (no loops, no 2-cycles, edge-labels of the specified format), and returns False otherwise.

    INPUT:

    - ``frozen`` -- (integer; default:0) The number of frozen vertices.

    EXAMPLES::

        sage: from sage.combinat.cluster_algebra_quiver.mutation_class import _is_valid_digraph_edge_set
        sage: _is_valid_digraph_edge_set( [[0,1,'a'],[2,3,(1,-1)]] )
        The given digraph has edge labels which are not integral or integral 2-tuples.
        False
        sage: _is_valid_digraph_edge_set( [[0,1],[2,3,(1,-1)]] )
        True
        sage: _is_valid_digraph_edge_set( [[0,1,'a'],[2,3,(1,-1)],[3,2,(1,-1)]] )
        The given digraph or edge list contains oriented 2-cycles.
        False
    """
    try:
        dg = DiGraph()
        dg.allow_multiple_edges(True)
        dg.add_edges( edges )

        # checks if the digraph contains loops
        if dg.has_loops():
            print "The given digraph or edge list contains loops."
            return False

        # checks if the digraph contains oriented 2-cycles
        if _has_two_cycles( dg ):
            print "The given digraph or edge list contains oriented 2-cycles."
            return False

        # checks if all edge labels are 'None', positive integers or tuples of positive integers
        if not all( i == None or ( i in ZZ and i > 0 ) or ( type(i) == tuple and len(i) == 2 and i[0] in ZZ and i[1] in ZZ ) for i in dg.edge_labels() ):
            print "The given digraph has edge labels which are not integral or integral 2-tuples."
            return False

        # checks if all edge labels for multiple edges are 'None' or positive integers
        if dg.has_multiple_edges():
            for e in set( dg.multiple_edges(labels=False) ):
                if not all( i == None or ( i in ZZ and i > 0 ) for i in dg.edge_label( e[0], e[1] ) ):
                    print "The given digraph or edge list contains multiple edges with non-integral labels."
                    return False

        n = dg.order() - frozen
        if n < 0:
            print "The number of frozen variables is larger than the number of vertices."
            return False

        if [ e for e in dg.edges(labels=False) if e[0] >= n] <> []:
            print "The given digraph or edge list contains edges within the frozen vertices."
            return False

        return True
    except StandardError:
        print "Could not even build a digraph from the input data."
        return False

# 需要导入模块: from sage.graphs.all import DiGraph [as 别名]
# 或者: from sage.graphs.all.DiGraph import add_edges [as 别名]
class NaiveCrystal(UniqueRepresentation, Parent):
    r"""
    This is an example of a "crystal" which does not come from any kind of
    representation, designed primarily to test the Stembridge local rules with.
    The crystal has vertices labeled 0 through 5, with 0 the highest weight.

    The code here could also possibly be generalized to create a class that
    automatically builds a crystal from an edge-colored digraph, if someone
    feels adventurous.

    Currently, only the methods :meth:`highest_weight_vector`, :meth:`e`, and :meth:`f` are
    guaranteed to work.

    EXAMPLES::

        sage: C = Crystals().example(choice='naive')
        sage: C.highest_weight_vector()
        0
    """
    def __init__(self):
        """
        EXAMPLES::

            sage: C = sage.categories.examples.crystals.NaiveCrystal()
            sage: C == Crystals().example(choice='naive')
            True
        """
        Parent.__init__(self, category = ClassicalCrystals())
        self.n = 2
        self._cartan_type = CartanType(['A',2])
        self.G = DiGraph(5)
        self.G.add_edges([ [0,1,1], [1,2,1], [2,3,1], [3,5,1],  [0,4,2], [4,5,2] ])
        self.module_generators = [ self(0) ]

    def __repr__(self):
        """
        EXAMPLES::

            sage: Crystals().example(choice='naive')
            A broken crystal, defined by digraph, of dimension five.
        """
        return "A broken crystal, defined by digraph, of dimension five."

    class Element(ElementWrapper):
        def e(self, i):
            r"""
            Returns the action of `e_i` on ``self``.

            EXAMPLES::

                sage: C = Crystals().example(choice='naive')
                sage: [[c,i,c.e(i)] for i in C.index_set() for c in [C(j) for j in [0..5]] if c.e(i) is not None]
                [[1, 1, 0], [2, 1, 1], [3, 1, 2], [5, 1, 3], [4, 2, 0], [5, 2, 4]]
            """
            assert i in self.index_set()
            for edge in self.parent().G.edges():
               if edge[1]==int(str(self)) and edge[2]==i:
                   return self.parent()(edge[0])
            return None

        def f(self, i):
            r"""
            Returns the action of `f_i` on ``self``.

            EXAMPLES::

                sage: C = Crystals().example(choice='naive')
                sage: [[c,i,c.f(i)] for i in C.index_set() for c in [C(j) for j in [0..5]] if c.f(i) is not None]
                [[0, 1, 1], [1, 1, 2], [2, 1, 3], [3, 1, 5], [0, 2, 4], [4, 2, 5]]
            """
            assert i in self.index_set()
            for edge in self.parent().G.edges_incident(int(str(self))):
                if edge[2] == i:
                    return self.parent()(edge[1])
            return None