graph dance moves.sagews

reset()
typeset_mode(True)

def all_paths(G,a,b):
    old_paths = G.all_paths( a, b ) # get all paths without edge multiplicity
    new_paths=[]
    for p in old_paths: # traverse each path replacing each edge by a list of (multi) edges
        multi_path=[]
        for i,u in enumerate(p):
            if i < len(p)-1:
                v = p[i+1]
                edges = G.edge_boundary([u], [v] )
                multi_path.append(edges)
        new_paths.extend( CartesianProduct(*multi_path )) # each sequence of (multi) edges will be a source of multiple paths
        #new_paths.extend( cartesian_product(*multi_path ))
    return new_paths

# start is at position 1 and end is position 5
_ = var('start')
_ = var('end')

# define all the positions
for i in ['A','B']:
    for j in [1..2]:
        for k in ['a','b']:
            for l in [1..8]:
                _ = var(str(i)+str(j)+str(k)+'Pos'+str(l))

#Add arrows for calls, small subset, rest are at end

reset('D')
# create the graph
D = DiGraph(multiedges=True)

for i in ['BRPT']:
    D.add_edge(start,A1aPos4,str(i))
    D.add_edge(B2aPos6,end,str(i))
    for j in [[1,4],[2,1],[3,2],[4,3],[5,8],[6,5],[7,6],[8,7]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['CL4','MAL1','MAR1','WAL1','WAR1','LL','MG1','WG1','MDsD1','WDsD1','NDsD1','NAL1','NAR1']:
    D.add_edge((start,A1aPos1,str(i)))
    D.add_edge((B2aPos5,end,str(i)))
    for j in [[1,1],[2,2],[3,3],[4,4],[5,5],[6,6],[7,7],[8,8]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['WHH','MHH']:
    D.add_edge((start,A1aPos7,str(i)))
    D.add_edge((B2aPos3,end,str(i)))
    D.add_edge((B2aPos7,end,str(i)))
    for j in [[1,7],[2,4],[3,5],[4,2],[5,7],[6,2],[7,5],[8,4]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['WAL1.5','WAR1.5']:
    D.add_edge((start,A1aPos8,str(i)))
    D.add_edge((B2aPos2,end,str(i)))
    for j in [[1,8],[2,5],[3,6],[4,7],[5,2],[6,3],[7,4],[8,1]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['MAL1.5','MAR1.5','MG1.5','MDsD1.5']:
    D.add_edge((start,A1aPos6,str(i)))
    D.add_edge((B2aPos4,end,str(i)))
    for j in [[1,6],[2,7],[3,8],[4,5],[5,4],[6,1],[7,2],[8,3]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['RsLs']:
    D.add_edge((start,A1aPos6,str(i)))
    D.add_edge((B2aPos4,end,str(i)))
    for j in [[1,6],[2,7],[3,8],[4,5],[5,4],[6,1],[7,2],[8,3]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['BRCT']:
    D.add_edge((start,A1aPos7,str(i)))
    D.add_edge((B2aPos3,end,str(i)))
    for j in [[1,7],[2,6],[3,5],[4,8],[5,3],[6,2],[7,1],[8,4]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['WG1.5','WDsD1.5']:
    D.add_edge((start,A1aPos8,str(i)))
    D.add_edge((B2aPos4,end,str(i)))
    for j in [[1,8],[2,7],[3,6],[4,5],[5,4],[6,3],[7,2],[8,1]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['LC']:
    D.add_edge((start,A1aPos2,str(i)))
    D.add_edge((B2aPos2,end,str(i)))
    D.add_edge((B2aPos8,end,str(i)))
    for j in [[1,2],[2,5],[3,4],[4,7],[5,2],[6,7],[7,4],[8,5]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['PS']:
    for j in [[2,2],[4,4],[6,4],[8,2]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['NS']:
    D.add_edge((start,A1aPos5,str(i)))
    D.add_edge((B2aPos1,end,str(i)))
    D.add_edge((B2aPos5,end,str(i)))
    for j in [[1,5],[3,7],[5,5],[7,7]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['PDsD1','PAL1','PAR1']:
    for j in [[2,2],[4,4],[6,6],[8,8]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['PDsD1.5','PAL1.5','PAR1.5']:
    for j in [[2,8],[4,6],[6,4],[8,2]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['NDsD1','NALR1']:
    D.add_edge((start,A1aPos1,str(i)))
    D.add_edge((B2aPos5,end,str(i)))
    for j in [[1,1],[3,3],[5,5],[7,7]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['NDsD1.5','NAL1.5','NAR1.5']:
    D.add_edge((start,A1aPos5,str(i)))
    D.add_edge((B2aPos1,end,str(i)))
    for j in [[1,5],[3,7],[5,1],[7,3]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b'],['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

# show the graph, it's not pretty...yet
len(set(D.vertices()))
#D.graphplot(edge_labels=True,layout='circular').show()
D.graphplot(edge_labels=True,layout='circular').show()
D.get_pos()
#positions = D.get_pos()
#positions
#D.get_pos()

$\displaystyle 58$

# count the dances
paths=all_paths(D,start,end)
len(paths)

D.set_pos({
        start:[0,4],
        A1aPos1:[1,7],
        A1aPos2:[1,6],
        A1aPos3:[1,5],
        A1aPos4:[1,4],
        A1aPos5:[1,3],
        A1aPos6:[1,2],
        A1aPos7:[1,1],
        A1aPos8:[1,0],
        A1bPos1:[2,7],
        A1bPos2:[2,6],
        A1bPos3:[2,5],
        A1bPos4:[2,4],
        A1bPos5:[2,3],
        A1bPos6:[2,2],
        A1bPos7:[2,1],
        A1bPos8:[2,0],
        A2aPos1:[3,7],
        A2aPos2:[3,6],
        A2aPos3:[3,5],
        A2aPos4:[3,4],
        A2aPos5:[3,3],
        A2aPos6:[3,2],
        A2aPos7:[3,1],
        A2aPos8:[3,0],
        A2bPos1:[4,7],
        A2bPos2:[4,6],
        A2bPos3:[4,5],
        A2bPos4:[4,4],
        A2bPos5:[4,3],
        A2bPos6:[4,2],
        A2bPos7:[4,1],
        A2bPos8:[4,0],
        B1aPos1:[5,7],
        B1aPos2:[5,6],
        B1aPos3:[5,5],
        B1aPos4:[5,4],
        B1aPos5:[5,3],
        B1aPos6:[5,2],
        B1aPos7:[5,1],
        B1aPos8:[5,0],
        B1bPos1:[6,7],
        B1bPos2:[6,6],
        B1bPos3:[6,5],
        B1bPos4:[6,4],
        B1bPos5:[6,3],
        B1bPos6:[6,2],
        B1bPos7:[6,1],
        B1bPos8:[6,0],
        B2aPos1:[7,7],
        B2aPos2:[7,6],
        B2aPos3:[7,5],
        B2aPos4:[7,4],
        B2aPos5:[7,3],
        B2aPos6:[7,2],
        B2aPos7:[7,1],
        B2aPos8:[7,0],
        end:[8,4]
    })

D.graphplot(edge_labels=True).show(figsize=32)

D.graphplot(edge_labels=True).show(figsize=128)

D.get_pos()

D.set_pos()
D.plot(save_pos=True)

for p in paths:
    print p

D.show(edge_labels=True,layout='spring',iterations=20000)

D.show()

digraphs.Circuit(100).show()
digraphs.Circuit(100).show(iterations=20000)