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Project: Contra Dance
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# This code accompanies work by Matt Thomas and Crystal Peebles at Ithaca College.
# Please contact [email protected] for information about this code.

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
# Graph D is the first half of dances

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

for i in ['BRPT']:
    D.add_edge(start,A1aPos4,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']]:
            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)))
    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']]:
            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)))
    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']]:
            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)))
    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']]:
            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)))
    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']]:
            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)))
    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']]:
            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)))
    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']]:
            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)))
    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']]:
            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)))
    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']]:
            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']]:
            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)))
    for j in [[1,5],[3,7],[5,5],[7,7]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b']]:
            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']]:
            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']]:
            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)))
    for j in [[1,1],[3,3],[5,5],[7,7]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b']]:
            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)))
    for j in [[1,5],[3,7],[5,1],[7,3]]:
        for k in [['A1a','A1b'],['A1b','A2a'],['A2a','A2b']]:
            D.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

# Graph E is the second half of dances
reset('E')
# create the graph
E = DiGraph(multiedges=True)

for i in ['BRPT']:
    E.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 [['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            E.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']:
    E.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 [['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            E.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']:
    E.add_edge((B2aPos3,end,str(i)))
    E.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 [['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            E.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']:
    E.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 [['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            E.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']:
    E.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 [['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            E.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['RsLs']:
    E.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 [['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            E.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['BRCT']:
    E.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 [['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            E.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']:
    E.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 [['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            E.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

for i in ['LC']:
    E.add_edge((B2aPos2,end,str(i)))
    E.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 [['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            E.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 [['A2b','B1a'],['B1a','B1b'],['B1b','B2a']]:
            E.add_edge(var(str(k[0])+'Pos'+str(j[0])),var(str(k[1])+'Pos'+str(j[1])),str(i))

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

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]
    })


E.set_pos({
        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, vertex_size=5000).show(figsize=4)

E.graphplot(edge_labels=True, vertex_size=3500).show(figsize=4)

D.get_pos()
E.get_pos()
{A2aPos7:[3,1],A1bPos2:[2,6],A1aPos4:[1,4],A2aPos5:[3,3],A1bPos7:[2,1],A2bPos8:[4,0],A1aPos2:[1,6],A1bPos5:[2,3],A2bPos6:[4,2],A1aPos7:[1,1],A2aPos8:[3,0],A1aPos5:[1,3],A2aPos6:[3,2],start:[0,4],A1bPos8:[2,0],A2bPos3:[4,5],A1bPos6:[2,2],A1aPos8:[1,0],A2bPos1:[4,7],A2aPos3:[3,5],A1aPos6:[1,2],A2aPos1:[3,7],A1bPos3:[2,5],A2bPos4:[4,4],A1bPos1:[2,7],A2bPos2:[4,6],A1aPos3:[1,5],A2aPos4:[3,4],A2bPos7:[4,1],A1aPos1:[1,7],A2aPos2:[3,6],A1bPos4:[2,4],A2bPos5:[4,3]}\displaystyle \left\{\mathit{A2aPos}_{7} : \left[3, 1\right], \mathit{A1bPos}_{2} : \left[2, 6\right], \mathit{A1aPos}_{4} : \left[1, 4\right], \mathit{A2aPos}_{5} : \left[3, 3\right], \mathit{A1bPos}_{7} : \left[2, 1\right], \mathit{A2bPos}_{8} : \left[4, 0\right], \mathit{A1aPos}_{2} : \left[1, 6\right], \mathit{A1bPos}_{5} : \left[2, 3\right], \mathit{A2bPos}_{6} : \left[4, 2\right], \mathit{A1aPos}_{7} : \left[1, 1\right], \mathit{A2aPos}_{8} : \left[3, 0\right], \mathit{A1aPos}_{5} : \left[1, 3\right], \mathit{A2aPos}_{6} : \left[3, 2\right], \mathit{start} : \left[0, 4\right], \mathit{A1bPos}_{8} : \left[2, 0\right], \mathit{A2bPos}_{3} : \left[4, 5\right], \mathit{A1bPos}_{6} : \left[2, 2\right], \mathit{A1aPos}_{8} : \left[1, 0\right], \mathit{A2bPos}_{1} : \left[4, 7\right], \mathit{A2aPos}_{3} : \left[3, 5\right], \mathit{A1aPos}_{6} : \left[1, 2\right], \mathit{A2aPos}_{1} : \left[3, 7\right], \mathit{A1bPos}_{3} : \left[2, 5\right], \mathit{A2bPos}_{4} : \left[4, 4\right], \mathit{A1bPos}_{1} : \left[2, 7\right], \mathit{A2bPos}_{2} : \left[4, 6\right], \mathit{A1aPos}_{3} : \left[1, 5\right], \mathit{A2aPos}_{4} : \left[3, 4\right], \mathit{A2bPos}_{7} : \left[4, 1\right], \mathit{A1aPos}_{1} : \left[1, 7\right], \mathit{A2aPos}_{2} : \left[3, 6\right], \mathit{A1bPos}_{4} : \left[2, 4\right], \mathit{A2bPos}_{5} : \left[4, 3\right]\right\}
{B1aPos8:[5,0],B2aPos3:[7,5],B1aPos6:[5,2],A2bPos8:[4,0],B2aPos1:[7,7],B1bPos3:[6,5],A2bPos6:[4,2],B1bPos1:[6,7],B1aPos3:[5,5],B2aPos4:[7,4],B1aPos1:[5,7],B2aPos2:[7,6],A2bPos3:[4,5],B1bPos4:[6,4],B2aPos7:[7,1],A2bPos1:[4,7],B1bPos2:[6,6],B1aPos4:[5,4],B2aPos5:[7,3],B1bPos7:[6,1],end:[8,4],B1aPos2:[5,6],A2bPos4:[4,4],B1bPos5:[6,3],B1aPos7:[5,1],B2aPos8:[7,0],A2bPos2:[4,6],B1aPos5:[5,3],B2aPos6:[7,2],A2bPos7:[4,1],B1bPos8:[6,0],A2bPos5:[4,3],B1bPos6:[6,2]}\displaystyle \left\{\mathit{B1aPos}_{8} : \left[5, 0\right], \mathit{B2aPos}_{3} : \left[7, 5\right], \mathit{B1aPos}_{6} : \left[5, 2\right], \mathit{A2bPos}_{8} : \left[4, 0\right], \mathit{B2aPos}_{1} : \left[7, 7\right], \mathit{B1bPos}_{3} : \left[6, 5\right], \mathit{A2bPos}_{6} : \left[4, 2\right], \mathit{B1bPos}_{1} : \left[6, 7\right], \mathit{B1aPos}_{3} : \left[5, 5\right], \mathit{B2aPos}_{4} : \left[7, 4\right], \mathit{B1aPos}_{1} : \left[5, 7\right], \mathit{B2aPos}_{2} : \left[7, 6\right], \mathit{A2bPos}_{3} : \left[4, 5\right], \mathit{B1bPos}_{4} : \left[6, 4\right], \mathit{B2aPos}_{7} : \left[7, 1\right], \mathit{A2bPos}_{1} : \left[4, 7\right], \mathit{B1bPos}_{2} : \left[6, 6\right], \mathit{B1aPos}_{4} : \left[5, 4\right], \mathit{B2aPos}_{5} : \left[7, 3\right], \mathit{B1bPos}_{7} : \left[6, 1\right], \mathit{end} : \left[8, 4\right], \mathit{B1aPos}_{2} : \left[5, 6\right], \mathit{A2bPos}_{4} : \left[4, 4\right], \mathit{B1bPos}_{5} : \left[6, 3\right], \mathit{B1aPos}_{7} : \left[5, 1\right], \mathit{B2aPos}_{8} : \left[7, 0\right], \mathit{A2bPos}_{2} : \left[4, 6\right], \mathit{B1aPos}_{5} : \left[5, 3\right], \mathit{B2aPos}_{6} : \left[7, 2\right], \mathit{A2bPos}_{7} : \left[4, 1\right], \mathit{B1bPos}_{8} : \left[6, 0\right], \mathit{A2bPos}_{5} : \left[4, 3\right], \mathit{B1bPos}_{6} : \left[6, 2\right]\right\}
# count the dances
#paths=all_paths(D,start,A2bPos1)
#len(paths)
#for p in paths:
#    print p

totaldances = 0
for i in [1..8]:
    for j in ['a','b']:
        _ = var(str(j)+str(i))

firstset = []
secondset = []
for i in [1..8]:
    paths=all_paths(D,start,var('A2bPos'+str(i)))
    firstset.append(len(paths))
    print "Start to A2b Position",i,"is",len(paths),"paths"
for i in [1..8]:
    paths=all_paths(E,var('A2bPos'+str(i)),end)
    secondset.append(len(paths))
    print "A2b Position",i,"to end is",len(paths),"paths"
<string>:11: DeprecationWarning: CartesianProduct is deprecated. Use cartesian_product instead See http://trac.sagemath.org/18411 for details.
Start to A2b Position 1 is 158191 paths Start to A2b Position 2 is 173187 paths Start to A2b Position 3 is 103870 paths Start to A2b Position 4 is 179807 paths Start to A2b Position 5 is 181266 paths Start to A2b Position 6 is 141273 paths Start to A2b Position 7 is 167723 paths Start to A2b Position 8 is 126958 paths A2b Position 1 to end is 181266 paths A2b Position 2 to end is 186557 paths A2b Position 3 to end is 167723 paths A2b Position 4 to end is 238817 paths A2b Position 5 to end is 238764 paths A2b Position 6 to end is 179931 paths A2b Position 7 to end is 178306 paths A2b Position 8 to end is 173131 paths 
firstset
secondset
[158191\displaystyle 158191, 173187\displaystyle 173187, 103870\displaystyle 103870, 179807\displaystyle 179807, 181266\displaystyle 181266, 141273\displaystyle 141273, 167723\displaystyle 167723, 126958\displaystyle 126958]
[181266\displaystyle 181266, 186557\displaystyle 186557, 167723\displaystyle 167723, 238817\displaystyle 238817, 238764\displaystyle 238764, 179931\displaystyle 179931, 178306\displaystyle 178306, 173131\displaystyle 173131]
totaldances=0
for i in [0..len(firstset)-1]:
    totaldances = totaldances + (firstset[i]*secondset[i])
totaldances
241931823417\displaystyle 241931823417
matrix(firstset)*transpose(matrix(secondset))
(241931823417)\displaystyle \left(\begin{array}{r} 241931823417 \end{array}\right)