Double Derived Markov chain w/ contexts

Double Derived Markov chain w/ contexts#

%%capture
%run receptor_tools_cycle_fluxes.ipynb

dG_house = {0: {1: 'a', 2: 'c', 4: 'f'}, 1: {0: 'A', 2: 'b'}, 2: {0: 'C', 1: 'B', 3: 'd'}, 3: {2: 'D', 4: 'e'}, 4: {3: 'E', 0: 'F'}}
dG_c3_handle = {0: {1: 'a', 2: 'c'}, 1: {0: 'A', 2: 'b'}, 2: {0: 'C', 1: 'B', 3: 'd'}, 3: {2: 'D'}}
dG_c4_chord = {0: {1: 'a', 2: 'c', 3: 'e'}, 1: {0: 'A', 2: 'b'}, 2: {0: 'C', 1: 'B', 3: 'd'}, 3: {0: 'E', 2: 'D'}}
dG_c3_tail = {0: {1: 'a', 2: 'C'}, 1: {0: 'A', 2: 'b'}, 2: {0: 'c', 1: 'B', 3: 'd'}, 3: {2: 'd'}}
dG_p2 = {0: {1: 'a'}, 1: {0: 'A'}}
dG_p3 = {0: {1: 'a'}, 1: {0: 'A', 2: 'b'}, 2: {1: 'B'}}
dG_p4 = {0: {1: 'a'}, 1: {0: 'A', 2: 'b'}, 2: {1: 'B', 3: 'c'}, 3: {2: 'C'}}
dG_c3 = {0: {1:'a', 2:'C'}, 1: {0:'A', 2:'b'}, 2: {0:'c', 1:'B'}}

dG = dG_c3 # choose graph here (dG may be used below)

G, Vg = graph_and_edge_ring_from_dict(dG)

nvG, neG, betaG, Tg, TG, cycleG_p, cycleG_m, cycleG_2, cycleG, Jg, dict_vG, inverted_dict_vG, d_cycleG, inverted_d_cycleG =  cycle_flux_analysis(G,str='G')

_images/c6d7849333426151770a367d16e3013bbc3f0c67bb5fee6d0faa47c39b2e68e1.png

[-C - a      a      C]
[     A -b - A      b]
[     c      B -B - c]

For root/cycle [0] : A*B + b*c + A*c 

For root/cycle [1] : C*B + a*B + a*c 

For root/cycle [2] : C*b + a*b + C*A 

G cycles p: [(0, 1, 2, 0)] 

G cycles m: [(0, 2, 1, 0)] 

G cycles 2: [(0, 1, 0), (0, 2, 0), (1, 2, 1)] 

G cycle flux 0 : a * b * c

G cycle flux 1 : C * A * B

G cycle flux 2 : a * A * (B + c)

G cycle flux 3 : C * (b + A) * c

G cycle flux 4 : (C + a) * b * B

dH_c5 = {0: {1: 'v', 2: 'x', 4: 'Z'}, 1: {0: 'V', 2: 'w'}, 2: {1: 'W', 3: 'x'}, 3: {2: 'X', 4: 'y'}, 4: {0: 'z', 3: 'Y'}}
dH_c3 = {0: {1: 'x', 2: 'Z'}, 1: {0: 'X', 2: 'y'}, 2: {0: 'z', 1: 'Y'}}
dH_p4 = {0: {1: 'x'}, 1: {0: 'X', 2: 'y'}, 2: {1: 'Y', 3: 'z'}, 3: {2: 'Z'}}
dH_p3 = {0: {1: 'x'}, 1: {0: 'X', 2: 'y'}, 2: {1: 'Y'}}
dH_p2 = {0: {1: 'x'}, 1: {0: 'X'}}

dH_p2_r2 = {2: {3: 'x'}, 3: {2: 'X'}}
dH_c3_r3 = {3: {4: 'x', 5: 'Z'}, 4: {3: 'X', 5: 'y'}, 5: {3: 'z', 4: 'Y'}}
dH_p3_r3 = {3: {4: 'x'}, 4: {3: 'X', 5: 'y'}, 5: {4: 'Y'}}

dH = copy(dG);
#dH = dH_p2_r2

H, Vh = graph_and_edge_ring_from_dict(dH)
nvH, neH, betaH, Th, TH, cycleH_p, cycleH_m, cycleH_2, cycleH, Jh, dict_vH, inverted_dict_vH, d_cycleH, inverted_d_cycleH =  cycle_flux_analysis(H,str='H')

_images/3034d3f6e9564c02da951de5311fd5612da0e1700e5e9f5858bdc82cf4ec25d5.png

[-C - a      a      C]
[     A -b - A      b]
[     c      B -B - c]

For root/cycle [0] : A*B + b*c + A*c 

For root/cycle [1] : C*B + a*B + a*c 

For root/cycle [2] : C*b + a*b + C*A 

H cycles p: [(0, 1, 2, 0)] 

H cycles m: [(0, 2, 1, 0)] 

H cycles 2: [(0, 1, 0), (0, 2, 0), (1, 2, 1)] 

H cycle flux 0 : a * b * c

H cycle flux 1 : C * A * B

H cycle flux 2 : a * A * (B + c)

H cycle flux 3 : C * (b + A) * c

H cycle flux 4 : (C + a) * b * B

for context in [ False, True ]:
    GH = Cartesian_product(G, H, context=context)
    print(edge_ring_from_graph(GH))
    GH.show(edge_labels=True,figsize=12,graph_border=True,\
           edge_colors=cartesian_edge_color(GH,verbose=False),\
            title='G box H, context = ' + str(context))

GH0 = GH.to_undirected()
GH0.show(edge_labels=False,vertex_labels=False,vertex_size=0,figsize=4,graph_border=True,edge_colors=cartesian_edge_color(GH0,verbose=False),title='G box H')

Multivariate Polynomial Ring in B, C, c, a, A, b over Integer Ring

_images/342fb4b0c22b83b3260ef973e07eb289ed20dbaae8a729be3fe5ec740304a67c.png

Multivariate Polynomial Ring in a2, b2, a0, A1, B0, A2, B2, a1, b1, b0, C1, C2, c0, c1, B1, A0, c2, C0 over Integer Ring

_images/227690c84f4c0d7050207decb9afdd7416db64c4a8520ac032175a739fa3d7f0.png

_images/8f5e653f1335836d762babd14ded40a3a38f9e05b941e211dc3e962e3a88e5fb.png

DerG = derived_graph(G)
DerG.show(edge_labels=True,figsize=8,graph_border=True,title='DerG')

_images/8a82b62c2eab15837a41f49a267350b27623b296027cfdde46097f20988d6dbc.png

DerGrate, DerGcyc = split_derived_graph(DerG)
DerGrate.show(edge_labels=True,figsize=8,graph_border=True,title='DerGrate')
DerGcyc.show(edge_labels=True,figsize=8,graph_border=True,title='DerGcyc')

_images/96fe94c25281945c0f7992fde763e51bb755550afee92791f5bcf2ff9522bbb5.png

_images/6b72d5e515ebd60a9317cd017fe1cf484816f2d1165a5ff6f79d33218a785806.png

dict_Jg = cycle_fluxes_from_derived_graph(DerG,verbose=True)

rooted spanning tree of derived graph T(0,0) = (A*B + b*c + A*c) * (A*B + C*B + a*B + b*c + A*c + a*c + C*b + a*b + C*A) 

J (0, 1, 0) = a * A * (B + c) * (A*B + b*c + A*c) 

J (0, 1, 2, 0) = a * b * c * (A*B + b*c + A*c) 

J (1, 2, 1) = a * b * B * (A*B + b*c + A*c) 

J (0, 2, 0) = C * (b + A) * c * (A*B + b*c + A*c) 

J (0, 2, 1, 0) = C * A * B * (A*B + b*c + A*c) 

J (2, 1, 2) = C * b * B * (A*B + b*c + A*c)

DerH = derived_graph(H)
DerH.show(edge_labels=True,figsize=8,graph_border=True,title='DerH')
DerHrate, DerHcyc = split_derived_graph(DerH)

_images/79ca6a402a6cba204dc34a4298c449b26768126fc2d4113d4d4d4424a358f56b.png

dict_Jh = cycle_fluxes_from_derived_graph(DerH,verbose=True)

rooted spanning tree of derived graph T(0,0) = (A*B + b*c + A*c) * (A*B + C*B + a*B + b*c + A*c + a*c + C*b + a*b + C*A) 

J (0, 1, 0) = a * A * (B + c) * (A*B + b*c + A*c) 

J (0, 1, 2, 0) = a * b * c * (A*B + b*c + A*c) 

J (1, 2, 1) = a * b * B * (A*B + b*c + A*c) 

J (0, 2, 0) = C * (b + A) * c * (A*B + b*c + A*c) 

J (0, 2, 1, 0) = C * A * B * (A*B + b*c + A*c) 

J (2, 1, 2) = C * b * B * (A*B + b*c + A*c)

for context in [ False, True]:
    for reduce in [ False, True]:
        print('***')
        print('*** context =', str(context), '  reduce =', str(reduce))
        print('***')
        DDerGH = double_derived_graph(DerG,DerH,context=context,reduce=reduce)
        print(edge_ring_from_derived_graph(DDerGH))
        DDerGH.show(edge_labels=True,figsize=12,graph_border=True,\
                title='DDerGH '+'nv ='+str(DDerGH.order())+'  ne = '+str(DDerGH.size()))
        DDerGH0 = DDerGH.to_undirected()
        if reduce==False:
            edge_colors=cartesian_edge_color(DDerGH0,verbose=False)
        else:
            edge_colors=None
        DDerGH0.show(edge_colors=edge_colors,vertex_size=0,\
                     vertex_labels=False,graph_border=True,title='DDer G box H')

***
*** context = False   reduce = False
***
Multivariate Polynomial Ring in B, C, c, a, A, b over Integer Ring

_images/99adc1f28b9c844d2a0b4400a3a531ebb7a0293cc7cab55c4f7688473480b663.png

_images/b1f3ef578de331ff2bb457677c64feb4524b4ad6890cdf7e6e51f28898bfcb95.png

***
*** context = False   reduce = True
***
Multivariate Polynomial Ring in B, C, c, a, A, b over Integer Ring

_images/60b771d948adccc62abb674cb4dcfdb699f8108cb91af7212dc2d30266831332.png

_images/95eb5dad02a9ab60e02e9bbf3c4509669e0ba0040e3d345b1f81ac789f572c5d.png

***
*** context = True   reduce = False
***
Multivariate Polynomial Ring in a2, b2, a0, A1, B0, A2, B2, a1, b1, b0, C1, C2, c0, c1, B1, A0, c2, C0 over Integer Ring

_images/fb7bde40c06ae6afc7c13bb4863988b06833b284c8e0403629fdbb17838fd2bc.png

_images/9e9860d6dbae70ffa0d08451ef7deb2576712d0138c01b0f15054667cbad94b9.png

***
*** context = True   reduce = True
***
Multivariate Polynomial Ring in a2, b2, a0, A1, B0, A2, B2, a1, b1, b0, C1, C2, c0, c1, B1, A0, c2, C0 over Integer Ring

_images/a1a97c4a86aeb9b21adb2d51d680793b75c2f085487cd1e75122dfc37a13adb0.png

_images/460c14a14cc44e55dbc6e2c247d06d5dae6c901dc9903e053f4f453dc49c7496.png

DDerGH = double_derived_graph(DerG,DerH,context=False,reduce=True)
dict_Jg_lumped_merge = cycle_fluxes_from_derived_graph(DDerGH,verbose=False,big=False)
for key in dict_Jg_lumped_merge:
    print(key,':',dict_Jg_lumped_merge[key],'\n')

(0, 1, 0) : 2^5 * A * a * (B + c) * (B + c + A + b) * (B + C + c + a + A + b) * (B*A + c*A + c*b)^2 * (B*C + B*a + c*a + B*A + C*A + c*A + C*b + c*b + a*b) * (2*B^3*C + 2*B^2*C^2 + 4*B^2*C*c + B*C^2*c + 2*B*C*c^2 + 2*B^3*a + 4*B^2*C*a + 6*B^2*c*a + 5*B*C*c*a + 6*B*c^2*a + C*c^2*a + 2*c^3*a + 2*B^2*a^2 + 4*B*c*a^2 + 2*c^2*a^2 + 4*B^3*A + 10*B^2*C*A + 5*B*C^2*A + 12*B^2*c*A + 16*B*C*c*A + 2*C^2*c*A + 12*B*c^2*A + 6*C*c^2*A + 4*c^3*A + 8*B^2*a*A + 7*B*C*a*A + 16*B*c*a*A + 6*C*c*a*A + 8*c^2*a*A + 2*B*a^2*A + 2*c*a^2*A + 8*B^2*A^2 + 10*B*C*A^2 + 2*C^2*A^2 + 16*B*c*A^2 + 8*C*c*A^2 + 8*c^2*A^2 + 6*B*a*A^2 + C*a*A^2 + 6*c*a*A^2 + 4*B*A^3 + 2*C*A^3 + 4*c*A^3 + 6*B^2*C*b + 4*B*C^2*b + 4*B^2*c*b + 12*B*C*c*b + 2*C^2*c*b + 8*B*c^2*b + 6*C*c^2*b + 4*c^3*b + 6*B^2*a*b + 8*B*C*a*b + 16*B*c*a*b + 7*C*c*a*b + 10*c^2*a*b + 4*B*a^2*b + 5*c*a^2*b + 8*B^2*A*b + 16*B*C*A*b + 4*C^2*A*b + 24*B*c*A*b + 16*C*c*A*b + 16*c^2*A*b + 12*B*a*A*b + 5*C*a*A*b + 16*c*a*A*b + a^2*A*b + 8*B*A^2*b + 6*C*A^2*b + 12*c*A^2*b + 2*a*A^2*b + 6*B*C*b^2 + 2*C^2*b^2 + 8*B*c*b^2 + 8*C*c*b^2 + 8*c^2*b^2 + 6*B*a*b^2 + 4*C*a*b^2 + 10*c*a*b^2 + 2*a^2*b^2 + 4*B*A*b^2 + 6*C*A*b^2 + 12*c*A*b^2 + 4*a*A*b^2 + 2*C*b^3 + 4*c*b^3 + 2*a*b^3) 

(0, 1, 2, 0) : 2^5 * b * a * c * (B + c + A + b) * (B + C + c + a + A + b) * (B*A + c*A + c*b)^2 * (B*C + B*a + c*a + B*A + C*A + c*A + C*b + c*b + a*b) * (2*B^3*C + 2*B^2*C^2 + 4*B^2*C*c + B*C^2*c + 2*B*C*c^2 + 2*B^3*a + 4*B^2*C*a + 6*B^2*c*a + 5*B*C*c*a + 6*B*c^2*a + C*c^2*a + 2*c^3*a + 2*B^2*a^2 + 4*B*c*a^2 + 2*c^2*a^2 + 4*B^3*A + 10*B^2*C*A + 5*B*C^2*A + 12*B^2*c*A + 16*B*C*c*A + 2*C^2*c*A + 12*B*c^2*A + 6*C*c^2*A + 4*c^3*A + 8*B^2*a*A + 7*B*C*a*A + 16*B*c*a*A + 6*C*c*a*A + 8*c^2*a*A + 2*B*a^2*A + 2*c*a^2*A + 8*B^2*A^2 + 10*B*C*A^2 + 2*C^2*A^2 + 16*B*c*A^2 + 8*C*c*A^2 + 8*c^2*A^2 + 6*B*a*A^2 + C*a*A^2 + 6*c*a*A^2 + 4*B*A^3 + 2*C*A^3 + 4*c*A^3 + 6*B^2*C*b + 4*B*C^2*b + 4*B^2*c*b + 12*B*C*c*b + 2*C^2*c*b + 8*B*c^2*b + 6*C*c^2*b + 4*c^3*b + 6*B^2*a*b + 8*B*C*a*b + 16*B*c*a*b + 7*C*c*a*b + 10*c^2*a*b + 4*B*a^2*b + 5*c*a^2*b + 8*B^2*A*b + 16*B*C*A*b + 4*C^2*A*b + 24*B*c*A*b + 16*C*c*A*b + 16*c^2*A*b + 12*B*a*A*b + 5*C*a*A*b + 16*c*a*A*b + a^2*A*b + 8*B*A^2*b + 6*C*A^2*b + 12*c*A^2*b + 2*a*A^2*b + 6*B*C*b^2 + 2*C^2*b^2 + 8*B*c*b^2 + 8*C*c*b^2 + 8*c^2*b^2 + 6*B*a*b^2 + 4*C*a*b^2 + 10*c*a*b^2 + 2*a^2*b^2 + 4*B*A*b^2 + 6*C*A*b^2 + 12*c*A*b^2 + 4*a*A*b^2 + 2*C*b^3 + 4*c*b^3 + 2*a*b^3) 

(1, 2, 1) : 2^5 * b * (C + a) * B * (B + c + A + b) * (B + C + c + a + A + b) * (B*A + c*A + c*b)^2 * (B*C + B*a + c*a + B*A + C*A + c*A + C*b + c*b + a*b) * (2*B^3*C + 2*B^2*C^2 + 4*B^2*C*c + B*C^2*c + 2*B*C*c^2 + 2*B^3*a + 4*B^2*C*a + 6*B^2*c*a + 5*B*C*c*a + 6*B*c^2*a + C*c^2*a + 2*c^3*a + 2*B^2*a^2 + 4*B*c*a^2 + 2*c^2*a^2 + 4*B^3*A + 10*B^2*C*A + 5*B*C^2*A + 12*B^2*c*A + 16*B*C*c*A + 2*C^2*c*A + 12*B*c^2*A + 6*C*c^2*A + 4*c^3*A + 8*B^2*a*A + 7*B*C*a*A + 16*B*c*a*A + 6*C*c*a*A + 8*c^2*a*A + 2*B*a^2*A + 2*c*a^2*A + 8*B^2*A^2 + 10*B*C*A^2 + 2*C^2*A^2 + 16*B*c*A^2 + 8*C*c*A^2 + 8*c^2*A^2 + 6*B*a*A^2 + C*a*A^2 + 6*c*a*A^2 + 4*B*A^3 + 2*C*A^3 + 4*c*A^3 + 6*B^2*C*b + 4*B*C^2*b + 4*B^2*c*b + 12*B*C*c*b + 2*C^2*c*b + 8*B*c^2*b + 6*C*c^2*b + 4*c^3*b + 6*B^2*a*b + 8*B*C*a*b + 16*B*c*a*b + 7*C*c*a*b + 10*c^2*a*b + 4*B*a^2*b + 5*c*a^2*b + 8*B^2*A*b + 16*B*C*A*b + 4*C^2*A*b + 24*B*c*A*b + 16*C*c*A*b + 16*c^2*A*b + 12*B*a*A*b + 5*C*a*A*b + 16*c*a*A*b + a^2*A*b + 8*B*A^2*b + 6*C*A^2*b + 12*c*A^2*b + 2*a*A^2*b + 6*B*C*b^2 + 2*C^2*b^2 + 8*B*c*b^2 + 8*C*c*b^2 + 8*c^2*b^2 + 6*B*a*b^2 + 4*C*a*b^2 + 10*c*a*b^2 + 2*a^2*b^2 + 4*B*A*b^2 + 6*C*A*b^2 + 12*c*A*b^2 + 4*a*A*b^2 + 2*C*b^3 + 4*c*b^3 + 2*a*b^3) 

(0, 2, 0) : 2^5 * (A + b) * c * C * (B + c + A + b) * (B + C + c + a + A + b) * (B*A + c*A + c*b)^2 * (B*C + B*a + c*a + B*A + C*A + c*A + C*b + c*b + a*b) * (2*B^3*C + 2*B^2*C^2 + 4*B^2*C*c + B*C^2*c + 2*B*C*c^2 + 2*B^3*a + 4*B^2*C*a + 6*B^2*c*a + 5*B*C*c*a + 6*B*c^2*a + C*c^2*a + 2*c^3*a + 2*B^2*a^2 + 4*B*c*a^2 + 2*c^2*a^2 + 4*B^3*A + 10*B^2*C*A + 5*B*C^2*A + 12*B^2*c*A + 16*B*C*c*A + 2*C^2*c*A + 12*B*c^2*A + 6*C*c^2*A + 4*c^3*A + 8*B^2*a*A + 7*B*C*a*A + 16*B*c*a*A + 6*C*c*a*A + 8*c^2*a*A + 2*B*a^2*A + 2*c*a^2*A + 8*B^2*A^2 + 10*B*C*A^2 + 2*C^2*A^2 + 16*B*c*A^2 + 8*C*c*A^2 + 8*c^2*A^2 + 6*B*a*A^2 + C*a*A^2 + 6*c*a*A^2 + 4*B*A^3 + 2*C*A^3 + 4*c*A^3 + 6*B^2*C*b + 4*B*C^2*b + 4*B^2*c*b + 12*B*C*c*b + 2*C^2*c*b + 8*B*c^2*b + 6*C*c^2*b + 4*c^3*b + 6*B^2*a*b + 8*B*C*a*b + 16*B*c*a*b + 7*C*c*a*b + 10*c^2*a*b + 4*B*a^2*b + 5*c*a^2*b + 8*B^2*A*b + 16*B*C*A*b + 4*C^2*A*b + 24*B*c*A*b + 16*C*c*A*b + 16*c^2*A*b + 12*B*a*A*b + 5*C*a*A*b + 16*c*a*A*b + a^2*A*b + 8*B*A^2*b + 6*C*A^2*b + 12*c*A^2*b + 2*a*A^2*b + 6*B*C*b^2 + 2*C^2*b^2 + 8*B*c*b^2 + 8*C*c*b^2 + 8*c^2*b^2 + 6*B*a*b^2 + 4*C*a*b^2 + 10*c*a*b^2 + 2*a^2*b^2 + 4*B*A*b^2 + 6*C*A*b^2 + 12*c*A*b^2 + 4*a*A*b^2 + 2*C*b^3 + 4*c*b^3 + 2*a*b^3) 

(0, 2, 1, 0) : 2^5 * A * C * B * (B + c + A + b) * (B + C + c + a + A + b) * (B*A + c*A + c*b)^2 * (B*C + B*a + c*a + B*A + C*A + c*A + C*b + c*b + a*b) * (2*B^3*C + 2*B^2*C^2 + 4*B^2*C*c + B*C^2*c + 2*B*C*c^2 + 2*B^3*a + 4*B^2*C*a + 6*B^2*c*a + 5*B*C*c*a + 6*B*c^2*a + C*c^2*a + 2*c^3*a + 2*B^2*a^2 + 4*B*c*a^2 + 2*c^2*a^2 + 4*B^3*A + 10*B^2*C*A + 5*B*C^2*A + 12*B^2*c*A + 16*B*C*c*A + 2*C^2*c*A + 12*B*c^2*A + 6*C*c^2*A + 4*c^3*A + 8*B^2*a*A + 7*B*C*a*A + 16*B*c*a*A + 6*C*c*a*A + 8*c^2*a*A + 2*B*a^2*A + 2*c*a^2*A + 8*B^2*A^2 + 10*B*C*A^2 + 2*C^2*A^2 + 16*B*c*A^2 + 8*C*c*A^2 + 8*c^2*A^2 + 6*B*a*A^2 + C*a*A^2 + 6*c*a*A^2 + 4*B*A^3 + 2*C*A^3 + 4*c*A^3 + 6*B^2*C*b + 4*B*C^2*b + 4*B^2*c*b + 12*B*C*c*b + 2*C^2*c*b + 8*B*c^2*b + 6*C*c^2*b + 4*c^3*b + 6*B^2*a*b + 8*B*C*a*b + 16*B*c*a*b + 7*C*c*a*b + 10*c^2*a*b + 4*B*a^2*b + 5*c*a^2*b + 8*B^2*A*b + 16*B*C*A*b + 4*C^2*A*b + 24*B*c*A*b + 16*C*c*A*b + 16*c^2*A*b + 12*B*a*A*b + 5*C*a*A*b + 16*c*a*A*b + a^2*A*b + 8*B*A^2*b + 6*C*A^2*b + 12*c*A^2*b + 2*a*A^2*b + 6*B*C*b^2 + 2*C^2*b^2 + 8*B*c*b^2 + 8*C*c*b^2 + 8*c^2*b^2 + 6*B*a*b^2 + 4*C*a*b^2 + 10*c*a*b^2 + 2*a^2*b^2 + 4*B*A*b^2 + 6*C*A*b^2 + 12*c*A*b^2 + 4*a*A*b^2 + 2*C*b^3 + 4*c*b^3 + 2*a*b^3)

DDerGH = double_derived_graph(DerG,DerH,context=True,reduce=True)
dict_Jg_lumped_merge = cycle_fluxes_from_derived_graph(DDerGH,verbose=False,big=False)
for key in dict_Jg_lumped_merge:
    print(key,':',dict_Jg_lumped_merge[key],'\n')

(0, 1, 0) : 2^5 * (B2 + c2) * A1 * (A1 + B2 + b1 + c2) * a0 * (a0 + A1 + B2 + b1 + c2 + C0) * (A1*B2 + A1*c2 + b1*c2)^2 * (a0*B2 + A1*B2 + a0*b1 + a0*c2 + A1*c2 + b1*c2 + A1*C0 + B2*C0 + b1*C0) * (2*a0^2*A1*B2 + 6*a0*A1^2*B2 + 4*A1^3*B2 + 2*a0^2*B2^2 + 8*a0*A1*B2^2 + 8*A1^2*B2^2 + 2*a0*B2^3 + 4*A1*B2^3 + a0^2*A1*b1 + 2*a0*A1^2*b1 + 4*a0^2*B2*b1 + 12*a0*A1*B2*b1 + 8*A1^2*B2*b1 + 6*a0*B2^2*b1 + 8*A1*B2^2*b1 + 2*a0^2*b1^2 + 4*a0*A1*b1^2 + 6*a0*B2*b1^2 + 4*A1*B2*b1^2 + 2*a0*b1^3 + 2*a0^2*A1*c2 + 6*a0*A1^2*c2 + 4*A1^3*c2 + 4*a0^2*B2*c2 + 16*a0*A1*B2*c2 + 16*A1^2*B2*c2 + 6*a0*B2^2*c2 + 12*A1*B2^2*c2 + 5*a0^2*b1*c2 + 16*a0*A1*b1*c2 + 12*A1^2*b1*c2 + 16*a0*B2*b1*c2 + 24*A1*B2*b1*c2 + 4*B2^2*b1*c2 + 10*a0*b1^2*c2 + 12*A1*b1^2*c2 + 8*B2*b1^2*c2 + 4*b1^3*c2 + 2*a0^2*c2^2 + 8*a0*A1*c2^2 + 8*A1^2*c2^2 + 6*a0*B2*c2^2 + 12*A1*B2*c2^2 + 10*a0*b1*c2^2 + 16*A1*b1*c2^2 + 8*B2*b1*c2^2 + 8*b1^2*c2^2 + 2*a0*c2^3 + 4*A1*c2^3 + 4*b1*c2^3 + a0*A1^2*C0 + 2*A1^3*C0 + 7*a0*A1*B2*C0 + 10*A1^2*B2*C0 + 4*a0*B2^2*C0 + 10*A1*B2^2*C0 + 2*B2^3*C0 + 5*a0*A1*b1*C0 + 6*A1^2*b1*C0 + 8*a0*B2*b1*C0 + 16*A1*B2*b1*C0 + 6*B2^2*b1*C0 + 4*a0*b1^2*C0 + 6*A1*b1^2*C0 + 6*B2*b1^2*C0 + 2*b1^3*C0 + 6*a0*A1*c2*C0 + 8*A1^2*c2*C0 + 5*a0*B2*c2*C0 + 16*A1*B2*c2*C0 + 4*B2^2*c2*C0 + 7*a0*b1*c2*C0 + 16*A1*b1*c2*C0 + 12*B2*b1*c2*C0 + 8*b1^2*c2*C0 + a0*c2^2*C0 + 6*A1*c2^2*C0 + 2*B2*c2^2*C0 + 6*b1*c2^2*C0 + 2*A1^2*C0^2 + 5*A1*B2*C0^2 + 2*B2^2*C0^2 + 4*A1*b1*C0^2 + 4*B2*b1*C0^2 + 2*b1^2*C0^2 + 2*A1*c2*C0^2 + B2*c2*C0^2 + 2*b1*c2*C0^2) 

(0, 1, 2, 0) : 2^5 * c2 * b1 * (A1 + B2 + b1 + c2) * a0 * (a0 + A1 + B2 + b1 + c2 + C0) * (A1*B2 + A1*c2 + b1*c2)^2 * (a0*B2 + A1*B2 + a0*b1 + a0*c2 + A1*c2 + b1*c2 + A1*C0 + B2*C0 + b1*C0) * (2*a0^2*A1*B2 + 6*a0*A1^2*B2 + 4*A1^3*B2 + 2*a0^2*B2^2 + 8*a0*A1*B2^2 + 8*A1^2*B2^2 + 2*a0*B2^3 + 4*A1*B2^3 + a0^2*A1*b1 + 2*a0*A1^2*b1 + 4*a0^2*B2*b1 + 12*a0*A1*B2*b1 + 8*A1^2*B2*b1 + 6*a0*B2^2*b1 + 8*A1*B2^2*b1 + 2*a0^2*b1^2 + 4*a0*A1*b1^2 + 6*a0*B2*b1^2 + 4*A1*B2*b1^2 + 2*a0*b1^3 + 2*a0^2*A1*c2 + 6*a0*A1^2*c2 + 4*A1^3*c2 + 4*a0^2*B2*c2 + 16*a0*A1*B2*c2 + 16*A1^2*B2*c2 + 6*a0*B2^2*c2 + 12*A1*B2^2*c2 + 5*a0^2*b1*c2 + 16*a0*A1*b1*c2 + 12*A1^2*b1*c2 + 16*a0*B2*b1*c2 + 24*A1*B2*b1*c2 + 4*B2^2*b1*c2 + 10*a0*b1^2*c2 + 12*A1*b1^2*c2 + 8*B2*b1^2*c2 + 4*b1^3*c2 + 2*a0^2*c2^2 + 8*a0*A1*c2^2 + 8*A1^2*c2^2 + 6*a0*B2*c2^2 + 12*A1*B2*c2^2 + 10*a0*b1*c2^2 + 16*A1*b1*c2^2 + 8*B2*b1*c2^2 + 8*b1^2*c2^2 + 2*a0*c2^3 + 4*A1*c2^3 + 4*b1*c2^3 + a0*A1^2*C0 + 2*A1^3*C0 + 7*a0*A1*B2*C0 + 10*A1^2*B2*C0 + 4*a0*B2^2*C0 + 10*A1*B2^2*C0 + 2*B2^3*C0 + 5*a0*A1*b1*C0 + 6*A1^2*b1*C0 + 8*a0*B2*b1*C0 + 16*A1*B2*b1*C0 + 6*B2^2*b1*C0 + 4*a0*b1^2*C0 + 6*A1*b1^2*C0 + 6*B2*b1^2*C0 + 2*b1^3*C0 + 6*a0*A1*c2*C0 + 8*A1^2*c2*C0 + 5*a0*B2*c2*C0 + 16*A1*B2*c2*C0 + 4*B2^2*c2*C0 + 7*a0*b1*c2*C0 + 16*A1*b1*c2*C0 + 12*B2*b1*c2*C0 + 8*b1^2*c2*C0 + a0*c2^2*C0 + 6*A1*c2^2*C0 + 2*B2*c2^2*C0 + 6*b1*c2^2*C0 + 2*A1^2*C0^2 + 5*A1*B2*C0^2 + 2*B2^2*C0^2 + 4*A1*b1*C0^2 + 4*B2*b1*C0^2 + 2*b1^2*C0^2 + 2*A1*c2*C0^2 + B2*c2*C0^2 + 2*b1*c2*C0^2) 

(1, 2, 1) : 2^5 * b1 * B2 * (A1 + B2 + b1 + c2) * (a0 + C0) * (a0 + A1 + B2 + b1 + c2 + C0) * (A1*B2 + A1*c2 + b1*c2)^2 * (a0*B2 + A1*B2 + a0*b1 + a0*c2 + A1*c2 + b1*c2 + A1*C0 + B2*C0 + b1*C0) * (2*a0^2*A1*B2 + 6*a0*A1^2*B2 + 4*A1^3*B2 + 2*a0^2*B2^2 + 8*a0*A1*B2^2 + 8*A1^2*B2^2 + 2*a0*B2^3 + 4*A1*B2^3 + a0^2*A1*b1 + 2*a0*A1^2*b1 + 4*a0^2*B2*b1 + 12*a0*A1*B2*b1 + 8*A1^2*B2*b1 + 6*a0*B2^2*b1 + 8*A1*B2^2*b1 + 2*a0^2*b1^2 + 4*a0*A1*b1^2 + 6*a0*B2*b1^2 + 4*A1*B2*b1^2 + 2*a0*b1^3 + 2*a0^2*A1*c2 + 6*a0*A1^2*c2 + 4*A1^3*c2 + 4*a0^2*B2*c2 + 16*a0*A1*B2*c2 + 16*A1^2*B2*c2 + 6*a0*B2^2*c2 + 12*A1*B2^2*c2 + 5*a0^2*b1*c2 + 16*a0*A1*b1*c2 + 12*A1^2*b1*c2 + 16*a0*B2*b1*c2 + 24*A1*B2*b1*c2 + 4*B2^2*b1*c2 + 10*a0*b1^2*c2 + 12*A1*b1^2*c2 + 8*B2*b1^2*c2 + 4*b1^3*c2 + 2*a0^2*c2^2 + 8*a0*A1*c2^2 + 8*A1^2*c2^2 + 6*a0*B2*c2^2 + 12*A1*B2*c2^2 + 10*a0*b1*c2^2 + 16*A1*b1*c2^2 + 8*B2*b1*c2^2 + 8*b1^2*c2^2 + 2*a0*c2^3 + 4*A1*c2^3 + 4*b1*c2^3 + a0*A1^2*C0 + 2*A1^3*C0 + 7*a0*A1*B2*C0 + 10*A1^2*B2*C0 + 4*a0*B2^2*C0 + 10*A1*B2^2*C0 + 2*B2^3*C0 + 5*a0*A1*b1*C0 + 6*A1^2*b1*C0 + 8*a0*B2*b1*C0 + 16*A1*B2*b1*C0 + 6*B2^2*b1*C0 + 4*a0*b1^2*C0 + 6*A1*b1^2*C0 + 6*B2*b1^2*C0 + 2*b1^3*C0 + 6*a0*A1*c2*C0 + 8*A1^2*c2*C0 + 5*a0*B2*c2*C0 + 16*A1*B2*c2*C0 + 4*B2^2*c2*C0 + 7*a0*b1*c2*C0 + 16*A1*b1*c2*C0 + 12*B2*b1*c2*C0 + 8*b1^2*c2*C0 + a0*c2^2*C0 + 6*A1*c2^2*C0 + 2*B2*c2^2*C0 + 6*b1*c2^2*C0 + 2*A1^2*C0^2 + 5*A1*B2*C0^2 + 2*B2^2*C0^2 + 4*A1*b1*C0^2 + 4*B2*b1*C0^2 + 2*b1^2*C0^2 + 2*A1*c2*C0^2 + B2*c2*C0^2 + 2*b1*c2*C0^2) 

(0, 2, 0) : 2^5 * C0 * c2 * (A1 + b1) * (A1 + B2 + b1 + c2) * (a0 + A1 + B2 + b1 + c2 + C0) * (A1*B2 + A1*c2 + b1*c2)^2 * (a0*B2 + A1*B2 + a0*b1 + a0*c2 + A1*c2 + b1*c2 + A1*C0 + B2*C0 + b1*C0) * (2*a0^2*A1*B2 + 6*a0*A1^2*B2 + 4*A1^3*B2 + 2*a0^2*B2^2 + 8*a0*A1*B2^2 + 8*A1^2*B2^2 + 2*a0*B2^3 + 4*A1*B2^3 + a0^2*A1*b1 + 2*a0*A1^2*b1 + 4*a0^2*B2*b1 + 12*a0*A1*B2*b1 + 8*A1^2*B2*b1 + 6*a0*B2^2*b1 + 8*A1*B2^2*b1 + 2*a0^2*b1^2 + 4*a0*A1*b1^2 + 6*a0*B2*b1^2 + 4*A1*B2*b1^2 + 2*a0*b1^3 + 2*a0^2*A1*c2 + 6*a0*A1^2*c2 + 4*A1^3*c2 + 4*a0^2*B2*c2 + 16*a0*A1*B2*c2 + 16*A1^2*B2*c2 + 6*a0*B2^2*c2 + 12*A1*B2^2*c2 + 5*a0^2*b1*c2 + 16*a0*A1*b1*c2 + 12*A1^2*b1*c2 + 16*a0*B2*b1*c2 + 24*A1*B2*b1*c2 + 4*B2^2*b1*c2 + 10*a0*b1^2*c2 + 12*A1*b1^2*c2 + 8*B2*b1^2*c2 + 4*b1^3*c2 + 2*a0^2*c2^2 + 8*a0*A1*c2^2 + 8*A1^2*c2^2 + 6*a0*B2*c2^2 + 12*A1*B2*c2^2 + 10*a0*b1*c2^2 + 16*A1*b1*c2^2 + 8*B2*b1*c2^2 + 8*b1^2*c2^2 + 2*a0*c2^3 + 4*A1*c2^3 + 4*b1*c2^3 + a0*A1^2*C0 + 2*A1^3*C0 + 7*a0*A1*B2*C0 + 10*A1^2*B2*C0 + 4*a0*B2^2*C0 + 10*A1*B2^2*C0 + 2*B2^3*C0 + 5*a0*A1*b1*C0 + 6*A1^2*b1*C0 + 8*a0*B2*b1*C0 + 16*A1*B2*b1*C0 + 6*B2^2*b1*C0 + 4*a0*b1^2*C0 + 6*A1*b1^2*C0 + 6*B2*b1^2*C0 + 2*b1^3*C0 + 6*a0*A1*c2*C0 + 8*A1^2*c2*C0 + 5*a0*B2*c2*C0 + 16*A1*B2*c2*C0 + 4*B2^2*c2*C0 + 7*a0*b1*c2*C0 + 16*A1*b1*c2*C0 + 12*B2*b1*c2*C0 + 8*b1^2*c2*C0 + a0*c2^2*C0 + 6*A1*c2^2*C0 + 2*B2*c2^2*C0 + 6*b1*c2^2*C0 + 2*A1^2*C0^2 + 5*A1*B2*C0^2 + 2*B2^2*C0^2 + 4*A1*b1*C0^2 + 4*B2*b1*C0^2 + 2*b1^2*C0^2 + 2*A1*c2*C0^2 + B2*c2*C0^2 + 2*b1*c2*C0^2) 

(0, 2, 1, 0) : 2^5 * C0 * B2 * A1 * (A1 + B2 + b1 + c2) * (a0 + A1 + B2 + b1 + c2 + C0) * (A1*B2 + A1*c2 + b1*c2)^2 * (a0*B2 + A1*B2 + a0*b1 + a0*c2 + A1*c2 + b1*c2 + A1*C0 + B2*C0 + b1*C0) * (2*a0^2*A1*B2 + 6*a0*A1^2*B2 + 4*A1^3*B2 + 2*a0^2*B2^2 + 8*a0*A1*B2^2 + 8*A1^2*B2^2 + 2*a0*B2^3 + 4*A1*B2^3 + a0^2*A1*b1 + 2*a0*A1^2*b1 + 4*a0^2*B2*b1 + 12*a0*A1*B2*b1 + 8*A1^2*B2*b1 + 6*a0*B2^2*b1 + 8*A1*B2^2*b1 + 2*a0^2*b1^2 + 4*a0*A1*b1^2 + 6*a0*B2*b1^2 + 4*A1*B2*b1^2 + 2*a0*b1^3 + 2*a0^2*A1*c2 + 6*a0*A1^2*c2 + 4*A1^3*c2 + 4*a0^2*B2*c2 + 16*a0*A1*B2*c2 + 16*A1^2*B2*c2 + 6*a0*B2^2*c2 + 12*A1*B2^2*c2 + 5*a0^2*b1*c2 + 16*a0*A1*b1*c2 + 12*A1^2*b1*c2 + 16*a0*B2*b1*c2 + 24*A1*B2*b1*c2 + 4*B2^2*b1*c2 + 10*a0*b1^2*c2 + 12*A1*b1^2*c2 + 8*B2*b1^2*c2 + 4*b1^3*c2 + 2*a0^2*c2^2 + 8*a0*A1*c2^2 + 8*A1^2*c2^2 + 6*a0*B2*c2^2 + 12*A1*B2*c2^2 + 10*a0*b1*c2^2 + 16*A1*b1*c2^2 + 8*B2*b1*c2^2 + 8*b1^2*c2^2 + 2*a0*c2^3 + 4*A1*c2^3 + 4*b1*c2^3 + a0*A1^2*C0 + 2*A1^3*C0 + 7*a0*A1*B2*C0 + 10*A1^2*B2*C0 + 4*a0*B2^2*C0 + 10*A1*B2^2*C0 + 2*B2^3*C0 + 5*a0*A1*b1*C0 + 6*A1^2*b1*C0 + 8*a0*B2*b1*C0 + 16*A1*B2*b1*C0 + 6*B2^2*b1*C0 + 4*a0*b1^2*C0 + 6*A1*b1^2*C0 + 6*B2*b1^2*C0 + 2*b1^3*C0 + 6*a0*A1*c2*C0 + 8*A1^2*c2*C0 + 5*a0*B2*c2*C0 + 16*A1*B2*c2*C0 + 4*B2^2*c2*C0 + 7*a0*b1*c2*C0 + 16*A1*b1*c2*C0 + 12*B2*b1*c2*C0 + 8*b1^2*c2*C0 + a0*c2^2*C0 + 6*A1*c2^2*C0 + 2*B2*c2^2*C0 + 6*b1*c2^2*C0 + 2*A1^2*C0^2 + 5*A1*B2*C0^2 + 2*B2^2*C0^2 + 4*A1*b1*C0^2 + 4*B2*b1*C0^2 + 2*b1^2*C0^2 + 2*A1*c2*C0^2 + B2*c2*C0^2 + 2*b1*c2*C0^2)