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Image: ubuntu2004
attach DATA+'poly.sage'
ver 2012.08.08
P=FundamentalPolygon([6,4,2])
Q=P.draw()
Q.show()
Q.save("figura1.eps")

a=latex(pi/2)

list(a)
['\\', 'f', 'r', 'a', 'c', '{', '1', '}', '{', '2', '}', ' ', '\\', ',', ' ', '\\', 'p', 'i']
angulos=[text("$\\frac{\\pi}{2}$",P[0]-0.02*i,fontsize=15)]
sum(angulos,Q)

Q

wc3=WeylGroup(['C',3])
R=Poly(wc3,[6,4,2])
wc3p=R._G  #permutation representation of the group
R.draw()
calculations took 0.630000 seconds of cputime
R.border[0].A()
0.805345730145 - 0.321899935909*I
etiquetas_vertices=sum([text('$P_{'+str(k.a().label)+'}$',(1.07*k.A().real(),1.05*k.A().imag()),rgbcolor=[0,0,0],fontsize=7) for k in R.border])

R.draw()+etiquetas_vertices

R.moebius_invariant()
[ r1 1/2*r1 - 1/2 -3/2*r1 - 1/2] [ 1/2*r1 - 1/2 r1 -r1] [-3/2*r1 - 1/2 -r1 3*r1 + 1]
find_generators(wc3p,[6,4,2])
[(1,2,5,8,7,4)(3,6), (1,3,5,2)(4,7,8,6), (3,4)(5,6)]
L=R.symplectic_group_generators()
L
[ [ 1 0 1 1 0 -1] [ 1 1 1 2 1 -2] [-2 0 -1 0 0 -1] [-1 0 0 0 -1 -1] [ 1 0 1 1 0 -1] [-1 -1 -1 0 0 -1] [-1 1 -1 0 0 0] [-3 -1 -2 -2 -2 1] [ 3 0 2 1 1 0] [ 0 0 0 0 1 1] [ 0 0 0 -1 1 1] [ 0 0 0 -2 -1 3] [ 0 0 0 -1 0 1] [ 0 0 0 -1 -1 2] [ 0 0 0 0 -1 0] [ 0 0 0 0 1 0], [ 0 0 0 -1 0 1], [ 0 0 0 -1 -1 2] ]
R.moebius_invariant()
[ r2 1/2*r2 - 1/2 -3/2*r2 - 1/2] [ 1/2*r2 - 1/2 r2 -r2] [-3/2*r2 - 1/2 -r2 3*r2 + 1]
R.border
[E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, -E2, E11, E12, E13, E14, E15, E16, E17, E18, E19, -E11, E20, E21, E22, E23, E24, E25, E26, E27, E28, -E20, E29, -E8, -E7, -E6, -E5, -E4, -E3, -E10, -E9, -E29, E30, -E17, -E16, -E15, -E14, -E13, -E12, -E19, -E18, -E30, -E1, -E26, -E25, -E24, -E23, -E22, -E21, -E28, -E27]
C7=CyclicPermutationGroup(7)
x=C7.0

R1=Poly(C7,[x,x,x^5])
R1.draw()
calculations took 0.120000 seconds of cputime
I1,m1=R1.moebius_invariant()
pretty_print(I1)
pretty_print(m1)
pretty_print(R1.symplectic_group_generators())
Since equations are not linear, it t can be to solve them. We return an ideal containing all the necessary equations (as polynomials) and a matrix of with the form of the invariant riemann matrices
(x0+125557652x57−4402059x56+17722059x55−165418236x54+74912059x53−271898236x52+221638236x5−1817994,x1+302957652x57−23294118x56+199578236x55−450158236x54+719938236x53−406134118x52+166572059x5−2084497,x2−183614413x57+52074118x56−101202059x55+418794118x54−694494118x53+720434118x52−292292059x5+3781497,x3−574118x57+13578236x56−33974118x55+186938236x54−342738236x53+451258236x52−110842059x5+25471,x4+167214413x57−23532059x56+179794118x55−179882059x54+588094118x53−609474118x52+499934118x5−3139497,x58−11x57+49x56−119x55+210x54−266x53+245x52−165x5+58)Q[x0,x1,x2,x3,x4,x5]\renewcommand{\Bold}[1]{\mathbf{#1}}\left(x_{0} + \frac{1255}{57652} x_{5}^{7} - \frac{440}{2059} x_{5}^{6} + \frac{1772}{2059} x_{5}^{5} - \frac{16541}{8236} x_{5}^{4} + \frac{7491}{2059} x_{5}^{3} - \frac{27189}{8236} x_{5}^{2} + \frac{22163}{8236} x_{5} - \frac{1817}{994}, x_{1} + \frac{3029}{57652} x_{5}^{7} - \frac{2329}{4118} x_{5}^{6} + \frac{19957}{8236} x_{5}^{5} - \frac{45015}{8236} x_{5}^{4} + \frac{71993}{8236} x_{5}^{3} - \frac{40613}{4118} x_{5}^{2} + \frac{16657}{2059} x_{5} - \frac{2084}{497}, x_{2} - \frac{1836}{14413} x_{5}^{7} + \frac{5207}{4118} x_{5}^{6} - \frac{10120}{2059} x_{5}^{5} + \frac{41879}{4118} x_{5}^{4} - \frac{69449}{4118} x_{5}^{3} + \frac{72043}{4118} x_{5}^{2} - \frac{29229}{2059} x_{5} + \frac{3781}{497}, x_{3} - \frac{57}{4118} x_{5}^{7} + \frac{1357}{8236} x_{5}^{6} - \frac{3397}{4118} x_{5}^{5} + \frac{18693}{8236} x_{5}^{4} - \frac{34273}{8236} x_{5}^{3} + \frac{45125}{8236} x_{5}^{2} - \frac{11084}{2059} x_{5} + \frac{254}{71}, x_{4} + \frac{1672}{14413} x_{5}^{7} - \frac{2353}{2059} x_{5}^{6} + \frac{17979}{4118} x_{5}^{5} - \frac{17988}{2059} x_{5}^{4} + \frac{58809}{4118} x_{5}^{3} - \frac{60947}{4118} x_{5}^{2} + \frac{49993}{4118} x_{5} - \frac{3139}{497}, x_{5}^{8} - 11 x_{5}^{7} + 49 x_{5}^{6} - 119 x_{5}^{5} + 210 x_{5}^{4} - 266 x_{5}^{3} + 245 x_{5}^{2} - 165 x_{5} + 58\right)\Bold{Q}[x_{0}, x_{1}, x_{2}, x_{3}, x_{4}, x_{5}]
(x0x1x2x1x3x4x2x4x5)\renewcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr} x_{0} & x_{1} & x_{2} \\ x_{1} & x_{3} & x_{4} \\ x_{2} & x_{4} & x_{5} \end{array}\right)
[(000−1000001−1000001−1111−100011000001000),(000−1000001−1000001−1111−100011000001000),(110−110001000−1−1−1000100−110100−101100−100)]\renewcommand{\Bold}[1]{\mathbf{#1}}\left[\left(\begin{array}{rrrrrr} 0 & 0 & 0 & -1 & 0 & 0 \\ 0 & 0 & 0 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 1 & -1 \\ 1 & 1 & 1 & -1 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \end{array}\right), \left(\begin{array}{rrrrrr} 0 & 0 & 0 & -1 & 0 & 0 \\ 0 & 0 & 0 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 1 & -1 \\ 1 & 1 & 1 & -1 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \end{array}\right), \left(\begin{array}{rrrrrr} 1 & 1 & 0 & -1 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ -1 & -1 & -1 & 0 & 0 & 0 \\ 1 & 0 & 0 & -1 & 1 & 0 \\ 1 & 0 & 0 & -1 & 0 & 1 \\ 1 & 0 & 0 & -1 & 0 & 0 \end{array}\right)\right]
R2=Poly(C7,[x,x^2,x^4])
I2,m2=R2.moebius_invariant()
pretty_print(I2)
pretty_print(m2)
pretty_print(R2.symplectic_group_generators())
calculations took 0.110000 seconds of cputime Since equations are not linear, it t can be to solve them. We return an ideal containing all the necessary equations (as polynomials) and a matrix of with the form of the invariant riemann matrices
(x0−21691x57−19013x56−40513x55−61013x54−256552x53−50513x52−26513x5−81191,x1−64273x57−5613x56−45839x55−81139x54−94439x53−3043156x52−13913x5−638273,x2+1112273x57+15413x56+88939x55+114839x54+4573156x53+153778x52+27726x5+643273,x3+94491x57+26813x56+47013x55+45413x54+71726x53+21726x52+1813x5−46391,x4−916273x57−6713x56−67978x55−25639x54−1579312x53−7156x52+213x5+526273,x58+114x57+498x56+354x55+32932x54+354x53+498x52+114x5+1)Q[x0,x1,x2,x3,x4,x5]\renewcommand{\Bold}[1]{\mathbf{#1}}\left(x_{0} - \frac{216}{91} x_{5}^{7} - \frac{190}{13} x_{5}^{6} - \frac{405}{13} x_{5}^{5} - \frac{610}{13} x_{5}^{4} - \frac{2565}{52} x_{5}^{3} - \frac{505}{13} x_{5}^{2} - \frac{265}{13} x_{5} - \frac{811}{91}, x_{1} - \frac{64}{273} x_{5}^{7} - \frac{56}{13} x_{5}^{6} - \frac{458}{39} x_{5}^{5} - \frac{811}{39} x_{5}^{4} - \frac{944}{39} x_{5}^{3} - \frac{3043}{156} x_{5}^{2} - \frac{139}{13} x_{5} - \frac{638}{273}, x_{2} + \frac{1112}{273} x_{5}^{7} + \frac{154}{13} x_{5}^{6} + \frac{889}{39} x_{5}^{5} + \frac{1148}{39} x_{5}^{4} + \frac{4573}{156} x_{5}^{3} + \frac{1537}{78} x_{5}^{2} + \frac{277}{26} x_{5} + \frac{643}{273}, x_{3} + \frac{944}{91} x_{5}^{7} + \frac{268}{13} x_{5}^{6} + \frac{470}{13} x_{5}^{5} + \frac{454}{13} x_{5}^{4} + \frac{717}{26} x_{5}^{3} + \frac{217}{26} x_{5}^{2} + \frac{18}{13} x_{5} - \frac{463}{91}, x_{4} - \frac{916}{273} x_{5}^{7} - \frac{67}{13} x_{5}^{6} - \frac{679}{78} x_{5}^{5} - \frac{256}{39} x_{5}^{4} - \frac{1579}{312} x_{5}^{3} - \frac{7}{156} x_{5}^{2} + \frac{2}{13} x_{5} + \frac{526}{273}, x_{5}^{8} + \frac{11}{4} x_{5}^{7} + \frac{49}{8} x_{5}^{6} + \frac{35}{4} x_{5}^{5} + \frac{329}{32} x_{5}^{4} + \frac{35}{4} x_{5}^{3} + \frac{49}{8} x_{5}^{2} + \frac{11}{4} x_{5} + 1\right)\Bold{Q}[x_{0}, x_{1}, x_{2}, x_{3}, x_{4}, x_{5}]
(x0x1x2x1x3x4x2x4x5)\renewcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr} x_{0} & x_{1} & x_{2} \\ x_{1} & x_{3} & x_{4} \\ x_{2} & x_{4} & x_{5} \end{array}\right)
[(0100000−10−10000010−1111−110111−101011001),(0−10−100−10−12−10100−11−10000−10−1001−10001000),(101−2200101−21−1−1−1000100−110110000100−11−1)]\renewcommand{\Bold}[1]{\mathbf{#1}}\left[\left(\begin{array}{rrrrrr} 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & -1 & 0 & -1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & -1 \\ 1 & 1 & 1 & -1 & 1 & 0 \\ 1 & 1 & 1 & -1 & 0 & 1 \\ 0 & 1 & 1 & 0 & 0 & 1 \end{array}\right), \left(\begin{array}{rrrrrr} 0 & -1 & 0 & -1 & 0 & 0 \\ -1 & 0 & -1 & 2 & -1 & 0 \\ 1 & 0 & 0 & -1 & 1 & -1 \\ 0 & 0 & 0 & 0 & -1 & 0 \\ -1 & 0 & 0 & 1 & -1 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \end{array}\right), \left(\begin{array}{rrrrrr} 1 & 0 & 1 & -2 & 2 & 0 \\ 0 & 1 & 0 & 1 & -2 & 1 \\ -1 & -1 & -1 & 0 & 0 & 0 \\ 1 & 0 & 0 & -1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & -1 & 1 & -1 \end{array}\right)\right]
riemann_hurwitz(48,3)
[[{'gamma': 0}, [[12, 3, 2], [6, 4, 2], [4, 3, 3]]], [{'gamma': 1}, []]]
suggest_signatures(wc3p,3)
[[6, 4, 2]]
find_generators(wc3p,[3,2,2,2])
[(2,3,4)(5,7,6), (3,4)(5,6), (1,3)(2,5)(4,7)(6,8), (1,3)(2,7)(4,5)(6,8)]
P3=GeodesicPolygon([i,(1+i)/3,(1+3*i)/4])
P3.draw()

G=SymmetricGroup(5)

suggest_signatures(G,34)
[[5, 4, 2, 2]]
P=Poly(G,[5,4,2,2])
P.draw()
calculations took 187.360000 seconds of cputime
Q=FundamentalPolygon([5,4,2,2])
Q.draw()

P.border
[E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E22, E23, E24, -E14, E25, E26, E27, E28, -E9, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E45, E46, E47, E48, E49, E50, -E25, E51, E52, E53, E54, E55, E56, E57, -E36, E58, E59, E60, E61, E62, -E38, -E37, E63, E64, E65, E66, E67, E68, E69, E70, -E18, -E17, E71, E72, -E55, -E54, E73, E74, -E27, -E26, -E50, -E49, E75, E76, E77, E78, E79, E80, E81, E82, -E40, -E39, -E62, E83, E84, E85, E86, E87, -E24, -E23, -E22, E88, E89, E90, -E83, E91, E92, E93, E94, -E81, -E46, -E45, E95, E96, E97, E98, E99, E100, E101, E102, E103, E104, E105, E106, E107, E108, E109, E110, -E64, E111, E112, E113, -E91, -E61, -E60, -E59, E114, E115, -E32, -E31, -E100, E116, E117, E118, E119, E120, -E102, -E101, E121, E122, E123, E124, -E74, E125, -E16, -E15, -E87, -E86, -E34, -E33, -E115, -E114, -E58, E126, -E93, -E92, -E113, -E112, E127, -E3, E128, E129, -E66, -E65, E130, -E5, -E104, -E103, -E120, E131, E132, E133, E134, E135, -E90, -E89, -E88, E136, E137, E138, -E131, E139, E140, E141, -E6, -E130, -E110, -E109, E142, E143, E144, E145, E146, E147, E148, E149, E150, E151, -E42, E152, -E48, E153, E154, E155, -E122, E156, E157, E158, -E139, -E119, -E118, -E117, E159, E160, -E96, -E95, -E147, E161, E162, E163, E164, E165, -E149, -E148, -E44, E166, E167, E168, -E126, -E35, -E85, -E84, -E135, -E134, -E98, -E97, -E160, -E159, -E116, E169, -E141, -E140, -E158, -E157, -E4, -E75, -E10, -E28, -E124, -E123, E170, -E77, -E151, -E150, -E165, E171, E172, E173, E174, E175, -E138, -E137, -E136, E176, E177, E178, -E171, E179, E180, E181, -E78, -E170, -E155, -E154, E182, E183, E184, E185, -E68, E186, E187, E188, E189, E190, -E106, -E41, -E111, -E63, E191, E192, -E166, -E43, E193, E194, -E179, -E164, -E163, -E162, E195, E196, -E143, -E142, -E186, E197, E198, E199, E200, E201, -E188, -E187, -E108, E202, -E8, -E7, -E169, -E99, -E133, -E132, -E175, -E174, -E145, -E144, -E196, -E195, -E161, E203, -E181, -E180, -E194, -E193, -E76, -E127, -E82, -E94, -E168, -E167, E204, -E128, -E190, -E189, -E201, E205, -E70, -E69, E206, E207, -E178, -E177, -E176, -E21, -E20, -E19, -E205, E208, E209, E210, -E129, -E204, -E192, -E191, -E57, -E56, -E72, -E71, -E125, E211, E212, E213, -E12, -E11, -E152, -E105, -E156, -E121, -E30, -E29, -E202, -E107, -E2, -E1, -E208, -E200, -E199, -E198, E214, E215, -E183, -E182, -E211, -E73, -E53, -E52, -E51, -E13, -E213, -E212, -E153, -E47, -E80, -E79, -E203, -E146, -E173, -E172, -E207, -E206, -E185, -E184, -E215, -E214, -E197, -E67, -E210, -E209]
P.loops
[[E24, E15, E16, E17, E18, E19, E20, E21, E22, E23], [E28, E10, E11, E12, E13, E25, E26, E27], [E48, -E10, -E9, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E45, E46, E47], [E50, -E25, -E13, -E12, -E11, E49], [E57, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, E9, E10, E11, E12, E13, E51, E52, E53, E54, E55, E56], [E62, -E38, -E37, -E36, E58, E59, E60, E61], [E70, -E18, -E17, -E16, -E15, -E14, -E13, -E12, -E11, -E10, -E9, E29, E30, E31, E32, E33, E34, E35, E36, E63, E64, E65, E66, E67, E68, E69], [E72, -E55, -E54, -E53, -E52, -E51, E14, E15, E16, E71], [E74, -E27, -E26, -E25, E51, E52, E53, E73], [E75, E4, E5, E6, E7, E8, E9, E10], [E76, -E42, -E41, -E40, -E39, -E38, -E37, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, -E8, -E7, -E6, -E5, -E4], [E80, -E46, -E45, -E44, -E43, E77, E78, E79], [E82, E41, E42, E43, E44, E45, E46, E81], [E85, E35, E58, E59, E60, E61, E83, E84], [E87, -E14, -E13, -E12, -E11, -E10, -E9, E29, E30, E31, E32, E33, E34, E86], [E90, -E83, -E61, -E60, -E59, -E58, -E35, -E34, -E33, -E32, -E31, -E30, -E29, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E88, E89], [E94, -E81, -E46, -E45, -E44, -E43, -E42, -E41, -E40, -E39, -E38, -E37, -E36, E58, E59, E60, E61, E91, E92, E93], [E100, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E95, E96, E97, E98, E99], [E104, E5, E6, E7, E8, E29, E30, E101, E102, E103], [E105, -E41, -E40, -E39, -E38, -E37, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, -E8, -E7, -E6, -E5], [E106, E3, E4, E5, E6, E7, E8, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41], [E110, -E64, -E63, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, -E8, -E7, -E6, -E5, -E4, -E3, E107, E108, E109], [E111, -E40, -E39, -E38, -E37, E63], [E113, -E91, -E61, -E60, -E59, -E58, E36, E37, E38, E39, E40, E112], [E115, E33, E34, E35, E58, E114], [E120, -E102, -E101, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E95, E96, E97, E98, E99, E116, E117, E118, E119], [E124, -E27, -E26, -E25, -E13, -E12, -E11, -E10, -E9, E29, E30, E121, E122, E123], [E125, -E16, -E15, -E14, E51, E52, E53, E73], [E126, -E93, -E92, -E91, -E61, -E60, -E59, -E58], [E127, E4, E5, E6, E7, E8, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40], [E129, -E66, -E65, -E64, -E63, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, -E8, -E7, -E6, -E5, -E4, -E3, E128], [E130, E6, E7, E8, E29, E30, E31, E32, E33, E34, E35, E36, E63, E64], [E133, E99, E116, E117, E118, E119, E131, E132], [E135, -E83, -E61, -E60, -E59, -E58, E36, E37, E38, E39, E40, E41, E42, E43, E44, E95, E96, E97, E98, E134], [E138, -E131, -E119, -E118, -E117, -E116, -E99, -E98, -E97, -E96, -E95, -E44, -E43, -E42, -E41, -E40, -E39, -E38, -E37, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E136, E137], [E141, E7, E8, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E95, E96, E97, E98, E99, E116, E117, E118, E119, E139, E140], [E147, -E44, -E43, -E42, -E41, -E40, -E39, -E38, -E37, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, -E8, -E7, -E6, -E5, -E4, -E3, E107, E108, E142, E143, E144, E145, E146], [E151, E43, E44, E148, E149, E150], [E152, -E10, -E9, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41], [E155, -E122, -E121, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E45, E46, E47, E153, E154], [E156, E5, E6, E7, E8, E29, E30, E121], [E158, -E139, -E119, -E118, -E117, -E116, -E99, -E98, -E97, -E96, -E95, -E44, -E43, -E42, -E41, -E40, -E39, -E38, -E37, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, -E8, -E7, -E6, -E5, E157], [E160, E97, E98, E99, E116, E159], [E165, -E149, -E148, -E44, -E43, -E42, -E41, -E40, -E39, -E38, -E37, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, -E8, -E7, -E6, -E5, -E4, -E3, E107, E108, E142, E143, E144, E145, E146, E161, E162, E163, E164], [E168, -E93, -E92, -E91, -E61, -E60, -E59, -E58, E36, E37, E38, E39, E40, E41, E42, E43, E166, E167], [E169, E7, E8, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E95, E96, E97, E98, E99], [E170, -E77, -E42, -E41, -E40, -E39, -E38, -E37, -E36, -E35, -E34, -E33, -E32, -E31, E121, E122], [E173, E146, E161, E162, E163, E164, E171, E172], [E175, -E131, -E119, -E118, -E117, -E116, -E99, -E98, -E97, -E96, -E95, -E44, -E43, -E42, -E41, -E40, -E39, -E38, -E37, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, -E8, -E7, -E6, -E5, -E4, -E3, E107, E108, E142, E143, E144, E145, E174], [E178, -E171, -E164, -E163, -E162, -E161, -E146, -E145, -E144, -E143, -E142, -E108, -E107, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21, E176, E177], [E181, -E78, -E77, -E42, -E41, -E40, -E39, -E38, -E37, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, -E8, -E7, -E6, -E5, -E4, -E3, E107, E108, E142, E143, E144, E145, E146, E161, E162, E163, E164, E179, E180], [E185, -E68, -E67, -E66, -E65, -E64, -E63, E37, E38, E39, E40, E41, E42, E43, E44, E45, E46, E47, E153, E182, E183, E184], [E186, -E108, -E107, E3, E4, E5, E6, E7, E8, E29, E30, E31, E32, E33, E34, E35, E36, E63, E64, E65, E66, E67], [E190, E107, E108, E187, E188, E189], [E192, -E166, -E43, -E42, -E41, -E40, -E39, -E38, -E37, E191], [E194, -E179, -E164, -E163, -E162, -E161, -E146, -E145, -E144, -E143, -E142, -E108, -E107, E3, E4, E5, E6, E7, E8, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E193], [E196, E144, E145, E146, E161, E195], [E201, -E188, -E187, -E108, -E107, E3, E4, E5, E6, E7, E8, E29, E30, E31, E32, E33, E34, E35, E36, E63, E64, E65, E66, E67, E197, E198, E199, E200], [E202, -E8, -E7, -E6, -E5, -E4, -E3, E107], [E203, -E78, -E77, -E42, -E41, -E40, -E39, -E38, -E37, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, -E8, -E7, -E6, -E5, -E4, -E3, E107, E108, E142, E143, E144, E145, E146], [E204, -E128, E3, E4, E5, E6, E7, E8, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E166], [E205, -E18, -E17, -E16, -E15, -E14, -E13, -E12, -E11, -E10, -E9, E29, E30, E31, E32, E33, E34, E35, E36, E63, E64, E65, E66, E67, E197, E198, E199, E200], [E207, -E171, -E164, -E163, -E162, -E161, -E146, -E145, -E144, -E143, -E142, -E108, -E107, E3, E4, E5, E6, E7, E8, E29, E30, E31, E32, E33, E34, E35, E36, E63, E64, E65, E66, E67, E68, E206], [E208, E1, E2, E3, E4, E5, E6, E7, E8, E29, E30, E31, E32, E33, E34, E35, E36, E63, E64, E65, E66, E67, E197, E198, E199, E200], [E210, -E66, -E65, -E64, -E63, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, -E8, -E7, -E6, -E5, -E4, -E3, -E2, -E1, E209], [E211, -E153, -E47, -E46, -E45, -E44, -E43, -E42, -E41, -E40, -E39, -E38, -E37, -E36, -E35, -E34, -E33, -E32, -E31, -E30, -E29, E9, E10, E11, E12, E13, E51, E52, E53, E73], [E213, -E12, -E11, -E10, -E9, E29, E30, E31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, E44, E45, E46, E47, E153, E212], [E215, -E183, -E182, -E153, -E47, -E46, -E45, -E44, -E43, -E42, -E41, -E40, -E39, -E38, -E37, E63, E64, E65, E66, E67, E197, E214]]
P.relations()
['a^4cba^2bca^2b^-2a^-4', 'a^4cba^2bc^-1a^2b^-2a^-4', 'a^4cba^2bab^-1a^-2b^-1c^-1a^-1', 'a^4cba^2ba^-1b^-1a^-2b^-1c^-1a^-2', 'a^4cba^2b^2a^2b^-1c^-1a^-1', 'a^4cba^2b^-1a^-2b^-1a^-2', 'a^4cba^2ca^-2c^-1a^-3', 'a^4cba^2c^-1a^-2c^-1a^-3', 'a^4cba^-2ba^-2b^-1', 'a^4cba^-2b^-2a^-2b^-1c^-1a^-2', 'a^4cba^-2cb^-1a^-2b^-2a^-4', 'a^4cba^-2c^-1b^-1a^-2b^-2a^-4', 'a^4cba^-1ba^-1c^-1a^-4', 'a^4cba^-1b^-1a^-1b^-1', 'a^4cba^-1ca^2c^-1a^-1', 'a^4cba^-1c^-1a^2c^-1a^-1', 'a^4cb^2ac^-1', 'a^4cb^-2ac^-1', 'a^4cb^-1cb^-1a^-4', 'a^4cb^-1c^-1b^-1a^-4', 'a^4cb^-1abc^-1a^-3', 'a^4cb^-1a^-1bc^-1', 'bcbc^-1', 'bc^-1bc^-1', 'babab^-1c^-1a^-4', 'bab^-1ab^-2', 'baca^-1b^-1c^-1', 'bac^-1a^-1b^-1c^-1', 'ba^2ba^-2b^-1c^-1a^-2', 'ba^2b^-1a^2b^-1c^-1a^-4', 'ba^2ca^-2b^-2a^-4', 'ba^2c^-1a^-2b^-2a^-4', 'ba^4ba^-1', 'ba^-1ba^-1', 'b^2cac^-1a^-1', 'b^2c^-1ac^-1a^-1', 'b^2aba^2c^-1a^-2', 'b^2ab^-1ab', 'b^2aca^-1c^-1', 'b^2ac^-1a^-1c^-1', 'b^2a^2bca^2b^-1c^-1', 'b^2a^2bc^-1a^2b^-1c^-1', 'b^2a^2bab^-1a^-2b^-2a^-3', 'b^2a^2ba^-1b^-1a^-2b^-2a^-2', 'b^2a^2b^2a^2b^-2a^-3', 'b^2a^2b^-1a^-2c^-1a^-2', 'b^2a^2ca^-2b^-1a^-1', 'b^2a^2c^-1a^-2b^-1a^-1', 'b^2a^-2ba^-2c^-1a^-4', 'b^2a^-2b^-2a^-2b^-2a^-2', 'b^2a^-2cb^-1a^-2b^-1c^-1', 'b^2a^-2c^-1b^-1a^-2b^-1c^-1', 'b^2a^-1ba^-1b^-1', 'b^2a^-1b^-1a^-1c^-1a^-4', 'b^2a^-1caba^-4', 'b^2a^-1c^-1aba^-4', 'b^-1cb^-1c^-1', 'b^-1c^-1b^-1c^-1', 'b^-1ab^-1a^-4', 'b^-1a^-4b^-1a^-4', 'b^-1a^-1ba^-1b^-2', 'b^-1a^-1b^-1a^-1b^-1c^-1a^-1', 'b^-1a^-1cab^-2a^-1', 'b^-1a^-1c^-1ab^-2a^-1', 'cabab^-2a^-1', 'cab^-1ab^-1c^-1', 'caca^-1b^-2', 'cac^-1a^-1b^-2', 'ca^2ba^-2b^-2a^-3', 'ca^2b^-1a^2b^-2a^-1', 'ca^2ca^-2b^-1c^-1a^-1', 'ca^2c^-1a^-2b^-1c^-1a^-1', 'ca^-2ba^-1b^-1c^-1a^-4', 'ca^-2b^-1a^-1b^-2a^-3', 'ca^-2cab^-1c^-1a^-3', 'ca^-2c^-1ab^-1c^-1a^-3', 'ca^-1b^2c^-1a^-4', 'ca^-1b^-2c^-1a^-4', 'ca^-1cb^-2a^-4', 'ca^-1c^-1b^-2a^-4', 'cbcb', 'cbc^-1b', 'cbababa^-4', 'cbab^-1a^2c^-1a^-1', 'cbaca^-1b^-1', 'cbac^-1a^-1b^-1']
find_generators(G,[5,4,2,2])
[(1,2,3,4,5), (2,3,4,5), (3,5), (1,5)(2,4)]
M=P.symplectic_group_generators()[0]

pretty_print(M)
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0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & -1 & -1 & -1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 2 & 0 & 0 & 0 & 1 & -1 & 1 & -2 & 1 & -1 & -1 & -1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & -1 & -1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & 1 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & -1 & -1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & -1 & 1 & 1 & 0 & -1 & -1 & -1 & 0 & -1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 0 & -1 & -1 & -1 & 0 & -1 & 0 & -1 & 1 & 1 & 0 & -1 & -1 & -1 & 0 & -1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & -1 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & -1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right)
A=P.moebius_invariant()

pretty_print(A)
WARNING: Output truncated! <html><a target='_new' href='/home/abehn/14/cells/35/full_output.txt' class='file_link'>full_output.txt</a></html>
$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr} -\frac{2}{3} \, r_{10} + \frac{8}{3} \, r_{11} - 2 \, r_{3} - 3 \, r_{4} + \frac{10}{3} \, r_{5} + \frac{19}{3} \, r_{6} + 12 \, r_{7} - \frac{4}{3} \, r_{8} + \frac{5}{3} \, r_{9} - \frac{5}{2} & \frac{5}{3} \, r_{10} - \frac{14}{3} \, r_{11} + 4 \, r_{3} + 5 \, r_{4} - \frac{19}{3} \, r_{5} - \frac{37}{3} \, r_{6} - 23 \, r_{7} + \frac{7}{3} \, r_{8} - \frac{11}{3} \, r_{9} + \frac{9}{2} & -\frac{11}{3} \, r_{10} + \frac{2}{3} \, r_{11} - 2 \, r_{3} - 2 \, r_{4} + \frac{4}{3} \, r_{5} + \frac{7}{3} \, r_{6} + 8 \, r_{7} - \frac{4}{3} \, r_{8} + \frac{5}{3} \, r_{9} - \frac{5}{2} & -3 \, r_{11} - 2 \, r_{3} - 2 \, r_{5} - \frac{9}{2} \, r_{6} - 5 \, r_{7} + \frac{1}{2} \, r_{9} - 1 & -\frac{1}{3} \, r_{10} - \frac{11}{3} \, r_{11} - 2 \, r_{3} + r_{4} - \frac{7}{3} \, r_{5} - \frac{16}{3} \, r_{6} - 6 \, r_{7} + \frac{1}{3} \, r_{8} + \frac{1}{3} \, r_{9} - 1 & \frac{8}{3} \, r_{10} - \frac{8}{3} \, r_{11} - 3 \, r_{3} - \frac{1}{3} \, r_{5} - \frac{5}{6} \, r_{6} - 2 \, r_{7} + \frac{1}{3} \, r_{8} + \frac{11}{6} \, r_{9} - \frac{1}{2} & -r_{10} + 2 \, r_{11} + 2 \, r_{5} + \frac{7}{2} \, r_{6} + 5 \, r_{7} - \frac{1}{2} \, r_{9} - \frac{1}{2} & r_{3} + r_{6} + 1 & -3 \, r_{10} + 2 \, r_{11} + 2 \, r_{3} - r_{4} + r_{5} + 2 \, r_{6} + 3 \, r_{7} - r_{8} - r_{9} + 1 & r_{11} - r_{3} - 2 \, r_{4} + r_{5} + 2 \, r_{6} + 4 \, r_{7} - r_{8} - 1 & -3 \, r_{10} - r_{11} + r_{3} + r_{4} - 2 \, r_{5} - \frac{9}{2} \, r_{6} - 5 \, r_{7} - \frac{3}{2} \, r_{9} + \frac{1}{2} & -2 \, r_{11} + 3 \, r_{3} + 6 \, r_{4} - 3 \, r_{5} - 8 \, r_{6} - 14 \, r_{7} + 2 \, r_{8} - 2 \, r_{9} + 3 & \frac{2}{3} \, r_{10} - \frac{8}{3} \, r_{11} + 3 \, r_{3} + 4 \, r_{4} - \frac{10}{3} \, r_{5} - \frac{53}{6} \, r_{6} - 15 \, r_{7} + \frac{4}{3} \, r_{8} - \frac{13}{6} \, r_{9} + 3 & -\frac{4}{3} \, r_{10} + \frac{1}{3} \, r_{11} - 2 \, r_{3} - 2 \, r_{4} + \frac{2}{3} \, r_{5} + \frac{13}{6} \, r_{6} + 5 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{5}{6} \, r_{9} - 2 & \frac{2}{3} \, r_{10} + \frac{1}{3} \, r_{11} + 2 \, r_{3} + 2 \, r_{4} - \frac{1}{3} \, r_{5} - \frac{7}{3} \, r_{6} - 4 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{5}{3} \, r_{9} + \frac{3}{2} & r_{10} - r_{3} - r_{4} + r_{5} + \frac{7}{2} \, r_{6} + 4 \, r_{7} + \frac{3}{2} \, r_{9} - \frac{1}{2} & -\frac{5}{3} \, r_{10} - \frac{4}{3} \, r_{11} - 3 \, r_{3} - 2 \, r_{4} - \frac{2}{3} \, r_{5} + \frac{5}{6} \, r_{6} + 4 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{13}{6} \, r_{9} - \frac{5}{2} & \frac{1}{3} \, r_{10} + \frac{2}{3} \, r_{11} + r_{3} - r_{4} + \frac{1}{3} \, r_{5} + \frac{5}{6} \, r_{6} + 2 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{1}{6} \, r_{9} + \frac{1}{2} & -\frac{1}{3} \, r_{10} + \frac{4}{3} \, r_{11} - r_{3} - 2 \, r_{4} + \frac{2}{3} \, r_{5} + \frac{5}{3} \, r_{6} + 5 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{1}{3} \, r_{9} - \frac{3}{2} & -2 \, r_{10} + r_{11} - r_{3} - 2 \, r_{4} + r_{5} + \frac{5}{2} \, r_{6} + 6 \, r_{7} - r_{8} + \frac{1}{2} \, r_{9} - \frac{3}{2} & -\frac{8}{3} \, r_{10} + \frac{2}{3} \, r_{11} - 2 \, r_{3} + \frac{1}{3} \, r_{5} + \frac{4}{3} \, r_{6} + 3 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{2}{3} \, r_{9} - \frac{3}{2} & r_{7} & -4 \, r_{10} + r_{11} - 2 \, r_{3} + r_{4} + \frac{1}{2} \, r_{6} + 3 \, r_{7} + \frac{1}{2} \, r_{9} - \frac{3}{2} & -\frac{1}{2} \, r_{6} - \frac{1}{2} \, r_{9} - 1 & -\frac{2}{3} \, r_{10} - \frac{10}{3} \, r_{11} - r_{3} + 2 \, r_{4} - \frac{8}{3} \, r_{5} - \frac{37}{6} \, r_{6} - 8 \, r_{7} + \frac{2}{3} \, r_{8} + \frac{1}{6} \, r_{9} + \frac{1}{2} & r_{11} + 2 \, r_{3} + r_{6} - r_{9} + 1 & \frac{2}{3} \, r_{10} - \frac{2}{3} \, r_{11} + r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{4}{3} \, r_{6} - 3 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{2}{3} \, r_{9} + 1 & -r_{11} - 2 \, r_{3} - r_{4} + \frac{3}{2} \, r_{6} + 3 \, r_{7} + \frac{3}{2} \, r_{9} - \frac{3}{2} & \frac{4}{3} \, r_{10} + \frac{2}{3} \, r_{11} + 2 \, r_{3} + 2 \, r_{4} - \frac{2}{3} \, r_{5} - \frac{13}{6} \, r_{6} - 4 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{11}{6} \, r_{9} + 1 & \frac{2}{3} \, r_{10} - \frac{5}{3} \, r_{11} - r_{3} - \frac{1}{3} \, r_{5} + \frac{1}{6} \, r_{6} - r_{7} + \frac{1}{3} \, r_{8} + \frac{5}{6} \, r_{9} + \frac{1}{2} & -r_{3} - r_{4} + \frac{3}{2} \, r_{6} + 2 \, r_{7} + \frac{3}{2} \, r_{9} - \frac{1}{2} & \frac{1}{3} \, r_{10} - \frac{4}{3} \, r_{11} - r_{3} + 2 \, r_{4} - \frac{2}{3} \, r_{5} - \frac{5}{3} \, r_{6} - 2 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{1}{3} \, r_{9} - \frac{1}{2} & \frac{8}{3} \, r_{10} - \frac{5}{3} \, r_{11} + r_{3} - \frac{1}{3} \, r_{5} - \frac{5}{6} \, r_{6} - 4 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{1}{6} \, r_{9} + \frac{3}{2} & \frac{2}{3} \, r_{10} - \frac{2}{3} \, r_{11} + r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{4}{3} \, r_{6} - 3 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{2}{3} \, r_{9} + 1 \\ \frac{5}{3} \, r_{10} - \frac{14}{3} \, r_{11} + 4 \, r_{3} + 5 \, r_{4} - \frac{19}{3} \, r_{5} - \frac{37}{3} \, r_{6} - 23 \, r_{7} + \frac{7}{3} \, r_{8} - \frac{11}{3} \, r_{9} + \frac{9}{2} & -\frac{14}{3} \, r_{10} + \frac{32}{3} \, r_{11} - 10 \, r_{3} - 11 \, r_{4} + \frac{46}{3} \, r_{5} + \frac{91}{3} \, r_{6} + 56 \, r_{7} - \frac{16}{3} \, r_{8} + \frac{29}{3} \, r_{9} - \frac{21}{2} & 8 \, r_{10} - 2 \, r_{11} + 4 \, r_{3} + 4 \, r_{4} - 4 \, r_{5} - 7 \, r_{6} - 20 \, r_{7} + 3 \, r_{8} - 4 \, r_{9} + 5 & \frac{1}{3} \, r_{10} + \frac{23}{3} \, r_{11} + 2 \, r_{3} - 4 \, r_{4} + \frac{19}{3} \, r_{5} + \frac{49}{3} \, r_{6} + 21 \, r_{7} - \frac{4}{3} \, r_{8} + \frac{5}{3} \, r_{9} + \frac{1}{2} & -\frac{1}{3} \, r_{10} + \frac{28}{3} \, r_{11} + 2 \, r_{3} - 5 \, r_{4} + \frac{20}{3} \, r_{5} + \frac{103}{6} \, r_{6} + 22 \, r_{7} - \frac{5}{3} \, r_{8} + \frac{11}{6} \, r_{9} + \frac{1}{2} & -\frac{20}{3} \, r_{10} + \frac{20}{3} \, r_{11} + 4 \, r_{3} - 3 \, r_{4} + \frac{10}{3} \, r_{5} + \frac{53}{6} \, r_{6} + 16 \, r_{7} - \frac{7}{3} \, r_{8} - \frac{5}{6} \, r_{9} & \frac{4}{3} \, r_{10} - \frac{10}{3} \, r_{11} - \frac{8}{3} \, r_{5} - \frac{17}{3} \, r_{6} - 8 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{2}{3} \, r_{9} + 1 & -\frac{1}{3} \, r_{10} - \frac{2}{3} \, r_{11} - 2 \, r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{17}{6} \, r_{6} - r_{7} + \frac{1}{3} \, r_{8} - \frac{1}{6} \, r_{9} - 2 & 4 \, r_{10} - 3 \, r_{11} - 6 \, r_{3} - \frac{1}{2} \, r_{6} + 2 \, r_{7} + r_{8} + \frac{5}{2} \, r_{9} - \frac{9}{2} & \frac{4}{3} \, r_{10} - \frac{7}{3} \, r_{11} + 6 \, r_{3} + 6 \, r_{4} - \frac{11}{3} \, r_{5} - \frac{23}{3} \, r_{6} - 16 \, r_{7} + \frac{8}{3} \, r_{8} - \frac{7}{3} \, r_{9} + \frac{11}{2} & \frac{16}{3} \, r_{10} + \frac{8}{3} \, r_{11} - 3 \, r_{3} - 3 \, r_{4} + \frac{16}{3} \, r_{5} + \frac{34}{3} \, r_{6} + 14 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{11}{3} \, r_{9} - 2 & \frac{1}{3} \, r_{10} + \frac{20}{3} \, r_{11} - 7 \, r_{3} - 13 \, r_{4} + \frac{25}{3} \, r_{5} + \frac{125}{6} \, r_{6} + 34 \, r_{7} - \frac{13}{3} \, r_{8} + \frac{25}{6} \, r_{9} - \frac{15}{2} & -\frac{2}{3} \, r_{10} + \frac{26}{3} \, r_{11} - 6 \, r_{3} - 10 \, r_{4} + \frac{28}{3} \, r_{5} + \frac{70}{3} \, r_{6} + 37 \, r_{7} - \frac{10}{3} \, r_{8} + \frac{14}{3} \, r_{9} - 7 & 2 \, r_{10} - r_{11} + 3 \, r_{3} + 3 \, r_{4} - r_{5} - \frac{7}{2} \, r_{6} - 7 \, r_{7} + r_{8} - \frac{1}{2} \, r_{9} + 3 & -\frac{1}{3} \, r_{10} + \frac{4}{3} \, r_{11} - 4 \, r_{3} - 4 \, r_{4} + \frac{5}{3} \, r_{5} + \frac{20}{3} \, r_{6} + 10 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{7}{3} \, r_{9} - 3 & -\frac{7}{3} \, r_{10} - \frac{2}{3} \, r_{11} - r_{4} - \frac{4}{3} \, r_{5} - \frac{29}{6} \, r_{6} - 4 \, r_{7} - \frac{2}{3} \, r_{8} - \frac{13}{6} \, r_{9} - 1 & \frac{7}{3} \, r_{10} + \frac{2}{3} \, r_{11} + 4 \, r_{3} + 3 \, r_{4} + \frac{1}{3} \, r_{5} - \frac{8}{3} \, r_{6} - 7 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{7}{3} \, r_{9} + \frac{7}{2} & -\frac{2}{3} \, r_{10} - \frac{1}{3} \, r_{11} - r_{3} + 2 \, r_{4} + \frac{1}{3} \, r_{5} + \frac{1}{3} \, r_{6} - 2 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{1}{3} \, r_{9} & \frac{7}{3} \, r_{10} - \frac{4}{3} \, r_{11} + 4 \, r_{3} + 5 \, r_{4} - \frac{2}{3} \, r_{5} - \frac{8}{3} \, r_{6} - 11 \, r_{7} + \frac{5}{3} \, r_{8} - \frac{4}{3} \, r_{9} + 5 & \frac{17}{3} \, r_{10} - \frac{2}{3} \, r_{11} + 5 \, r_{3} + 5 \, r_{4} - \frac{4}{3} \, r_{5} - \frac{23}{6} \, r_{6} - 13 \, r_{7} + \frac{7}{3} \, r_{8} - \frac{7}{6} \, r_{9} + 6 & \frac{20}{3} \, r_{10} + \frac{1}{3} \, r_{11} + 4 \, r_{3} - r_{4} + \frac{2}{3} \, r_{5} + \frac{1}{6} \, r_{6} - 3 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{1}{6} \, r_{9} + 3 & -\frac{1}{3} \, r_{10} + \frac{1}{3} \, r_{11} + r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{5}{6} \, r_{6} - 4 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{7}{6} \, r_{9} + 1 & \frac{29}{3} \, r_{10} + \frac{1}{3} \, r_{11} + 6 \, r_{3} - r_{4} + \frac{2}{3} \, r_{5} - \frac{1}{3} \, r_{6} - 8 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{5}{3} \, r_{9} + 5 & \frac{4}{3} \, r_{10} + \frac{2}{3} \, r_{11} + 2 \, r_{3} + 2 \, r_{4} - \frac{2}{3} \, r_{5} - \frac{7}{6} \, r_{6} - 4 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{5}{6} \, r_{9} + 3 & 6 \, r_{11} - 5 \, r_{4} + 6 \, r_{5} + 14 \, r_{6} + 20 \, r_{7} - 2 \, r_{8} + r_{9} - \frac{5}{2} & -\frac{1}{3} \, r_{10} - \frac{8}{3} \, r_{11} - 4 \, r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{10}{3} \, r_{6} - r_{7} + \frac{1}{3} \, r_{8} + \frac{4}{3} \, r_{9} - 2 & -\frac{2}{3} \, r_{10} + \frac{2}{3} \, r_{11} - r_{4} + \frac{1}{3} \, r_{5} + \frac{5}{6} \, r_{6} + r_{7} - \frac{1}{3} \, r_{8} + \frac{1}{6} \, r_{9} & -\frac{4}{3} \, r_{10} + \frac{4}{3} \, r_{11} - r_{4} + \frac{2}{3} \, r_{5} + \frac{1}{6} \, r_{6} + 2 \, r_{7} - \frac{2}{3} \, r_{8} - \frac{1}{6} \, r_{9} - \frac{1}{2} & -\frac{10}{3} \, r_{10} - \frac{2}{3} \, r_{11} - 5 \, r_{3} - 5 \, r_{4} + \frac{5}{3} \, r_{5} + \frac{17}{3} \, r_{6} + 11 \, r_{7} - \frac{5}{3} \, r_{8} + \frac{13}{3} \, r_{9} - 3 & -\frac{5}{3} \, r_{10} + \frac{11}{3} \, r_{11} + r_{3} + \frac{4}{3} \, r_{5} + \frac{11}{6} \, r_{6} + 5 \, r_{7} - \frac{1}{3} \, r_{8} - \frac{5}{6} \, r_{9} - 2 & -r_{10} - r_{11} + 2 \, r_{3} + 2 \, r_{4} - r_{5} - 4 \, r_{6} - 5 \, r_{7} - 2 \, r_{9} + 1 & -\frac{5}{3} \, r_{10} + \frac{8}{3} \, r_{11} + r_{3} - 4 \, r_{4} + \frac{1}{3} \, r_{5} + \frac{11}{6} \, r_{6} + 3 \, r_{7} - \frac{4}{3} \, r_{8} + \frac{1}{6} \, r_{9} & -7 \, r_{10} + r_{11} - 4 \, r_{3} - r_{4} + r_{6} + 9 \, r_{7} - r_{8} + r_{9} - 5 & -\frac{2}{3} \, r_{10} + \frac{5}{3} \, r_{11} - r_{3} - r_{4} + \frac{1}{3} \, r_{5} + \frac{11}{6} \, r_{6} + 4 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{7}{6} \, r_{9} - 1 \\ -\frac{11}{3} \, r_{10} + \frac{2}{3} \, r_{11} - 2 \, r_{3} - 2 \, r_{4} + \frac{4}{3} \, r_{5} + \frac{7}{3} \, r_{6} + 8 \, r_{7} - \frac{4}{3} \, r_{8} + \frac{5}{3} \, r_{9} - \frac{5}{2} & 8 \, r_{10} - 2 \, r_{11} + 4 \, r_{3} + 4 \, r_{4} - 4 \, r_{5} - 7 \, r_{6} - 20 \, r_{7} + 3 \, r_{8} - 4 \, r_{9} + 5 & -\frac{20}{3} \, r_{10} + \frac{8}{3} \, r_{11} - 4 \, r_{3} - 11 \, r_{4} + \frac{22}{3} \, r_{5} + \frac{43}{3} \, r_{6} + 30 \, r_{7} - \frac{16}{3} \, r_{8} + \frac{23}{3} \, r_{9} - \frac{7}{2} & \frac{2}{3} \, r_{10} - \frac{11}{3} \, r_{11} + r_{3} + 5 \, r_{4} - \frac{10}{3} \, r_{5} - \frac{59}{6} \, r_{6} - 15 \, r_{7} + \frac{4}{3} \, r_{8} - \frac{19}{6} \, r_{9} + 1 & \frac{2}{3} \, r_{10} - \frac{14}{3} \, r_{11} + 4 \, r_{4} - \frac{10}{3} \, r_{5} - \frac{28}{3} \, r_{6} - 13 \, r_{7} + \frac{4}{3} \, r_{8} - \frac{8}{3} \, r_{9} & \frac{4}{3} \, r_{10} - \frac{7}{3} \, r_{11} + r_{3} + 13 \, r_{4} - \frac{23}{3} \, r_{5} - \frac{97}{6} \, r_{6} - 28 \, r_{7} + \frac{17}{3} \, r_{8} - \frac{35}{6} \, r_{9} + \frac{1}{2} & r_{8} & -\frac{1}{3} \, r_{10} + \frac{4}{3} \, r_{11} - 2 \, r_{4} + \frac{2}{3} \, r_{5} + \frac{19}{6} \, r_{6} + 4 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{5}{6} \, r_{9} & -\frac{8}{3} \, r_{10} + \frac{8}{3} \, r_{11} - r_{3} - 11 \, r_{4} + \frac{16}{3} \, r_{5} + \frac{71}{6} \, r_{6} + 20 \, r_{7} - \frac{13}{3} \, r_{8} + \frac{37}{6} \, r_{9} + \frac{1}{2} & -\frac{2}{3} \, r_{10} - \frac{1}{3} \, r_{11} - 3 \, r_{3} + \frac{1}{3} \, r_{5} + \frac{1}{3} \, r_{6} + 2 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{2}{3} \, r_{9} - 2 & -\frac{4}{3} \, r_{10} + \frac{4}{3} \, r_{11} - 2 \, r_{3} - 9 \, r_{4} + \frac{14}{3} \, r_{5} + \frac{29}{3} \, r_{6} + 17 \, r_{7} - \frac{11}{3} \, r_{8} + \frac{16}{3} \, r_{9} & \frac{7}{3} \, r_{10} - \frac{4}{3} \, r_{11} + 4 \, r_{3} + 3 \, r_{4} - \frac{5}{3} \, r_{5} - \frac{17}{3} \, r_{6} - 12 \, r_{7} + \frac{5}{3} \, r_{8} - \frac{4}{3} \, r_{9} + \frac{9}{2} & \frac{8}{3} \, r_{10} - \frac{8}{3} \, r_{11} + 3 \, r_{3} + 3 \, r_{4} - \frac{7}{3} \, r_{5} - \frac{22}{3} \, r_{6} - 14 \, r_{7} + \frac{4}{3} \, r_{8} - \frac{2}{3} \, r_{9} + \frac{9}{2} & -\frac{1}{3} \, r_{10} + \frac{1}{3} \, r_{11} - r_{3} - 2 \, r_{4} + \frac{2}{3} \, r_{5} + \frac{13}{6} \, r_{6} + 4 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{5}{6} \, r_{9} - 1 & r_{5} & 2 \, r_{10} - 4 \, r_{11} + r_{3} + 6 \, r_{4} - 4 \, r_{5} - 8 \, r_{6} - 13 \, r_{7} + 2 \, r_{8} - r_{9} + 1 & -\frac{2}{3} \, r_{10} + \frac{2}{3} \, r_{11} - 2 \, r_{3} - 3 \, r_{4} + \frac{4}{3} \, r_{5} + \frac{29}{6} \, r_{6} + 9 \, r_{7} - \frac{4}{3} \, r_{8} + \frac{13}{6} \, r_{9} - 2 & -\frac{1}{3} \, r_{10} + \frac{7}{3} \, r_{11} - 6 \, r_{4} + \frac{8}{3} \, r_{5} + \frac{43}{6} \, r_{6} + 12 \, r_{7} - \frac{5}{3} \, r_{8} + \frac{11}{6} \, r_{9} - 1 & -2 \, r_{10} + 2 \, r_{11} - 3 \, r_{3} - 7 \, r_{4} + 3 \, r_{5} + 8 \, r_{6} + 16 \, r_{7} - 2 \, r_{8} + 3 \, r_{9} - 3 & -4 \, r_{10} + 2 \, r_{11} - 5 \, r_{3} - 6 \, r_{4} + 3 \, r_{5} + \frac{15}{2} \, r_{6} + 16 \, r_{7} - 2 \, r_{8} + \frac{5}{2} \, r_{9} - 5 & -\frac{4}{3} \, r_{10} + \frac{1}{3} \, r_{11} - 5 \, r_{3} - r_{4} + \frac{5}{3} \, r_{5} + \frac{19}{6} \, r_{6} + 6 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{17}{6} \, r_{9} - 2 & \frac{1}{3} \, r_{10} - \frac{1}{3} \, r_{11} - 2 \, r_{4} + \frac{1}{3} \, r_{5} + \frac{4}{3} \, r_{6} + 3 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{2}{3} \, r_{9} & -\frac{8}{3} \, r_{10} - \frac{1}{3} \, r_{11} - 7 \, r_{3} - 4 \, r_{4} + \frac{7}{3} \, r_{5} + \frac{16}{3} \, r_{6} + 12 \, r_{7} - \frac{4}{3} \, r_{8} + \frac{17}{3} \, r_{9} - 3 & -\frac{7}{3} \, r_{10} + \frac{1}{3} \, r_{11} - 2 \, r_{3} - 2 \, r_{4} + \frac{2}{3} \, r_{5} + \frac{5}{3} \, r_{6} + 5 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{1}{3} \, r_{9} - 3 & -\frac{1}{3} \, r_{10} + \frac{1}{3} \, r_{11} + 3 \, r_{4} - \frac{4}{3} \, r_{5} - \frac{17}{6} \, r_{6} - 5 \, r_{7} + \frac{4}{3} \, r_{8} + \frac{5}{6} \, r_{9} + \frac{3}{2} & r_{10} + r_{11} - 3 \, r_{4} + r_{5} + 4 \, r_{6} + 5 \, r_{7} - r_{8} - 1 & \frac{1}{3} \, r_{10} - \frac{1}{3} \, r_{11} + 2 \, r_{4} - \frac{2}{3} \, r_{5} - \frac{7}{6} \, r_{6} - 2 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{5}{6} \, r_{9} & \frac{5}{3} \, r_{10} - \frac{5}{3} \, r_{11} + r_{3} + 4 \, r_{4} - \frac{7}{3} \, r_{5} - \frac{29}{6} \, r_{6} - 9 \, r_{7} + \frac{4}{3} \, r_{8} - \frac{13}{6} \, r_{9} & \frac{7}{3} \, r_{10} - \frac{1}{3} \, r_{11} + 3 \, r_{3} + 2 \, r_{4} - \frac{2}{3} \, r_{5} - \frac{19}{6} \, r_{6} - 7 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{17}{6} \, r_{9} + 2 & r_{10} - 3 \, r_{11} - r_{3} + 3 \, r_{4} - 3 \, r_{5} - \frac{11}{2} \, r_{6} - 9 \, r_{7} + r_{8} - \frac{3}{2} \, r_{9} - \frac{1}{2} & \frac{1}{3} \, r_{10} - \frac{1}{3} \, r_{11} + 2 \, r_{4} - \frac{5}{3} \, r_{5} - \frac{8}{3} \, r_{6} - 5 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{1}{3} \, r_{9} & r_{10} - 4 \, r_{11} - r_{3} + 6 \, r_{4} - 3 \, r_{5} - \frac{15}{2} \, r_{6} - 11 \, r_{7} + 2 \, r_{8} - \frac{5}{2} \, r_{9} - 1 & 4 \, r_{10} - r_{11} + 6 \, r_{3} + 6 \, r_{4} - 3 \, r_{5} - 7 \, r_{6} - 16 \, r_{7} + 2 \, r_{8} - 5 \, r_{9} + 4 & -\frac{1}{3} \, r_{10} + \frac{1}{3} \, r_{11} + r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{5} ... 1}{3} \, r_{5} - \frac{23}{3} \, r_{6} - 15 \, r_{7} + \frac{5}{3} \, r_{8} - \frac{4}{3} \, r_{9} + \frac{9}{2} & -\frac{4}{3} \, r_{10} - \frac{5}{3} \, r_{11} + r_{3} + r_{4} - \frac{7}{3} \, r_{5} - \frac{13}{3} \, r_{6} - 5 \, r_{7} + \frac{1}{3} \, r_{8} + \frac{1}{3} \, r_{9} + \frac{3}{2} & r_{10} + \frac{1}{2} \, r_{6} + \frac{1}{2} \, r_{9} & -\frac{5}{3} \, r_{10} - \frac{4}{3} \, r_{11} - \frac{5}{3} \, r_{5} - \frac{5}{3} \, r_{6} - r_{7} - \frac{1}{3} \, r_{8} + \frac{8}{3} \, r_{9} + \frac{3}{2} & r_{10} - r_{11} - r_{7} + 1 & -r_{10} + r_{11} - r_{3} - 3 \, r_{4} + r_{5} + 3 \, r_{6} + 6 \, r_{7} - r_{8} + r_{9} - \frac{3}{2} & \frac{1}{3} \, r_{10} - \frac{4}{3} \, r_{11} + 2 \, r_{4} - \frac{2}{3} \, r_{5} - \frac{8}{3} \, r_{6} - 4 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{4}{3} \, r_{9} & -2 \, r_{10} + r_{11} - 4 \, r_{3} - 3 \, r_{4} + r_{5} + \frac{7}{2} \, r_{6} + 9 \, r_{7} - r_{8} + \frac{5}{2} \, r_{9} - 3 & \frac{2}{3} \, r_{10} + \frac{1}{3} \, r_{11} + 5 \, r_{3} + 4 \, r_{4} - \frac{1}{3} \, r_{5} - \frac{29}{6} \, r_{6} - 10 \, r_{7} + \frac{4}{3} \, r_{8} - \frac{25}{6} \, r_{9} + 3 & -\frac{2}{3} \, r_{10} - \frac{1}{3} \, r_{11} - r_{3} - r_{4} + \frac{1}{3} \, r_{5} + \frac{4}{3} \, r_{6} + 3 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{2}{3} \, r_{9} - 1 & 2 \, r_{10} + r_{11} + 4 \, r_{3} + 3 \, r_{4} - 3 \, r_{6} - 7 \, r_{7} + r_{8} - 4 \, r_{9} + 3 & -\frac{10}{3} \, r_{10} + \frac{4}{3} \, r_{11} - 2 \, r_{3} - r_{4} + \frac{8}{3} \, r_{5} + \frac{8}{3} \, r_{6} + 8 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{4}{3} \, r_{9} - \frac{3}{2} & \frac{10}{3} \, r_{10} + \frac{8}{3} \, r_{11} + 5 \, r_{3} + r_{4} + \frac{4}{3} \, r_{5} + \frac{4}{3} \, r_{6} - 3 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{7}{3} \, r_{9} + \frac{7}{2} & -\frac{2}{3} \, r_{10} + \frac{5}{3} \, r_{11} - r_{3} - r_{4} + \frac{7}{3} \, r_{5} + \frac{10}{3} \, r_{6} + 6 \, r_{7} - \frac{1}{3} \, r_{8} - \frac{4}{3} \, r_{9} - \frac{5}{2} & -\frac{1}{3} \, r_{10} - \frac{2}{3} \, r_{11} - 2 \, r_{3} - 2 \, r_{4} + \frac{2}{3} \, r_{5} + \frac{13}{6} \, r_{6} + 4 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{5}{6} \, r_{9} - 2 \\ \frac{1}{3} \, r_{10} - \frac{4}{3} \, r_{11} - r_{3} + 2 \, r_{4} - \frac{2}{3} \, r_{5} - \frac{5}{3} \, r_{6} - 2 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{1}{3} \, r_{9} - \frac{1}{2} & -\frac{5}{3} \, r_{10} + \frac{8}{3} \, r_{11} + r_{3} - 4 \, r_{4} + \frac{1}{3} \, r_{5} + \frac{11}{6} \, r_{6} + 3 \, r_{7} - \frac{4}{3} \, r_{8} + \frac{1}{6} \, r_{9} & r_{10} - 4 \, r_{11} - r_{3} + 6 \, r_{4} - 3 \, r_{5} - \frac{15}{2} \, r_{6} - 11 \, r_{7} + 2 \, r_{8} - \frac{5}{2} \, r_{9} - 1 & \frac{1}{3} \, r_{10} + \frac{2}{3} \, r_{11} + 2 \, r_{3} + \frac{1}{3} \, r_{5} + \frac{1}{3} \, r_{6} - r_{7} + \frac{2}{3} \, r_{8} - \frac{1}{3} \, r_{9} + \frac{3}{2} & \frac{2}{3} \, r_{10} - \frac{2}{3} \, r_{11} + r_{3} + \frac{2}{3} \, r_{5} + \frac{7}{6} \, r_{6} + \frac{1}{3} \, r_{8} + \frac{5}{6} \, r_{9} + \frac{3}{2} & -\frac{2}{3} \, r_{10} + \frac{5}{3} \, r_{11} - 8 \, r_{4} + \frac{10}{3} \, r_{5} + \frac{25}{3} \, r_{6} + 13 \, r_{7} - \frac{7}{3} \, r_{8} + \frac{8}{3} \, r_{9} & -3 \, r_{10} - r_{11} - 4 \, r_{3} - r_{4} - r_{5} - \frac{1}{2} \, r_{6} + 4 \, r_{7} - r_{8} + \frac{3}{2} \, r_{9} - \frac{7}{2} & \frac{1}{3} \, r_{10} + \frac{2}{3} \, r_{11} - r_{4} + \frac{1}{3} \, r_{5} + \frac{5}{6} \, r_{6} + r_{7} - \frac{1}{3} \, r_{8} + \frac{1}{6} \, r_{9} & r_{10} - 2 \, r_{11} - 2 \, r_{3} + 6 \, r_{4} - 4 \, r_{5} - \frac{17}{2} \, r_{6} - 11 \, r_{7} + 2 \, r_{8} - \frac{5}{2} \, r_{9} - 2 & \frac{4}{3} \, r_{10} + \frac{2}{3} \, r_{11} - r_{3} - 2 \, r_{4} + \frac{4}{3} \, r_{5} + \frac{17}{6} \, r_{6} + 4 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{7}{6} \, r_{9} - \frac{1}{2} & -\frac{2}{3} \, r_{10} - \frac{7}{3} \, r_{11} - r_{3} + 5 \, r_{4} - \frac{11}{3} \, r_{5} - \frac{49}{6} \, r_{6} - 11 \, r_{7} + \frac{5}{3} \, r_{8} - \frac{17}{6} \, r_{9} - \frac{3}{2} & \frac{5}{3} \, r_{10} - \frac{8}{3} \, r_{11} + 2 \, r_{3} + 2 \, r_{4} - \frac{7}{3} \, r_{5} - \frac{35}{6} \, r_{6} - 9 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{13}{6} \, r_{9} + \frac{3}{2} & \frac{7}{3} \, r_{10} - \frac{4}{3} \, r_{11} + 3 \, r_{3} + 2 \, r_{4} - \frac{5}{3} \, r_{5} - \frac{14}{3} \, r_{6} - 9 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{7}{3} \, r_{9} + \frac{5}{2} & -\frac{2}{3} \, r_{10} + \frac{5}{3} \, r_{11} - r_{3} + \frac{1}{3} \, r_{5} + \frac{5}{6} \, r_{6} + 2 \, r_{7} - \frac{1}{3} \, r_{8} - \frac{5}{6} \, r_{9} - 2 & -\frac{2}{3} \, r_{10} - \frac{13}{3} \, r_{11} - r_{3} + r_{4} - \frac{8}{3} \, r_{5} - \frac{31}{6} \, r_{6} - 5 \, r_{7} + \frac{2}{3} \, r_{8} + \frac{7}{6} \, r_{9} + \frac{1}{2} & r_{10} + 3 \, r_{11} + 3 \, r_{3} + r_{4} + 2 \, r_{5} + \frac{7}{2} \, r_{6} + 3 \, r_{7} - \frac{1}{2} \, r_{9} + 2 & -r_{10} + 2 \, r_{11} + r_{3} + r_{4} + r_{5} + \frac{3}{2} \, r_{6} + r_{7} - \frac{3}{2} \, r_{9} - \frac{1}{2} & -3 \, r_{11} - 2 \, r_{3} + 3 \, r_{4} - 3 \, r_{5} - \frac{13}{2} \, r_{6} - 9 \, r_{7} + r_{8} - \frac{1}{2} \, r_{9} - \frac{1}{2} & -\frac{4}{3} \, r_{10} - \frac{5}{3} \, r_{11} - 3 \, r_{3} + r_{4} - \frac{7}{3} \, r_{5} - \frac{23}{6} \, r_{6} - 3 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{1}{6} \, r_{9} - \frac{5}{2} & -\frac{7}{3} \, r_{10} - \frac{8}{3} \, r_{11} - 4 \, r_{3} + r_{4} - \frac{7}{3} \, r_{5} - \frac{13}{3} \, r_{6} - 3 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{2}{3} \, r_{9} - \frac{7}{2} & -r_{10} - 2 \, r_{11} + 3 \, r_{3} + 2 \, r_{4} - 3 \, r_{5} - \frac{13}{2} \, r_{6} - 9 \, r_{7} + r_{8} - \frac{7}{2} \, r_{9} + \frac{3}{2} & -\frac{1}{3} \, r_{10} - \frac{2}{3} \, r_{11} - 2 \, r_{3} - r_{4} + \frac{2}{3} \, r_{5} + \frac{5}{3} \, r_{6} + 4 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{7}{3} \, r_{9} - 1 & -\frac{4}{3} \, r_{10} - \frac{8}{3} \, r_{11} + 2 \, r_{3} + r_{4} - \frac{7}{3} \, r_{5} - \frac{29}{6} \, r_{6} - 5 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{13}{6} \, r_{9} + \frac{1}{2} & -2 \, r_{3} + r_{7} + r_{9} - 1 & \frac{1}{3} \, r_{10} - \frac{1}{3} \, r_{11} - 2 \, r_{4} + \frac{1}{3} \, r_{5} + \frac{5}{6} \, r_{6} + r_{7} - \frac{1}{3} \, r_{8} - \frac{5}{6} \, r_{9} - \frac{1}{2} & r_{11} + r_{3} - r_{7} + 1 & \frac{1}{3} \, r_{10} + \frac{2}{3} \, r_{11} - r_{4} + \frac{1}{3} \, r_{5} + \frac{5}{6} \, r_{6} + r_{7} - \frac{1}{3} \, r_{8} + \frac{1}{6} \, r_{9} & -r_{10} + 2 \, r_{11} + 3 \, r_{3} + r_{4} + r_{5} + \frac{3}{2} \, r_{6} + r_{7} - \frac{1}{2} \, r_{9} + 2 & \frac{2}{3} \, r_{10} - \frac{2}{3} \, r_{11} + r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{4}{3} \, r_{6} - 3 \, r_{7} + \frac{1}{3} \, r_{8} + \frac{1}{3} \, r_{9} + 2 & \frac{1}{3} \, r_{10} + \frac{5}{3} \, r_{11} + 2 \, r_{3} - r_{4} + \frac{4}{3} \, r_{5} + \frac{11}{6} \, r_{6} + 2 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{1}{6} \, r_{9} + 1 & \frac{10}{3} \, r_{10} + \frac{8}{3} \, r_{11} + 5 \, r_{3} + r_{4} + \frac{4}{3} \, r_{5} + \frac{4}{3} \, r_{6} - 3 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{7}{3} \, r_{9} + \frac{7}{2} & 2 \, r_{11} - 5 \, r_{4} + 4 \, r_{5} + 8 \, r_{6} + 14 \, r_{7} - 2 \, r_{8} + 4 \, r_{9} + \frac{1}{2} & \frac{4}{3} \, r_{10} + \frac{8}{3} \, r_{11} + 2 \, r_{3} - r_{4} + \frac{7}{3} \, r_{5} + \frac{13}{3} \, r_{6} + 3 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{2}{3} \, r_{9} + \frac{5}{2} & -r_{4} + r_{9} \\ \frac{8}{3} \, r_{10} - \frac{5}{3} \, r_{11} + r_{3} - \frac{1}{3} \, r_{5} - \frac{5}{6} \, r_{6} - 4 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{1}{6} \, r_{9} + \frac{3}{2} & -7 \, r_{10} + r_{11} - 4 \, r_{3} - r_{4} + r_{6} + 9 \, r_{7} - r_{8} + r_{9} - 5 & 4 \, r_{10} - r_{11} + 6 \, r_{3} + 6 \, r_{4} - 3 \, r_{5} - 7 \, r_{6} - 16 \, r_{7} + 2 \, r_{8} - 5 \, r_{9} + 4 & \frac{8}{3} \, r_{10} + \frac{1}{3} \, r_{11} + 3 \, r_{3} + r_{4} + \frac{2}{3} \, r_{5} + \frac{1}{6} \, r_{6} - 2 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{1}{6} \, r_{9} + \frac{5}{2} & 3 \, r_{10} + r_{11} + 2 \, r_{3} + r_{5} + \frac{3}{2} \, r_{6} + r_{7} + \frac{1}{2} \, r_{9} + \frac{3}{2} & 4 \, r_{10} - 3 \, r_{11} - r_{3} - 4 \, r_{4} + 2 \, r_{5} + \frac{5}{2} \, r_{6} + 4 \, r_{7} - r_{8} + \frac{7}{2} \, r_{9} + 1 & -\frac{2}{3} \, r_{10} - \frac{4}{3} \, r_{11} - r_{3} - r_{4} - \frac{5}{3} \, r_{5} - \frac{13}{6} \, r_{6} - 2 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{1}{6} \, r_{9} - \frac{1}{2} & -\frac{5}{3} \, r_{10} + \frac{2}{3} \, r_{11} - 2 \, r_{3} - r_{4} + \frac{1}{3} \, r_{5} + \frac{5}{6} \, r_{6} + 3 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{1}{6} \, r_{9} - 2 & -\frac{10}{3} \, r_{10} - \frac{2}{3} \, r_{11} - r_{3} + r_{4} - \frac{7}{3} \, r_{5} - \frac{11}{6} \, r_{6} - r_{7} + \frac{1}{3} \, r_{8} - \frac{13}{6} \, r_{9} - 3 & r_{11} - 2 \, r_{4} + r_{5} + \frac{7}{2} \, r_{6} + 3 \, r_{7} + \frac{3}{2} \, r_{9} + \frac{3}{2} & -2 \, r_{10} + 2 \, r_{3} + 4 \, r_{4} - 3 \, r_{5} - 5 \, r_{6} - 7 \, r_{7} + r_{8} - 4 \, r_{9} - \frac{1}{2} & -\frac{7}{3} \, r_{10} - \frac{5}{3} \, r_{11} - 2 \, r_{3} - \frac{4}{3} \, r_{5} - \frac{7}{3} \, r_{6} + r_{7} - \frac{2}{3} \, r_{8} + \frac{1}{3} \, r_{9} - \frac{5}{2} & -r_{10} - 2 \, r_{11} - r_{3} + r_{4} - r_{5} - 2 \, r_{6} - \frac{3}{2} & -\frac{1}{3} \, r_{10} + \frac{1}{3} \, r_{11} + r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{4}{3} \, r_{6} - 2 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{5}{3} \, r_{9} & -\frac{1}{3} \, r_{10} - \frac{8}{3} \, r_{11} + r_{4} - \frac{7}{3} \, r_{5} - \frac{17}{6} \, r_{6} - 5 \, r_{7} + \frac{1}{3} \, r_{8} + \frac{11}{6} \, r_{9} + \frac{3}{2} & r_{10} + 2 \, r_{11} + r_{3} + 2 \, r_{5} + 2 \, r_{6} + 3 \, r_{7} + r_{9} + 1 & r_{10} + 2 \, r_{11} + 4 \, r_{3} + 4 \, r_{4} - 3 \, r_{6} - 6 \, r_{7} + r_{8} - 4 \, r_{9} + \frac{3}{2} & -\frac{2}{3} \, r_{10} - \frac{10}{3} \, r_{11} + 2 \, r_{4} - \frac{8}{3} \, r_{5} - \frac{17}{3} \, r_{6} - 8 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{1}{3} \, r_{9} + \frac{1}{2} & -\frac{2}{3} \, r_{10} - \frac{7}{3} \, r_{11} + r_{3} + 2 \, r_{4} - \frac{8}{3} \, r_{5} - \frac{14}{3} \, r_{6} - 8 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{1}{3} \, r_{9} + \frac{3}{2} & 2 \, r_{10} - r_{11} + 5 \, r_{3} + 4 \, r_{4} - 4 \, r_{5} - \frac{17}{2} \, r_{6} - 17 \, r_{7} + 2 \, r_{8} - \frac{7}{2} \, r_{9} + \frac{9}{2} & \frac{2}{3} \, r_{10} - \frac{2}{3} \, r_{11} + 3 \, r_{3} + 3 \, r_{4} - \frac{10}{3} \, r_{5} - \frac{19}{3} \, r_{6} - 10 \, r_{7} + \frac{4}{3} \, r_{8} - \frac{11}{3} \, r_{9} + \frac{3}{2} & \frac{1}{2} \, r_{6} + \frac{1}{2} \, r_{9} + 1 & \frac{2}{3} \, r_{10} + \frac{1}{3} \, r_{11} + 4 \, r_{3} + 3 \, r_{4} - \frac{10}{3} \, r_{5} - \frac{29}{6} \, r_{6} - 10 \, r_{7} + \frac{4}{3} \, r_{8} - \frac{31}{6} \, r_{9} + \frac{7}{2} & r_{3} - 2 \, r_{7} + 2 & r_{10} - r_{11} + r_{7} - \frac{1}{2} & -\frac{13}{3} \, r_{10} + \frac{7}{3} \, r_{11} - 4 \, r_{3} - 2 \, r_{4} + \frac{2}{3} \, r_{5} + \frac{8}{3} \, r_{6} + 8 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{4}{3} \, r_{9} - 4 & \frac{1}{3} \, r_{10} - \frac{1}{3} \, r_{11} - r_{3} - r_{4} + \frac{1}{3} \, r_{5} + \frac{5}{6} \, r_{6} + 2 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{7}{6} \, r_{9} & \frac{1}{3} \, r_{10} + \frac{2}{3} \, r_{11} + 2 \, r_{3} + 3 \, r_{4} + \frac{1}{3} \, r_{5} - \frac{13}{6} \, r_{6} - 3 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{5}{6} \, r_{9} + 1 & -\frac{5}{3} \, r_{10} + \frac{2}{3} \, r_{11} - r_{3} - r_{4} + \frac{1}{3} \, r_{5} + \frac{4}{3} \, r_{6} + 3 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{2}{3} \, r_{9} - 1 & \frac{1}{3} \, r_{10} + \frac{2}{3} \, r_{11} - r_{3} - r_{4} + \frac{4}{3} \, r_{5} + \frac{4}{3} \, r_{6} + 3 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{5}{3} \, r_{9} & -\frac{2}{3} \, r_{10} + \frac{5}{3} \, r_{11} - r_{3} - r_{4} + \frac{7}{3} \, r_{5} + \frac{10}{3} \, r_{6} + 6 \, r_{7} - \frac{1}{3} \, r_{8} - \frac{4}{3} \, r_{9} - \frac{5}{2} & \frac{4}{3} \, r_{10} + \frac{8}{3} \, r_{11} + 2 \, r_{3} - r_{4} + \frac{7}{3} \, r_{5} + \frac{13}{3} \, r_{6} + 3 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{2}{3} \, r_{9} + \frac{5}{2} & -\frac{2}{3} \, r_{10} + \frac{2}{3} \, r_{11} - 4 \, r_{3} - 3 \, r_{4} + \frac{10}{3} \, r_{5} + \frac{16}{3} \, r_{6} + 12 \, r_{7} - \frac{4}{3} \, r_{8} + \frac{14}{3} \, r_{9} - \frac{9}{2} & -\frac{1}{3} \, r_{10} - \frac{2}{3} \, r_{11} - 2 \, r_{3} - 2 \, r_{4} + \frac{2}{3} \, r_{5} + \frac{13}{6} \, r_{6} + 4 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{11}{6} \, r_{9} - 1 \\ \frac{2}{3} \, r_{10} - \frac{2}{3} \, r_{11} + r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{4}{3} \, r_{6} - 3 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{2}{3} \, r_{9} + 1 & -\frac{2}{3} \, r_{10} + \frac{5}{3} \, r_{11} - r_{3} - r_{4} + \frac{1}{3} \, r_{5} + \frac{11}{6} \, r_{6} + 4 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{7}{6} \, r_{9} - 1 & -\frac{1}{3} \, r_{10} + \frac{1}{3} \, r_{11} + r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{5}{6} \, r_{6} - 2 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{13}{6} \, r_{9} & r_{3} - \frac{1}{2} \, r_{6} - 2 \, r_{7} - \frac{1}{2} \, r_{9} + 1 & r_{3} - \frac{1}{2} \, r_{6} - 2 \, r_{7} - \frac{1}{2} \, r_{9} + 1 & \frac{8}{3} \, r_{10} - \frac{5}{3} \, r_{11} + r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{11}{6} \, r_{6} - 4 \, r_{7} + \frac{1}{3} \, r_{8} + \frac{5}{6} \, r_{9} + 2 & -\frac{1}{3} \, r_{10} + \frac{1}{3} \, r_{11} + r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{1}{3} \, r_{6} - r_{7} + \frac{1}{3} \, r_{8} + \frac{1}{3} \, r_{9} + 1 & r_{10} & \frac{1}{3} \, r_{10} + \frac{5}{3} \, r_{11} + 2 \, r_{3} + 2 \, r_{4} - \frac{2}{3} \, r_{5} - \frac{5}{3} \, r_{6} - 4 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{7}{3} \, r_{9} + 1 & -r_{3} - \frac{1}{2} \, r_{6} - \frac{1}{2} \, r_{9} - 1 & -\frac{4}{3} \, r_{10} + \frac{4}{3} \, r_{11} + r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{1}{3} \, r_{6} - r_{7} + \frac{1}{3} \, r_{8} - \frac{5}{3} \, r_{9} & -\frac{4}{3} \, r_{10} - \frac{2}{3} \, r_{11} + r_{4} - \frac{1}{3} \, r_{5} - \frac{1}{3} \, r_{6} + \frac{1}{3} \, r_{8} + \frac{1}{3} \, r_{9} & -2 \, r_{10} - r_{3} + \frac{1}{2} \, r_{6} + 2 \, r_{7} + \frac{1}{2} \, r_{9} - 1 & r_{6} & \frac{1}{3} \, r_{10} + \frac{2}{3} \, r_{11} + 2 \, r_{3} + 2 \, r_{4} - \frac{2}{3} \, r_{5} - \frac{19}{6} \, r_{6} - 4 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{11}{6} \, r_{9} + 1 & -\frac{1}{3} \, r_{10} - \frac{2}{3} \, r_{11} - 2 \, r_{3} - 2 \, r_{4} + \frac{2}{3} \, r_{5} + \frac{8}{3} \, r_{6} + 4 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{1}{3} \, r_{9} - 2 & -\frac{1}{3} \, r_{10} + \frac{1}{3} \, r_{11} - r_{3} - 2 \, r_{4} + \frac{2}{3} \, r_{5} + \frac{19}{6} \, r_{6} + 4 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{5}{6} \, r_{9} - 1 & r_{4} & -r_{10} + r_{4} & r_{4} & -\frac{2}{3} \, r_{10} + \frac{2}{3} \, r_{11} + 2 \, r_{3} + 2 \, r_{4} - \frac{2}{3} \, r_{5} - \frac{13}{6} \, r_{6} - 4 \, r_{7} + \frac{2}{3} \, r_{8} - \frac{11}{6} \, r_{9} + 1 & 0 & \frac{2}{3} \, r_{10} + \frac{4}{3} \, r_{11} + 4 \, r_{3} + 3 \, r_{4} - \frac{4}{3} \, r_{5} - \frac{13}{3} \, r_{6} - 8 \, r_{7} + \frac{4}{3} \, r_{8} - \frac{11}{3} \, r_{9} + 2 & r_{10} & \frac{2}{3} \, r_{10} - \frac{2}{3} \, r_{11} + r_{3} + r_{4} - \frac{1}{3} \, r_{5} - \frac{4}{3} \, r_{6} - 3 \, r_{7} + \frac{1}{3} \, r_{8} - \frac{2}{3} \, r_{9} + 1 & 0 & -r_{11} & -\frac{1}{3} \, r_{10} + \frac{1}{3} \, r_{11} - r_{3} - 2 \, r_{4} + \frac{2}{3} \, r_{5} + \frac{8}{3} \, r_{6} + 4 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{4}{3} \, r_{9} - 1 & r_{3} - r_{7} + 1 & -\frac{2}{3} \, r_{10} - \frac{1}{3} \, r_{11} - r_{3} - r_{4} + \frac{1}{3} \, r_{5} + \frac{5}{6} \, r_{6} + 2 \, r_{7} - \frac{1}{3} \, r_{8} + \frac{7}{6} \, r_{9} - 1 & -\frac{1}{3} \, r_{10} - \frac{2}{3} \, r_{11} - 2 \, r_{3} - 2 \, r_{4} + \frac{2}{3} \, r_{5} + \frac{13}{6} \, r_{6} + 4 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{5}{6} \, r_{9} - 2 & -r_{4} + r_{9} & -\frac{1}{3} \, r_{10} - \frac{2}{3} \, r_{11} - 2 \, r_{3} - 2 \, r_{4} + \frac{2}{3} \, r_{5} + \frac{13}{6} \, r_{6} + 4 \, r_{7} - \frac{2}{3} \, r_{8} + \frac{11}{6} \, r_{9} - 1 & -r_{6} + r_{9} \end{array}\right)$
J=P.J
pretty_print(J)
68 x 68 dense matrix over Integer Ring