--This file was prepared by Federico Galetto using Macaulay2. Contact the author at galetto.federico [(AT)] gmail.com for questions, comments or bug reports. A=QQ[x_111, x_112, x_113, x_121, x_122, x_123, x_131, x_132, x_133, x_211, x_212, x_213, x_221, x_222, x_223, x_231, x_232, x_233] I14=ideal(x_212*x_113*x_213*x_121*x_221*x_122-x_112*x_213^2*x_121*x_221*x_122-x_212*x_113^2*x_221^2*x_122+x_112*x_113*x_213*x_221^2*x_122-x_211*x_113*x_213*x_221*x_122^2+x_111*x_213^2*x_221*x_122^2-x_212*x_113*x_213*x_121^2*x_222+x_112*x_213^2*x_121^2*x_222+x_212*x_113^2*x_121*x_221*x_222-x_112*x_113*x_213*x_121*x_221*x_222+x_211*x_113*x_213*x_121*x_122*x_222-x_111*x_213^2*x_121*x_122*x_222+x_211*x_113^2*x_221*x_122*x_222-x_111*x_113*x_213*x_221*x_122*x_222-x_211*x_113^2*x_121*x_222^2+x_111*x_113*x_213*x_121*x_222^2-x_212^2*x_113*x_121*x_221*x_123+x_112*x_212*x_213*x_121*x_221*x_123+x_112*x_212*x_113*x_221^2*x_123-x_112^2*x_213*x_221^2*x_123+x_211*x_212*x_113*x_221*x_122*x_123+x_211*x_112*x_213*x_221*x_122*x_123-2*x_111*x_212*x_213*x_221*x_122*x_123+x_211*x_212*x_113*x_121*x_222*x_123-2*x_211*x_112*x_213*x_121*x_222*x_123+x_111*x_212*x_213*x_121*x_222*x_123-x_211*x_112*x_113*x_221*x_222*x_123-x_111*x_212*x_113*x_221*x_222*x_123+2*x_111*x_112*x_213*x_221*x_222*x_123-x_211^2*x_113*x_122*x_222*x_123+x_111*x_211*x_213*x_122*x_222*x_123+x_111*x_211*x_113*x_222^2*x_123-x_111^2*x_213*x_222^2*x_123-x_211*x_112*x_212*x_221*x_123^2+x_111*x_212^2*x_221*x_123^2+x_211^2*x_112*x_222*x_123^2-x_111*x_211*x_212*x_222*x_123^2+x_212^2*x_113*x_121^2*x_223-x_112*x_212*x_213*x_121^2*x_223-x_112*x_212*x_113*x_121*x_221*x_223+x_112^2*x_213*x_121*x_221*x_223-2*x_211*x_212*x_113*x_121*x_122*x_223+x_211*x_112*x_213*x_121*x_122*x_223+x_111*x_212*x_213*x_121*x_122*x_223-x_211*x_112*x_113*x_221*x_122*x_223+2*x_111*x_212*x_113*x_221*x_122*x_223-x_111*x_112*x_213*x_221*x_122*x_223+x_211^2*x_113*x_122^2*x_223-x_111*x_211*x_213*x_122^2*x_223+2*x_211*x_112*x_113*x_121*x_222*x_223-x_111*x_212*x_113*x_121*x_222*x_223-x_111*x_112*x_213*x_121*x_222*x_223-x_111*x_211*x_113*x_122*x_222*x_223+x_111^2*x_213*x_122*x_222*x_223+x_211*x_112*x_212*x_121*x_123*x_223-x_111*x_212^2*x_121*x_123*x_223+x_211*x_112^2*x_221*x_123*x_223-x_111*x_112*x_212*x_221*x_123*x_223-x_211^2*x_112*x_122*x_123*x_223+x_111*x_211*x_212*x_122*x_123*x_223-x_111*x_211*x_112*x_222*x_123*x_223+x_111^2*x_212*x_222*x_123*x_223-x_211*x_112^2*x_121*x_223^2+x_111*x_112*x_212*x_121*x_223^2+x_111*x_211*x_112*x_122*x_223^2-x_111^2*x_212*x_122*x_223^2,x_212^2*x_113^2*x_221*x_131-2*x_112*x_212*x_113*x_213*x_221*x_131+x_112^2*x_213^2*x_221*x_131-x_211*x_212*x_113^2*x_222*x_131+x_211*x_112*x_113*x_213*x_222*x_131+x_111*x_212*x_113*x_213*x_222*x_131-x_111*x_112*x_213^2*x_222*x_131+x_211*x_112*x_212*x_113*x_223*x_131-x_111*x_212^2*x_113*x_223*x_131-x_211*x_112^2*x_213*x_223*x_131+x_111*x_112*x_212*x_213*x_223*x_131-x_212^2*x_113^2*x_121*x_231+2*x_112*x_212*x_113*x_213*x_121*x_231-x_112^2*x_213^2*x_121*x_231+x_211*x_212*x_113^2*x_122*x_231-x_211*x_112*x_113*x_213*x_122*x_231-x_111*x_212*x_113*x_213*x_122*x_231+x_111*x_112*x_213^2*x_122*x_231-x_211*x_112*x_212*x_113*x_123*x_231+x_111*x_212^2*x_113*x_123*x_231+x_211*x_112^2*x_213*x_123*x_231-x_111*x_112*x_212*x_213*x_123*x_231-x_211*x_212*x_113^2*x_221*x_132+x_211*x_112*x_113*x_213*x_221*x_132+x_111*x_212*x_113*x_213*x_221*x_132-x_111*x_112*x_213^2*x_221*x_132+x_211^2*x_113^2*x_222*x_132-2*x_111*x_211*x_113*x_213*x_222*x_132+x_111^2*x_213^2*x_222*x_132-x_211^2*x_112*x_113*x_223*x_132+x_111*x_211*x_212*x_113*x_223*x_132+x_111*x_211*x_112*x_213*x_223*x_132-x_111^2*x_212*x_213*x_223*x_132+x_211*x_212*x_113^2*x_121*x_232-x_211*x_112*x_113*x_213*x_121*x_232-x_111*x_212*x_113*x_213*x_121*x_232+x_111*x_112*x_213^2*x_121*x_232-x_211^2*x_113^2*x_122*x_232+2*x_111*x_211*x_113*x_213*x_122*x_232-x_111^2*x_213^2*x_122*x_232+x_211^2*x_112*x_113*x_123*x_232-x_111*x_211*x_212*x_113*x_123*x_232-x_111*x_211*x_112*x_213*x_123*x_232+x_111^2*x_212*x_213*x_123*x_232+x_211*x_112*x_212*x_113*x_221*x_133-x_111*x_212^2*x_113*x_221*x_133-x_211*x_112^2*x_213*x_221*x_133+x_111*x_112*x_212*x_213*x_221*x_133-x_211^2*x_112*x_113*x_222*x_133+x_111*x_211*x_212*x_113*x_222*x_133+x_111*x_211*x_112*x_213*x_222*x_133-x_111^2*x_212*x_213*x_222*x_133+x_211^2*x_112^2*x_223*x_133-2*x_111*x_211*x_112*x_212*x_223*x_133+x_111^2*x_212^2*x_223*x_133-x_211*x_112*x_212*x_113*x_121*x_233+x_111*x_212^2*x_113*x_121*x_233+x_211*x_112^2*x_213*x_121*x_233-x_111*x_112*x_212*x_213*x_121*x_233+x_211^2*x_112*x_113*x_122*x_233-x_111*x_211*x_212*x_113*x_122*x_233-x_111*x_211*x_112*x_213*x_122*x_233+x_111^2*x_212*x_213*x_122*x_233-x_211^2*x_112^2*x_123*x_233+2*x_111*x_211*x_112*x_212*x_123*x_233-x_111^2*x_212^2*x_123*x_233,x_212^2*x_113*x_121*x_221*x_131-x_112*x_212*x_213*x_121*x_221*x_131-x_112*x_212*x_113*x_221^2*x_131+x_112^2*x_213*x_221^2*x_131-x_211*x_112*x_213*x_221*x_122*x_131+x_111*x_212*x_213*x_221*x_122*x_131-x_211*x_212*x_113*x_121*x_222*x_131+x_211*x_112*x_213*x_121*x_222*x_131+x_211*x_112*x_113*x_221*x_222*x_131-x_111*x_112*x_213*x_221*x_222*x_131+x_211*x_112*x_212*x_221*x_123*x_131-x_111*x_212^2*x_221*x_123*x_131-x_211^2*x_112*x_222*x_123*x_131+x_111*x_211*x_212*x_222*x_123*x_131-x_211*x_112^2*x_221*x_223*x_131+x_111*x_112*x_212*x_221*x_223*x_131+x_211^2*x_112*x_122*x_223*x_131-x_111*x_211*x_212*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211*x_122*x_131*x_132*x_233^2+x_111*x_222*x_131*x_132*x_233^2+x_211*x_121*x_132^2*x_233^2-x_111*x_221*x_132^2*x_233^2) N14=cokernel map(A^{{-2},{-2},{-2},{-2},{-2},{-2},{-2},{-2},{-2},{0}},A^{{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3}},{{-x_131, -(1/4)*x_231, 0, 0, x_121, (1/4)*x_221, x_113, (1/4)*x_213, -x_112, -(1/4)*x_212, 0, 0, x_111, x_111, (1/4)*x_211, (1/4)*x_211, -x_111, -(1/4)*x_211, 0, 0, 0, 0, x_111, (1/4)*x_211, 0, 0, 0, 0, 0, 0, 0, 0}, {x_132, (1/4)*x_232, 0, 0, -x_122, -(1/4)*x_222, 0, 0, 0, 0, x_113, (1/4)*x_213, 0, -x_112, 0, -(1/4)*x_212, 0, 0, 0, 0, 0, 0, 0, 0, -x_111, -(1/4)*x_211, 0, 0, 0, 0, 0, 0}, {0, 0, -x_131, -(1/4)*x_231, 0, 0, -x_123, -(1/4)*x_223, x_122, (1/4)*x_222, 0, 0, -x_121, 0, -(1/4)*x_221, 0, 0, 0, 0, 0, x_111, (1/4)*x_211, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {x_133, (1/4)*x_233, 0, 0, -x_123, -(1/4)*x_223, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_113, (1/4)*x_213, -x_112, -(1/4)*x_212, 0, 0, 0, 0, 0, 0, x_111, (1/4)*x_211, 0, 0, 0, 0}, {0, 0, x_133, (1/4)*x_233, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_123, 0, -(1/4)*x_223, 0, 0, x_122, (1/4)*x_222, -x_113, -(1/4)*x_213, -x_123, -(1/4)*x_223, 0, 0, -x_121, -(1/4)*x_221, 0, 0, 0, 0}, {0, 0, -x_132, -(1/4)*x_232, 0, 0, 0, 0, 0, 0, x_123, (1/4)*x_223, 0, 0, 0, 0, -x_122, -(1/4)*x_222, 0, 0, x_112, (1/4)*x_212, x_122, (1/4)*x_222, -x_121, -(1/4)*x_221, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, x_133, (1/4)*x_233, -x_132, -(1/4)*x_232, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_131, (1/4)*x_231, 0, 0, 0, 0, -x_121, -(1/4)*x_221, x_111, (1/4)*x_211}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_133, -(1/4)*x_233, -x_132, 0, -(1/4)*x_232, 0, x_132, (1/4)*x_232, 0, 0, 0, 0, 0, 0, x_131, (1/4)*x_231, 0, 0, -x_122, -(1/4)*x_222, x_112, (1/4)*x_212}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_133, x_133, (1/4)*x_233, (1/4)*x_233, 0, 0, -x_132, -(1/4)*x_232, 0, 0, 0, 0, 0, 0, x_131, (1/4)*x_231, x_123, (1/4)*x_223, -x_113, -(1/4)*x_213}, {0, -x_133*x_222*x_231+x_132*x_223*x_231+x_133*x_221*x_232-x_131*x_223*x_232-x_132*x_221*x_233+x_131*x_222*x_233, 0, -x_133*x_212*x_231+x_132*x_213*x_231+x_133*x_211*x_232-x_131*x_213*x_232-x_132*x_211*x_233+x_131*x_212*x_233, 0, x_123*x_222*x_231-x_122*x_223*x_231-x_123*x_221*x_232+x_121*x_223*x_232+x_122*x_221*x_233-x_121*x_222*x_233, 0, x_133*x_213*x_222-x_133*x_212*x_223-x_123*x_213*x_232+x_113*x_223*x_232+x_123*x_212*x_233-x_113*x_222*x_233, 0, -x_132*x_213*x_222+x_132*x_212*x_223+x_122*x_213*x_232-x_112*x_223*x_232-x_122*x_212*x_233+x_112*x_222*x_233, 0, x_133*x_213*x_221-x_133*x_211*x_223-x_123*x_213*x_231+x_113*x_223*x_231+x_123*x_211*x_233-x_113*x_221*x_233, 0, 0, -x_133*x_212*x_221+x_132*x_213*x_221+x_133*x_211*x_222-x_132*x_211*x_223-x_121*x_213*x_232+x_111*x_223*x_232+x_121*x_212*x_233-x_111*x_222*x_233, -x_133*x_212*x_221+x_133*x_211*x_222+x_123*x_212*x_231-x_112*x_223*x_231-x_123*x_211*x_232+x_111*x_223*x_232+x_112*x_221*x_233-x_111*x_222*x_233, 0, -x_132*x_213*x_221+x_132*x_211*x_223+x_122*x_213*x_231-x_113*x_222*x_231+x_113*x_221*x_232-x_111*x_223*x_232-x_122*x_211*x_233+x_111*x_222*x_233, 0, x_132*x_212*x_221-x_132*x_211*x_222-x_122*x_212*x_231+x_112*x_222*x_231+x_122*x_211*x_232-x_112*x_221*x_232, 0, x_113*x_212*x_231-x_112*x_213*x_231-x_113*x_211*x_232+x_111*x_213*x_232+x_112*x_211*x_233-x_111*x_212*x_233, 0, x_131*x_213*x_222-x_131*x_212*x_223+x_123*x_212*x_231-x_122*x_213*x_231-x_123*x_211*x_232+x_111*x_223*x_232+x_122*x_211*x_233-x_111*x_222*x_233, 0, -x_131*x_213*x_221+x_131*x_211*x_223+x_121*x_213*x_231-x_111*x_223*x_231-x_121*x_211*x_233+x_111*x_221*x_233, 0, -x_131*x_212*x_221+x_131*x_211*x_222+x_121*x_212*x_231-x_111*x_222*x_231-x_121*x_211*x_232+x_111*x_221*x_232, 0, -x_123*x_212*x_221+x_122*x_213*x_221+x_123*x_211*x_222-x_121*x_213*x_222-x_122*x_211*x_223+x_121*x_212*x_223, 0, x_113*x_212*x_221-x_112*x_213*x_221-x_113*x_211*x_222+x_111*x_213*x_222+x_112*x_211*x_223-x_111*x_212*x_223}}) C14=cokernel map(A^{{-2},{-2},{-2},{-2},{-2},{-2},{-2},{-2},{-2}},A^{{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3},{-3}},{{x_111, 0, 0, 0, 0, x_112, 0, 0, x_113, 0, 0, x_121, 0, 0, x_131, 0, x_211, 0, 0, 0, 0, x_212, 0, 0, x_213, 0, 0, x_221, 0, 0, x_231, 0}, {0, x_111, 0, 0, 0, 0, x_112, 0, 0, x_113, 0, -x_122, 0, 0, -x_132, 0, 0, x_211, 0, 0, 0, 0, x_212, 0, 0, x_213, 0, -x_222, 0, 0, -x_232, 0}, {0, 0, x_111, 0, 0, -x_122, 0, 0, -x_123, 0, 0, 0, x_121, 0, 0, x_131, 0, 0, x_211, 0, 0, -x_222, 0, 0, -x_223, 0, 0, 0, x_221, 0, 0, x_231}, {0, 0, 0, x_111, 0, 0, 0, x_112, 0, 0, x_113, -x_123, 0, 0, -x_133, 0, 0, 0, 0, x_211, 0, 0, 0, x_212, 0, 0, x_213, -x_223, 0, 0, -x_233, 0}, {-x_123, 0, -x_113, -x_121, 0, 0, 0, -x_122, 0, 0, -x_123, 0, -x_123, 0, 0, -x_133, -x_223, 0, -x_213, -x_221, 0, 0, 0, -x_222, 0, 0, -x_223, 0, -x_223, 0, 0, -x_233}, {x_122, x_121, x_112, 0, 0, 0, x_122, 0, 0, x_123, 0, 0, x_122, 0, 0, x_132, x_222, x_221, x_212, 0, 0, 0, x_222, 0, 0, x_223, 0, 0, x_222, 0, 0, x_232}, {x_131, 0, 0, 0, x_111, x_132, x_131, 0, x_133, 0, x_131, 0, x_131, x_121, 0, 0, x_231, 0, 0, 0, x_211, x_232, x_231, 0, x_233, 0, x_231, 0, x_231, x_221, 0, 0}, {0, -x_131, 0, 0, x_112, 0, 0, 0, 0, -x_133, x_132, 0, x_132, x_122, 0, 0, 0, -x_231, 0, 0, x_212, 0, 0, 0, 0, -x_233, x_232, 0, x_232, x_222, 0, 0}, {0, 0, 0, x_131, -x_113, 0, -x_133, x_132, 0, 0, 0, 0, -x_133, -x_123, 0, 0, 0, 0, 0, x_231, -x_213, 0, -x_233, x_232, 0, 0, 0, 0, -x_233, -x_223, 0, 0}})