# A codimension 5 example with details -- Constructing a minimal resolution for a codimension 5 cyclic polytope detailed.

We give all the details of the unprojection construction of a codim 5 example.

Δ(2,7):

 `i1 : R=QQ[x_1..x_7];` ```i2 : cc=cycRes(2,R,verbose=>2); ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ delta(2,{x_1, x_2, x_3, x_4, x_5}) + delta(0,{z, x_2, x_3, x_4}) -> delta(2,{x_1, x_2, x_3, x_4, x_5, x_6}) ------------------------------------------------------------------------------------------------------------------------ res(I): a_1 = | x_2x_4 x_3x_5 x_1x_4 x_2x_5 x_1x_3 | a_2 = {2} | 0 x_1 0 0 -x_5 | {2} | -x_1 0 x_2 0 0 | {2} | 0 -x_2 0 x_3 0 | {2} | 0 0 -x_3 0 x_4 | {2} | x_5 0 0 -x_4 0 | a_3 = {3} | x_2x_4 | {3} | x_3x_5 | {3} | x_1x_4 | {3} | x_2x_5 | {3} | x_1x_3 | ------------------------------------------------------------------------------------------------------------------------ res(J): b_1 = | z x_3 x_4 x_2 | b_2 = {1} | x_3 x_4 x_2 0 0 0 | {1} | -z 0 0 0 x_2 -x_4 | {1} | 0 -z 0 -x_2 0 x_3 | {1} | 0 0 -z x_4 -x_3 0 | b_3 = {2} | 0 x_2 -x_4 0 | {2} | -x_2 0 x_3 0 | {2} | x_4 -x_3 0 0 | {2} | z 0 0 x_3 | {2} | 0 z 0 x_4 | {2} | 0 0 z x_2 | b_4 = {3} | x_3 | {3} | x_4 | {3} | x_2 | {3} | -z | ------------------------------------------------------------------------------------------------------------------------ phi: {z, x_3, x_4, x_2} -> {x_1*x_5, 0, 0, 0} ------------------------------------------------------------------------------------------------------------------------ alpha_1 = {1} | 0 0 0 0 0 | {1} | 0 x_5 0 0 x_1 | {1} | 0 0 x_1 0 0 | {1} | x_4 0 0 x_5 0 | alpha_2 = {2} | 0 0 0 0 0 | {2} | 0 0 0 0 0 | {2} | 0 0 0 0 0 | {2} | 0 x_1 0 0 0 | {2} | 0 0 x_5 0 0 | {2} | 0 0 0 x_1 0 | alpha_3 = {3} | 0 | {3} | 0 | {3} | 0 | {3} | x_1x_5 | ------------------------------------------------------------------------------------------------------------------------ beta_1 = | -x_1x_5 0 0 0 | beta_2 = {2} | 0 0 0 0 0 0 | {2} | -x_1 0 0 0 0 0 | {2} | 0 -x_5 0 0 0 0 | {2} | 0 0 -x_1 0 0 0 | {2} | 0 0 0 0 0 0 | beta_3 = {3} | 0 0 -x_4 0 | {3} | -x_5 0 0 0 | {3} | 0 -x_1 0 0 | {3} | 0 0 -x_5 0 | {3} | -x_1 0 0 0 | ------------------------------------------------------------------------------------------------------------------------ u = -1 ------------------------------------------------------------------------------------------------------------------------ h_1 = 0 h_2 = 0 h_3 = 0 ------------------------------------------------------------------------------------------------------------------------ f_1 = | x_2x_4 x_3x_5 x_1x_4 x_2x_5 x_1x_3 x_6z-x_1x_5 x_6x_3 x_6x_4 x_6x_2 | f_2 = | 0 x_1 0 0 -x_5 0 0 0 0 0 0 x_6 0 0 0 0 | | -x_1 0 x_2 0 0 -x_1 0 0 0 0 0 0 x_6 0 0 0 | | 0 -x_2 0 x_3 0 0 -x_5 0 0 0 0 0 0 x_6 0 0 | | 0 0 -x_3 0 x_4 0 0 -x_1 0 0 0 0 0 0 x_6 0 | | x_5 0 0 -x_4 0 0 0 0 0 0 0 0 0 0 0 x_6 | | 0 0 0 0 0 -x_3 -x_4 -x_2 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 z 0 0 0 -x_2 x_4 0 -x_5 0 0 -x_1 | | 0 0 0 0 0 0 z 0 x_2 0 -x_3 0 0 -x_1 0 0 | | 0 0 0 0 0 0 0 z -x_4 x_3 0 -x_4 0 0 -x_5 0 | f_3 = | 0 0 -x_4 0 -x_6 0 0 0 0 | | -x_5 0 0 0 0 -x_6 0 0 0 | | 0 -x_1 0 0 0 0 -x_6 0 0 | | 0 0 -x_5 0 0 0 0 -x_6 0 | | -x_1 0 0 0 0 0 0 0 -x_6 | | 0 -x_2 x_4 0 0 0 0 0 0 | | x_2 0 -x_3 0 0 0 0 0 0 | | -x_4 x_3 0 0 0 0 0 0 0 | | -z 0 0 -x_3 0 -x_1 0 0 0 | | 0 -z 0 -x_4 0 0 -x_5 0 0 | | 0 0 -z -x_2 0 0 0 -x_1 0 | | 0 0 0 0 0 x_1 0 0 -x_5 | | 0 0 0 0 -x_1 0 x_2 0 0 | | 0 0 0 0 0 -x_2 0 x_3 0 | | 0 0 0 0 0 0 -x_3 0 x_4 | | 0 0 0 0 x_5 0 0 -x_4 0 | f_4 = | -x_6x_3 | | -x_6x_4 | | -x_6x_2 | | x_6z-x_1x_5 | | x_2x_4 | | x_3x_5 | | x_1x_4 | | x_2x_5 | | x_1x_3 | ------------------------------------------------------------------------------------------------------------------------ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ delta(2,{x_1, x_2, x_3, x_4, x_5, x_6}) + delta(0,{z, x_2, x_3, x_4, x_5}) -> delta(2,{x_1, x_2, x_3, x_4, x_5, x_6, x_7}) ------------------------------------------------------------------------------------------------------------------------ res(I): a_1 = | x_2x_4 x_3x_5 x_1x_4 x_2x_5 x_1x_3 -x_1x_5 x_3x_6 x_4x_6 x_2x_6 | a_2 = {2} | 0 x_1 0 0 -x_5 0 0 0 0 0 0 x_6 0 0 0 0 | {2} | -x_1 0 x_2 0 0 -x_1 0 0 0 0 0 0 x_6 0 0 0 | {2} | 0 -x_2 0 x_3 0 0 -x_5 0 0 0 0 0 0 x_6 0 0 | {2} | 0 0 -x_3 0 x_4 0 0 -x_1 0 0 0 0 0 0 x_6 0 | {2} | x_5 0 0 -x_4 0 0 0 0 0 0 0 0 0 0 0 x_6 | {2} | 0 0 0 0 0 -x_3 -x_4 -x_2 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 0 0 -x_2 x_4 0 -x_5 0 0 -x_1 | {2} | 0 0 0 0 0 0 0 0 x_2 0 -x_3 0 0 -x_1 0 0 | {2} | 0 0 0 0 0 0 0 0 -x_4 x_3 0 -x_4 0 0 -x_5 0 | a_3 = {3} | 0 0 -x_4 0 -x_6 0 0 0 0 | {3} | -x_5 0 0 0 0 -x_6 0 0 0 | {3} | 0 -x_1 0 0 0 0 -x_6 0 0 | {3} | 0 0 -x_5 0 0 0 0 -x_6 0 | {3} | -x_1 0 0 0 0 0 0 0 -x_6 | {3} | 0 -x_2 x_4 0 0 0 0 0 0 | {3} | x_2 0 -x_3 0 0 0 0 0 0 | {3} | -x_4 x_3 0 0 0 0 0 0 0 | {3} | 0 0 0 -x_3 0 -x_1 0 0 0 | {3} | 0 0 0 -x_4 0 0 -x_5 0 0 | {3} | 0 0 0 -x_2 0 0 0 -x_1 0 | {3} | 0 0 0 0 0 x_1 0 0 -x_5 | {3} | 0 0 0 0 -x_1 0 x_2 0 0 | {3} | 0 0 0 0 0 -x_2 0 x_3 0 | {3} | 0 0 0 0 0 0 -x_3 0 x_4 | {3} | 0 0 0 0 x_5 0 0 -x_4 0 | a_4 = {4} | -x_3x_6 | {4} | -x_4x_6 | {4} | -x_2x_6 | {4} | -x_1x_5 | {4} | x_2x_4 | {4} | x_3x_5 | {4} | x_1x_4 | {4} | x_2x_5 | {4} | x_1x_3 | ------------------------------------------------------------------------------------------------------------------------ res(J): b_1 = | z x_2 x_4 x_5 x_3 | b_2 = {1} | x_2 x_4 x_5 x_3 0 0 0 0 0 0 | {1} | -z 0 0 0 x_4 x_5 x_3 0 0 0 | {1} | 0 -z 0 0 -x_2 0 0 0 x_3 -x_5 | {1} | 0 0 -z 0 0 -x_2 0 -x_3 0 x_4 | {1} | 0 0 0 -z 0 0 -x_2 x_5 -x_4 0 | b_3 = {2} | x_4 x_5 x_3 0 0 0 0 0 0 0 | {2} | -x_2 0 0 0 x_3 -x_5 0 0 0 0 | {2} | 0 -x_2 0 -x_3 0 x_4 0 0 0 0 | {2} | 0 0 -x_2 x_5 -x_4 0 0 0 0 0 | {2} | z 0 0 0 0 0 0 x_3 -x_5 0 | {2} | 0 z 0 0 0 0 -x_3 0 x_4 0 | {2} | 0 0 z 0 0 0 x_5 -x_4 0 0 | {2} | 0 0 0 z 0 0 x_2 0 0 x_4 | {2} | 0 0 0 0 z 0 0 x_2 0 x_5 | {2} | 0 0 0 0 0 z 0 0 x_2 x_3 | b_4 = {3} | 0 x_3 -x_5 0 0 | {3} | -x_3 0 x_4 0 0 | {3} | x_5 -x_4 0 0 0 | {3} | x_2 0 0 x_4 0 | {3} | 0 x_2 0 x_5 0 | {3} | 0 0 x_2 x_3 0 | {3} | -z 0 0 0 x_4 | {3} | 0 -z 0 0 x_5 | {3} | 0 0 -z 0 x_3 | {3} | 0 0 0 -z -x_2 | b_5 = {4} | x_4 | {4} | x_5 | {4} | x_3 | {4} | -x_2 | {4} | z | ------------------------------------------------------------------------------------------------------------------------ phi: {z, x_2, x_4, x_5, x_3} -> {x_1*x_6, 0, 0, 0, 0} ------------------------------------------------------------------------------------------------------------------------ alpha_1 = {1} | 0 0 0 0 0 0 0 0 0 | {1} | x_4 0 0 x_5 0 0 0 0 x_6 | {1} | 0 0 x_1 0 0 0 0 x_6 0 | {1} | 0 0 0 0 0 -x_1 0 0 0 | {1} | 0 x_5 0 0 x_1 0 x_6 0 0 | alpha_2 = {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {2} | 0 x_1 0 0 0 0 0 0 -x_6 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 -x_1 0 0 0 0 0 0 0 0 | {2} | 0 0 -x_5 0 0 0 0 0 0 x_6 0 0 0 0 0 0 | {2} | 0 0 0 0 0 -x_1 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 x_1 0 0 0 0 0 0 -x_6 0 0 0 0 0 | {2} | 0 0 0 0 0 0 x_1 0 0 0 0 0 0 0 0 0 | alpha_3 = {3} | 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 | {3} | 0 x_1 0 0 0 0 0 0 0 | {3} | 0 0 0 x_6 0 0 0 0 0 | {3} | x_1 0 0 0 0 0 0 0 0 | {3} | 0 0 -x_1 0 0 0 0 0 0 | alpha_4 = {4} | 0 | {4} | 0 | {4} | 0 | {4} | 0 | {4} | -x_1x_6 | ------------------------------------------------------------------------------------------------------------------------ beta_1 = | -x_1x_6 0 0 0 0 | beta_2 = {2} | 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 x_6 0 0 0 0 0 0 0 | {2} | 0 0 0 -x_1 0 0 0 0 0 0 | {2} | 0 -x_1 0 0 0 0 0 0 0 0 | {2} | -x_1 0 0 0 0 0 0 0 0 0 | beta_3 = {3} | 0 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 x_6 0 0 0 0 0 0 | {3} | 0 0 0 0 0 -x_6 0 0 0 0 | {3} | 0 x_6 0 0 0 0 0 0 0 0 | {3} | x_1 0 0 0 0 0 0 0 0 0 | {3} | 0 0 -x_1 0 0 0 0 0 0 0 | {3} | 0 0 0 0 x_1 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 x_1 0 0 0 0 0 0 | {3} | 0 0 0 0 0 -x_5 0 0 0 0 | {3} | 0 x_1 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 0 | beta_4 = {4} | 0 0 -x_6 0 0 | {4} | -x_6 0 0 0 0 | {4} | 0 0 0 x_6 0 | {4} | 0 -x_1 0 0 0 | {4} | 0 0 0 -x_4 0 | {4} | 0 0 x_5 0 0 | {4} | x_1 0 0 0 0 | {4} | 0 0 0 -x_5 0 | {4} | 0 0 x_1 0 0 | ------------------------------------------------------------------------------------------------------------------------ u = 1 ------------------------------------------------------------------------------------------------------------------------ h_1 = 0 h_2 = 0 h_3 = 0 h_4 = 0 ------------------------------------------------------------------------------------------------------------------------ f_1 = | x_2x_4 x_3x_5 x_1x_4 x_2x_5 x_1x_3 -x_1x_5 x_3x_6 x_4x_6 x_2x_6 x_7z-x_1x_6 x_7x_2 x_7x_4 x_7x_5 x_7x_3 | f_2 = | 0 x_1 0 0 -x_5 0 0 0 0 0 0 x_6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x_7 0 0 0 0 0 0 0 0 | | -x_1 0 x_2 0 0 -x_1 0 0 0 0 0 0 x_6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x_7 0 0 0 0 0 0 0 | | 0 -x_2 0 x_3 0 0 -x_5 0 0 0 0 0 0 x_6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x_7 0 0 0 0 0 0 | | 0 0 -x_3 0 x_4 0 0 -x_1 0 0 0 0 0 0 x_6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x_7 0 0 0 0 0 | | x_5 0 0 -x_4 0 0 0 0 0 0 0 0 0 0 0 x_6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x_7 0 0 0 0 | | 0 0 0 0 0 -x_3 -x_4 -x_2 0 0 0 0 0 0 0 0 0 0 x_6 0 0 0 0 0 0 0 0 0 0 0 0 x_7 0 0 0 | | 0 0 0 0 0 0 0 0 0 -x_2 x_4 0 -x_5 0 0 -x_1 0 0 0 -x_1 0 0 0 0 0 0 0 0 0 0 0 0 x_7 0 0 | | 0 0 0 0 0 0 0 0 x_2 0 -x_3 0 0 -x_1 0 0 0 -x_1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x_7 0 | | 0 0 0 0 0 0 0 0 -x_4 x_3 0 -x_4 0 0 -x_5 0 -x_1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x_7 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_2 -x_4 -x_5 -x_3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 z 0 0 0 -x_4 -x_5 -x_3 0 0 0 -x_4 0 0 -x_5 0 0 0 0 -x_6 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 z 0 0 x_2 0 0 0 -x_3 x_5 0 0 -x_1 0 0 0 0 -x_6 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 z 0 0 x_2 0 x_3 0 -x_4 0 0 0 0 0 x_1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 z 0 0 x_2 -x_5 x_4 0 0 -x_5 0 0 -x_1 0 -x_6 0 0 | f_3 = | 0 0 -x_4 0 -x_6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | -x_5 0 0 0 0 -x_6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 -x_1 0 0 0 0 -x_6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 -x_5 0 0 0 0 -x_6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 0 0 0 0 0 0 0 0 0 0 | | -x_1 0 0 0 0 0 0 0 -x_6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 0 0 0 0 0 0 0 0 0 | | 0 -x_2 x_4 0 0 0 0 0 0 0 0 0 x_6 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 0 0 0 0 0 0 0 0 | | x_2 0 -x_3 0 0 0 0 0 0 0 0 0 0 0 -x_6 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 0 0 0 0 0 0 0 | | -x_4 x_3 0 0 0 0 0 0 0 0 x_6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 0 0 0 0 0 0 | | 0 0 0 -x_3 0 -x_1 0 0 0 x_1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 0 0 0 0 0 | | 0 0 0 -x_4 0 0 -x_5 0 0 0 0 -x_1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 0 0 0 0 | | 0 0 0 -x_2 0 0 0 -x_1 0 0 0 0 0 x_1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 0 0 0 | | 0 0 0 0 0 x_1 0 0 -x_5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 0 0 | | 0 0 0 0 -x_1 0 x_2 0 0 0 0 0 x_1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 0 | | 0 0 0 0 0 -x_2 0 x_3 0 0 0 0 0 0 -x_5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 0 | | 0 0 0 0 0 0 -x_3 0 x_4 0 x_1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 0 | | 0 0 0 0 x_5 0 0 -x_4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_7 | | 0 0 0 0 0 0 0 0 0 -x_4 -x_5 -x_3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 x_2 0 0 0 -x_3 x_5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 x_2 0 x_3 0 -x_4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 x_2 -x_5 x_4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 -z 0 0 0 0 0 0 -x_3 x_5 0 0 -x_1 0 0 0 0 0 0 x_6 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 -z 0 0 0 0 x_3 0 -x_4 0 0 0 0 0 0 0 0 x_1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 -z 0 0 0 -x_5 x_4 0 0 0 0 x_5 0 0 0 0 0 0 -x_6 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 -z 0 0 -x_2 0 0 -x_4 0 0 0 0 0 x_1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 -z 0 0 -x_2 0 -x_5 0 0 0 -x_1 0 0 0 0 0 0 x_6 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -z 0 0 -x_2 -x_3 0 0 0 0 0 0 -x_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 x_1 0 0 -x_5 0 0 0 0 0 0 x_6 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_1 0 x_2 0 0 -x_1 0 0 0 0 0 0 x_6 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_2 0 x_3 0 0 -x_5 0 0 0 0 0 0 x_6 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_3 0 x_4 0 0 -x_1 0 0 0 0 0 0 x_6 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x_5 0 0 -x_4 0 0 0 0 0 0 0 0 0 0 0 x_6 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_3 -x_4 -x_2 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -x_2 x_4 0 -x_5 0 0 -x_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 x_2 0 -x_3 0 0 -x_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 -x_4 x_3 0 -x_4 0 0 -x_5 0 | f_4 = | 0 0 -x_6 0 0 x_7 0 0 0 0 0 0 0 0 | | -x_6 0 0 0 0 0 x_7 0 0 0 0 0 0 0 | | 0 0 0 x_6 0 0 0 x_7 0 0 0 0 0 0 | | 0 -x_1 0 0 0 0 0 0 x_7 0 0 0 0 0 | | 0 0 0 -x_4 0 0 0 0 0 x_7 0 0 0 0 | | 0 0 x_5 0 0 0 0 0 0 0 x_7 0 0 0 | | x_1 0 0 0 0 0 0 0 0 0 0 x_7 0 0 | | 0 0 0 -x_5 0 0 0 0 0 0 0 0 x_7 0 | | 0 0 x_1 0 0 0 0 0 0 0 0 0 0 x_7 | | 0 -x_3 x_5 0 0 0 0 0 0 0 0 0 0 0 | | x_3 0 -x_4 0 0 0 0 0 0 0 0 0 0 0 | | -x_5 x_4 0 0 0 0 0 0 0 0 0 0 0 0 | | -x_2 0 0 -x_4 0 0 0 0 0 0 0 0 0 0 | | 0 -x_2 0 -x_5 0 0 0 0 0 0 0 0 0 0 | | 0 0 -x_2 -x_3 0 0 0 0 0 0 0 0 0 0 | | z 0 0 0 -x_4 0 -x_1 0 0 0 0 0 0 0 | | 0 z 0 0 -x_5 0 0 0 -x_6 0 0 0 0 0 | | 0 0 z 0 -x_3 -x_1 0 0 0 0 0 0 0 0 | | 0 0 0 z x_2 0 0 x_1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 -x_4 0 -x_6 0 0 0 0 | | 0 0 0 0 0 -x_5 0 0 0 0 -x_6 0 0 0 | | 0 0 0 0 0 0 -x_1 0 0 0 0 -x_6 0 0 | | 0 0 0 0 0 0 0 -x_5 0 0 0 0 -x_6 0 | | 0 0 0 0 0 -x_1 0 0 0 0 0 0 0 -x_6 | | 0 0 0 0 0 0 -x_2 x_4 0 0 0 0 0 0 | | 0 0 0 0 0 x_2 0 -x_3 0 0 0 0 0 0 | | 0 0 0 0 0 -x_4 x_3 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 -x_3 0 -x_1 0 0 0 | | 0 0 0 0 0 0 0 0 -x_4 0 0 -x_5 0 0 | | 0 0 0 0 0 0 0 0 -x_2 0 0 0 -x_1 0 | | 0 0 0 0 0 0 0 0 0 0 x_1 0 0 -x_5 | | 0 0 0 0 0 0 0 0 0 -x_1 0 x_2 0 0 | | 0 0 0 0 0 0 0 0 0 0 -x_2 0 x_3 0 | | 0 0 0 0 0 0 0 0 0 0 0 -x_3 0 x_4 | | 0 0 0 0 0 0 0 0 0 x_5 0 0 -x_4 0 | f_5 = | -x_7x_4 | | -x_7x_5 | | -x_7x_3 | | x_7x_2 | | -x_7z+x_1x_6 | | -x_3x_6 | | -x_4x_6 | | -x_2x_6 | | -x_1x_5 | | x_2x_4 | | x_3x_5 | | x_1x_4 | | x_2x_5 | | x_1x_3 | ------------------------------------------------------------------------------------------------------------------------```