Description of fast matrix multiplication algorithm: ⟨19×19×27:5679⟩

Algorithm type

X^{7} Y^{8} Z^{11} + 7 X^{8} Y^{8} Z^{8} + X^{7} Y^{7} Z^{10} + X^{8} Y^{8} Z^{7} + 3 X^{14} Y^{4} Z^{4} + 3 X^{8} Y^{7} Z^{7} + 3 X^{7} Y^{8} Z^{7} + 3 X^{7} Y^{7} Z^{8} + 2 X^{4} Y^{14} Z^{4} + X^{4} Y^{4} Z^{14} + X^{13} Y^{4} Z^{4} + X^{8} Y^{7} Z^{6} + 2 X^{7} Y^{7} Z^{7} + X^{4} Y^{14} Z^{3} + X^{3} Y^{4} Z^{14} + X^{14} Y^{2} Z^{4} + X^{11} Y^{2} Z^{7} + X^{8} Y^{6} Z^{6} + 9 X^{7} Y^{6} Z^{7} + 3 X^{6} Y^{7} Z^{7} + 9 X^{6} Y^{6} Z^{8} + X^{4} Y^{9} Z^{7} + X^{4} Y^{8} Z^{8} + 6 X^{4} Y^{4} Z^{12} + X^{2} Y^{14} Z^{4} + X^{12} Y^{3} Z^{4} + 3 X^{7} Y^{6} Z^{6} + 7 X^{6} Y^{6} Z^{7} + 3 X^{4} Y^{8} Z^{7} + X^{4} Y^{4} Z^{11} + X^{12} Y^{3} Z^{3} + 2 X^{11} Y^{4} Z^{3} + X^{7} Y^{5} Z^{6} + 2 X^{6} Y^{5} Z^{7} + X^{4} Y^{11} Z^{3} + 2 X^{4} Y^{10} Z^{4} + X^{4} Y^{7} Z^{7} + 2 X^{4} Y^{6} Z^{8} + 4 X^{4} Y^{4} Z^{10} + X^{4} Y^{3} Z^{11} + 2 X^{4} Y^{2} Z^{12} + X^{3} Y^{8} Z^{7} + 4 X^{3} Y^{4} Z^{11} + 2 X^{10} Y^{4} Z^{3} + X^{8} Y^{3} Z^{6} + X^{5} Y^{5} Z^{7} + X^{4} Y^{10} Z^{3} + X^{4} Y^{7} Z^{6} + X^{4} Y^{6} Z^{7} + X^{4} Y^{2} Z^{11} + X^{3} Y^{6} Z^{8} + 5 X^{2} Y^{13} Z^{2} + X^{2} Y^{11} Z^{4} + X^{12} Y Z^{3} + X^{10} Y^{3} Z^{3} + X^{7} Y^{2} Z^{7} + 3 X^{6} Y^{4} Z^{6} + 2 X^{5} Y^{4} Z^{7} + X^{4} Y^{9} Z^{3} + 10 X^{4} Y^{8} Z^{4} + 65 X^{4} Y^{6} Z^{6} + 2 X^{4} Y^{4} Z^{8} + X^{4} Y^{3} Z^{9} + 2 X^{4} Y^{2} Z^{10} + X^{3} Y^{10} Z^{3} + X^{3} Y^{9} Z^{4} + X^{3} Y^{8} Z^{5} + 2 X^{3} Y^{3} Z^{10} + X^{2} Y^{13} Z + 2 X^{2} Y^{12} Z^{2} + X^{2} Y^{11} Z^{3} + X^{2} Y^{10} Z^{4} + X^{2} Y^{6} Z^{8} + 2 X^{5} Y^{4} Z^{6} + 35 X^{4} Y^{7} Z^{4} + X^{4} Y^{5} Z^{6} + 4 X^{4} Y^{4} Z^{7} + X^{3} Y^{9} Z^{3} + 2 X^{3} Y^{8} Z^{4} + X^{3} Y^{5} Z^{7} + 2 X^{3} Y^{2} Z^{10} + 7 X^{2} Y^{11} Z^{2} + 2 X^{2} Y^{6} Z^{7} + 3 X^{8} Y^{4} Z^{2} + X^{7} Y^{3} Z^{4} + X^{5} Y^{3} Z^{6} + 7 X^{4} Y^{7} Z^{3} + 14 X^{4} Y^{6} Z^{4} + X^{4} Y^{4} Z^{6} + 4 X^{4} Y^{3} Z^{7} + X^{4} Y Z^{9} + 2 X^{3} Y^{8} Z^{3} + 8 X^{3} Y^{7} Z^{4} + 2 X^{3} Y^{4} Z^{7} + 7 X^{2} Y^{10} Z^{2} + 2 X^{2} Y^{9} Z^{3} + 2 X^{2} Y^{8} Z^{4} + 96 X^{2} Y^{6} Z^{6} + 4 X^{2} Y^{4} Z^{8} + X^{8} Y^{3} Z^{2} + X^{7} Y^{4} Z^{2} + 2 X^{6} Y^{3} Z^{4} + 2 X^{5} Y^{4} Z^{4} + 2 X^{4} Y^{7} Z^{2} + 15 X^{4} Y^{5} Z^{4} + X^{4} Y^{4} Z^{5} + 4 X^{4} Y^{3} Z^{6} + X^{4} Y^{2} Z^{7} + 5 X^{3} Y^{7} Z^{3} + X^{3} Y^{3} Z^{7} + X^{2} Y^{8} Z^{3} + 7 X^{2} Y^{7} Z^{4} + X^{2} Y^{5} Z^{6} + 7 X^{8} Y^{2} Z^{2} + X^{7} Y^{3} Z^{2} + 10 X^{6} Y^{4} Z^{2} + 7 X^{6} Y^{2} Z^{4} + 2 X^{4} Y^{6} Z^{2} + X^{4} Y^{5} Z^{3} + 250 X^{4} Y^{4} Z^{4} + 19 X^{3} Y^{6} Z^{3} + X^{3} Y^{5} Z^{4} + X^{3} Y^{2} Z^{7} + 2 X^{2} Y^{9} Z + 10 X^{2} Y^{8} Z^{2} + 3 X^{2} Y^{7} Z^{3} + 12 X^{2} Y^{6} Z^{4} + 16 X^{2} Y^{4} Z^{6} + X^{2} Y^{3} Z^{7} + 19 X^{2} Y^{2} Z^{8} + 2 X Y^{9} Z^{2} + X Y^{5} Z^{6} + 2 X^{8} Y Z^{2} + X^{7} Y^{2} Z^{2} + 2 X^{6} Y Z^{4} + 2 X^{5} Y^{4} Z^{2} + 13 X^{4} Y^{4} Z^{3} + 57 X^{4} Y^{3} Z^{4} + 4 X^{3} Y^{6} Z^{2} + 10 X^{3} Y^{4} Z^{4} + X^{2} Y^{8} Z + 3 X^{2} Y^{7} Z^{2} + 5 X^{2} Y^{5} Z^{4} + 7 X^{2} Y^{3} Z^{6} + 2 X^{2} Y^{2} Z^{7} + 2 X Y^{9} Z + X Y^{7} Z^{3} + 2 X Y^{6} Z^{4} + 2 X Y^{4} Z^{6} + 65 X^{6} Y^{2} Z^{2} + X^{6} Y Z^{3} + 8 X^{5} Y^{4} Z + 2 X^{5} Y^{3} Z^{2} + 2 X^{5} Y^{2} Z^{3} + 9 X^{4} Y^{4} Z^{2} + 163 X^{4} Y^{3} Z^{3} + 33 X^{4} Y^{2} Z^{4} + 2 X^{3} Y^{4} Z^{3} + 19 X^{3} Y^{3} Z^{4} + 46 X^{2} Y^{6} Z^{2} + 53 X^{2} Y^{4} Z^{4} + X^{2} Y^{3} Z^{5} + 48 X^{2} Y^{2} Z^{6} + X Y^{8} Z + X Y^{6} Z^{3} + 3 X Y^{4} Z^{5} + X^{5} Y^{3} Z + 4 X^{5} Y^{2} Z^{2} + 7 X^{4} Y^{3} Z^{2} + 4 X^{4} Y Z^{4} + 2 X^{3} Y^{4} Z^{2} + 5 X^{3} Y^{3} Z^{3} + 2 X^{3} Y^{2} Z^{4} + 16 X^{2} Y^{5} Z^{2} + 14 X^{2} Y^{4} Z^{3} + 22 X^{2} Y^{3} Z^{4} + 7 X^{2} Y^{2} Z^{5} + 7 X^{2} Y Z^{6} + 12 X Y^{6} Z^{2} + 2 X Y^{4} Z^{4} + 6 X Y^{2} Z^{6} + 2 X^{5} Y^{2} Z + X^{5} Y Z^{2} + 43 X^{4} Y^{2} Z^{2} + X^{4} Y Z^{3} + 2 X^{3} Y^{3} Z^{2} + 2 X^{3} Y^{2} Z^{3} + 2 X^{2} Y^{5} Z + 370 X^{2} Y^{4} Z^{2} + 407 X^{2} Y^{3} Z^{3} + 252 X^{2} Y^{2} Z^{4} + 72 X Y^{6} Z + 2 X Y^{3} Z^{4} + 30 X Y Z^{6} + X^{5} Y Z + 2 X^{4} Y Z^{2} + 38 X^{3} Y^{2} Z^{2} + 11 X^{2} Y^{4} Z + 41 X^{2} Y^{3} Z^{2} + 3 X^{2} Y^{2} Z^{3} + 22 X^{2} Y Z^{4} + 46 X Y^{4} Z^{2} + 243 X Y^{3} Z^{3} + 40 X Y^{2} Z^{4} + 86 X^{3} Y^{2} Z + 42 X^{3} Y Z^{2} + 2 X^{2} Y^{3} Z + 653 X^{2} Y^{2} Z^{2} + 38 X Y^{4} Z + 18 X Y^{3} Z^{2} + 30 X Y^{2} Z^{3} + 33 X Y Z^{4} + 110 X^{3} Y Z + 82 X^{2} Y^{2} Z + 86 X^{2} Y Z^{2} + 82 X Y^{3} Z + 316 X Y^{2} Z^{2} + 53 X Y Z^{3} + 94 X^{2} Y Z + 266 X Y^{2} Z + 276 X Y Z^{2} + 256 X Y Z

Algorithm definition

The algorithm ⟨19×19×27:5679⟩ could be constructed using the following decomposition:

⟨19×19×27:5679⟩ = ⟨10×9×15:870⟩ + ⟨10×9×15:870⟩ + ⟨9×10×12:696⟩ + ⟨10×10×12:795⟩ + ⟨9×10×15:870⟩ + ⟨9×9×12:600⟩ + ⟨10×10×15:978⟩.

This decomposition is defined by the following equality:

Trace (Mul ((\begin{matrix} A_1_1 & A_1_2 & A_1_3 & A_1_4 & A_1_5 & A_1_6 & A_1_7 & A_1_8 & A_1_9 & A_1_10 & A_1_11 & A_1_12 & A_1_13 & A_1_14 & A_1_15 & A_1_16 & A_1_17 & A_1_18 & A_1_19 \\ A_2_1 & A_2_2 & A_2_3 & A_2_4 & A_2_5 & A_2_6 & A_2_7 & A_2_8 & A_2_9 & A_2_10 & A_2_11 & A_2_12 & A_2_13 & A_2_14 & A_2_15 & A_2_16 & A_2_17 & A_2_18 & A_2_19 \\ A_3_1 & A_3_2 & A_3_3 & A_3_4 & A_3_5 & A_3_6 & A_3_7 & A_3_8 & A_3_9 & A_3_10 & A_3_11 & A_3_12 & A_3_13 & A_3_14 & A_3_15 & A_3_16 & A_3_17 & A_3_18 & A_3_19 \\ A_4_1 & A_4_2 & A_4_3 & A_4_4 & A_4_5 & A_4_6 & A_4_7 & A_4_8 & A_4_9 & A_4_10 & A_4_11 & A_4_12 & A_4_13 & A_4_14 & A_4_15 & A_4_16 & A_4_17 & A_4_18 & A_4_19 \\ A_5_1 & A_5_2 & A_5_3 & A_5_4 & A_5_5 & A_5_6 & A_5_7 & A_5_8 & A_5_9 & A_5_10 & A_5_11 & A_5_12 & A_5_13 & A_5_14 & A_5_15 & A_5_16 & A_5_17 & A_5_18 & A_5_19 \\ A_6_1 & A_6_2 & A_6_3 & A_6_4 & A_6_5 & A_6_6 & A_6_7 & A_6_8 & A_6_9 & A_6_10 & A_6_11 & A_6_12 & A_6_13 & A_6_14 & A_6_15 & A_6_16 & A_6_17 & A_6_18 & A_6_19 \\ A_7_1 & A_7_2 & A_7_3 & A_7_4 & A_7_5 & A_7_6 & A_7_7 & A_7_8 & A_7_9 & A_7_10 & A_7_11 & A_7_12 & A_7_13 & A_7_14 & A_7_15 & A_7_16 & A_7_17 & A_7_18 & A_7_19 \\ A_8_1 & A_8_2 & A_8_3 & A_8_4 & A_8_5 & A_8_6 & A_8_7 & A_8_8 & A_8_9 & A_8_10 & A_8_11 & A_8_12 & A_8_13 & A_8_14 & A_8_15 & A_8_16 & A_8_17 & A_8_18 & A_8_19 \\ A_9_1 & A_9_2 & A_9_3 & A_9_4 & A_9_5 & A_9_6 & A_9_7 & A_9_8 & A_9_9 & A_9_10 & A_9_11 & A_9_12 & A_9_13 & A_9_14 & A_9_15 & A_9_16 & A_9_17 & A_9_18 & A_9_19 \\ A_10_1 & A_10_2 & A_10_3 & A_10_4 & A_10_5 & A_10_6 & A_10_7 & A_10_8 & A_10_9 & A_10_10 & A_10_11 & A_10_12 & A_10_13 & A_10_14 & A_10_15 & A_10_16 & A_10_17 & A_10_18 & A_10_19 \\ A_11_1 & A_11_2 & A_11_3 & A_11_4 & A_11_5 & A_11_6 & A_11_7 & A_11_8 & A_11_9 & A_11_10 & A_11_11 & A_11_12 & A_11_13 & A_11_14 & A_11_15 & A_11_16 & A_11_17 & A_11_18 & A_11_19 \\ A_12_1 & A_12_2 & A_12_3 & A_12_4 & A_12_5 & A_12_6 & A_12_7 & A_12_8 & A_12_9 & A_12_10 & A_12_11 & A_12_12 & A_12_13 & A_12_14 & A_12_15 & A_12_16 & A_12_17 & A_12_18 & A_12_19 \\ A_13_1 & A_13_2 & A_13_3 & A_13_4 & A_13_5 & A_13_6 & A_13_7 & A_13_8 & A_13_9 & A_13_10 & A_13_11 & A_13_12 & A_13_13 & A_13_14 & A_13_15 & A_13_16 & A_13_17 & A_13_18 & A_13_19 \\ A_14_1 & A_14_2 & A_14_3 & A_14_4 & A_14_5 & A_14_6 & A_14_7 & A_14_8 & A_14_9 & A_14_10 & A_14_11 & A_14_12 & A_14_13 & A_14_14 & A_14_15 & A_14_16 & A_14_17 & A_14_18 & A_14_19 \\ A_15_1 & A_15_2 & A_15_3 & A_15_4 & A_15_5 & A_15_6 & A_15_7 & A_15_8 & A_15_9 & A_15_10 & A_15_11 & A_15_12 & A_15_13 & A_15_14 & A_15_15 & A_15_16 & A_15_17 & A_15_18 & A_15_19 \\ A_16_1 & A_16_2 & A_16_3 & A_16_4 & A_16_5 & A_16_6 & A_16_7 & A_16_8 & A_16_9 & A_16_10 & A_16_11 & A_16_12 & A_16_13 & A_16_14 & A_16_15 & A_16_16 & A_16_17 & A_16_18 & A_16_19 \\ A_17_1 & A_17_2 & A_17_3 & A_17_4 & A_17_5 & A_17_6 & A_17_7 & A_17_8 & A_17_9 & A_17_10 & A_17_11 & A_17_12 & A_17_13 & A_17_14 & A_17_15 & A_17_16 & A_17_17 & A_17_18 & A_17_19 \\ A_18_1 & A_18_2 & A_18_3 & A_18_4 & A_18_5 & A_18_6 & A_18_7 & A_18_8 & A_18_9 & A_18_10 & A_18_11 & A_18_12 & A_18_13 & A_18_14 & A_18_15 & A_18_16 & A_18_17 & A_18_18 & A_18_19 \\ A_19_1 & A_19_2 & A_19_3 & A_19_4 & A_19_5 & A_19_6 & A_19_7 & A_19_8 & A_19_9 & A_19_10 & A_19_11 & A_19_12 & A_19_13 & A_19_14 & A_19_15 & A_19_16 & A_19_17 & A_19_18 & A_19_19 \end{matrix}), (\begin{matrix} B_1_1 & B_1_2 & B_1_3 & B_1_4 & B_1_5 & B_1_6 & B_1_7 & B_1_8 & B_1_9 & B_1_10 & B_1_11 & B_1_12 & B_1_13 & B_1_14 & B_1_15 & B_1_16 & B_1_17 & B_1_18 & B_1_19 & B_1_20 & B_1_21 & B_1_22 & B_1_23 & B_1_24 & B_1_25 & B_1_26 & B_1_27 \\ B_2_1 & B_2_2 & B_2_3 & B_2_4 & B_2_5 & B_2_6 & B_2_7 & B_2_8 & B_2_9 & B_2_10 & B_2_11 & B_2_12 & B_2_13 & B_2_14 & B_2_15 & B_2_16 & B_2_17 & B_2_18 & B_2_19 & B_2_20 & B_2_21 & B_2_22 & B_2_23 & B_2_24 & B_2_25 & B_2_26 & B_2_27 \\ B_3_1 & B_3_2 & B_3_3 & B_3_4 & B_3_5 & B_3_6 & B_3_7 & B_3_8 & B_3_9 & B_3_10 & B_3_11 & B_3_12 & B_3_13 & B_3_14 & B_3_15 & B_3_16 & B_3_17 & B_3_18 & B_3_19 & B_3_20 & B_3_21 & B_3_22 & B_3_23 & B_3_24 & B_3_25 & B_3_26 & B_3_27 \\ B_4_1 & B_4_2 & B_4_3 & B_4_4 & B_4_5 & B_4_6 & B_4_7 & B_4_8 & B_4_9 & B_4_10 & B_4_11 & B_4_12 & B_4_13 & B_4_14 & B_4_15 & B_4_16 & B_4_17 & B_4_18 & B_4_19 & B_4_20 & B_4_21 & B_4_22 & B_4_23 & B_4_24 & B_4_25 & B_4_26 & B_4_27 \\ B_5_1 & B_5_2 & B_5_3 & B_5_4 & B_5_5 & B_5_6 & B_5_7 & B_5_8 & B_5_9 & B_5_10 & B_5_11 & B_5_12 & B_5_13 & B_5_14 & B_5_15 & B_5_16 & B_5_17 & B_5_18 & B_5_19 & B_5_20 & B_5_21 & B_5_22 & B_5_23 & B_5_24 & B_5_25 & B_5_26 & B_5_27 \\ B_6_1 & B_6_2 & B_6_3 & B_6_4 & B_6_5 & B_6_6 & B_6_7 & B_6_8 & B_6_9 & B_6_10 & B_6_11 & B_6_12 & B_6_13 & B_6_14 & B_6_15 & B_6_16 & B_6_17 & B_6_18 & B_6_19 & B_6_20 & B_6_21 & B_6_22 & B_6_23 & B_6_24 & B_6_25 & B_6_26 & B_6_27 \\ B_7_1 & B_7_2 & B_7_3 & B_7_4 & B_7_5 & B_7_6 & B_7_7 & B_7_8 & B_7_9 & B_7_10 & B_7_11 & B_7_12 & B_7_13 & B_7_14 & B_7_15 & B_7_16 & B_7_17 & B_7_18 & B_7_19 & B_7_20 & B_7_21 & B_7_22 & B_7_23 & B_7_24 & B_7_25 & B_7_26 & B_7_27 \\ B_8_1 & B_8_2 & B_8_3 & B_8_4 & B_8_5 & B_8_6 & B_8_7 & B_8_8 & B_8_9 & B_8_10 & B_8_11 & B_8_12 & B_8_13 & B_8_14 & B_8_15 & B_8_16 & B_8_17 & B_8_18 & B_8_19 & B_8_20 & B_8_21 & B_8_22 & B_8_23 & B_8_24 & B_8_25 & B_8_26 & B_8_27 \\ B_9_1 & B_9_2 & B_9_3 & B_9_4 & B_9_5 & B_9_6 & B_9_7 & B_9_8 & B_9_9 & B_9_10 & B_9_11 & B_9_12 & B_9_13 & B_9_14 & B_9_15 & B_9_16 & B_9_17 & B_9_18 & B_9_19 & B_9_20 & B_9_21 & B_9_22 & B_9_23 & B_9_24 & B_9_25 & B_9_26 & B_9_27 \\ B_10_1 & B_10_2 & B_10_3 & B_10_4 & B_10_5 & B_10_6 & B_10_7 & B_10_8 & B_10_9 & B_10_10 & B_10_11 & B_10_12 & B_10_13 & B_10_14 & B_10_15 & B_10_16 & B_10_17 & B_10_18 & B_10_19 & B_10_20 & B_10_21 & B_10_22 & B_10_23 & B_10_24 & B_10_25 & B_10_26 & B_10_27 \\ B_11_1 & B_11_2 & B_11_3 & B_11_4 & B_11_5 & B_11_6 & B_11_7 & B_11_8 & B_11_9 & B_11_10 & B_11_11 & B_11_12 & B_11_13 & B_11_14 & B_11_15 & B_11_16 & B_11_17 & B_11_18 & B_11_19 & B_11_20 & B_11_21 & B_11_22 & B_11_23 & B_11_24 & B_11_25 & B_11_26 & B_11_27 \\ B_12_1 & B_12_2 & B_12_3 & B_12_4 & B_12_5 & B_12_6 & B_12_7 & B_12_8 & B_12_9 & B_12_10 & B_12_11 & B_12_12 & B_12_13 & B_12_14 & B_12_15 & B_12_16 & B_12_17 & B_12_18 & B_12_19 & B_12_20 & B_12_21 & B_12_22 & B_12_23 & B_12_24 & B_12_25 & B_12_26 & B_12_27 \\ B_13_1 & B_13_2 & B_13_3 & B_13_4 & B_13_5 & B_13_6 & B_13_7 & B_13_8 & B_13_9 & B_13_10 & B_13_11 & B_13_12 & B_13_13 & B_13_14 & B_13_15 & B_13_16 & B_13_17 & B_13_18 & B_13_19 & B_13_20 & B_13_21 & B_13_22 & B_13_23 & B_13_24 & B_13_25 & B_13_26 & B_13_27 \\ B_14_1 & B_14_2 & B_14_3 & B_14_4 & B_14_5 & B_14_6 & B_14_7 & B_14_8 & B_14_9 & B_14_10 & B_14_11 & B_14_12 & B_14_13 & B_14_14 & B_14_15 & B_14_16 & B_14_17 & B_14_18 & B_14_19 & B_14_20 & B_14_21 & B_14_22 & B_14_23 & B_14_24 & B_14_25 & B_14_26 & B_14_27 \\ B_15_1 & B_15_2 & B_15_3 & B_15_4 & B_15_5 & B_15_6 & B_15_7 & B_15_8 & B_15_9 & B_15_10 & B_15_11 & B_15_12 & B_15_13 & B_15_14 & B_15_15 & B_15_16 & B_15_17 & B_15_18 & B_15_19 & B_15_20 & B_15_21 & B_15_22 & B_15_23 & B_15_24 & B_15_25 & B_15_26 & B_15_27 \\ B_16_1 & B_16_2 & B_16_3 & B_16_4 & B_16_5 & B_16_6 & B_16_7 & B_16_8 & B_16_9 & B_16_10 & B_16_11 & B_16_12 & B_16_13 & B_16_14 & B_16_15 & B_16_16 & B_16_17 & B_16_18 & B_16_19 & B_16_20 & B_16_21 & B_16_22 & B_16_23 & B_16_24 & B_16_25 & B_16_26 & B_16_27 \\ B_17_1 & B_17_2 & B_17_3 & B_17_4 & B_17_5 & B_17_6 & B_17_7 & B_17_8 & B_17_9 & B_17_10 & B_17_11 & B_17_12 & B_17_13 & B_17_14 & B_17_15 & B_17_16 & B_17_17 & B_17_18 & B_17_19 & B_17_20 & B_17_21 & B_17_22 & B_17_23 & B_17_24 & B_17_25 & B_17_26 & B_17_27 \\ B_18_1 & B_18_2 & B_18_3 & B_18_4 & B_18_5 & B_18_6 & B_18_7 & B_18_8 & B_18_9 & B_18_10 & B_18_11 & B_18_12 & B_18_13 & B_18_14 & B_18_15 & B_18_16 & B_18_17 & B_18_18 & B_18_19 & B_18_20 & B_18_21 & B_18_22 & B_18_23 & B_18_24 & B_18_25 & B_18_26 & B_18_27 \\ B_19_1 & B_19_2 & B_19_3 & B_19_4 & B_19_5 & B_19_6 & B_19_7 & B_19_8 & B_19_9 & B_19_10 & B_19_11 & B_19_12 & B_19_13 & B_19_14 & B_19_15 & B_19_16 & B_19_17 & B_19_18 & B_19_19 & B_19_20 & B_19_21 & B_19_22 & B_19_23 & B_19_24 & B_19_25 & B_19_26 & B_19_27 \end{matrix}), (\begin{matrix} C_1_1 & C_1_2 & C_1_3 & C_1_4 & C_1_5 & C_1_6 & C_1_7 & C_1_8 & C_1_9 & C_1_10 & C_1_11 & C_1_12 & C_1_13 & C_1_14 & C_1_15 & C_1_16 & C_1_17 & C_1_18 & C_1_19 \\ C_2_1 & C_2_2 & C_2_3 & C_2_4 & C_2_5 & C_2_6 & C_2_7 & C_2_8 & C_2_9 & C_2_10 & C_2_11 & C_2_12 & C_2_13 & C_2_14 & C_2_15 & C_2_16 & C_2_17 & C_2_18 & C_2_19 \\ C_3_1 & C_3_2 & C_3_3 & C_3_4 & C_3_5 & C_3_6 & C_3_7 & C_3_8 & C_3_9 & C_3_10 & C_3_11 & C_3_12 & C_3_13 & C_3_14 & C_3_15 & C_3_16 & C_3_17 & C_3_18 & C_3_19 \\ C_4_1 & C_4_2 & C_4_3 & C_4_4 & C_4_5 & C_4_6 & C_4_7 & C_4_8 & C_4_9 & C_4_10 & C_4_11 & C_4_12 & C_4_13 & C_4_14 & C_4_15 & C_4_16 & C_4_17 & C_4_18 & C_4_19 \\ C_5_1 & C_5_2 & C_5_3 & C_5_4 & C_5_5 & C_5_6 & C_5_7 & C_5_8 & C_5_9 & C_5_10 & C_5_11 & C_5_12 & C_5_13 & C_5_14 & C_5_15 & C_5_16 & C_5_17 & C_5_18 & C_5_19 \\ C_6_1 & C_6_2 & C_6_3 & C_6_4 & C_6_5 & C_6_6 & C_6_7 & C_6_8 & C_6_9 & C_6_10 & C_6_11 & C_6_12 & C_6_13 & C_6_14 & C_6_15 & C_6_16 & C_6_17 & C_6_18 & C_6_19 \\ C_7_1 & C_7_2 & C_7_3 & C_7_4 & C_7_5 & C_7_6 & C_7_7 & C_7_8 & C_7_9 & C_7_10 & C_7_11 & C_7_12 & C_7_13 & C_7_14 & C_7_15 & C_7_16 & C_7_17 & C_7_18 & C_7_19 \\ C_8_1 & C_8_2 & C_8_3 & C_8_4 & C_8_5 & C_8_6 & C_8_7 & C_8_8 & C_8_9 & C_8_10 & C_8_11 & C_8_12 & C_8_13 & C_8_14 & C_8_15 & C_8_16 & C_8_17 & C_8_18 & C_8_19 \\ C_9_1 & C_9_2 & C_9_3 & C_9_4 & C_9_5 & C_9_6 & C_9_7 & C_9_8 & C_9_9 & C_9_10 & C_9_11 & C_9_12 & C_9_13 & C_9_14 & C_9_15 & C_9_16 & C_9_17 & C_9_18 & C_9_19 \\ C_10_1 & C_10_2 & C_10_3 & C_10_4 & C_10_5 & C_10_6 & C_10_7 & C_10_8 & C_10_9 & C_10_10 & C_10_11 & C_10_12 & C_10_13 & C_10_14 & C_10_15 & C_10_16 & C_10_17 & C_10_18 & C_10_19 \\ C_11_1 & C_11_2 & C_11_3 & C_11_4 & C_11_5 & C_11_6 & C_11_7 & C_11_8 & C_11_9 & C_11_10 & C_11_11 & C_11_12 & C_11_13 & C_11_14 & C_11_15 & C_11_16 & C_11_17 & C_11_18 & C_11_19 \\ C_12_1 & C_12_2 & C_12_3 & C_12_4 & C_12_5 & C_12_6 & C_12_7 & C_12_8 & C_12_9 & C_12_10 & C_12_11 & C_12_12 & C_12_13 & C_12_14 & C_12_15 & C_12_16 & C_12_17 & C_12_18 & C_12_19 \\ C_13_1 & C_13_2 & C_13_3 & C_13_4 & C_13_5 & C_13_6 & C_13_7 & C_13_8 & C_13_9 & C_13_10 & C_13_11 & C_13_12 & C_13_13 & C_13_14 & C_13_15 & C_13_16 & C_13_17 & C_13_18 & C_13_19 \\ C_14_1 & C_14_2 & C_14_3 & C_14_4 & C_14_5 & C_14_6 & C_14_7 & C_14_8 & C_14_9 & C_14_10 & C_14_11 & C_14_12 & C_14_13 & C_14_14 & C_14_15 & C_14_16 & C_14_17 & C_14_18 & C_14_19 \\ C_15_1 & C_15_2 & C_15_3 & C_15_4 & C_15_5 & C_15_6 & C_15_7 & C_15_8 & C_15_9 & C_15_10 & C_15_11 & C_15_12 & C_15_13 & C_15_14 & C_15_15 & C_15_16 & C_15_17 & C_15_18 & C_15_19 \\ C_16_1 & C_16_2 & C_16_3 & C_16_4 & C_16_5 & C_16_6 & C_16_7 & C_16_8 & C_16_9 & C_16_10 & C_16_11 & C_16_12 & C_16_13 & C_16_14 & C_16_15 & C_16_16 & C_16_17 & C_16_18 & C_16_19 \\ C_17_1 & C_17_2 & C_17_3 & C_17_4 & C_17_5 & C_17_6 & C_17_7 & C_17_8 & C_17_9 & C_17_10 & C_17_11 & C_17_12 & C_17_13 & C_17_14 & C_17_15 & C_17_16 & C_17_17 & C_17_18 & C_17_19 \\ C_18_1 & C_18_2 & C_18_3 & C_18_4 & C_18_5 & C_18_6 & C_18_7 & C_18_8 & C_18_9 & C_18_10 & C_18_11 & C_18_12 & C_18_13 & C_18_14 & C_18_15 & C_18_16 & C_18_17 & C_18_18 & C_18_19 \\ C_19_1 & C_19_2 & C_19_3 & C_19_4 & C_19_5 & C_19_6 & C_19_7 & C_19_8 & C_19_9 & C_19_10 & C_19_11 & C_19_12 & C_19_13 & C_19_14 & C_19_15 & C_19_16 & C_19_17 & C_19_18 & C_19_19 \\ C_20_1 & C_20_2 & C_20_3 & C_20_4 & C_20_5 & C_20_6 & C_20_7 & C_20_8 & C_20_9 & C_20_10 & C_20_11 & C_20_12 & C_20_13 & C_20_14 & C_20_15 & C_20_16 & C_20_17 & C_20_18 & C_20_19 \\ C_21_1 & C_21_2 & C_21_3 & C_21_4 & C_21_5 & C_21_6 & C_21_7 & C_21_8 & C_21_9 & C_21_10 & C_21_11 & C_21_12 & C_21_13 & C_21_14 & C_21_15 & C_21_16 & C_21_17 & C_21_18 & C_21_19 \\ C_22_1 & C_22_2 & C_22_3 & C_22_4 & C_22_5 & C_22_6 & C_22_7 & C_22_8 & C_22_9 & C_22_10 & C_22_11 & C_22_12 & C_22_13 & C_22_14 & C_22_15 & C_22_16 & C_22_17 & C_22_18 & C_22_19 \\ C_23_1 & C_23_2 & C_23_3 & C_23_4 & C_23_5 & C_23_6 & C_23_7 & C_23_8 & C_23_9 & C_23_10 & C_23_11 & C_23_12 & C_23_13 & C_23_14 & C_23_15 & C_23_16 & C_23_17 & C_23_18 & C_23_19 \\ C_24_1 & C_24_2 & C_24_3 & C_24_4 & C_24_5 & C_24_6 & C_24_7 & C_24_8 & C_24_9 & C_24_10 & C_24_11 & C_24_12 & C_24_13 & C_24_14 & C_24_15 & C_24_16 & C_24_17 & C_24_18 & C_24_19 \\ C_25_1 & C_25_2 & C_25_3 & C_25_4 & C_25_5 & C_25_6 & C_25_7 & C_25_8 & C_25_9 & C_25_10 & C_25_11 & C_25_12 & C_25_13 & C_25_14 & C_25_15 & C_25_16 & C_25_17 & C_25_18 & C_25_19 \\ C_26_1 & C_26_2 & C_26_3 & C_26_4 & C_26_5 & C_26_6 & C_26_7 & C_26_8 & C_26_9 & C_26_10 & C_26_11 & C_26_12 & C_26_13 & C_26_14 & C_26_15 & C_26_16 & C_26_17 & C_26_18 & C_26_19 \\ C_27_1 & C_27_2 & C_27_3 & C_27_4 & C_27_5 & C_27_6 & C_27_7 & C_27_8 & C_27_9 & C_27_10 & C_27_11 & C_27_12 & C_27_13 & C_27_14 & C_27_15 & C_27_16 & C_27_17 & C_27_18 & C_27_19 \end{matrix}))) = Trace (Mul ((\begin{matrix} A_5_6 - A_5_11 & A_5_7 - A_5_12 & A_5_8 - A_5_13 & A_5_9 - A_5_14 & A_5_10 - A_5_15 & A_5_1 - A_5_16 & A_5_2 - A_5_17 & A_5_3 - A_5_18 & A_5_4 - A_5_19 \\ A_11_6 - A_11_11 & A_11_7 - A_11_12 & A_11_8 - A_11_13 & A_11_9 - A_11_14 & A_11_10 - A_11_15 & A_11_1 - A_11_16 & A_11_2 - A_11_17 & A_11_3 - A_11_18 & A_11_4 - A_11_19 \\ A_12_6 - A_12_11 & A_12_7 - A_12_12 & A_12_8 - A_12_13 & A_12_9 - A_12_14 & A_12_10 - A_12_15 & A_12_1 - A_12_16 & A_12_2 - A_12_17 & A_12_3 - A_12_18 & A_12_4 - A_12_19 \\ A_13_6 - A_13_11 & A_13_7 - A_13_12 & A_13_8 - A_13_13 & A_13_9 - A_13_14 & A_13_10 - A_13_15 & A_13_1 - A_13_16 & A_13_2 - A_13_17 & A_13_3 - A_13_18 & A_13_4 - A_13_19 \\ A_14_6 - A_14_11 & A_14_7 - A_14_12 & A_14_8 - A_14_13 & A_14_9 - A_14_14 & A_14_10 - A_14_15 & A_14_1 - A_14_16 & A_14_2 - A_14_17 & A_14_3 - A_14_18 & A_14_4 - A_14_19 \\ A_15_6 - A_15_11 & A_15_7 - A_15_12 & A_15_8 - A_15_13 & A_15_9 - A_15_14 & A_15_10 - A_15_15 & A_15_1 - A_15_16 & A_15_2 - A_15_17 & A_15_3 - A_15_18 & A_15_4 - A_15_19 \\ A_16_6 - A_16_11 & A_16_7 - A_16_12 & A_16_8 - A_16_13 & A_16_9 - A_16_14 & A_16_10 - A_16_15 & A_16_1 - A_16_16 & A_16_2 - A_16_17 & A_16_3 - A_16_18 & A_16_4 - A_16_19 \\ A_17_6 - A_17_11 & A_17_7 - A_17_12 & A_17_8 - A_17_13 & A_17_9 - A_17_14 & A_17_10 - A_17_15 & A_17_1 - A_17_16 & A_17_2 - A_17_17 & A_17_3 - A_17_18 & A_17_4 - A_17_19 \\ A_18_6 - A_18_11 & A_18_7 - A_18_12 & A_18_8 - A_18_13 & A_18_9 - A_18_14 & A_18_10 - A_18_15 & A_18_1 - A_18_16 & A_18_2 - A_18_17 & A_18_3 - A_18_18 & A_18_4 - A_18_19 \\ A_19_6 - A_19_11 & A_19_7 - A_19_12 & A_19_8 - A_19_13 & A_19_9 - A_19_14 & A_19_10 - A_19_15 & A_19_1 - A_19_16 & A_19_2 - A_19_17 & A_19_3 - A_19_18 & A_19_4 - A_19_19 \end{matrix}), (\begin{matrix} B_6_13 & B_6_14 & B_6_15 & - B_6_1 + B_6_16 & - B_6_2 + B_6_17 & - B_6_3 + B_6_18 & - B_6_4 + B_6_19 & - B_6_5 + B_6_20 & - B_6_6 + B_6_21 & - B_6_7 + B_6_22 & - B_6_8 + B_6_23 & - B_6_9 + B_6_24 & - B_6_10 + B_6_25 & - B_6_11 + B_6_26 & - B_6_12 + B_6_27 \\ B_7_13 & B_7_14 & B_7_15 & - B_7_1 + B_7_16 & - B_7_2 + B_7_17 & - B_7_3 + B_7_18 & - B_7_4 + B_7_19 & - B_7_5 + B_7_20 & - B_7_6 + B_7_21 & - B_7_7 + B_7_22 & - B_7_8 + B_7_23 & - B_7_9 + B_7_24 & - B_7_10 + B_7_25 & - B_7_11 + B_7_26 & - B_7_12 + B_7_27 \\ B_8_13 & B_8_14 & B_8_15 & - B_8_1 + B_8_16 & - B_8_2 + B_8_17 & - B_8_3 + B_8_18 & - B_8_4 + B_8_19 & - B_8_5 + B_8_20 & - B_8_6 + B_8_21 & - B_8_7 + B_8_22 & - B_8_8 + B_8_23 & - B_8_9 + B_8_24 & - B_8_10 + B_8_25 & - B_8_11 + B_8_26 & - B_8_12 + B_8_27 \\ B_9_13 & B_9_14 & B_9_15 & - B_9_1 + B_9_16 & - B_9_2 + B_9_17 & - B_9_3 + B_9_18 & - B_9_4 + B_9_19 & - B_9_5 + B_9_20 & - B_9_6 + B_9_21 & - B_9_7 + B_9_22 & - B_9_8 + B_9_23 & - B_9_9 + B_9_24 & - B_9_10 + B_9_25 & - B_9_11 + B_9_26 & - B_9_12 + B_9_27 \\ B_10_13 & B_10_14 & B_10_15 & - B_10_1 + B_10_16 & - B_10_2 + B_10_17 & - B_10_3 + B_10_18 & - B_10_4 + B_10_19 & - B_10_5 + B_10_20 & - B_10_6 + B_10_21 & - B_10_7 + B_10_22 & - B_10_8 + B_10_23 & - B_10_9 + B_10_24 & - B_10_10 + B_10_25 & - B_10_11 + B_10_26 & - B_10_12 + B_10_27 \\ B_1_13 & B_1_14 & B_1_15 & - B_1_1 + B_1_16 & - B_1_2 + B_1_17 & - B_1_3 + B_1_18 & - B_1_4 + B_1_19 & - B_1_5 + B_1_20 & - B_1_6 + B_1_21 & - B_1_7 + B_1_22 & - B_1_8 + B_1_23 & - B_1_9 + B_1_24 & - B_1_10 + B_1_25 & - B_1_11 + B_1_26 & - B_1_12 + B_1_27 \\ B_2_13 & B_2_14 & B_2_15 & - B_2_1 + B_2_16 & - B_2_2 + B_2_17 & - B_2_3 + B_2_18 & - B_2_4 + B_2_19 & - B_2_5 + B_2_20 & - B_2_6 + B_2_21 & - B_2_7 + B_2_22 & - B_2_8 + B_2_23 & - B_2_9 + B_2_24 & - B_2_10 + B_2_25 & - B_2_11 + B_2_26 & - B_2_12 + B_2_27 \\ B_3_13 & B_3_14 & B_3_15 & - B_3_1 + B_3_16 & - B_3_2 + B_3_17 & - B_3_3 + B_3_18 & - B_3_4 + B_3_19 & - B_3_5 + B_3_20 & - B_3_6 + B_3_21 & - B_3_7 + B_3_22 & - B_3_8 + B_3_23 & - B_3_9 + B_3_24 & - B_3_10 + B_3_25 & - B_3_11 + B_3_26 & - B_3_12 + B_3_27 \\ B_4_13 & B_4_14 & B_4_15 & - B_4_1 + B_4_16 & - B_4_2 + B_4_17 & - B_4_3 + B_4_18 & - B_4_4 + B_4_19 & - B_4_5 + B_4_20 & - B_4_6 + B_4_21 & - B_4_7 + B_4_22 & - B_4_8 + B_4_23 & - B_4_9 + B_4_24 & - B_4_10 + B_4_25 & - B_4_11 + B_4_26 & - B_4_12 + B_4_27 \end{matrix}), (\begin{matrix} C_13_5 & - C_13_6 + C_13_11 & - C_13_7 + C_13_12 & - C_13_8 + C_13_13 & - C_13_9 + C_13_14 & - C_13_10 + C_13_15 & - C_13_1 + C_13_16 & - C_13_2 + C_13_17 & - C_13_3 + C_13_18 & - C_13_4 + C_13_19 \\ C_14_5 & - C_14_6 + C_14_11 & - C_14_7 + C_14_12 & - C_14_8 + C_14_13 & - C_14_9 + C_14_14 & - C_14_10 + C_14_15 & - C_14_1 + C_14_16 & - C_14_2 + C_14_17 & - C_14_3 + C_14_18 & - C_14_4 + C_14_19 \\ C_15_5 & - C_15_6 + C_15_11 & - C_15_7 + C_15_12 & - C_15_8 + C_15_13 & - C_15_9 + C_15_14 & - C_15_10 + C_15_15 & - C_15_1 + C_15_16 & - C_15_2 + C_15_17 & - C_15_3 + C_15_18 & - C_15_4 + C_15_19 \\ C_16_5 & - C_16_6 + C_16_11 & - C_16_7 + C_16_12 & - C_16_8 + C_16_13 & - C_16_9 + C_16_14 & - C_16_10 + C_16_15 & - C_16_1 + C_16_16 & - C_16_2 + C_16_17 & - C_16_3 + C_16_18 & - C_16_4 + C_16_19 \\ C_17_5 & - C_17_6 + C_17_11 & - C_17_7 + C_17_12 & - C_17_8 + C_17_13 & - C_17_9 + C_17_14 & - C_17_10 + C_17_15 & - C_17_1 + C_17_16 & - C_17_2 + C_17_17 & - C_17_3 + C_17_18 & - C_17_4 + C_17_19 \\ C_18_5 & - C_18_6 + C_18_11 & - C_18_7 + C_18_12 & - C_18_8 + C_18_13 & - C_18_9 + C_18_14 & - C_18_10 + C_18_15 & - C_18_1 + C_18_16 & - C_18_2 + C_18_17 & - C_18_3 + C_18_18 & - C_18_4 + C_18_19 \\ C_19_5 & - C_19_6 + C_19_11 & - C_19_7 + C_19_12 & - C_19_8 + C_19_13 & - C_19_9 + C_19_14 & - C_19_10 + C_19_15 & - C_19_1 + C_19_16 & - C_19_2 + C_19_17 & - C_19_3 + C_19_18 & - C_19_4 + C_19_19 \\ C_20_5 & - C_20_6 + C_20_11 & - C_20_7 + C_20_12 & - C_20_8 + C_20_13 & - C_20_9 + C_20_14 & - C_20_10 + C_20_15 & - C_20_1 + C_20_16 & - C_20_2 + C_20_17 & - C_20_3 + C_20_18 & - C_20_4 + C_20_19 \\ C_21_5 & - C_21_6 + C_21_11 & - C_21_7 + C_21_12 & - C_21_8 + C_21_13 & - C_21_9 + C_21_14 & - C_21_10 + C_21_15 & - C_21_1 + C_21_16 & - C_21_2 + C_21_17 & - C_21_3 + C_21_18 & - C_21_4 + C_21_19 \\ C_22_5 & - C_22_6 + C_22_11 & - C_22_7 + C_22_12 & - C_22_8 + C_22_13 & - C_22_9 + C_22_14 & - C_22_10 + C_22_15 & - C_22_1 + C_22_16 & - C_22_2 + C_22_17 & - C_22_3 + C_22_18 & - C_22_4 + C_22_19 \\ C_23_5 & - C_23_6 + C_23_11 & - C_23_7 + C_23_12 & - C_23_8 + C_23_13 & - C_23_9 + C_23_14 & - C_23_10 + C_23_15 & - C_23_1 + C_23_16 & - C_23_2 + C_23_17 & - C_23_3 + C_23_18 & - C_23_4 + C_23_19 \\ C_24_5 & - C_24_6 + C_24_11 & - C_24_7 + C_24_12 & - C_24_8 + C_24_13 & - C_24_9 + C_24_14 & - C_24_10 + C_24_15 & - C_24_1 + C_24_16 & - C_24_2 + C_24_17 & - C_24_3 + C_24_18 & - C_24_4 + C_24_19 \\ C_25_5 & - C_25_6 + C_25_11 & - C_25_7 + C_25_12 & - C_25_8 + C_25_13 & - C_25_9 + C_25_14 & - C_25_10 + C_25_15 & - C_25_1 + C_25_16 & - C_25_2 + C_25_17 & - C_25_3 + C_25_18 & - C_25_4 + C_25_19 \\ C_26_5 & - C_26_6 + C_26_11 & - C_26_7 + C_26_12 & - C_26_8 + C_26_13 & - C_26_9 + C_26_14 & - C_26_10 + C_26_15 & - C_26_1 + C_26_16 & - C_26_2 + C_26_17 & - C_26_3 + C_26_18 & - C_26_4 + C_26_19 \\ C_27_5 & - C_27_6 + C_27_11 & - C_27_7 + C_27_12 & - C_27_8 + C_27_13 & - C_27_9 + C_27_14 & - C_27_10 + C_27_15 & - C_27_1 + C_27_16 & - C_27_2 + C_27_17 & - C_27_3 + C_27_18 & - C_27_4 + C_27_19 \end{matrix}))) + Trace (Mul ((\begin{matrix} A_5_6 & A_5_7 & A_5_8 & A_5_9 & A_5_10 & A_5_1 & A_5_2 & A_5_3 & A_5_4 \\ A_6_6 + A_11_6 & A_6_7 + A_11_7 & A_6_8 + A_11_8 & A_6_9 + A_11_9 & A_6_10 + A_11_10 & A_6_1 + A_11_1 & A_6_2 + A_11_2 & A_6_3 + A_11_3 & A_6_4 + A_11_4 \\ A_7_6 + A_12_6 & A_7_7 + A_12_7 & A_7_8 + A_12_8 & A_7_9 + A_12_9 & A_7_10 + A_12_10 & A_7_1 + A_12_1 & A_7_2 + A_12_2 & A_7_3 + A_12_3 & A_7_4 + A_12_4 \\ A_8_6 + A_13_6 & A_8_7 + A_13_7 & A_8_8 + A_13_8 & A_8_9 + A_13_9 & A_8_10 + A_13_10 & A_8_1 + A_13_1 & A_8_2 + A_13_2 & A_8_3 + A_13_3 & A_8_4 + A_13_4 \\ A_9_6 + A_14_6 & A_9_7 + A_14_7 & A_9_8 + A_14_8 & A_9_9 + A_14_9 & A_9_10 + A_14_10 & A_9_1 + A_14_1 & A_9_2 + A_14_2 & A_9_3 + A_14_3 & A_9_4 + A_14_4 \\ A_10_6 + A_15_6 & A_10_7 + A_15_7 & A_10_8 + A_15_8 & A_10_9 + A_15_9 & A_10_10 + A_15_10 & A_10_1 + A_15_1 & A_10_2 + A_15_2 & A_10_3 + A_15_3 & A_10_4 + A_15_4 \\ A_1_6 + A_16_6 & A_1_7 + A_16_7 & A_1_8 + A_16_8 & A_1_9 + A_16_9 & A_1_10 + A_16_10 & A_1_1 + A_16_1 & A_1_2 + A_16_2 & A_1_3 + A_16_3 & A_1_4 + A_16_4 \\ A_2_6 + A_17_6 & A_2_7 + A_17_7 & A_2_8 + A_17_8 & A_2_9 + A_17_9 & A_2_10 + A_17_10 & A_2_1 + A_17_1 & A_2_2 + A_17_2 & A_2_3 + A_17_3 & A_2_4 + A_17_4 \\ A_3_6 + A_18_6 & A_3_7 + A_18_7 & A_3_8 + A_18_8 & A_3_9 + A_18_9 & A_3_10 + A_18_10 & A_3_1 + A_18_1 & A_3_2 + A_18_2 & A_3_3 + A_18_3 & A_3_4 + A_18_4 \\ A_4_6 + A_19_6 & A_4_7 + A_19_7 & A_4_8 + A_19_8 & A_4_9 + A_19_9 & A_4_10 + A_19_10 & A_4_1 + A_19_1 & A_4_2 + A_19_2 & A_4_3 + A_19_3 & A_4_4 + A_19_4 \end{matrix}), (\begin{matrix} B_6_13 + B_11_13 & B_6_14 + B_11_14 & B_6_15 + B_11_15 & B_6_16 + B_11_16 & B_6_17 + B_11_17 & B_6_18 + B_11_18 & B_6_19 + B_11_19 & B_6_20 + B_11_20 & B_6_21 + B_11_21 & B_6_22 + B_11_22 & B_6_23 + B_11_23 & B_6_24 + B_11_24 & B_6_25 + B_11_25 & B_6_26 + B_11_26 & B_6_27 + B_11_27 \\ B_7_13 + B_12_13 & B_7_14 + B_12_14 & B_7_15 + B_12_15 & B_7_16 + B_12_16 & B_7_17 + B_12_17 & B_7_18 + B_12_18 & B_7_19 + B_12_19 & B_7_20 + B_12_20 & B_7_21 + B_12_21 & B_7_22 + B_12_22 & B_7_23 + B_12_23 & B_7_24 + B_12_24 & B_7_25 + B_12_25 & B_7_26 + B_12_26 & B_7_27 + B_12_27 \\ B_8_13 + B_13_13 & B_8_14 + B_13_14 & B_8_15 + B_13_15 & B_8_16 + B_13_16 & B_8_17 + B_13_17 & B_8_18 + B_13_18 & B_8_19 + B_13_19 & B_8_20 + B_13_20 & B_8_21 + B_13_21 & B_8_22 + B_13_22 & B_8_23 + B_13_23 & B_8_24 + B_13_24 & B_8_25 + B_13_25 & B_8_26 + B_13_26 & B_8_27 + B_13_27 \\ B_9_13 + B_14_13 & B_9_14 + B_14_14 & B_9_15 + B_14_15 & B_9_16 + B_14_16 & B_9_17 + B_14_17 & B_9_18 + B_14_18 & B_9_19 + B_14_19 & B_9_20 + B_14_20 & B_9_21 + B_14_21 & B_9_22 + B_14_22 & B_9_23 + B_14_23 & B_9_24 + B_14_24 & B_9_25 + B_14_25 & B_9_26 + B_14_26 & B_9_27 + B_14_27 \\ B_10_13 + B_15_13 & B_10_14 + B_15_14 & B_10_15 + B_15_15 & B_10_16 + B_15_16 & B_10_17 + B_15_17 & B_10_18 + B_15_18 & B_10_19 + B_15_19 & B_10_20 + B_15_20 & B_10_21 + B_15_21 & B_10_22 + B_15_22 & B_10_23 + B_15_23 & B_10_24 + B_15_24 & B_10_25 + B_15_25 & B_10_26 + B_15_26 & B_10_27 + B_15_27 \\ B_1_13 + B_16_13 & B_1_14 + B_16_14 & B_1_15 + B_16_15 & B_1_16 + B_16_16 & B_1_17 + B_16_17 & B_1_18 + B_16_18 & B_1_19 + B_16_19 & B_1_20 + B_16_20 & B_1_21 + B_16_21 & B_1_22 + B_16_22 & B_1_23 + B_16_23 & B_1_24 + B_16_24 & B_1_25 + B_16_25 & B_1_26 + B_16_26 & B_1_27 + B_16_27 \\ B_2_13 + B_17_13 & B_2_14 + B_17_14 & B_2_15 + B_17_15 & B_2_16 + B_17_16 & B_2_17 + B_17_17 & B_2_18 + B_17_18 & B_2_19 + B_17_19 & B_2_20 + B_17_20 & B_2_21 + B_17_21 & B_2_22 + B_17_22 & B_2_23 + B_17_23 & B_2_24 + B_17_24 & B_2_25 + B_17_25 & B_2_26 + B_17_26 & B_2_27 + B_17_27 \\ B_3_13 + B_18_13 & B_3_14 + B_18_14 & B_3_15 + B_18_15 & B_3_16 + B_18_16 & B_3_17 + B_18_17 & B_3_18 + B_18_18 & B_3_19 + B_18_19 & B_3_20 + B_18_20 & B_3_21 + B_18_21 & B_3_22 + B_18_22 & B_3_23 + B_18_23 & B_3_24 + B_18_24 & B_3_25 + B_18_25 & B_3_26 + B_18_26 & B_3_27 + B_18_27 \\ B_4_13 + B_19_13 & B_4_14 + B_19_14 & B_4_15 + B_19_15 & B_4_16 + B_19_16 & B_4_17 + B_19_17 & B_4_18 + B_19_18 & B_4_19 + B_19_19 & B_4_20 + B_19_20 & B_4_21 + B_19_21 & B_4_22 + B_19_22 & B_4_23 + B_19_23 & B_4_24 + B_19_24 & B_4_25 + B_19_25 & B_4_26 + B_19_26 & B_4_27 + B_19_27 \end{matrix}), (\begin{matrix} C_13_5 & C_13_11 & C_13_12 & C_13_13 & C_13_14 & C_13_15 & C_13_16 & C_13_17 & C_13_18 & C_13_19 \\ C_14_5 & C_14_11 & C_14_12 & C_14_13 & C_14_14 & C_14_15 & C_14_16 & C_14_17 & C_14_18 & C_14_19 \\ C_15_5 & C_15_11 & C_15_12 & C_15_13 & C_15_14 & C_15_15 & C_15_16 & C_15_17 & C_15_18 & C_15_19 \\ C_1_5 + C_16_5 & C_1_11 + C_16_11 & C_1_12 + C_16_12 & C_1_13 + C_16_13 & C_1_14 + C_16_14 & C_1_15 + C_16_15 & C_1_16 + C_16_16 & C_1_17 + C_16_17 & C_1_18 + C_16_18 & C_1_19 + C_16_19 \\ C_2_5 + C_17_5 & C_2_11 + C_17_11 & C_2_12 + C_17_12 & C_2_13 + C_17_13 & C_2_14 + C_17_14 & C_2_15 + C_17_15 & C_2_16 + C_17_16 & C_2_17 + C_17_17 & C_2_18 + C_17_18 & C_2_19 + C_17_19 \\ C_3_5 + C_18_5 & C_3_11 + C_18_11 & C_3_12 + C_18_12 & C_3_13 + C_18_13 & C_3_14 + C_18_14 & C_3_15 + C_18_15 & C_3_16 + C_18_16 & C_3_17 + C_18_17 & C_3_18 + C_18_18 & C_3_19 + C_18_19 \\ C_4_5 + C_19_5 & C_4_11 + C_19_11 & C_4_12 + C_19_12 & C_4_13 + C_19_13 & C_4_14 + C_19_14 & C_4_15 + C_19_15 & C_4_16 + C_19_16 & C_4_17 + C_19_17 & C_4_18 + C_19_18 & C_4_19 + C_19_19 \\ C_5_5 + C_20_5 & C_5_11 + C_20_11 & C_5_12 + C_20_12 & C_5_13 + C_20_13 & C_5_14 + C_20_14 & C_5_15 + C_20_15 & C_5_16 + C_20_16 & C_5_17 + C_20_17 & C_5_18 + C_20_18 & C_5_19 + C_20_19 \\ C_6_5 + C_21_5 & C_6_11 + C_21_11 & C_6_12 + C_21_12 & C_6_13 + C_21_13 & C_6_14 + C_21_14 & C_6_15 + C_21_15 & C_6_16 + C_21_16 & C_6_17 + C_21_17 & C_6_18 + C_21_18 & C_6_19 + C_21_19 \\ C_7_5 + C_22_5 & C_7_11 + C_22_11 & C_7_12 + C_22_12 & C_7_13 + C_22_13 & C_7_14 + C_22_14 & C_7_15 + C_22_15 & C_7_16 + C_22_16 & C_7_17 + C_22_17 & C_7_18 + C_22_18 & C_7_19 + C_22_19 \\ C_8_5 + C_23_5 & C_8_11 + C_23_11 & C_8_12 + C_23_12 & C_8_13 + C_23_13 & C_8_14 + C_23_14 & C_8_15 + C_23_15 & C_8_16 + C_23_16 & C_8_17 + C_23_17 & C_8_18 + C_23_18 & C_8_19 + C_23_19 \\ C_9_5 + C_24_5 & C_9_11 + C_24_11 & C_9_12 + C_24_12 & C_9_13 + C_24_13 & C_9_14 + C_24_14 & C_9_15 + C_24_15 & C_9_16 + C_24_16 & C_9_17 + C_24_17 & C_9_18 + C_24_18 & C_9_19 + C_24_19 \\ C_10_5 + C_25_5 & C_10_11 + C_25_11 & C_10_12 + C_25_12 & C_10_13 + C_25_13 & C_10_14 + C_25_14 & C_10_15 + C_25_15 & C_10_16 + C_25_16 & C_10_17 + C_25_17 & C_10_18 + C_25_18 & C_10_19 + C_25_19 \\ C_11_5 + C_26_5 & C_11_11 + C_26_11 & C_11_12 + C_26_12 & C_11_13 + C_26_13 & C_11_14 + C_26_14 & C_11_15 + C_26_15 & C_11_16 + C_26_16 & C_11_17 + C_26_17 & C_11_18 + C_26_18 & C_11_19 + C_26_19 \\ C_12_5 + C_27_5 & C_12_11 + C_27_11 & C_12_12 + C_27_12 & C_12_13 + C_27_13 & C_12_14 + C_27_14 & C_12_15 + C_27_15 & C_12_16 + C_27_16 & C_12_17 + C_27_17 & C_12_18 + C_27_18 & C_12_19 + C_27_19 \end{matrix}))) + Trace (Mul ((\begin{matrix} A_6_5 & A_6_11 & A_6_12 & A_6_13 & A_6_14 & A_6_15 & A_6_16 & A_6_17 & A_6_18 & A_6_19 \\ A_7_5 & A_7_11 & A_7_12 & A_7_13 & A_7_14 & A_7_15 & A_7_16 & A_7_17 & A_7_18 & A_7_19 \\ A_8_5 & A_8_11 & A_8_12 & A_8_13 & A_8_14 & A_8_15 & A_8_16 & A_8_17 & A_8_18 & A_8_19 \\ A_9_5 & A_9_11 & A_9_12 & A_9_13 & A_9_14 & A_9_15 & A_9_16 & A_9_17 & A_9_18 & A_9_19 \\ A_10_5 & A_10_11 & A_10_12 & A_10_13 & A_10_14 & A_10_15 & A_10_16 & A_10_17 & A_10_18 & A_10_19 \\ A_1_5 & A_1_11 & A_1_12 & A_1_13 & A_1_14 & A_1_15 & A_1_16 & A_1_17 & A_1_18 & A_1_19 \\ A_2_5 & A_2_11 & A_2_12 & A_2_13 & A_2_14 & A_2_15 & A_2_16 & A_2_17 & A_2_18 & A_2_19 \\ A_3_5 & A_3_11 & A_3_12 & A_3_13 & A_3_14 & A_3_15 & A_3_16 & A_3_17 & A_3_18 & A_3_19 \\ A_4_5 & A_4_11 & A_4_12 & A_4_13 & A_4_14 & A_4_15 & A_4_16 & A_4_17 & A_4_18 & A_4_19 \end{matrix}), (\begin{matrix} B_5_1 & B_5_2 & B_5_3 & B_5_4 & B_5_5 & B_5_6 & B_5_7 & B_5_8 & B_5_9 & B_5_10 & B_5_11 & B_5_12 \\ B_11_1 & B_11_2 & B_11_3 & B_11_4 & B_11_5 & B_11_6 & B_11_7 & B_11_8 & B_11_9 & B_11_10 & B_11_11 & B_11_12 \\ B_12_1 & B_12_2 & B_12_3 & B_12_4 & B_12_5 & B_12_6 & B_12_7 & B_12_8 & B_12_9 & B_12_10 & B_12_11 & B_12_12 \\ B_13_1 & B_13_2 & B_13_3 & B_13_4 & B_13_5 & B_13_6 & B_13_7 & B_13_8 & B_13_9 & B_13_10 & B_13_11 & B_13_12 \\ B_14_1 & B_14_2 & B_14_3 & B_14_4 & B_14_5 & B_14_6 & B_14_7 & B_14_8 & B_14_9 & B_14_10 & B_14_11 & B_14_12 \\ B_15_1 & B_15_2 & B_15_3 & B_15_4 & B_15_5 & B_15_6 & B_15_7 & B_15_8 & B_15_9 & B_15_10 & B_15_11 & B_15_12 \\ B_16_1 & B_16_2 & B_16_3 & B_16_4 & B_16_5 & B_16_6 & B_16_7 & B_16_8 & B_16_9 & B_16_10 & B_16_11 & B_16_12 \\ B_17_1 & B_17_2 & B_17_3 & B_17_4 & B_17_5 & B_17_6 & B_17_7 & B_17_8 & B_17_9 & B_17_10 & B_17_11 & B_17_12 \\ B_18_1 & B_18_2 & B_18_3 & B_18_4 & B_18_5 & B_18_6 & B_18_7 & B_18_8 & B_18_9 & B_18_10 & B_18_11 & B_18_12 \\ B_19_1 & B_19_2 & B_19_3 & B_19_4 & B_19_5 & B_19_6 & B_19_7 & B_19_8 & B_19_9 & B_19_10 & B_19_11 & B_19_12 \end{matrix}), (\begin{matrix} C_1_6 & C_1_7 & C_1_8 & C_1_9 & C_1_10 & C_1_1 & C_1_2 & C_1_3 & C_1_4 \\ C_2_6 & C_2_7 & C_2_8 & C_2_9 & C_2_10 & C_2_1 & C_2_2 & C_2_3 & C_2_4 \\ C_3_6 & C_3_7 & C_3_8 & C_3_9 & C_3_10 & C_3_1 & C_3_2 & C_3_3 & C_3_4 \\ C_4_6 & C_4_7 & C_4_8 & C_4_9 & C_4_10 & C_4_1 & C_4_2 & C_4_3 & C_4_4 \\ C_5_6 & C_5_7 & C_5_8 & C_5_9 & C_5_10 & C_5_1 & C_5_2 & C_5_3 & C_5_4 \\ C_6_6 & C_6_7 & C_6_8 & C_6_9 & C_6_10 & C_6_1 & C_6_2 & C_6_3 & C_6_4 \\ C_7_6 & C_7_7 & C_7_8 & C_7_9 & C_7_10 & C_7_1 & C_7_2 & C_7_3 & C_7_4 \\ C_8_6 & C_8_7 & C_8_8 & C_8_9 & C_8_10 & C_8_1 & C_8_2 & C_8_3 & C_8_4 \\ C_9_6 & C_9_7 & C_9_8 & C_9_9 & C_9_10 & C_9_1 & C_9_2 & C_9_3 & C_9_4 \\ C_10_6 & C_10_7 & C_10_8 & C_10_9 & C_10_10 & C_10_1 & C_10_2 & C_10_3 & C_10_4 \\ C_11_6 & C_11_7 & C_11_8 & C_11_9 & C_11_10 & C_11_1 & C_11_2 & C_11_3 & C_11_4 \\ C_12_6 & C_12_7 & C_12_8 & C_12_9 & C_12_10 & C_12_1 & C_12_2 & C_12_3 & C_12_4 \end{matrix}))) + Trace (Mul ((\begin{matrix} A_5_5 & A_5_11 & A_5_12 & A_5_13 & A_5_14 & A_5_15 & A_5_16 & A_5_17 & A_5_18 & A_5_19 \\ A_11_5 & A_11_11 & A_11_12 & A_11_13 & A_11_14 & A_11_15 & A_11_16 & A_11_17 & A_11_18 & A_11_19 \\ A_12_5 & A_12_11 & A_12_12 & A_12_13 & A_12_14 & A_12_15 & A_12_16 & A_12_17 & A_12_18 & A_12_19 \\ A_13_5 & A_13_11 & A_13_12 & A_13_13 & A_13_14 & A_13_15 & A_13_16 & A_13_17 & A_13_18 & A_13_19 \\ A_14_5 & A_14_11 & A_14_12 & A_14_13 & A_14_14 & A_14_15 & A_14_16 & A_14_17 & A_14_18 & A_14_19 \\ A_15_5 & A_15_11 & A_15_12 & A_15_13 & A_15_14 & A_15_15 & A_15_16 & A_15_17 & A_15_18 & A_15_19 \\ A_16_5 & A_16_11 & A_16_12 & A_16_13 & A_16_14 & A_16_15 & A_16_16 & A_16_17 & A_16_18 & A_16_19 \\ A_17_5 & A_17_11 & A_17_12 & A_17_13 & A_17_14 & A_17_15 & A_17_16 & A_17_17 & A_17_18 & A_17_19 \\ A_18_5 & A_18_11 & A_18_12 & A_18_13 & A_18_14 & A_18_15 & A_18_16 & A_18_17 & A_18_18 & A_18_19 \\ A_19_5 & A_19_11 & A_19_12 & A_19_13 & A_19_14 & A_19_15 & A_19_16 & A_19_17 & A_19_18 & A_19_19 \end{matrix}), (\begin{matrix} B_5_1 - B_5_16 & B_5_2 - B_5_17 & B_5_3 - B_5_18 & B_5_4 - B_5_19 & B_5_5 - B_5_20 & B_5_6 - B_5_21 & B_5_7 - B_5_22 & B_5_8 - B_5_23 & B_5_9 - B_5_24 & B_5_10 - B_5_25 & B_5_11 - B_5_26 & B_5_12 - B_5_27 \\ B_6_1 + B_11_1 - B_6_16 - B_11_16 & B_6_2 + B_11_2 - B_6_17 - B_11_17 & B_6_3 + B_11_3 - B_6_18 - B_11_18 & B_6_4 + B_11_4 - B_6_19 - B_11_19 & B_6_5 + B_11_5 - B_6_20 - B_11_20 & B_6_6 + B_11_6 - B_6_21 - B_11_21 & B_6_7 + B_11_7 - B_6_22 - B_11_22 & B_6_8 + B_11_8 - B_6_23 - B_11_23 & B_6_9 + B_11_9 - B_6_24 - B_11_24 & B_6_10 + B_11_10 - B_6_25 - B_11_25 & B_6_11 + B_11_11 - B_6_26 - B_11_26 & B_6_12 + B_11_12 - B_6_27 - B_11_27 \\ B_7_1 + B_12_1 - B_7_16 - B_12_16 & B_7_2 + B_12_2 - B_7_17 - B_12_17 & B_7_3 + B_12_3 - B_7_18 - B_12_18 & B_7_4 + B_12_4 - B_7_19 - B_12_19 & B_7_5 + B_12_5 - B_7_20 - B_12_20 & B_7_6 + B_12_6 - B_12_21 - B_7_21 & B_7_7 + B_12_7 - B_12_22 - B_7_22 & B_7_8 + B_12_8 - B_7_23 - B_12_23 & B_7_9 + B_12_9 - B_7_24 - B_12_24 & B_7_10 + B_12_10 - B_7_25 - B_12_25 & B_7_11 + B_12_11 - B_7_26 - B_12_26 & B_7_12 + B_12_12 - B_7_27 - B_12_27 \\ B_8_1 + B_13_1 - B_8_16 - B_13_16 & B_8_2 + B_13_2 - B_8_17 - B_13_17 & B_8_3 + B_13_3 - B_8_18 - B_13_18 & B_8_4 + B_13_4 - B_8_19 - B_13_19 & B_8_5 + B_13_5 - B_8_20 - B_13_20 & B_8_6 + B_13_6 - B_8_21 - B_13_21 & B_8_7 + B_13_7 - B_8_22 - B_13_22 & B_8_8 + B_13_8 - B_8_23 - B_13_23 & B_8_9 + B_13_9 - B_8_24 - B_13_24 & B_8_10 + B_13_10 - B_8_25 - B_13_25 & B_8_11 + B_13_11 - B_8_26 - B_13_26 & B_8_12 + B_13_12 - B_8_27 - B_13_27 \\ B_9_1 + B_14_1 - B_9_16 - B_14_16 & B_9_2 + B_14_2 - B_9_17 - B_14_17 & B_9_3 + B_14_3 - B_9_18 - B_14_18 & B_9_4 + B_14_4 - B_9_19 - B_14_19 & B_9_5 + B_14_5 - B_9_20 - B_14_20 & B_9_6 + B_14_6 - B_9_21 - B_14_21 & B_9_7 + B_14_7 - B_9_22 - B_14_22 & B_9_8 + B_14_8 - B_9_23 - B_14_23 & B_9_9 + B_14_9 - B_9_24 - B_14_24 & B_9_10 + B_14_10 - B_9_25 - B_14_25 & B_9_11 + B_14_11 - B_9_26 - B_14_26 & B_9_12 + B_14_12 - B_9_27 - B_14_27 \\ B_10_1 + B_15_1 - B_10_16 - B_15_16 & B_10_2 + B_15_2 - B_10_17 - B_15_17 & B_10_3 + B_15_3 - B_10_18 - B_15_18 & B_10_4 + B_15_4 - B_10_19 - B_15_19 & B_10_5 + B_15_5 - B_10_20 - B_15_20 & B_10_6 + B_15_6 - B_10_21 - B_15_21 & B_10_7 + B_15_7 - B_10_22 - B_15_22 & B_10_8 + B_15_8 - B_10_23 - B_15_23 & B_10_9 + B_15_9 - B_10_24 - B_15_24 & B_10_10 + B_15_10 - B_10_25 - B_15_25 & B_10_11 + B_15_11 - B_10_26 - B_15_26 & B_10_12 + B_15_12 - B_10_27 - B_15_27 \\ B_1_1 + B_16_1 - B_1_16 - B_16_16 & B_1_2 + B_16_2 - B_1_17 - B_16_17 & B_1_3 + B_16_3 - B_1_18 - B_16_18 & B_1_4 + B_16_4 - B_1_19 - B_16_19 & B_1_5 + B_16_5 - B_1_20 - B_16_20 & B_1_6 + B_16_6 - B_1_21 - B_16_21 & B_1_7 + B_16_7 - B_1_22 - B_16_22 & B_1_8 + B_16_8 - B_1_23 - B_16_23 & B_1_9 + B_16_9 - B_1_24 - B_16_24 & B_1_10 + B_16_10 - B_1_25 - B_16_25 & B_1_11 + B_16_11 - B_1_26 - B_16_26 & B_1_12 + B_16_12 - B_1_27 - B_16_27 \\ B_2_1 + B_17_1 - B_2_16 - B_17_16 & B_2_2 + B_17_2 - B_2_17 - B_17_17 & B_2_3 + B_17_3 - B_2_18 - B_17_18 & B_2_4 + B_17_4 - B_2_19 - B_17_19 & B_2_5 + B_17_5 - B_2_20 - B_17_20 & B_2_6 + B_17_6 - B_2_21 - B_17_21 & B_2_7 + B_17_7 - B_2_22 - B_17_22 & B_2_8 + B_17_8 - B_2_23 - B_17_23 & B_2_9 + B_17_9 - B_2_24 - B_17_24 & B_2_10 + B_17_10 - B_2_25 - B_17_25 & B_2_11 + B_17_11 - B_2_26 - B_17_26 & B_2_12 + B_17_12 - B_2_27 - B_17_27 \\ B_3_1 + B_18_1 - B_3_16 - B_18_16 & B_3_2 + B_18_2 - B_3_17 - B_18_17 & B_3_3 + B_18_3 - B_3_18 - B_18_18 & B_3_4 + B_18_4 - B_3_19 - B_18_19 & B_3_5 + B_18_5 - B_3_20 - B_18_20 & B_3_6 + B_18_6 - B_3_21 - B_18_21 & B_3_7 + B_18_7 - B_3_22 - B_18_22 & B_3_8 + B_18_8 - B_3_23 - B_18_23 & B_3_9 + B_18_9 - B_3_24 - B_18_24 & B_3_10 + B_18_10 - B_3_25 - B_18_25 & B_3_11 + B_18_11 - B_3_26 - B_18_26 & B_3_12 + B_18_12 - B_3_27 - B_18_27 \\ B_4_1 + B_19_1 - B_4_16 - B_19_16 & B_4_2 + B_19_2 - B_4_17 - B_19_17 & B_4_3 + B_19_3 - B_4_18 - B_19_18 & B_4_4 + B_19_4 - B_4_19 - B_19_19 & B_4_5 + B_19_5 - B_4_20 - B_19_20 & B_4_6 + B_19_6 - B_4_21 - B_19_21 & B_4_7 + B_19_7 - B_4_22 - B_19_22 & B_4_8 + B_19_8 - B_4_23 - B_19_23 & B_4_9 + B_19_9 - B_4_24 - B_19_24 & B_4_10 + B_19_10 - B_4_25 - B_19_25 & B_4_11 + B_19_11 - B_4_26 - B_19_26 & B_4_12 + B_19_12 - B_4_27 - B_19_27 \end{matrix}), (\begin{matrix} C_1_5 & C_1_11 & C_1_12 & C_1_13 & C_1_14 & C_1_15 & C_1_16 & C_1_17 & C_1_18 & C_1_19 \\ C_2_5 & C_2_11 & C_2_12 & C_2_13 & C_2_14 & C_2_15 & C_2_16 & C_2_17 & C_2_18 & C_2_19 \\ C_3_5 & C_3_11 & C_3_12 & C_3_13 & C_3_14 & C_3_15 & C_3_16 & C_3_17 & C_3_18 & C_3_19 \\ C_4_5 & C_4_11 & C_4_12 & C_4_13 & C_4_14 & C_4_15 & C_4_16 & C_4_17 & C_4_18 & C_4_19 \\ C_5_5 & C_5_11 & C_5_12 & C_5_13 & C_5_14 & C_5_15 & C_5_16 & C_5_17 & C_5_18 & C_5_19 \\ C_6_5 & C_6_11 & C_6_12 & C_6_13 & C_6_14 & C_6_15 & C_6_16 & C_6_17 & C_6_18 & C_6_19 \\ C_7_5 & C_7_11 & C_7_12 & C_7_13 & C_7_14 & C_7_15 & C_7_16 & C_7_17 & C_7_18 & C_7_19 \\ C_8_5 & C_8_11 & C_8_12 & C_8_13 & C_8_14 & C_8_15 & C_8_16 & C_8_17 & C_8_18 & C_8_19 \\ C_9_5 & C_9_11 & C_9_12 & C_9_13 & C_9_14 & C_9_15 & C_9_16 & C_9_17 & C_9_18 & C_9_19 \\ C_10_5 & C_10_11 & C_10_12 & C_10_13 & C_10_14 & C_10_15 & C_10_16 & C_10_17 & C_10_18 & C_10_19 \\ C_11_5 & C_11_11 & C_11_12 & C_11_13 & C_11_14 & C_11_15 & C_11_16 & C_11_17 & C_11_18 & C_11_19 \\ C_12_5 & C_12_11 & C_12_12 & C_12_13 & C_12_14 & C_12_15 & C_12_16 & C_12_17 & C_12_18 & C_12_19 \end{matrix}))) + Trace (Mul ((\begin{matrix} A_6_5 + A_11_5 & - A_6_6 - A_11_6 + A_6_11 + A_11_11 & - A_6_7 - A_11_7 + A_6_12 + A_11_12 & - A_6_8 - A_11_8 + A_6_13 + A_11_13 & - A_6_9 - A_11_9 + A_6_14 + A_11_14 & - A_6_10 - A_11_10 + A_6_15 + A_11_15 & - A_6_1 - A_11_1 + A_6_16 + A_11_16 & - A_6_2 - A_11_2 + A_6_17 + A_11_17 & - A_6_3 - A_11_3 + A_6_18 + A_11_18 & - A_6_4 - A_11_4 + A_6_19 + A_11_19 \\ A_7_5 + A_12_5 & - A_7_6 - A_12_6 + A_7_11 + A_12_11 & - A_7_7 - A_12_7 + A_7_12 + A_12_12 & - A_7_8 - A_12_8 + A_7_13 + A_12_13 & - A_7_9 - A_12_9 + A_7_14 + A_12_14 & - A_7_10 - A_12_10 + A_7_15 + A_12_15 & - A_7_1 - A_12_1 + A_7_16 + A_12_16 & - A_7_2 - A_12_2 + A_7_17 + A_12_17 & - A_7_3 - A_12_3 + A_7_18 + A_12_18 & - A_7_4 - A_12_4 + A_7_19 + A_12_19 \\ A_8_5 + A_13_5 & - A_8_6 - A_13_6 + A_8_11 + A_13_11 & - A_8_7 - A_13_7 + A_8_12 + A_13_12 & - A_8_8 - A_13_8 + A_8_13 + A_13_13 & - A_8_9 - A_13_9 + A_8_14 + A_13_14 & - A_8_10 - A_13_10 + A_8_15 + A_13_15 & - A_8_1 - A_13_1 + A_8_16 + A_13_16 & - A_8_2 - A_13_2 + A_8_17 + A_13_17 & - A_8_3 - A_13_3 + A_8_18 + A_13_18 & - A_8_4 - A_13_4 + A_8_19 + A_13_19 \\ A_9_5 + A_14_5 & - A_9_6 - A_14_6 + A_9_11 + A_14_11 & - A_9_7 - A_14_7 + A_9_12 + A_14_12 & - A_9_8 - A_14_8 + A_9_13 + A_14_13 & - A_9_9 - A_14_9 + A_9_14 + A_14_14 & - A_9_10 - A_14_10 + A_9_15 + A_14_15 & - A_9_1 - A_14_1 + A_9_16 + A_14_16 & - A_9_2 - A_14_2 + A_9_17 + A_14_17 & - A_9_3 - A_14_3 + A_9_18 + A_14_18 & - A_9_4 - A_14_4 + A_9_19 + A_14_19 \\ A_10_5 + A_15_5 & - A_10_6 - A_15_6 + A_10_11 + A_15_11 & - A_10_7 - A_15_7 + A_10_12 + A_15_12 & - A_10_8 - A_15_8 + A_10_13 + A_15_13 & - A_10_9 - A_15_9 + A_10_14 + A_15_14 & - A_10_10 - A_15_10 + A_10_15 + A_15_15 & - A_10_1 - A_15_1 + A_10_16 + A_15_16 & - A_10_2 - A_15_2 + A_10_17 + A_15_17 & - A_10_3 - A_15_3 + A_10_18 + A_15_18 & - A_10_4 - A_15_4 + A_10_19 + A_15_19 \\ A_1_5 + A_16_5 & - A_1_6 - A_16_6 + A_1_11 + A_16_11 & - A_1_7 - A_16_7 + A_1_12 + A_16_12 & - A_1_8 - A_16_8 + A_1_13 + A_16_13 & - A_1_9 - A_16_9 + A_1_14 + A_16_14 & - A_1_10 - A_16_10 + A_1_15 + A_16_15 & - A_1_1 - A_16_1 + A_1_16 + A_16_16 & - A_1_2 - A_16_2 + A_1_17 + A_16_17 & - A_1_3 - A_16_3 + A_1_18 + A_16_18 & - A_1_4 - A_16_4 + A_1_19 + A_16_19 \\ A_2_5 + A_17_5 & - A_2_6 - A_17_6 + A_2_11 + A_17_11 & - A_2_7 - A_17_7 + A_2_12 + A_17_12 & - A_2_8 - A_17_8 + A_2_13 + A_17_13 & - A_2_9 - A_17_9 + A_2_14 + A_17_14 & - A_2_10 - A_17_10 + A_2_15 + A_17_15 & - A_2_1 - A_17_1 + A_2_16 + A_17_16 & - A_2_2 - A_17_2 + A_2_17 + A_17_17 & - A_2_3 - A_17_3 + A_2_18 + A_17_18 & - A_2_4 - A_17_4 + A_2_19 + A_17_19 \\ A_3_5 + A_18_5 & - A_3_6 - A_18_6 + A_3_11 + A_18_11 & - A_3_7 - A_18_7 + A_3_12 + A_18_12 & - A_3_8 - A_18_8 + A_3_13 + A_18_13 & - A_3_9 - A_18_9 + A_3_14 + A_18_14 & - A_3_10 - A_18_10 + A_3_15 + A_18_15 & - A_3_1 - A_18_1 + A_3_16 + A_18_16 & - A_3_2 - A_18_2 + A_3_17 + A_18_17 & - A_3_3 - A_18_3 + A_3_18 + A_18_18 & - A_3_4 - A_18_4 + A_3_19 + A_18_19 \\ A_4_5 + A_19_5 & - A_4_6 - A_19_6 + A_4_11 + A_19_11 & - A_4_7 - A_19_7 + A_4_12 + A_19_12 & - A_4_8 - A_19_8 + A_4_13 + A_19_13 & - A_4_9 - A_19_9 + A_4_14 + A_19_14 & - A_4_10 - A_19_10 + A_4_15 + A_19_15 & - A_4_1 - A_19_1 + A_4_16 + A_19_16 & - A_4_2 - A_19_2 + A_4_17 + A_19_17 & - A_4_3 - A_19_3 + A_4_18 + A_19_18 & - A_4_4 - A_19_4 + A_4_19 + A_19_19 \end{matrix}), (\begin{matrix} B_5_13 & B_5_14 & B_5_15 & B_5_16 & B_5_17 & B_5_18 & B_5_19 & B_5_20 & B_5_21 & B_5_22 & B_5_23 & B_5_24 & B_5_25 & B_5_26 & B_5_27 \\ B_11_13 & B_11_14 & B_11_15 & B_11_16 & B_11_17 & B_11_18 & B_11_19 & B_11_20 & B_11_21 & B_11_22 & B_11_23 & B_11_24 & B_11_25 & B_11_26 & B_11_27 \\ B_12_13 & B_12_14 & B_12_15 & B_12_16 & B_12_17 & B_12_18 & B_12_19 & B_12_20 & B_12_21 & B_12_22 & B_12_23 & B_12_24 & B_12_25 & B_12_26 & B_12_27 \\ B_13_13 & B_13_14 & B_13_15 & B_13_16 & B_13_17 & B_13_18 & B_13_19 & B_13_20 & B_13_21 & B_13_22 & B_13_23 & B_13_24 & B_13_25 & B_13_26 & B_13_27 \\ B_14_13 & B_14_14 & B_14_15 & B_14_16 & B_14_17 & B_14_18 & B_14_19 & B_14_20 & B_14_21 & B_14_22 & B_14_23 & B_14_24 & B_14_25 & B_14_26 & B_14_27 \\ B_15_13 & B_15_14 & B_15_15 & B_15_16 & B_15_17 & B_15_18 & B_15_19 & B_15_20 & B_15_21 & B_15_22 & B_15_23 & B_15_24 & B_15_25 & B_15_26 & B_15_27 \\ B_16_13 & B_16_14 & B_16_15 & B_16_16 & B_16_17 & B_16_18 & B_16_19 & B_16_20 & B_16_21 & B_16_22 & B_16_23 & B_16_24 & B_16_25 & B_16_26 & B_16_27 \\ B_17_13 & B_17_14 & B_17_15 & B_17_16 & B_17_17 & B_17_18 & B_17_19 & B_17_20 & B_17_21 & B_17_22 & B_17_23 & B_17_24 & B_17_25 & B_17_26 & B_17_27 \\ B_18_13 & B_18_14 & B_18_15 & B_18_16 & B_18_17 & B_18_18 & B_18_19 & B_18_20 & B_18_21 & B_18_22 & B_18_23 & B_18_24 & B_18_25 & B_18_26 & B_18_27 \\ B_19_13 & B_19_14 & B_19_15 & B_19_16 & B_19_17 & B_19_18 & B_19_19 & B_19_20 & B_19_21 & B_19_22 & B_19_23 & B_19_24 & B_19_25 & B_19_26 & B_19_27 \end{matrix}), (\begin{matrix} C_13_6 & C_13_7 & C_13_8 & C_13_9 & C_13_10 & C_13_1 & C_13_2 & C_13_3 & C_13_4 \\ C_14_6 & C_14_7 & C_14_8 & C_14_9 & C_14_10 & C_14_1 & C_14_2 & C_14_3 & C_14_4 \\ C_15_6 & C_15_7 & C_15_8 & C_15_9 & C_15_10 & C_15_1 & C_15_2 & C_15_3 & C_15_4 \\ C_16_6 & C_16_7 & C_16_8 & C_16_9 & C_16_10 & C_16_1 & C_16_2 & C_16_3 & C_16_4 \\ C_17_6 & C_17_7 & C_17_8 & C_17_9 & C_17_10 & C_17_1 & C_17_2 & C_17_3 & C_17_4 \\ C_18_6 & C_18_7 & C_18_8 & C_18_9 & C_18_10 & C_18_1 & C_18_2 & C_18_3 & C_18_4 \\ C_19_6 & C_19_7 & C_19_8 & C_19_9 & C_19_10 & C_19_1 & C_19_2 & C_19_3 & C_19_4 \\ C_20_6 & C_20_7 & C_20_8 & C_20_9 & C_20_10 & C_20_1 & C_20_2 & C_20_3 & C_20_4 \\ C_21_6 & C_21_7 & C_21_8 & C_21_9 & C_21_10 & C_21_1 & C_21_2 & C_21_3 & C_21_4 \\ C_22_6 & C_22_7 & C_22_8 & C_22_9 & C_22_10 & C_22_1 & C_22_2 & C_22_3 & C_22_4 \\ C_23_6 & C_23_7 & C_23_8 & C_23_9 & C_23_10 & C_23_1 & C_23_2 & C_23_3 & C_23_4 \\ C_24_6 & C_24_7 & C_24_8 & C_24_9 & C_24_10 & C_24_1 & C_24_2 & C_24_3 & C_24_4 \\ C_25_6 & C_25_7 & C_25_8 & C_25_9 & C_25_10 & C_25_1 & C_25_2 & C_25_3 & C_25_4 \\ C_26_6 & C_26_7 & C_26_8 & C_26_9 & C_26_10 & C_26_1 & C_26_2 & C_26_3 & C_26_4 \\ C_27_6 & C_27_7 & C_27_8 & C_27_9 & C_27_10 & C_27_1 & C_27_2 & C_27_3 & C_27_4 \end{matrix}))) + Trace (Mul ((\begin{matrix} A_6_6 & A_6_7 & A_6_8 & A_6_9 & A_6_10 & A_6_1 & A_6_2 & A_6_3 & A_6_4 \\ A_7_6 & A_7_7 & A_7_8 & A_7_9 & A_7_10 & A_7_1 & A_7_2 & A_7_3 & A_7_4 \\ A_8_6 & A_8_7 & A_8_8 & A_8_9 & A_8_10 & A_8_1 & A_8_2 & A_8_3 & A_8_4 \\ A_9_6 & A_9_7 & A_9_8 & A_9_9 & A_9_10 & A_9_1 & A_9_2 & A_9_3 & A_9_4 \\ A_10_6 & A_10_7 & A_10_8 & A_10_9 & A_10_10 & A_10_1 & A_10_2 & A_10_3 & A_10_4 \\ A_1_6 & A_1_7 & A_1_8 & A_1_9 & A_1_10 & A_1_1 & A_1_2 & A_1_3 & A_1_4 \\ A_2_6 & A_2_7 & A_2_8 & A_2_9 & A_2_10 & A_2_1 & A_2_2 & A_2_3 & A_2_4 \\ A_3_6 & A_3_7 & A_3_8 & A_3_9 & A_3_10 & A_3_1 & A_3_2 & A_3_3 & A_3_4 \\ A_4_6 & A_4_7 & A_4_8 & A_4_9 & A_4_10 & A_4_1 & A_4_2 & A_4_3 & A_4_4 \end{matrix}), (\begin{matrix} B_6_1 & B_6_2 & B_6_3 & B_6_4 & B_6_5 & B_6_6 & B_6_7 & B_6_8 & B_6_9 & B_6_10 & B_6_11 & B_6_12 \\ B_7_1 & B_7_2 & B_7_3 & B_7_4 & B_7_5 & B_7_6 & B_7_7 & B_7_8 & B_7_9 & B_7_10 & B_7_11 & B_7_12 \\ B_8_1 & B_8_2 & B_8_3 & B_8_4 & B_8_5 & B_8_6 & B_8_7 & B_8_8 & B_8_9 & B_8_10 & B_8_11 & B_8_12 \\ B_9_1 & B_9_2 & B_9_3 & B_9_4 & B_9_5 & B_9_6 & B_9_7 & B_9_8 & B_9_9 & B_9_10 & B_9_11 & B_9_12 \\ B_10_1 & B_10_2 & B_10_3 & B_10_4 & B_10_5 & B_10_6 & B_10_7 & B_10_8 & B_10_9 & B_10_10 & B_10_11 & B_10_12 \\ B_1_1 & B_1_2 & B_1_3 & B_1_4 & B_1_5 & B_1_6 & B_1_7 & B_1_8 & B_1_9 & B_1_10 & B_1_11 & B_1_12 \\ B_2_1 & B_2_2 & B_2_3 & B_2_4 & B_2_5 & B_2_6 & B_2_7 & B_2_8 & B_2_9 & B_2_10 & B_2_11 & B_2_12 \\ B_3_1 & B_3_2 & B_3_3 & B_3_4 & B_3_5 & B_3_6 & B_3_7 & B_3_8 & B_3_9 & B_3_10 & B_3_11 & B_3_12 \\ B_4_1 & B_4_2 & B_4_3 & B_4_4 & B_4_5 & B_4_6 & B_4_7 & B_4_8 & B_4_9 & B_4_10 & B_4_11 & B_4_12 \end{matrix}), (\begin{matrix} C_1_6 + C_16_6 - C_1_11 - C_16_11 & C_1_7 + C_16_7 - C_1_12 - C_16_12 & C_1_8 + C_16_8 - C_1_13 - C_16_13 & C_1_9 + C_16_9 - C_1_14 - C_16_14 & C_1_10 + C_16_10 - C_1_15 - C_16_15 & C_1_1 + C_16_1 - C_1_16 - C_16_16 & C_1_2 + C_16_2 - C_1_17 - C_16_17 & C_1_3 + C_16_3 - C_1_18 - C_16_18 & C_1_4 + C_16_4 - C_1_19 - C_16_19 \\ C_2_6 + C_17_6 - C_2_11 - C_17_11 & C_2_7 + C_17_7 - C_2_12 - C_17_12 & C_2_8 + C_17_8 - C_2_13 - C_17_13 & C_2_9 + C_17_9 - C_2_14 - C_17_14 & C_2_10 + C_17_10 - C_2_15 - C_17_15 & C_2_1 + C_17_1 - C_2_16 - C_17_16 & C_2_2 + C_17_2 - C_2_17 - C_17_17 & C_2_3 + C_17_3 - C_2_18 - C_17_18 & C_2_4 + C_17_4 - C_2_19 - C_17_19 \\ C_3_6 + C_18_6 - C_3_11 - C_18_11 & C_3_7 + C_18_7 - C_3_12 - C_18_12 & C_3_8 + C_18_8 - C_3_13 - C_18_13 & C_3_9 + C_18_9 - C_3_14 - C_18_14 & C_3_10 + C_18_10 - C_3_15 - C_18_15 & C_3_1 + C_18_1 - C_3_16 - C_18_16 & C_3_2 + C_18_2 - C_3_17 - C_18_17 & C_3_3 + C_18_3 - C_3_18 - C_18_18 & C_3_4 + C_18_4 - C_3_19 - C_18_19 \\ C_4_6 + C_19_6 - C_4_11 - C_19_11 & C_4_7 + C_19_7 - C_4_12 - C_19_12 & C_4_8 + C_19_8 - C_4_13 - C_19_13 & C_4_9 + C_19_9 - C_4_14 - C_19_14 & C_4_10 + C_19_10 - C_4_15 - C_19_15 & C_4_1 + C_19_1 - C_4_16 - C_19_16 & C_4_2 + C_19_2 - C_4_17 - C_19_17 & C_4_3 + C_19_3 - C_4_18 - C_19_18 & C_4_4 + C_19_4 - C_4_19 - C_19_19 \\ C_5_6 + C_20_6 - C_5_11 - C_20_11 & C_5_7 + C_20_7 - C_5_12 - C_20_12 & C_5_8 + C_20_8 - C_5_13 - C_20_13 & C_5_9 + C_20_9 - C_5_14 - C_20_14 & C_5_10 + C_20_10 - C_5_15 - C_20_15 & C_5_1 + C_20_1 - C_5_16 - C_20_16 & C_5_2 + C_20_2 - C_5_17 - C_20_17 & C_5_3 + C_20_3 - C_5_18 - C_20_18 & C_5_4 + C_20_4 - C_5_19 - C_20_19 \\ C_6_6 + C_21_6 - C_6_11 - C_21_11 & C_6_7 + C_21_7 - C_6_12 - C_21_12 & C_6_8 + C_21_8 - C_6_13 - C_21_13 & C_6_9 + C_21_9 - C_6_14 - C_21_14 & C_6_10 + C_21_10 - C_6_15 - C_21_15 & C_6_1 + C_21_1 - C_6_16 - C_21_16 & C_6_2 + C_21_2 - C_6_17 - C_21_17 & C_6_3 + C_21_3 - C_6_18 - C_21_18 & C_6_4 + C_21_4 - C_6_19 - C_21_19 \\ C_7_6 + C_22_6 - C_7_11 - C_22_11 & C_7_7 + C_22_7 - C_7_12 - C_22_12 & C_7_8 + C_22_8 - C_7_13 - C_22_13 & C_7_9 + C_22_9 - C_7_14 - C_22_14 & C_7_10 + C_22_10 - C_7_15 - C_22_15 & C_7_1 + C_22_1 - C_7_16 - C_22_16 & C_7_2 + C_22_2 - C_7_17 - C_22_17 & C_7_3 + C_22_3 - C_7_18 - C_22_18 & C_7_4 + C_22_4 - C_7_19 - C_22_19 \\ C_8_6 + C_23_6 - C_8_11 - C_23_11 & C_8_7 + C_23_7 - C_8_12 - C_23_12 & C_8_8 + C_23_8 - C_8_13 - C_23_13 & C_8_9 + C_23_9 - C_8_14 - C_23_14 & C_8_10 + C_23_10 - C_8_15 - C_23_15 & C_8_1 + C_23_1 - C_8_16 - C_23_16 & C_8_2 + C_23_2 - C_8_17 - C_23_17 & C_8_3 + C_23_3 - C_8_18 - C_23_18 & C_8_4 + C_23_4 - C_8_19 - C_23_19 \\ C_9_6 + C_24_6 - C_9_11 - C_24_11 & C_9_7 + C_24_7 - C_9_12 - C_24_12 & C_9_8 + C_24_8 - C_9_13 - C_24_13 & C_9_9 + C_24_9 - C_9_14 - C_24_14 & C_9_10 + C_24_10 - C_9_15 - C_24_15 & C_9_1 + C_24_1 - C_9_16 - C_24_16 & C_9_2 + C_24_2 - C_9_17 - C_24_17 & C_9_3 + C_24_3 - C_9_18 - C_24_18 & C_9_4 + C_24_4 - C_9_19 - C_24_19 \\ C_10_6 + C_25_6 - C_10_11 - C_25_11 & C_10_7 + C_25_7 - C_10_12 - C_25_12 & C_10_8 + C_25_8 - C_10_13 - C_25_13 & C_10_9 + C_25_9 - C_10_14 - C_25_14 & C_10_10 + C_25_10 - C_10_15 - C_25_15 & C_10_1 + C_25_1 - C_10_16 - C_25_16 & C_10_2 + C_25_2 - C_10_17 - C_25_17 & C_10_3 + C_25_3 - C_10_18 - C_25_18 & C_10_4 + C_25_4 - C_10_19 - C_25_19 \\ C_11_6 + C_26_6 - C_11_11 - C_26_11 & C_11_7 + C_26_7 - C_11_12 - C_26_12 & C_11_8 + C_26_8 - C_11_13 - C_26_13 & C_11_9 + C_26_9 - C_11_14 - C_26_14 & C_11_10 + C_26_10 - C_11_15 - C_26_15 & C_11_1 + C_26_1 - C_11_16 - C_26_16 & C_11_2 + C_26_2 - C_11_17 - C_26_17 & C_11_3 + C_26_3 - C_11_18 - C_26_18 & C_11_4 + C_26_4 - C_11_19 - C_26_19 \\ C_12_6 + C_27_6 - C_12_11 - C_27_11 & C_12_7 + C_27_7 - C_12_12 - C_27_12 & C_12_8 + C_27_8 - C_12_13 - C_27_13 & C_12_9 + C_27_9 - C_12_14 - C_27_14 & C_12_10 + C_27_10 - C_12_15 - C_27_15 & C_12_1 + C_27_1 - C_12_16 - C_27_16 & C_12_2 + C_27_2 - C_12_17 - C_27_17 & C_12_3 + C_27_3 - C_12_18 - C_27_18 & C_12_4 + C_27_4 - C_12_19 - C_27_19 \end{matrix}))) + Trace (Mul ((\begin{matrix} A_5_5 & - A_5_6 + A_5_11 & - A_5_7 + A_5_12 & - A_5_8 + A_5_13 & - A_5_9 + A_5_14 & - A_5_10 + A_5_15 & - A_5_1 + A_5_16 & - A_5_2 + A_5_17 & - A_5_3 + A_5_18 & - A_5_4 + A_5_19 \\ A_11_5 & - A_6_6 - A_11_6 + A_11_11 & - A_6_7 - A_11_7 + A_11_12 & - A_6_8 - A_11_8 + A_11_13 & - A_6_9 - A_11_9 + A_11_14 & - A_6_10 - A_11_10 + A_11_15 & - A_6_1 - A_11_1 + A_11_16 & - A_6_2 - A_11_2 + A_11_17 & - A_6_3 - A_11_3 + A_11_18 & - A_6_4 - A_11_4 + A_11_19 \\ A_12_5 & - A_7_6 - A_12_6 + A_12_11 & - A_7_7 - A_12_7 + A_12_12 & - A_7_8 - A_12_8 + A_12_13 & - A_7_9 - A_12_9 + A_12_14 & - A_7_10 - A_12_10 + A_12_15 & - A_7_1 - A_12_1 + A_12_16 & - A_7_2 - A_12_2 + A_12_17 & - A_7_3 - A_12_3 + A_12_18 & - A_7_4 - A_12_4 + A_12_19 \\ A_13_5 & - A_8_6 - A_13_6 + A_13_11 & - A_8_7 - A_13_7 + A_13_12 & - A_8_8 - A_13_8 + A_13_13 & - A_8_9 - A_13_9 + A_13_14 & - A_8_10 - A_13_10 + A_13_15 & - A_8_1 - A_13_1 + A_13_16 & - A_8_2 - A_13_2 + A_13_17 & - A_8_3 - A_13_3 + A_13_18 & - A_8_4 - A_13_4 + A_13_19 \\ A_14_5 & - A_9_6 - A_14_6 + A_14_11 & - A_9_7 - A_14_7 + A_14_12 & - A_9_8 - A_14_8 + A_14_13 & - A_9_9 - A_14_9 + A_14_14 & - A_9_10 - A_14_10 + A_14_15 & - A_9_1 - A_14_1 + A_14_16 & - A_9_2 - A_14_2 + A_14_17 & - A_9_3 - A_14_3 + A_14_18 & - A_9_4 - A_14_4 + A_14_19 \\ A_15_5 & - A_10_6 - A_15_6 + A_15_11 & - A_10_7 - A_15_7 + A_15_12 & - A_10_8 - A_15_8 + A_15_13 & - A_10_9 - A_15_9 + A_15_14 & - A_10_10 - A_15_10 + A_15_15 & - A_10_1 - A_15_1 + A_15_16 & - A_10_2 - A_15_2 + A_15_17 & - A_10_3 - A_15_3 + A_15_18 & - A_10_4 - A_15_4 + A_15_19 \\ A_16_5 & - A_1_6 - A_16_6 + A_16_11 & - A_1_7 - A_16_7 + A_16_12 & - A_1_8 - A_16_8 + A_16_13 & - A_1_9 - A_16_9 + A_16_14 & - A_1_10 - A_16_10 + A_16_15 & - A_1_1 - A_16_1 + A_16_16 & - A_1_2 - A_16_2 + A_16_17 & - A_1_3 - A_16_3 + A_16_18 & - A_1_4 - A_16_4 + A_16_19 \\ A_17_5 & - A_2_6 - A_17_6 + A_17_11 & - A_2_7 - A_17_7 + A_17_12 & - A_2_8 - A_17_8 + A_17_13 & - A_2_9 - A_17_9 + A_17_14 & - A_2_10 - A_17_10 + A_17_15 & - A_2_1 - A_17_1 + A_17_16 & - A_2_2 - A_17_2 + A_17_17 & - A_2_3 - A_17_3 + A_17_18 & - A_2_4 - A_17_4 + A_17_19 \\ A_18_5 & - A_3_6 - A_18_6 + A_18_11 & - A_3_7 - A_18_7 + A_18_12 & - A_3_8 - A_18_8 + A_18_13 & - A_3_9 - A_18_9 + A_18_14 & - A_3_10 - A_18_10 + A_18_15 & - A_3_1 - A_18_1 + A_18_16 & - A_3_2 - A_18_2 + A_18_17 & - A_3_3 - A_18_3 + A_18_18 & - A_3_4 - A_18_4 + A_18_19 \\ A_19_5 & - A_4_6 - A_19_6 + A_19_11 & - A_4_7 - A_19_7 + A_19_12 & - A_4_8 - A_19_8 + A_19_13 & - A_4_9 - A_19_9 + A_19_14 & - A_4_10 - A_19_10 + A_19_15 & - A_4_1 - A_19_1 + A_19_16 & - A_4_2 - A_19_2 + A_19_17 & - A_4_3 - A_19_3 + A_19_18 & - A_4_4 - A_19_4 + A_19_19 \end{matrix}), (\begin{matrix} B_5_13 & B_5_14 & B_5_15 & B_5_16 & B_5_17 & B_5_18 & B_5_19 & B_5_20 & B_5_21 & B_5_22 & B_5_23 & B_5_24 & B_5_25 & B_5_26 & B_5_27 \\ B_6_13 + B_11_13 & B_6_14 + B_11_14 & B_6_15 + B_11_15 & - B_6_1 + B_6_16 + B_11_16 & - B_6_2 + B_6_17 + B_11_17 & - B_6_3 + B_6_18 + B_11_18 & - B_6_4 + B_6_19 + B_11_19 & - B_6_5 + B_6_20 + B_11_20 & - B_6_6 + B_6_21 + B_11_21 & - B_6_7 + B_6_22 + B_11_22 & - B_6_8 + B_6_23 + B_11_23 & - B_6_9 + B_6_24 + B_11_24 & - B_6_10 + B_6_25 + B_11_25 & - B_6_11 + B_6_26 + B_11_26 & - B_6_12 + B_6_27 + B_11_27 \\ B_7_13 + B_12_13 & B_7_14 + B_12_14 & B_7_15 + B_12_15 & - B_7_1 + B_7_16 + B_12_16 & - B_7_2 + B_7_17 + B_12_17 & - B_7_3 + B_7_18 + B_12_18 & - B_7_4 + B_7_19 + B_12_19 & - B_7_5 + B_7_20 + B_12_20 & - B_7_6 + B_7_21 + B_12_21 & - B_7_7 + B_7_22 + B_12_22 & - B_7_8 + B_7_23 + B_12_23 & - B_7_9 + B_7_24 + B_12_24 & - B_7_10 + B_7_25 + B_12_25 & - B_7_11 + B_7_26 + B_12_26 & - B_7_12 + B_7_27 + B_12_27 \\ B_8_13 + B_13_13 & B_8_14 + B_13_14 & B_8_15 + B_13_15 & - B_8_1 + B_8_16 + B_13_16 & - B_8_2 + B_8_17 + B_13_17 & - B_8_3 + B_8_18 + B_13_18 & - B_8_4 + B_8_19 + B_13_19 & - B_8_5 + B_8_20 + B_13_20 & - B_8_6 + B_8_21 + B_13_21 & - B_8_7 + B_8_22 + B_13_22 & - B_8_8 + B_8_23 + B_13_23 & - B_8_9 + B_8_24 + B_13_24 & - B_8_10 + B_8_25 + B_13_25 & - B_8_11 + B_8_26 + B_13_26 & - B_8_12 + B_8_27 + B_13_27 \\ B_9_13 + B_14_13 & B_9_14 + B_14_14 & B_9_15 + B_14_15 & - B_9_1 + B_9_16 + B_14_16 & - B_9_2 + B_9_17 + B_14_17 & - B_9_3 + B_9_18 + B_14_18 & - B_9_4 + B_9_19 + B_14_19 & - B_9_5 + B_9_20 + B_14_20 & - B_9_6 + B_9_21 + B_14_21 & - B_9_7 + B_9_22 + B_14_22 & - B_9_8 + B_9_23 + B_14_23 & - B_9_9 + B_9_24 + B_14_24 & - B_9_10 + B_9_25 + B_14_25 & - B_9_11 + B_9_26 + B_14_26 & - B_9_12 + B_9_27 + B_14_27 \\ B_10_13 + B_15_13 & B_10_14 + B_15_14 & B_10_15 + B_15_15 & - B_10_1 + B_10_16 + B_15_16 & - B_10_2 + B_10_17 + B_15_17 & - B_10_3 + B_10_18 + B_15_18 & - B_10_4 + B_10_19 + B_15_19 & - B_10_5 + B_10_20 + B_15_20 & - B_10_6 + B_10_21 + B_15_21 & - B_10_7 + B_10_22 + B_15_22 & - B_10_8 + B_10_23 + B_15_23 & - B_10_9 + B_10_24 + B_15_24 & - B_10_10 + B_10_25 + B_15_25 & - B_10_11 + B_10_26 + B_15_26 & - B_10_12 + B_10_27 + B_15_27 \\ B_1_13 + B_16_13 & B_1_14 + B_16_14 & B_1_15 + B_16_15 & - B_1_1 + B_1_16 + B_16_16 & - B_1_2 + B_1_17 + B_16_17 & - B_1_3 + B_1_18 + B_16_18 & - B_1_4 + B_1_19 + B_16_19 & - B_1_5 + B_1_20 + B_16_20 & - B_1_6 + B_1_21 + B_16_21 & - B_1_7 + B_1_22 + B_16_22 & - B_1_8 + B_1_23 + B_16_23 & - B_1_9 + B_1_24 + B_16_24 & - B_1_10 + B_1_25 + B_16_25 & - B_1_11 + B_1_26 + B_16_26 & - B_1_12 + B_1_27 + B_16_27 \\ B_2_13 + B_17_13 & B_2_14 + B_17_14 & B_2_15 + B_17_15 & - B_2_1 + B_2_16 + B_17_16 & - B_2_2 + B_2_17 + B_17_17 & - B_2_3 + B_2_18 + B_17_18 & - B_2_4 + B_2_19 + B_17_19 & - B_2_5 + B_2_20 + B_17_20 & - B_2_6 + B_2_21 + B_17_21 & - B_2_7 + B_2_22 + B_17_22 & - B_2_8 + B_2_23 + B_17_23 & - B_2_9 + B_2_24 + B_17_24 & - B_2_10 + B_2_25 + B_17_25 & - B_2_11 + B_2_26 + B_17_26 & - B_2_12 + B_2_27 + B_17_27 \\ B_3_13 + B_18_13 & B_3_14 + B_18_14 & B_3_15 + B_18_15 & - B_3_1 + B_3_16 + B_18_16 & - B_3_2 + B_3_17 + B_18_17 & - B_3_3 + B_3_18 + B_18_18 & - B_3_4 + B_3_19 + B_18_19 & - B_3_5 + B_3_20 + B_18_20 & - B_3_6 + B_3_21 + B_18_21 & - B_3_7 + B_3_22 + B_18_22 & - B_3_8 + B_3_23 + B_18_23 & - B_3_9 + B_3_24 + B_18_24 & - B_3_10 + B_3_25 + B_18_25 & - B_3_11 + B_3_26 + B_18_26 & - B_3_12 + B_3_27 + B_18_27 \\ B_4_13 + B_19_13 & B_4_14 + B_19_14 & B_4_15 + B_19_15 & - B_4_1 + B_4_16 + B_19_16 & - B_4_2 + B_4_17 + B_19_17 & - B_4_3 + B_4_18 + B_19_18 & - B_4_4 + B_4_19 + B_19_19 & - B_4_5 + B_4_20 + B_19_20 & - B_4_6 + B_4_21 + B_19_21 & - B_4_7 + B_4_22 + B_19_22 & - B_4_8 + B_4_23 + B_19_23 & - B_4_9 + B_4_24 + B_19_24 & - B_4_10 + B_4_25 + B_19_25 & - B_4_11 + B_4_26 + B_19_26 & - B_4_12 + B_4_27 + B_19_27 \end{matrix}), (\begin{matrix} C_13_5 & - C_13_6 + C_13_11 & - C_13_7 + C_13_12 & - C_13_8 + C_13_13 & - C_13_9 + C_13_14 & - C_13_10 + C_13_15 & - C_13_1 + C_13_16 & - C_13_2 + C_13_17 & - C_13_3 + C_13_18 & - C_13_4 + C_13_19 \\ C_14_5 & - C_14_6 + C_14_11 & - C_14_7 + C_14_12 & - C_14_8 + C_14_13 & - C_14_9 + C_14_14 & - C_14_10 + C_14_15 & - C_14_1 + C_14_16 & - C_14_2 + C_14_17 & - C_14_3 + C_14_18 & - C_14_4 + C_14_19 \\ C_15_5 & - C_15_6 + C_15_11 & - C_15_7 + C_15_12 & - C_15_8 + C_15_13 & - C_15_9 + C_15_14 & - C_15_10 + C_15_15 & - C_15_1 + C_15_16 & - C_15_2 + C_15_17 & - C_15_3 + C_15_18 & - C_15_4 + C_15_19 \\ C_1_5 + C_16_5 & - C_16_6 + C_1_11 + C_16_11 & - C_16_7 + C_1_12 + C_16_12 & - C_16_8 + C_1_13 + C_16_13 & - C_16_9 + C_1_14 + C_16_14 & - C_16_10 + C_1_15 + C_16_15 & - C_16_1 + C_1_16 + C_16_16 & - C_16_2 + C_1_17 + C_16_17 & - C_16_3 + C_1_18 + C_16_18 & - C_16_4 + C_1_19 + C_16_19 \\ C_2_5 + C_17_5 & - C_17_6 + C_2_11 + C_17_11 & - C_17_7 + C_2_12 + C_17_12 & - C_17_8 + C_2_13 + C_17_13 & - C_17_9 + C_2_14 + C_17_14 & - C_17_10 + C_2_15 + C_17_15 & - C_17_1 + C_2_16 + C_17_16 & - C_17_2 + C_2_17 + C_17_17 & - C_17_3 + C_2_18 + C_17_18 & - C_17_4 + C_2_19 + C_17_19 \\ C_3_5 + C_18_5 & - C_18_6 + C_3_11 + C_18_11 & - C_18_7 + C_3_12 + C_18_12 & - C_18_8 + C_3_13 + C_18_13 & - C_18_9 + C_3_14 + C_18_14 & - C_18_10 + C_3_15 + C_18_15 & - C_18_1 + C_3_16 + C_18_16 & - C_18_2 + C_3_17 + C_18_17 & - C_18_3 + C_3_18 + C_18_18 & - C_18_4 + C_3_19 + C_18_19 \\ C_4_5 + C_19_5 & - C_19_6 + C_4_11 + C_19_11 & - C_19_7 + C_4_12 + C_19_12 & - C_19_8 + C_4_13 + C_19_13 & - C_19_9 + C_4_14 + C_19_14 & - C_19_10 + C_4_15 + C_19_15 & - C_19_1 + C_4_16 + C_19_16 & - C_19_2 + C_4_17 + C_19_17 & - C_19_3 + C_4_18 + C_19_18 & - C_19_4 + C_4_19 + C_19_19 \\ C_5_5 + C_20_5 & - C_20_6 + C_5_11 + C_20_11 & - C_20_7 + C_5_12 + C_20_12 & - C_20_8 + C_5_13 + C_20_13 & - C_20_9 + C_5_14 + C_20_14 & - C_20_10 + C_5_15 + C_20_15 & - C_20_1 + C_5_16 + C_20_16 & - C_20_2 + C_5_17 + C_20_17 & - C_20_3 + C_5_18 + C_20_18 & - C_20_4 + C_5_19 + C_20_19 \\ C_6_5 + C_21_5 & - C_21_6 + C_6_11 + C_21_11 & - C_21_7 + C_6_12 + C_21_12 & - C_21_8 + C_6_13 + C_21_13 & - C_21_9 + C_6_14 + C_21_14 & - C_21_10 + C_6_15 + C_21_15 & - C_21_1 + C_6_16 + C_21_16 & - C_21_2 + C_6_17 + C_21_17 & - C_21_3 + C_6_18 + C_21_18 & - C_21_4 + C_6_19 + C_21_19 \\ C_7_5 + C_22_5 & - C_22_6 + C_7_11 + C_22_11 & - C_22_7 + C_7_12 + C_22_12 & - C_22_8 + C_7_13 + C_22_13 & - C_22_9 + C_7_14 + C_22_14 & - C_22_10 + C_7_15 + C_22_15 & - C_22_1 + C_7_16 + C_22_16 & - C_22_2 + C_7_17 + C_22_17 & - C_22_3 + C_7_18 + C_22_18 & - C_22_4 + C_7_19 + C_22_19 \\ C_8_5 + C_23_5 & - C_23_6 + C_8_11 + C_23_11 & - C_23_7 + C_8_12 + C_23_12 & - C_23_8 + C_8_13 + C_23_13 & - C_23_9 + C_8_14 + C_23_14 & - C_23_10 + C_8_15 + C_23_15 & - C_23_1 + C_8_16 + C_23_16 & - C_23_2 + C_8_17 + C_23_17 & - C_23_3 + C_8_18 + C_23_18 & - C_23_4 + C_8_19 + C_23_19 \\ C_9_5 + C_24_5 & - C_24_6 + C_9_11 + C_24_11 & - C_24_7 + C_9_12 + C_24_12 & - C_24_8 + C_9_13 + C_24_13 & - C_24_9 + C_9_14 + C_24_14 & - C_24_10 + C_9_15 + C_24_15 & - C_24_1 + C_9_16 + C_24_16 & - C_24_2 + C_9_17 + C_24_17 & - C_24_3 + C_9_18 + C_24_18 & - C_24_4 + C_9_19 + C_24_19 \\ C_10_5 + C_25_5 & - C_25_6 + C_10_11 + C_25_11 & - C_25_7 + C_10_12 + C_25_12 & - C_25_8 + C_10_13 + C_25_13 & - C_25_9 + C_10_14 + C_25_14 & - C_25_10 + C_10_15 + C_25_15 & - C_25_1 + C_10_16 + C_25_16 & - C_25_2 + C_10_17 + C_25_17 & - C_25_3 + C_10_18 + C_25_18 & - C_25_4 + C_10_19 + C_25_19 \\ C_11_5 + C_26_5 & - C_26_6 + C_11_11 + C_26_11 & - C_26_7 + C_11_12 + C_26_12 & - C_26_8 + C_11_13 + C_26_13 & - C_26_9 + C_11_14 + C_26_14 & - C_26_10 + C_11_15 + C_26_15 & - C_26_1 + C_11_16 + C_26_16 & - C_26_2 + C_11_17 + C_26_17 & - C_26_3 + C_11_18 + C_26_18 & - C_26_4 + C_11_19 + C_26_19 \\ C_12_5 + C_27_5 & - C_27_6 + C_12_11 + C_27_11 & - C_27_7 + C_12_12 + C_27_12 & - C_27_8 + C_12_13 + C_27_13 & - C_27_9 + C_12_14 + C_27_14 & - C_27_10 + C_12_15 + C_27_15 & - C_27_1 + C_12_16 + C_27_16 & - C_27_2 + C_12_17 + C_27_17 & - C_27_3 + C_12_18 + C_27_18 & - C_27_4 + C_12_19 + C_27_19 \end{matrix})))

N.B.: for any matrices A, B and C such that the expression Tr(Mul(A,B,C)) is defined, one can construct several trilinear homogeneous polynomials P(A,B,C) such that P(A,B,C)=Tr(Mul(A,B,C)) (P(A,B,C) variables are A,B and C's coefficients). Each trilinear P expression encodes a matrix multiplication algorithm: the coefficient in C_i_j of P(A,B,C) is the (i,j)-th entry of the matrix product Mul(A,B)=Transpose(C).

Algorithm description

These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.

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