Description of fast matrix multiplication algorithm: ⟨3×24×24:1272⟩

Algorithm type

6XY9Z+90X3Y4Z3+33X2Y6Z2+6X2Y6Z+6XY6Z2+96X2Y4Z2+42XY6Z+12X2Y4Z+12XY4Z2+147X2Y2Z2+60XY4Z+24X2Y2Z+90XY3Z+24XY2Z2+324XY2Z+300XYZ6XY9Z90X3Y4Z333X2Y6Z26X2Y6Z6XY6Z296X2Y4Z242XY6Z12X2Y4Z12XY4Z2147X2Y2Z260XY4Z24X2Y2Z90XY3Z24XY2Z2324XY2Z300XYZ6*X*Y^9*Z+90*X^3*Y^4*Z^3+33*X^2*Y^6*Z^2+6*X^2*Y^6*Z+6*X*Y^6*Z^2+96*X^2*Y^4*Z^2+42*X*Y^6*Z+12*X^2*Y^4*Z+12*X*Y^4*Z^2+147*X^2*Y^2*Z^2+60*X*Y^4*Z+24*X^2*Y^2*Z+90*X*Y^3*Z+24*X*Y^2*Z^2+324*X*Y^2*Z+300*X*Y*Z

Algorithm definition

The algorithm ⟨3×24×24:1272⟩ could be constructed using the following decomposition:

⟨3×24×24:1272⟩ = ⟨2×6×6:57⟩ + ⟨1×6×6:36⟩ + ⟨1×6×6:36⟩ + ⟨2×6×6:57⟩ + ⟨2×6×6:57⟩ + ⟨1×6×6:36⟩ + ⟨1×6×6:36⟩ + ⟨1×6×6:36⟩ + ⟨2×6×6:57⟩ + ⟨2×6×6:57⟩ + ⟨1×6×6:36⟩ + ⟨2×6×6:57⟩ + ⟨2×6×6:57⟩ + ⟨2×6×6:57⟩ + ⟨1×6×6:36⟩ + ⟨1×6×6:36⟩ + ⟨2×6×6:57⟩ + ⟨2×6×6:57⟩ + ⟨2×6×6:57⟩ + ⟨2×6×6:57⟩ + ⟨1×6×6:36⟩ + ⟨2×6×6:57⟩ + ⟨2×6×6:57⟩ + ⟨1×6×6:36⟩ + ⟨2×6×6:57⟩ + ⟨2×6×6:57⟩.

This decomposition is defined by the following equality:

TraceMulA_1_1A_1_2A_1_3A_1_4A_1_5A_1_6A_1_7A_1_8A_1_9A_1_10A_1_11A_1_12A_1_13A_1_14A_1_15A_1_16A_1_17A_1_18A_1_19A_1_20A_1_21A_1_22A_1_23A_1_24A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_2_7A_2_8A_2_9A_2_10A_2_11A_2_12A_2_13A_2_14A_2_15A_2_16A_2_17A_2_18A_2_19A_2_20A_2_21A_2_22A_2_23A_2_24A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_3_7A_3_8A_3_9A_3_10A_3_11A_3_12A_3_13A_3_14A_3_15A_3_16A_3_17A_3_18A_3_19A_3_20A_3_21A_3_22A_3_23A_3_24B_1_1B_1_2B_1_3B_1_4B_1_5B_1_6B_1_7B_1_8B_1_9B_1_10B_1_11B_1_12B_1_13B_1_14B_1_15B_1_16B_1_17B_1_18B_1_19B_1_20B_1_21B_1_22B_1_23B_1_24B_2_1B_2_2B_2_3B_2_4B_2_5B_2_6B_2_7B_2_8B_2_9B_2_10B_2_11B_2_12B_2_13B_2_14B_2_15B_2_16B_2_17B_2_18B_2_19B_2_20B_2_21B_2_22B_2_23B_2_24B_3_1B_3_2B_3_3B_3_4B_3_5B_3_6B_3_7B_3_8B_3_9B_3_10B_3_11B_3_12B_3_13B_3_14B_3_15B_3_16B_3_17B_3_18B_3_19B_3_20B_3_21B_3_22B_3_23B_3_24B_4_1B_4_2B_4_3B_4_4B_4_5B_4_6B_4_7B_4_8B_4_9B_4_10B_4_11B_4_12B_4_13B_4_14B_4_15B_4_16B_4_17B_4_18B_4_19B_4_20B_4_21B_4_22B_4_23B_4_24B_5_1B_5_2B_5_3B_5_4B_5_5B_5_6B_5_7B_5_8B_5_9B_5_10B_5_11B_5_12B_5_13B_5_14B_5_15B_5_16B_5_17B_5_18B_5_19B_5_20B_5_21B_5_22B_5_23B_5_24B_6_1B_6_2B_6_3B_6_4B_6_5B_6_6B_6_7B_6_8B_6_9B_6_10B_6_11B_6_12B_6_13B_6_14B_6_15B_6_16B_6_17B_6_18B_6_19B_6_20B_6_21B_6_22B_6_23B_6_24B_7_1B_7_2B_7_3B_7_4B_7_5B_7_6B_7_7B_7_8B_7_9B_7_10B_7_11B_7_12B_7_13B_7_14B_7_15B_7_16B_7_17B_7_18B_7_19B_7_20B_7_21B_7_22B_7_23B_7_24B_8_1B_8_2B_8_3B_8_4B_8_5B_8_6B_8_7B_8_8B_8_9B_8_10B_8_11B_8_12B_8_13B_8_14B_8_15B_8_16B_8_17B_8_18B_8_19B_8_20B_8_21B_8_22B_8_23B_8_24B_9_1B_9_2B_9_3B_9_4B_9_5B_9_6B_9_7B_9_8B_9_9B_9_10B_9_11B_9_12B_9_13B_9_14B_9_15B_9_16B_9_17B_9_18B_9_19B_9_20B_9_21B_9_22B_9_23B_9_24B_10_1B_10_2B_10_3B_10_4B_10_5B_10_6B_10_7B_10_8B_10_9B_10_10B_10_11B_10_12B_10_13B_10_14B_10_15B_10_16B_10_17B_10_18B_10_19B_10_20B_10_21B_10_22B_10_23B_10_24B_11_1B_11_2B_11_3B_11_4B_11_5B_11_6B_11_7B_11_8B_11_9B_11_10B_11_11B_11_12B_11_13B_11_14B_11_15B_11_16B_11_17B_11_18B_11_19B_11_20B_11_21B_11_22B_11_23B_11_24B_12_1B_12_2B_12_3B_12_4B_12_5B_12_6B_12_7B_12_8B_12_9B_12_10B_12_11B_12_12B_12_13B_12_14B_12_15B_12_16B_12_17B_12_18B_12_19B_12_20B_12_21B_12_22B_12_23B_12_24B_13_1B_13_2B_13_3B_13_4B_13_5B_13_6B_13_7B_13_8B_13_9B_13_10B_13_11B_13_12B_13_13B_13_14B_13_15B_13_16B_13_17B_13_18B_13_19B_13_20B_13_21B_13_22B_13_23B_13_24B_14_1B_14_2B_14_3B_14_4B_14_5B_14_6B_14_7B_14_8B_14_9B_14_10B_14_11B_14_12B_14_13B_14_14B_14_15B_14_16B_14_17B_14_18B_14_19B_14_20B_14_21B_14_22B_14_23B_14_24B_15_1B_15_2B_15_3B_15_4B_15_5B_15_6B_15_7B_15_8B_15_9B_15_10B_15_11B_15_12B_15_13B_15_14B_15_15B_15_16B_15_17B_15_18B_15_19B_15_20B_15_21B_15_22B_15_23B_15_24B_16_1B_16_2B_16_3B_16_4B_16_5B_16_6B_16_7B_16_8B_16_9B_16_10B_16_11B_16_12B_16_13B_16_14B_16_15B_16_16B_16_17B_16_18B_16_19B_16_20B_16_21B_16_22B_16_23B_16_24B_17_1B_17_2B_17_3B_17_4B_17_5B_17_6B_17_7B_17_8B_17_9B_17_10B_17_11B_17_12B_17_13B_17_14B_17_15B_17_16B_17_17B_17_18B_17_19B_17_20B_17_21B_17_22B_17_23B_17_24B_18_1B_18_2B_18_3B_18_4B_18_5B_18_6B_18_7B_18_8B_18_9B_18_10B_18_11B_18_12B_18_13B_18_14B_18_15B_18_16B_18_17B_18_18B_18_19B_18_20B_18_21B_18_22B_18_23B_18_24B_19_1B_19_2B_19_3B_19_4B_19_5B_19_6B_19_7B_19_8B_19_9B_19_10B_19_11B_19_12B_19_13B_19_14B_19_15B_19_16B_19_17B_19_18B_19_19B_19_20B_19_21B_19_22B_19_23B_19_24B_20_1B_20_2B_20_3B_20_4B_20_5B_20_6B_20_7B_20_8B_20_9B_20_10B_20_11B_20_12B_20_13B_20_14B_20_15B_20_16B_20_17B_20_18B_20_19B_20_20B_20_21B_20_22B_20_23B_20_24B_21_1B_21_2B_21_3B_21_4B_21_5B_21_6B_21_7B_21_8B_21_9B_21_10B_21_11B_21_12B_21_13B_21_14B_21_15B_21_16B_21_17B_21_18B_21_19B_21_20B_21_21B_21_22B_21_23B_21_24B_22_1B_22_2B_22_3B_22_4B_22_5B_22_6B_22_7B_22_8B_22_9B_22_10B_22_11B_22_12B_22_13B_22_14B_22_15B_22_16B_22_17B_22_18B_22_19B_22_20B_22_21B_22_22B_22_23B_22_24B_23_1B_23_2B_23_3B_23_4B_23_5B_23_6B_23_7B_23_8B_23_9B_23_10B_23_11B_23_12B_23_13B_23_14B_23_15B_23_16B_23_17B_23_18B_23_19B_23_20B_23_21B_23_22B_23_23B_23_24B_24_1B_24_2B_24_3B_24_4B_24_5B_24_6B_24_7B_24_8B_24_9B_24_10B_24_11B_24_12B_24_13B_24_14B_24_15B_24_16B_24_17B_24_18B_24_19B_24_20B_24_21B_24_22B_24_23B_24_24C_1_1C_1_2C_1_3C_2_1C_2_2C_2_3C_3_1C_3_2C_3_3C_4_1C_4_2C_4_3C_5_1C_5_2C_5_3C_6_1C_6_2C_6_3C_7_1C_7_2C_7_3C_8_1C_8_2C_8_3C_9_1C_9_2C_9_3C_10_1C_10_2C_10_3C_11_1C_11_2C_11_3C_12_1C_12_2C_12_3C_13_1C_13_2C_13_3C_14_1C_14_2C_14_3C_15_1C_15_2C_15_3C_16_1C_16_2C_16_3C_17_1C_17_2C_17_3C_18_1C_18_2C_18_3C_19_1C_19_2C_19_3C_20_1C_20_2C_20_3C_21_1C_21_2C_21_3C_22_1C_22_2C_22_3C_23_1C_23_2C_23_3C_24_1C_24_2C_24_3=TraceMulA_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6B_1_1-B_7_1-B_1_13B_1_2-B_7_2-B_1_14B_1_3-B_7_3-B_1_15B_1_4-B_7_4-B_1_16B_1_5-B_7_5-B_1_17B_1_6-B_7_6-B_1_18B_2_1-B_8_1-B_2_13B_2_2-B_8_2-B_2_14B_2_3-B_8_3-B_2_15B_2_4-B_8_4-B_2_16B_2_5-B_8_5-B_2_17B_2_6-B_8_6-B_2_18B_3_1-B_9_1-B_3_13B_3_2-B_9_2-B_3_14B_3_3-B_9_3-B_3_15B_3_4-B_9_4-B_3_16B_3_5-B_9_5-B_3_17B_3_6-B_9_6-B_3_18B_4_1-B_10_1-B_4_13B_4_2-B_10_2-B_4_14B_4_3-B_10_3-B_4_15B_4_4-B_10_4-B_4_16B_4_5-B_10_5-B_4_17B_4_6-B_10_6-B_4_18B_5_1-B_11_1-B_5_13B_5_2-B_11_2-B_5_14B_5_3-B_11_3-B_5_15B_5_4-B_11_4-B_5_1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3_24B_1_19B_1_20B_1_21B_1_22B_1_23B_1_24B_2_19B_2_20B_2_21B_2_22B_2_23B_2_24B_3_19B_3_20B_3_21B_3_22B_3_23B_3_24B_4_19B_4_20B_4_21B_4_22B_4_23B_4_24B_5_19B_5_20B_5_21B_5_22B_5_23B_5_24B_6_19B_6_20B_6_21B_6_22B_6_23B_6_24C_1_2C_7_2C_19_2C_1_3C_7_3C_19_3C_2_2C_8_2C_20_2C_2_3C_8_3C_20_3C_3_2C_9_2C_21_2C_3_3C_9_3C_21_3C_4_2C_10_2C_22_2C_4_3C_10_3C_22_3C_11_2C_5_2C_23_2C_11_3C_5_3C_23_3C_6_2C_12_2C_24_2C_6_3C_12_3C_24_3TraceMulA_1_1A_1_7A_1_19A_1_2A_1_8A_1_20A_1_3A_1_9A_1_21A_1_4A_1_10A_1_22A_1_5A_1_11A_1_23A_1_6A_1_12A_1_24B_19_1B_19_2B_19_3B_19_4B_19_5B_19_6B_20_1B_20_2B_20_3B_20_4B_20_5B_20_6B_21_1B_21_2B_21_3B_21_4B_21_5B_21_6B_22_1B_22_2B_22_3B_22_4B_22_5B_22_6B_23_1B_23_2B_23_3B_23_4B_23_5B_23_6B_24_1B_24_2B_24_3B_24_4B_24_5B_24_6C_1_1C_7_1C_19_1C_1_3C_7_3C_19_3C_2_1C_8_1C_20_1C_2_3C_8_3C_20_3C_3_1C_9_1C_21_1C_3_3C_9_3C_21_3C_4_1C_10_1C_22_1C_4_3C_10_3C_22_3C_11_1C_5_1C_23_1C_5_3C_11_3C_23_3C_6_1C_12_1C_24_1C_6_3C_12_3C_24_3TraceMulA_2_1A_2_13A_2_2A_2_14A_2_3A_2_15A_2_4A_2_16A_2_5A_2_17A_2_6A_2_18A_1_1A_3_1A_1_13A_3_13A_1_2A_3_2A_1_14A_3_14A_1_3A_3_3A_1_15A_3_15A_1_4A_3_4A_1_16A_3_16A_1_5A_3_5A_1_17A_3_17A_1_6A_3_6A_1_18A_3_18B_13_1B_13_2B_13_3B_13_4B_13_5B_13_6B_14_1B_14_2B_14_3B_14_4B_14_5B_14_6B_15_1B_15_2B_15_3B_15_4B_15_5B_15_6B_16_1B_16_2B_16_3B_16_4B_16_5B_16_6B_17_1B_17_2B_17_3B_17_4B_17_5B_17_6B_18_1B_18_2B_18_3B_18_4B_18_5B_18_6C_1_2C_13_2C_1_3C_13_3C_2_2C_14_2C_2_3C_14_3C_3_2C_15_2C_3_3C_15_3C_4_2C_16_2C_4_3C_16_3C_5_2C_17_2C_5_3C_17_3C_6_2C_18_2C_6_3C_18_3TraceMulA_2_13A_2_19A_2_14A_2_20A_2_15A_2_21A_2_16A_2_22A_2_17A_2_23A_2_18A_2_24A_1_13A_3_13A_1_19A_3_19A_1_14A_3_14A_1_20A_3_20A_1_15A_3_15A_1_21A_3_21A_1_16A_3_16A_1_22A_3_22A_1_17A_3_17A_1_23A_3_23A_3_18A_1_18A_1_24A_3_24B_13_19B_13_20B_13_21B_13_22B_13_23B_13_24B_14_19B_14_20B_14_21B_14_22B_14_23B_14_24B_15_19B_15_20B_15_21B_15_22B_15_23B_15_24B_16_19B_16_20B_16_21B_16_22B_16_23B_16_24B_17_19B_17_20B_17_21B_17_22B_17_23B_17_24B_18_19B_18_20B_18_21B_18_22B_18_23B_18_24C_13_2C_19_2C_13_3C_19_3C_14_2C_20_2C_14_3C_20_3C_15_2C_21_2C_15_3C_21_3C_16_2C_22_2C_16_3C_22_3C_17_2C_23_2C_17_3C_23_3C_18_2C_24_2C_18_3C_24_3Trace(Mul(Matrix(3, 24, [[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_1_20,A_1_21,A_1_22,A_1_23,A_1_24],[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_2_20,A_2_21,A_2_22,A_2_23,A_2_24],[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_3_20,A_3_21,A_3_22,A_3_23,A_3_24]]),Matrix(24, 24, [[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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_20_1,B_20_2,B_20_3,B_20_4,B_20_5,B_20_6,B_20_7,B_20_8,B_20_9,B_20_10,B_20_11,B_20_12,B_20_13,B_20_14,B_20_15,B_20_16,B_20_17,B_20_18,B_20_19,B_20_20,B_20_21,B_20_22,B_20_23,B_20_24],[B_21_1,B_21_2,B_21_3,B_21_4,B_21_5,B_21_6,B_21_7,B_21_8,B_21_9,B_21_10,B_21_11,B_21_12,B_21_13,B_21_14,B_21_15,B_21_16,B_21_17,B_21_18,B_21_19,B_21_20,B_21_21,B_21_22,B_21_23,B_21_24],[B_22_1,B_22_2,B_22_3,B_22_4,B_22_5,B_22_6,B_22_7,B_22_8,B_22_9,B_22_10,B_22_11,B_22_12,B_22_13,B_22_14,B_22_15,B_22_16,B_22_17,B_22_18,B_22_19,B_22_20,B_22_21,B_22_22,B_22_23,B_22_24],[B_23_1,B_23_2,B_23_3,B_23_4,B_23_5,B_23_6,B_23_7,B_23_8,B_23_9,B_23_10,B_23_11,B_23_12,B_23_13,B_23_14,B_23_15,B_23_16,B_23_17,B_23_18,B_23_19,B_23_20,B_23_21,B_23_22,B_23_23,B_23_24],[B_24_1,B_24_2,B_24_3,B_24_4,B_24_5,B_24_6,B_24_7,B_24_8,B_24_9,B_24_10,B_24_11,B_24_12,B_24_13,B_24_14,B_24_15,B_24_16,B_24_17,B_24_18,B_24_19,B_24_20,B_24_21,B_24_22,B_24_23,B_24_24]]),Matrix(24, 3, [[C_1_1,C_1_2,C_1_3],[C_2_1,C_2_2,C_2_3],[C_3_1,C_3_2,C_3_3],[C_4_1,C_4_2,C_4_3],[C_5_1,C_5_2,C_5_3],[C_6_1,C_6_2,C_6_3],[C_7_1,C_7_2,C_7_3],[C_8_1,C_8_2,C_8_3],[C_9_1,C_9_2,C_9_3],[C_10_1,C_10_2,C_10_3],[C_11_1,C_11_2,C_11_3],[C_12_1,C_12_2,C_12_3],[C_13_1,C_13_2,C_13_3],[C_14_1,C_14_2,C_14_3],[C_15_1,C_15_2,C_15_3],[C_16_1,C_16_2,C_16_3],[C_17_1,C_17_2,C_17_3],[C_18_1,C_18_2,C_18_3],[C_19_1,C_19_2,C_19_3],[C_20_1,C_20_2,C_20_3],[C_21_1,C_21_2,C_21_3],[C_22_1,C_22_2,C_22_3],[C_23_1,C_23_2,C_23_3],[C_24_1,C_24_2,C_24_3]]))) = Trace(Mul(Matrix(2, 6, [[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6],[A_3_1,A_3_2,A_3_3,A_3_4,A_3_5,A_3_6]]),Matrix(6, 6, [[B_1_1-B_7_1-B_1_13,B_1_2-B_7_2-B_1_14,B_1_3-B_7_3-B_1_15,B_1_4-B_7_4-B_1_16,B_1_5-B_7_5-B_1_17,B_1_6-B_7_6-B_1_18],[B_2_1-B_8_1-B_2_13,B_2_2-B_8_2-B_2_14,B_2_3-B_8_3-B_2_15,B_2_4-B_8_4-B_2_16,B_2_5-B_8_5-B_2_17,B_2_6-B_8_6-B_2_18],[B_3_1-B_9_1-B_3_13,B_3_2-B_9_2-B_3_14,B_3_3-B_9_3-B_3_15,B_3_4-B_9_4-B_3_16,B_3_5-B_9_5-B_3_17,B_3_6-B_9_6-B_3_18],[B_4_1-B_10_1-B_4_13,B_4_2-B_10_2-B_4_14,B_4_3-B_10_3-B_4_15,B_4_4-B_10_4-B_4_16,B_4_5-B_10_5-B_4_17,B_4_6-B_10_6-B_4_18],[B_5_1-B_11_1-B_5_13,B_5_2-B_11_2-B_5_14,B_5_3-B_11_3-B_5_15,B_5_4-B_11_4-B_5_16,B_5_5-B_11_5-B_5_17,B_5_6-B_11_6-B_5_18],[B_6_1-B_12_1-B_6_13,B_6_2-B_12_2-B_6_14,B_6_3-B_12_3-B_6_15,B_6_4-B_12_4-B_6_16,B_6_5-B_12_5-B_6_17,B_6_6-B_12_6-B_6_18]]),Matrix(6, 2, [[C_1_2,C_1_1+C_1_3],[C_2_2,C_2_1+C_2_3],[C_3_2,C_3_1+C_3_3],[C_4_2,C_4_1+C_4_3],[C_5_2,C_5_1+C_5_3],[C_6_2,C_6_1+C_6_3]])))+Trace(Mul(Matrix(1, 6, [[A_1_7,A_1_8,A_1_9,A_1_10,A_1_11,A_1_12]]),Matrix(6, 6, [[B_19_1-B_1_7+B_7_7-B_19_7-B_7_13,B_19_2-B_1_8+B_7_8-B_19_8-B_7_14,B_19_3-B_1_9+B_7_9-B_19_9-B_7_15,B_19_4-B_1_10+B_7_10-B_19_10-B_7_16,B_19_5-B_1_11+B_7_11-B_19_11-B_7_17,B_19_6-B_1_12+B_7_12-B_19_12-B_7_18],[B_20_1-B_2_7+B_8_7-B_20_7-B_8_13,B_20_2-B_2_8+B_8_8-B_20_8-B_8_14,B_20_3-B_2_9+B_8_9-B_20_9-B_8_15,B_20_4-B_2_10+B_8_10-B_20_10-B_8_16,B_20_5-B_2_11+B_8_11-B_20_11-B_8_17,B_20_6-B_2_12+B_8_12-B_20_12-B_8_18],[B_21_1-B_3_7+B_9_7-B_21_7-B_9_13,B_21_2-B_3_8+B_9_8-B_21_8-B_9_14,B_21_3-B_3_9+B_9_9-B_21_9-B_9_15,B_21_4-B_3_10+B_9_10-B_21_10-B_9_16,B_21_5-B_3_11+B_9_11-B_21_11-B_9_17,B_21_6-B_3_12+B_9_12-B_21_12-B_9_18],[B_22_1-B_4_7+B_10_7-B_22_7-B_10_13,B_22_2-B_4_8+B_10_8-B_22_8-B_10_14,B_22_3-B_4_9+B_10_9-B_22_9-B_10_15,B_22_4-B_4_10+B_10_10-B_22_10-B_10_16,B_22_5-B_4_11+B_10_11-B_22_11-B_10_17,B_22_6-B_4_12+B_10_12-B_22_12-B_10_18],[B_23_1-B_5_7+B_11_7-B_23_7-B_11_13,B_23_2-B_5_8+B_11_8-B_23_8-B_11_14,B_23_3-B_5_9+B_11_9-B_23_9-B_11_15,B_23_4-B_5_10+B_11_10-B_23_10-B_11_16,B_23_5-B_5_11+B_11_11-B_23_11-B_11_17,B_23_6-B_5_12+B_11_12-B_23_12-B_11_18],[B_24_1-B_6_7+B_12_7-B_24_7-B_12_13,B_24_2-B_6_8+B_12_8-B_24_8-B_12_14,B_24_3-B_6_9+B_12_9-B_24_9-B_12_15,B_24_4-B_6_10+B_12_10-B_24_10-B_12_16,B_24_5-B_6_11+B_12_11-B_24_11-B_12_17,B_24_6-B_6_12+B_12_12-B_24_12-B_12_18]]),Matrix(6, 1, [[C_7_1+C_7_3],[C_8_1+C_8_3],[C_9_1+C_9_3],[C_10_1+C_10_3],[C_11_1+C_11_3],[C_12_1+C_12_3]])))+Trace(Mul(Matrix(1, 6, [[A_1_13,A_1_14,A_1_15,A_1_16,A_1_17,A_1_18]]),Matrix(6, 6, [[-B_13_7-B_1_13+B_13_13-B_19_13,-B_13_8-B_1_14+B_13_14-B_19_14,-B_13_9-B_1_15+B_13_15-B_19_15,-B_13_10-B_1_16+B_13_16-B_19_16,-B_13_11-B_1_17+B_13_17-B_19_17,-B_13_12-B_1_18+B_13_18-B_19_18],[-B_14_7-B_2_13+B_14_13-B_20_13,-B_14_8-B_2_14+B_14_14-B_20_14,-B_14_9-B_2_15+B_14_15-B_20_15,-B_14_10-B_2_16+B_14_16-B_20_16,-B_14_11-B_2_17+B_14_17-B_20_17,-B_14_12-B_2_18+B_14_18-B_20_18],[-B_15_7-B_3_13+B_15_13-B_21_13,-B_15_8-B_3_14+B_15_14-B_21_14,-B_15_9-B_3_15+B_15_15-B_21_15,-B_15_10-B_3_16+B_15_16-B_21_16,-B_15_11-B_3_17+B_15_17-B_21_17,-B_15_12-B_3_18+B_15_18-B_21_18],[-B_16_7-B_4_13+B_16_13-B_22_13,-B_16_8-B_4_14+B_16_14-B_22_14,-B_16_9-B_4_15+B_16_15-B_22_15,-B_16_10-B_4_16+B_16_16-B_22_16,-B_16_11-B_4_17+B_16_17-B_22_17,-B_16_12-B_4_18+B_16_18-B_22_18],[-B_17_7-B_5_13+B_17_13-B_23_13,-B_17_8-B_5_14+B_17_14-B_23_14,-B_17_9-B_5_15+B_17_15-B_23_15,-B_17_10-B_5_16+B_17_16-B_23_16,-B_17_11-B_5_17+B_17_17-B_23_17,-B_17_12-B_5_18+B_17_18-B_23_18],[-B_18_7-B_6_13+B_18_13-B_24_13,-B_18_8-B_6_14+B_18_14-B_24_14,-B_18_9-B_6_15+B_18_15-B_24_15,-B_18_10-B_6_16+B_18_16-B_24_16,-B_18_11-B_6_17+B_18_17-B_24_17,-B_18_12-B_6_18+B_18_18-B_24_18]]),Matrix(6, 1, [[C_13_1],[C_14_1],[C_15_1],[C_16_1],[C_17_1],[C_18_1]])))+Trace(Mul(Matrix(2, 6, [[A_2_13,A_2_14,A_2_15,A_2_16,A_2_17,A_2_18],[A_3_13,A_3_14,A_3_15,A_3_16,A_3_17,A_3_18]]),Matrix(6, 6, [[-B_13_1-B_7_13+B_13_13-B_13_19,-B_13_2-B_7_14+B_13_14-B_13_20,-B_13_3-B_7_15+B_13_15-B_13_21,-B_13_4-B_7_16+B_13_16-B_13_22,-B_13_5-B_7_17+B_13_17-B_13_23,-B_13_6-B_7_18+B_13_18-B_13_24],[-B_14_1-B_8_13+B_14_13-B_14_19,-B_14_2-B_8_14+B_14_14-B_14_20,-B_14_3-B_8_15+B_14_15-B_14_21,-B_14_4-B_8_16+B_14_16-B_14_22,-B_14_5-B_8_17+B_14_17-B_14_23,-B_14_6-B_8_18+B_14_18-B_14_24],[-B_15_1-B_9_13+B_15_13-B_15_19,-B_15_2-B_9_14+B_15_14-B_15_20,-B_15_3-B_9_15+B_15_15-B_15_21,-B_15_4-B_9_16+B_15_16-B_15_22,-B_15_5-B_9_17+B_15_17-B_15_23,-B_15_6-B_9_18+B_15_18-B_15_24],[-B_16_1-B_10_13+B_16_13-B_16_19,-B_16_2-B_10_14+B_16_14-B_16_20,-B_16_3-B_10_15+B_16_15-B_16_21,-B_16_4-B_10_16+B_16_16-B_16_22,-B_16_5-B_10_17+B_16_17-B_16_23,-B_16_6-B_10_18+B_16_18-B_16_24],[-B_17_1-B_11_13+B_17_13-B_17_19,-B_17_2-B_11_14+B_17_14-B_17_20,-B_17_3-B_11_15+B_17_15-B_17_21,-B_17_4-B_11_16+B_17_16-B_17_22,-B_17_5-B_11_17+B_17_17-B_17_23,-B_17_6-B_11_18+B_17_18-B_17_24],[-B_18_1-B_12_13+B_18_13-B_18_19,-B_18_2-B_12_14+B_18_14-B_18_20,-B_18_3-B_12_15+B_18_15-B_18_21,-B_18_4-B_12_16+B_18_16-B_18_22,-B_18_5-B_12_17+B_18_17-B_18_23,-B_18_6-B_12_18+B_18_18-B_18_24]]),Matrix(6, 2, [[C_13_2,C_13_3],[C_14_2,C_14_3],[C_15_2,C_15_3],[C_16_2,C_16_3],[C_17_2,C_17_3],[C_18_2,C_18_3]])))+Trace(Mul(Matrix(2, 6, [[A_2_19,A_2_20,A_2_21,A_2_22,A_2_23,A_2_24],[A_3_19,A_3_20,A_3_21,A_3_22,A_3_23,A_3_24]]),Matrix(6, 6, [[B_19_1-B_19_13+B_1_19-B_7_19+B_19_19,B_19_2-B_19_14+B_1_20-B_7_20+B_19_20,B_19_3-B_19_15+B_1_21-B_7_21+B_19_21,B_19_4-B_19_16+B_1_22-B_7_22+B_19_22,B_19_5-B_19_17+B_1_23-B_7_23+B_19_23,B_19_6-B_19_18+B_1_24-B_7_24+B_19_24],[B_20_1-B_20_13+B_2_19-B_8_19+B_20_19,B_20_2-B_20_14+B_2_20-B_8_20+B_20_20,B_20_3-B_20_15+B_2_21-B_8_21+B_20_21,B_20_4-B_20_16+B_2_22-B_8_22+B_20_22,B_20_5-B_20_17+B_2_23-B_8_23+B_20_23,B_20_6-B_20_18+B_2_24-B_8_24+B_20_24],[B_21_1-B_21_13+B_3_19-B_9_19+B_21_19,B_21_2-B_21_14+B_3_20-B_9_20+B_21_20,B_21_3-B_21_15+B_3_21-B_9_21+B_21_21,B_21_4-B_21_16+B_3_22-B_9_22+B_21_22,B_21_5-B_21_17+B_3_23-B_9_23+B_21_23,B_21_6-B_21_18+B_3_24-B_9_24+B_21_24],[B_22_1-B_22_13+B_4_19-B_10_19+B_22_19,B_22_2-B_22_14+B_4_20-B_10_20+B_22_20,B_22_3-B_22_15+B_4_21-B_10_21+B_22_21,B_22_4-B_22_16+B_4_22-B_10_22+B_22_22,B_22_5-B_22_17+B_4_23-B_10_23+B_22_23,B_22_6-B_22_18+B_4_24-B_10_24+B_22_24],[B_23_1-B_23_13+B_5_19-B_11_19+B_23_19,B_23_2-B_23_14+B_5_20-B_11_20+B_23_20,B_23_3-B_23_15+B_5_21-B_11_21+B_23_21,B_23_4-B_23_16+B_5_22-B_11_22+B_23_22,B_23_5-B_23_17+B_5_23-B_11_23+B_23_23,B_23_6-B_23_18+B_5_24-B_11_24+B_23_24],[B_24_1-B_24_13+B_6_19-B_12_19+B_24_19,B_24_2-B_24_14+B_6_20-B_12_20+B_24_20,B_24_3-B_24_15+B_6_21-B_12_21+B_24_21,B_24_4-B_24_16+B_6_22-B_12_22+B_24_22,B_24_5-B_24_17+B_6_23-B_12_23+B_24_23,B_24_6-B_24_18+B_6_24-B_12_24+B_24_24]]),Matrix(6, 2, [[C_19_2,C_19_1+C_19_3],[C_20_2,C_20_1+C_20_3],[C_21_2,C_21_1+C_21_3],[C_22_2,C_22_1+C_22_3],[C_23_2,C_23_1+C_23_3],[C_24_2,C_24_1+C_24_3]])))+Trace(Mul(Matrix(1, 6, [[A_1_1+A_1_7,A_1_2+A_1_8,A_1_3+A_1_9,A_1_4+A_1_10,A_1_5+A_1_11,A_1_6+A_1_12]]),Matrix(6, 6, [[B_19_1+B_1_7,B_19_2+B_1_8,B_19_3+B_1_9,B_19_4+B_1_10,B_19_5+B_1_11,B_19_6+B_1_12],[B_20_1+B_2_7,B_20_2+B_2_8,B_20_3+B_2_9,B_20_4+B_2_10,B_20_5+B_2_11,B_20_6+B_2_12],[B_21_1+B_3_7,B_21_2+B_3_8,B_21_3+B_3_9,B_21_4+B_3_10,B_21_5+B_3_11,B_21_6+B_3_12],[B_22_1+B_4_7,B_22_2+B_4_8,B_22_3+B_4_9,B_22_4+B_4_10,B_22_5+B_4_11,B_22_6+B_4_12],[B_23_1+B_5_7,B_23_2+B_5_8,B_23_3+B_5_9,B_23_4+B_5_10,B_23_5+B_5_11,B_23_6+B_5_12],[B_24_1+B_6_7,B_24_2+B_6_8,B_24_3+B_6_9,B_24_4+B_6_10,B_24_5+B_6_11,B_24_6+B_6_12]]),Matrix(6, 1, [[C_1_1+C_7_1],[C_2_1+C_8_1],[C_3_1+C_9_1],[C_4_1+C_10_1],[C_11_1+C_5_1],[C_6_1+C_12_1]])))+Trace(Mul(Matrix(1, 6, [[A_1_1+A_1_13,A_1_2+A_1_14,A_1_3+A_1_15,A_1_4+A_1_16,A_1_5+A_1_17,A_1_6+A_1_18]]),Matrix(6, 6, [[B_1_13,B_1_14,B_1_15,B_1_16,B_1_17,B_1_18],[B_2_13,B_2_14,B_2_15,B_2_16,B_2_17,B_2_18],[B_3_13,B_3_14,B_3_15,B_3_16,B_3_17,B_3_18],[B_4_13,B_4_14,B_4_15,B_4_16,B_4_17,B_4_18],[B_5_13,B_5_14,B_5_15,B_5_16,B_5_17,B_5_18],[B_6_13,B_6_14,B_6_15,B_6_16,B_6_17,B_6_18]]),Matrix(6, 1, [[C_1_1+C_13_1+C_1_3+C_13_3],[C_2_1+C_14_1+C_2_3+C_14_3],[C_3_1+C_15_1+C_3_3+C_15_3],[C_4_1+C_16_1+C_4_3+C_16_3],[C_5_1+C_17_1+C_5_3+C_17_3],[C_6_1+C_18_1+C_6_3+C_18_3]])))+Trace(Mul(Matrix(1, 6, [[A_1_1-A_3_1,A_1_2-A_3_2,A_1_3-A_3_3,A_1_4-A_3_4,A_1_5-A_3_5,A_1_6-A_3_6]]),Matrix(6, 6, [[B_1_1-B_13_1-B_1_7,B_1_2-B_13_2-B_1_8,B_1_3-B_13_3-B_1_9,B_1_4-B_13_4-B_1_10,B_1_5-B_13_5-B_1_11,B_1_6-B_13_6-B_1_12],[B_2_1-B_14_1-B_2_7,B_2_2-B_14_2-B_2_8,B_2_3-B_14_3-B_2_9,B_2_4-B_14_4-B_2_10,B_2_5-B_14_5-B_2_11,B_2_6-B_14_6-B_2_12],[B_3_1-B_15_1-B_3_7,B_3_2-B_15_2-B_3_8,B_3_3-B_15_3-B_3_9,B_3_4-B_15_4-B_3_10,B_3_5-B_15_5-B_3_11,B_3_6-B_15_6-B_3_12],[B_4_1-B_16_1-B_4_7,B_4_2-B_16_2-B_4_8,B_4_3-B_16_3-B_4_9,B_4_4-B_16_4-B_4_10,B_4_5-B_16_5-B_4_11,B_4_6-B_16_6-B_4_12],[B_5_1-B_17_1-B_5_7,B_5_2-B_17_2-B_5_8,B_5_3-B_17_3-B_5_9,B_5_4-B_17_4-B_5_10,B_5_5-B_17_5-B_5_11,B_5_6-B_17_6-B_5_12],[B_6_1-B_18_1-B_6_7,B_6_2-B_18_2-B_6_8,B_6_3-B_18_3-B_6_9,B_6_4-B_18_4-B_6_10,B_6_5-B_18_5-B_6_11,B_6_6-B_18_6-B_6_12]]),Matrix(6, 1, [[C_1_1],[C_2_1],[C_3_1],[C_4_1],[C_5_1],[C_6_1]])))+Trace(Mul(Matrix(2, 6, [[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6],[A_3_1+A_1_7,A_3_2+A_1_8,A_3_3+A_1_9,A_3_4+A_1_10,A_3_5+A_1_11,A_3_6+A_1_12]]),Matrix(6, 6, [[B_7_1-B_1_7,B_7_2-B_1_8,B_7_3-B_1_9,B_7_4-B_1_10,B_7_5-B_1_11,B_7_6-B_1_12],[B_8_1-B_2_7,B_8_2-B_2_8,B_8_3-B_2_9,B_8_4-B_2_10,B_8_5-B_2_11,B_8_6-B_2_12],[B_9_1-B_3_7,B_9_2-B_3_8,B_9_3-B_3_9,B_9_4-B_3_10,B_9_5-B_3_11,B_9_6-B_3_12],[B_10_1-B_4_7,B_10_2-B_4_8,B_10_3-B_4_9,B_10_4-B_4_10,B_10_5-B_4_11,B_10_6-B_4_12],[B_11_1-B_5_7,B_11_2-B_5_8,B_11_3-B_5_9,B_11_4-B_5_10,B_11_5-B_5_11,B_11_6-B_5_12],[B_12_1-B_6_7,B_12_2-B_6_8,B_12_3-B_6_9,B_12_4-B_6_10,B_12_5-B_6_11,B_12_6-B_6_12]]),Matrix(6, 2, [[-C_7_2,C_1_1-C_7_3],[-C_8_2,C_2_1-C_8_3],[-C_9_2,C_3_1-C_9_3],[-C_10_2,C_4_1-C_10_3],[-C_11_2,C_5_1-C_11_3],[-C_12_2,C_6_1-C_12_3]])))+Trace(Mul(Matrix(2, 6, [[A_2_1+A_2_7,A_2_2+A_2_8,A_2_3+A_2_9,A_2_4+A_2_10,A_2_5+A_2_11,A_2_6+A_2_12],[A_3_1+A_3_7,A_3_2+A_3_8,A_3_3+A_3_9,A_3_4+A_3_10,A_3_5+A_3_11,A_3_6+A_3_12]]),Matrix(6, 6, [[B_7_1+B_1_19,B_7_2+B_1_20,B_7_3+B_1_21,B_7_4+B_1_22,B_7_5+B_1_23,B_7_6+B_1_24],[B_8_1+B_2_19,B_8_2+B_2_20,B_8_3+B_2_21,B_8_4+B_2_22,B_8_5+B_2_23,B_8_6+B_2_24],[B_9_1+B_3_19,B_9_2+B_3_20,B_9_3+B_3_21,B_9_4+B_3_22,B_9_5+B_3_23,B_9_6+B_3_24],[B_10_1+B_4_19,B_10_2+B_4_20,B_10_3+B_4_21,B_10_4+B_4_22,B_10_5+B_4_23,B_10_6+B_4_24],[B_11_1+B_5_19,B_11_2+B_5_20,B_11_3+B_5_21,B_11_4+B_5_22,B_11_5+B_5_23,B_11_6+B_5_24],[B_12_1+B_6_19,B_12_2+B_6_20,B_12_3+B_6_21,B_12_4+B_6_22,B_12_5+B_6_23,B_12_6+B_6_24]]),Matrix(6, 2, [[C_1_2+C_7_2,C_1_3+C_7_3],[C_2_2+C_8_2,C_2_3+C_8_3],[C_3_2+C_9_2,C_3_3+C_9_3],[C_4_2+C_10_2,C_4_3+C_10_3],[C_11_2+C_5_2,C_11_3+C_5_3],[C_6_2+C_12_2,C_6_3+C_12_3]])))+Trace(Mul(Matrix(1, 6, [[A_1_7+A_1_19,A_1_8+A_1_20,A_1_9+A_1_21,A_1_10+A_1_22,A_1_11+A_1_23,A_1_12+A_1_24]]),Matrix(6, 6, [[-B_19_1+B_19_7,-B_19_2+B_19_8,-B_19_3+B_19_9,-B_19_4+B_19_10,-B_19_5+B_19_11,-B_19_6+B_19_12],[-B_20_1+B_20_7,-B_20_2+B_20_8,-B_20_3+B_20_9,-B_20_4+B_20_10,-B_20_5+B_20_11,-B_20_6+B_20_12],[-B_21_1+B_21_7,-B_21_2+B_21_8,-B_21_3+B_21_9,-B_21_4+B_21_10,-B_21_5+B_21_11,-B_21_6+B_21_12],[-B_22_1+B_22_7,-B_22_2+B_22_8,-B_22_3+B_22_9,-B_22_4+B_22_10,-B_22_5+B_22_11,-B_22_6+B_22_12],[-B_23_1+B_23_7,-B_23_2+B_23_8,-B_23_3+B_23_9,-B_23_4+B_23_10,-B_23_5+B_23_11,-B_23_6+B_23_12],[-B_24_1+B_24_7,-B_24_2+B_24_8,-B_24_3+B_24_9,-B_24_4+B_24_10,-B_24_5+B_24_11,-B_24_6+B_24_12]]),Matrix(6, 1, [[C_7_1+C_19_1],[C_8_1+C_20_1],[C_9_1+C_21_1],[C_10_1+C_22_1],[C_11_1+C_23_1],[C_12_1+C_24_1]])))+Trace(Mul(Matrix(2, 6, [[-A_2_7,-A_2_8,-A_2_9,-A_2_10,-A_2_11,-A_2_12],[A_1_7-A_3_7,A_1_8-A_3_8,A_1_9-A_3_9,A_1_10-A_3_10,A_1_11-A_3_11,A_1_12-A_3_12]]),Matrix(6, 6, [[B_7_1-B_7_7+B_13_7-B_1_19+B_7_19,B_7_2-B_7_8+B_13_8-B_1_20+B_7_20,B_7_3-B_7_9+B_13_9-B_1_21+B_7_21,B_7_4-B_7_10+B_13_10-B_1_22+B_7_22,B_7_5-B_7_11+B_13_11-B_1_23+B_7_23,B_7_6-B_7_12+B_13_12-B_1_24+B_7_24],[B_8_1-B_8_7+B_14_7-B_2_19+B_8_19,B_8_2-B_8_8+B_14_8-B_2_20+B_8_20,B_8_3-B_8_9+B_14_9-B_2_21+B_8_21,-B_8_10+B_8_4+B_14_10-B_2_22+B_8_22,B_8_5-B_8_11+B_14_11-B_2_23+B_8_23,B_8_6-B_8_12+B_14_12-B_2_24+B_8_24],[B_9_1-B_9_7+B_15_7-B_3_19+B_9_19,B_9_2-B_9_8+B_15_8-B_3_20+B_9_20,B_9_3-B_9_9+B_15_9-B_3_21+B_9_21,B_9_4-B_9_10+B_15_10-B_3_22+B_9_22,-B_9_11+B_9_5+B_15_11-B_3_23+B_9_23,B_9_6-B_9_12+B_15_12-B_3_24+B_9_24],[B_10_1-B_10_7+B_16_7-B_4_19+B_10_19,B_10_2-B_10_8+B_16_8-B_4_20+B_10_20,B_10_3-B_10_9+B_16_9-B_4_21+B_10_21,B_10_4-B_10_10+B_16_10-B_4_22+B_10_22,B_10_5-B_10_11+B_16_11-B_4_23+B_10_23,B_10_6-B_10_12+B_16_12-B_4_24+B_10_24],[B_11_1-B_11_7+B_17_7-B_5_19+B_11_19,B_11_2-B_11_8+B_17_8-B_5_20+B_11_20,B_11_3-B_11_9+B_17_9-B_5_21+B_11_21,B_11_4-B_11_10+B_17_10-B_5_22+B_11_22,B_11_5-B_11_11+B_17_11-B_5_23+B_11_23,B_11_6-B_11_12+B_17_12-B_5_24+B_11_24],[B_12_1-B_12_7+B_18_7-B_6_19+B_12_19,B_12_2-B_12_8+B_18_8-B_6_20+B_12_20,B_12_3-B_12_9+B_18_9-B_6_21+B_12_21,B_12_4-B_12_10+B_18_10-B_6_22+B_12_22,B_12_5-B_12_11+B_18_11-B_6_23+B_12_23,B_12_6-B_12_12+B_18_12-B_6_24+B_12_24]]),Matrix(6, 2, [[C_7_2,C_7_3],[C_8_2,C_8_3],[C_9_2,C_9_3],[C_10_2,C_10_3],[C_11_2,C_11_3],[C_12_2,C_12_3]])))+Trace(Mul(Matrix(2, 6, [[A_2_7+A_2_13,A_2_8+A_2_14,A_2_9+A_2_15,A_2_10+A_2_16,A_2_11+A_2_17,A_2_12+A_2_18],[A_3_7+A_3_13,A_3_8+A_3_14,A_3_9+A_3_15,A_3_10+A_3_16,A_3_11+A_3_17,A_3_12+A_3_18]]),Matrix(6, 6, [[B_7_13,B_7_14,B_7_15,B_7_16,B_7_17,B_7_18],[B_8_13,B_8_14,B_8_15,B_8_16,B_8_17,B_8_18],[B_9_13,B_9_14,B_9_15,B_9_16,B_9_17,B_9_18],[B_10_13,B_10_14,B_10_15,B_10_16,B_10_17,B_10_18],[B_11_13,B_11_14,B_11_15,B_11_16,B_11_17,B_11_18],[B_12_13,B_12_14,B_12_15,B_12_16,B_12_17,B_12_18]]),Matrix(6, 2, [[C_7_2+C_13_2,C_7_1+C_13_1+C_7_3+C_13_3],[C_8_2+C_14_2,C_8_1+C_14_1+C_8_3+C_14_3],[C_9_2+C_15_2,C_9_1+C_15_1+C_9_3+C_15_3],[C_10_2+C_16_2,C_10_1+C_16_1+C_10_3+C_16_3],[C_11_2+C_17_2,C_11_1+C_17_1+C_11_3+C_17_3],[C_12_2+C_18_2,C_12_1+C_18_1+C_12_3+C_18_3]])))+Trace(Mul(Matrix(2, 6, [[A_2_7+A_2_19,A_2_8+A_2_20,A_2_9+A_2_21,A_2_10+A_2_22,A_2_11+A_2_23,A_2_12+A_2_24],[A_3_7+A_3_19,A_3_8+A_3_20,A_3_9+A_3_21,A_3_10+A_3_22,A_3_11+A_3_23,A_3_12+A_3_24]]),Matrix(6, 6, [[-B_1_19+B_7_19,-B_1_20+B_7_20,-B_1_21+B_7_21,-B_1_22+B_7_22,-B_1_23+B_7_23,-B_1_24+B_7_24],[-B_2_19+B_8_19,-B_2_20+B_8_20,-B_2_21+B_8_21,-B_2_22+B_8_22,-B_2_23+B_8_23,-B_2_24+B_8_24],[-B_3_19+B_9_19,-B_3_20+B_9_20,-B_3_21+B_9_21,-B_3_22+B_9_22,-B_3_23+B_9_23,-B_3_24+B_9_24],[-B_4_19+B_10_19,-B_4_20+B_10_20,-B_4_21+B_10_21,-B_4_22+B_10_22,-B_4_23+B_10_23,-B_4_24+B_10_24],[-B_5_19+B_11_19,-B_5_20+B_11_20,-B_5_21+B_11_21,-B_5_22+B_11_22,-B_5_23+B_11_23,-B_5_24+B_11_24],[-B_6_19+B_12_19,-B_6_20+B_12_20,-B_6_21+B_12_21,-B_6_22+B_12_22,-B_6_23+B_12_23,-B_6_24+B_12_24]]),Matrix(6, 2, [[C_7_2+C_19_2,C_7_3+C_19_3],[C_8_2+C_20_2,C_8_3+C_20_3],[C_9_2+C_21_2,C_9_3+C_21_3],[C_10_2+C_22_2,C_10_3+C_22_3],[C_11_2+C_23_2,C_11_3+C_23_3],[C_12_2+C_24_2,C_12_3+C_24_3]])))+Trace(Mul(Matrix(1, 6, [[A_1_13+A_1_19,A_1_14+A_1_20,A_1_15+A_1_21,A_1_16+A_1_22,A_1_17+A_1_23,A_1_18+A_1_24]]),Matrix(6, 6, [[B_19_13,B_19_14,B_19_15,B_19_16,B_19_17,B_19_18],[B_20_13,B_20_14,B_20_15,B_20_16,B_20_17,B_20_18],[B_21_13,B_21_14,B_21_15,B_21_16,B_21_17,B_21_18],[B_22_13,B_22_14,B_22_15,B_22_16,B_22_17,B_22_18],[B_23_13,B_23_14,B_23_15,B_23_16,B_23_17,B_23_18],[B_24_13,B_24_14,B_24_15,B_24_16,B_24_17,B_24_18]]),Matrix(6, 1, [[C_13_1+C_19_1+C_13_3+C_19_3],[C_14_1+C_20_1+C_14_3+C_20_3],[C_15_1+C_21_1+C_15_3+C_21_3],[C_16_1+C_22_1+C_16_3+C_22_3],[C_17_1+C_23_1+C_17_3+C_23_3],[C_18_1+C_24_1+C_18_3+C_24_3]])))+Trace(Mul(Matrix(1, 6, [[A_1_19-A_3_19,A_1_20-A_3_20,A_1_21-A_3_21,A_1_22-A_3_22,A_1_23-A_3_23,A_1_24-A_3_24]]),Matrix(6, 6, [[B_19_1-B_19_7+B_1_19-B_13_19+B_19_19,B_19_2-B_19_8+B_1_20-B_13_20+B_19_20,B_19_3-B_19_9+B_1_21-B_13_21+B_19_21,B_19_4-B_19_10+B_1_22-B_13_22+B_19_22,B_19_5-B_19_11+B_1_23-B_13_23+B_19_23,B_19_6-B_19_12+B_1_24-B_13_24+B_19_24],[B_20_1-B_20_7+B_2_19-B_14_19+B_20_19,B_20_2-B_20_8+B_2_20-B_14_20+B_20_20,B_20_3-B_20_9+B_2_21-B_14_21+B_20_21,B_20_4-B_20_10+B_2_22-B_14_22+B_20_22,B_20_5-B_20_11+B_2_23-B_14_23+B_20_23,B_20_6-B_20_12+B_2_24-B_14_24+B_20_24],[B_21_1-B_21_7+B_3_19-B_15_19+B_21_19,B_21_2-B_21_8+B_3_20-B_15_20+B_21_20,B_21_3-B_21_9+B_3_21-B_15_21+B_21_21,B_21_4-B_21_10+B_3_22-B_15_22+B_21_22,B_21_5-B_21_11+B_3_23-B_15_23+B_21_23,B_21_6-B_21_12+B_3_24-B_15_24+B_21_24],[B_22_1-B_22_7+B_4_19-B_16_19+B_22_19,B_22_2-B_22_8+B_4_20-B_16_20+B_22_20,B_22_3-B_22_9+B_4_21-B_16_21+B_22_21,B_22_4-B_22_10+B_4_22-B_16_22+B_22_22,B_22_5-B_22_11+B_4_23-B_16_23+B_22_23,B_22_6-B_22_12+B_4_24-B_16_24+B_22_24],[B_23_1-B_23_7+B_5_19-B_17_19+B_23_19,B_23_2-B_23_8+B_5_20-B_17_20+B_23_20,B_23_3-B_23_9+B_5_21-B_17_21+B_23_21,B_23_4-B_23_10+B_5_22-B_17_22+B_23_22,B_23_5-B_23_11+B_5_23-B_17_23+B_23_23,B_23_6-B_23_12+B_5_24-B_17_24+B_23_24],[B_24_1-B_24_7+B_6_19-B_18_19+B_24_19,B_24_2-B_24_8+B_6_20-B_18_20+B_24_20,B_24_3-B_24_9+B_6_21-B_18_21+B_24_21,B_24_4-B_24_10+B_6_22-B_18_22+B_24_22,B_24_5-B_24_11+B_6_23-B_18_23+B_24_23,B_24_6-B_24_12+B_6_24-B_18_24+B_24_24]]),Matrix(6, 1, [[C_19_1],[C_20_1],[C_21_1],[C_22_1],[C_23_1],[C_24_1]])))+Trace(Mul(Matrix(2, 6, [[A_2_19,A_2_20,A_2_21,A_2_22,A_2_23,A_2_24],[A_1_7+A_3_19,A_1_8+A_3_20,A_1_9+A_3_21,A_1_10+A_3_22,A_1_11+A_3_23,A_1_12+A_3_24]]),Matrix(6, 6, [[B_19_1-B_19_7-B_1_19+B_7_19,B_19_2-B_19_8-B_1_20+B_7_20,B_19_3-B_19_9-B_1_21+B_7_21,B_19_4-B_19_10-B_1_22+B_7_22,B_19_5-B_19_11-B_1_23+B_7_23,B_19_6-B_19_12-B_1_24+B_7_24],[B_20_1-B_20_7-B_2_19+B_8_19,B_20_2-B_20_8-B_2_20+B_8_20,B_20_3-B_20_9-B_2_21+B_8_21,B_20_4-B_20_10-B_2_22+B_8_22,B_20_5-B_20_11-B_2_23+B_8_23,B_20_6-B_20_12-B_2_24+B_8_24],[B_21_1-B_21_7-B_3_19+B_9_19,B_21_2-B_21_8-B_3_20+B_9_20,B_21_3-B_21_9-B_3_21+B_9_21,B_21_4-B_21_10-B_3_22+B_9_22,B_21_5-B_21_11-B_3_23+B_9_23,B_21_6-B_21_12-B_3_24+B_9_24],[B_22_1-B_22_7-B_4_19+B_10_19,B_22_2-B_22_8-B_4_20+B_10_20,B_22_3-B_22_9-B_4_21+B_10_21,B_22_4-B_22_10-B_4_22+B_10_22,B_22_5-B_22_11-B_4_23+B_10_23,B_22_6-B_22_12-B_4_24+B_10_24],[B_23_1-B_23_7-B_5_19+B_11_19,B_23_2-B_23_8-B_5_20+B_11_20,B_23_3-B_23_9-B_5_21+B_11_21,B_23_4-B_23_10-B_5_22+B_11_22,B_23_5-B_23_11-B_5_23+B_11_23,B_23_6-B_23_12-B_5_24+B_11_24],[B_24_1-B_24_7-B_6_19+B_12_19,B_24_2-B_24_8-B_6_20+B_12_20,B_24_3-B_24_9-B_6_21+B_12_21,B_24_4-B_24_10-B_6_22+B_12_22,B_24_5-B_24_11-B_6_23+B_12_23,B_24_6-B_24_12-B_6_24+B_12_24]]),Matrix(6, 2, [[-C_7_2,C_19_1-C_7_3],[-C_8_2,C_20_1-C_8_3],[-C_9_2,C_21_1-C_9_3],[-C_10_2,C_22_1-C_10_3],[-C_11_2,C_23_1-C_11_3],[-C_12_2,C_24_1-C_12_3]])))+Trace(Mul(Matrix(2, 6, [[-A_2_1,-A_2_2,-A_2_3,-A_2_4,-A_2_5,-A_2_6],[A_1_1-A_3_1+A_1_13,A_1_2-A_3_2+A_1_14,A_1_3-A_3_3+A_1_15,A_1_4-A_3_4+A_1_16,A_1_5-A_3_5+A_1_17,A_1_6-A_3_6+A_1_18]]),Matrix(6, 6, [[B_13_1-B_1_13,B_13_2-B_1_14,B_13_3-B_1_15,B_13_4-B_1_16,B_13_5-B_1_17,B_13_6-B_1_18],[B_14_1-B_2_13,B_14_2-B_2_14,B_14_3-B_2_15,B_14_4-B_2_16,B_14_5-B_2_17,B_14_6-B_2_18],[B_15_1-B_3_13,B_15_2-B_3_14,B_15_3-B_3_15,B_15_4-B_3_16,B_15_5-B_3_17,B_15_6-B_3_18],[B_16_1-B_4_13,B_16_2-B_4_14,B_16_3-B_4_15,B_16_4-B_4_16,B_16_5-B_4_17,B_16_6-B_4_18],[B_17_1-B_5_13,B_17_2-B_5_14,B_17_3-B_5_15,B_17_4-B_5_16,B_17_5-B_5_17,B_17_6-B_5_18],[B_18_1-B_6_13,B_18_2-B_6_14,B_18_3-B_6_15,B_18_4-B_6_16,B_18_5-B_6_17,B_18_6-B_6_18]]),Matrix(6, 2, [[C_1_2+C_13_2,C_1_1+C_1_3+C_13_3],[C_2_2+C_14_2,C_2_1+C_2_3+C_14_3],[C_3_2+C_15_2,C_3_1+C_3_3+C_15_3],[C_4_2+C_16_2,C_4_1+C_4_3+C_16_3],[C_5_2+C_17_2,C_5_1+C_5_3+C_17_3],[C_6_2+C_18_2,C_6_1+C_6_3+C_18_3]])))+Trace(Mul(Matrix(2, 6, [[-A_2_7-A_2_13,-A_2_8-A_2_14,-A_2_9-A_2_15,-A_2_10-A_2_16,-A_2_11-A_2_17,-A_2_12-A_2_18],[A_1_7-A_3_7-A_3_13,A_1_8-A_3_8-A_3_14,A_1_9-A_3_9-A_3_15,A_1_10-A_3_10-A_3_16,A_1_11-A_3_11-A_3_17,A_1_12-A_3_12-A_3_18]]),Matrix(6, 6, [[-B_13_7+B_7_13,-B_13_8+B_7_14,-B_13_9+B_7_15,-B_13_10+B_7_16,-B_13_11+B_7_17,-B_13_12+B_7_18],[-B_14_7+B_8_13,-B_14_8+B_8_14,-B_14_9+B_8_15,-B_14_10+B_8_16,-B_14_11+B_8_17,-B_14_12+B_8_18],[-B_15_7+B_9_13,-B_15_8+B_9_14,-B_15_9+B_9_15,-B_15_10+B_9_16,-B_15_11+B_9_17,-B_15_12+B_9_18],[-B_16_7+B_10_13,-B_16_8+B_10_14,-B_16_9+B_10_15,-B_16_10+B_10_16,-B_16_11+B_10_17,-B_16_12+B_10_18],[-B_17_7+B_11_13,-B_17_8+B_11_14,-B_17_9+B_11_15,-B_17_10+B_11_16,-B_17_11+B_11_17,-B_17_12+B_11_18],[-B_18_7+B_12_13,-B_18_8+B_12_14,-B_18_9+B_12_15,-B_18_10+B_12_16,-B_18_11+B_12_17,-B_18_12+B_12_18]]),Matrix(6, 2, [[C_7_2,C_7_1+C_13_1+C_7_3],[C_8_2,C_8_1+C_14_1+C_8_3],[C_9_2,C_9_1+C_15_1+C_9_3],[C_10_2,C_10_1+C_16_1+C_10_3],[C_11_2,C_11_1+C_17_1+C_11_3],[C_12_2,C_12_1+C_18_1+C_12_3]])))+Trace(Mul(Matrix(2, 6, [[-A_2_19,-A_2_20,-A_2_21,-A_2_22,-A_2_23,-A_2_24],[A_1_13+A_1_19-A_3_19,A_1_14+A_1_20-A_3_20,A_1_15+A_1_21-A_3_21,A_1_16+A_1_22-A_3_22,A_1_17+A_1_23-A_3_23,A_1_18+A_1_24-A_3_24]]),Matrix(6, 6, [[-B_19_13+B_13_19,-B_19_14+B_13_20,-B_19_15+B_13_21,-B_19_16+B_13_22,-B_19_17+B_13_23,-B_19_18+B_13_24],[-B_20_13+B_14_19,-B_20_14+B_14_20,-B_20_15+B_14_21,-B_20_16+B_14_22,-B_20_17+B_14_23,-B_20_18+B_14_24],[-B_21_13+B_15_19,-B_21_14+B_15_20,-B_21_15+B_15_21,-B_21_16+B_15_22,-B_21_17+B_15_23,-B_21_18+B_15_24],[-B_22_13+B_16_19,-B_22_14+B_16_20,-B_22_15+B_16_21,-B_22_16+B_16_22,-B_22_17+B_16_23,-B_22_18+B_16_24],[-B_23_13+B_17_19,-B_23_14+B_17_20,-B_23_15+B_17_21,-B_23_16+B_17_22,-B_23_17+B_17_23,-B_23_18+B_17_24],[-B_24_13+B_18_19,-B_24_14+B_18_20,-B_24_15+B_18_21,-B_24_16+B_18_22,-B_24_17+B_18_23,-B_24_18+B_18_24]]),Matrix(6, 2, [[C_13_2+C_19_2,C_13_3+C_19_1+C_19_3],[C_14_2+C_20_2,C_20_1+C_14_3+C_20_3],[C_15_2+C_21_2,C_21_1+C_15_3+C_21_3],[C_16_2+C_22_2,C_22_1+C_16_3+C_22_3],[C_17_2+C_23_2,C_23_1+C_17_3+C_23_3],[C_18_2+C_24_2,C_24_1+C_18_3+C_24_3]])))+Trace(Mul(Matrix(1, 6, [[A_1_7-A_3_7+A_1_13-A_3_13,A_1_8-A_3_8+A_1_14-A_3_14,A_1_9-A_3_9+A_1_15-A_3_15,A_1_10-A_3_10+A_1_16-A_3_16,A_1_11-A_3_11+A_1_17-A_3_17,A_1_12-A_3_12+A_1_18-A_3_18]]),Matrix(6, 6, [[B_13_7,B_13_8,B_13_9,B_13_10,B_13_11,B_13_12],[B_14_7,B_14_8,B_14_9,B_14_10,B_14_11,B_14_12],[B_15_7,B_15_8,B_15_9,B_15_10,B_15_11,B_15_12],[B_16_7,B_16_8,B_16_9,B_16_10,B_16_11,B_16_12],[B_17_7,B_17_8,B_17_9,B_17_10,B_17_11,B_17_12],[B_18_7,B_18_8,B_18_9,B_18_10,B_18_11,B_18_12]]),Matrix(6, 1, [[C_7_1+C_13_1],[C_8_1+C_14_1],[C_9_1+C_15_1],[C_10_1+C_16_1],[C_11_1+C_17_1],[C_12_1+C_18_1]])))+Trace(Mul(Matrix(2, 6, [[A_2_19,A_2_20,A_2_21,A_2_22,A_2_23,A_2_24],[A_1_1+A_1_7-A_1_19+A_3_19,A_1_2+A_1_8-A_1_20+A_3_20,A_1_3+A_1_9-A_1_21+A_3_21,A_1_4+A_1_10-A_1_22+A_3_22,A_1_5+A_1_11-A_1_23+A_3_23,A_1_6+A_1_12-A_1_24+A_3_24]]),Matrix(6, 6, [[-B_19_1+B_1_19,-B_19_2+B_1_20,-B_19_3+B_1_21,-B_19_4+B_1_22,-B_19_5+B_1_23,-B_19_6+B_1_24],[-B_20_1+B_2_19,-B_20_2+B_2_20,-B_20_3+B_2_21,-B_20_4+B_2_22,-B_20_5+B_2_23,-B_20_6+B_2_24],[-B_21_1+B_3_19,-B_21_2+B_3_20,-B_21_3+B_3_21,-B_21_4+B_3_22,-B_21_5+B_3_23,-B_21_6+B_3_24],[-B_22_1+B_4_19,-B_22_2+B_4_20,-B_22_3+B_4_21,-B_22_4+B_4_22,-B_22_5+B_4_23,-B_22_6+B_4_24],[-B_23_1+B_5_19,-B_23_2+B_5_20,-B_23_3+B_5_21,-B_23_4+B_5_22,-B_23_5+B_5_23,-B_23_6+B_5_24],[-B_24_1+B_6_19,-B_24_2+B_6_20,-B_24_3+B_6_21,-B_24_4+B_6_22,-B_24_5+B_6_23,-B_24_6+B_6_24]]),Matrix(6, 2, [[-C_1_2-C_7_2+C_19_2,C_19_1-C_1_3-C_7_3+C_19_3],[-C_2_2-C_8_2+C_20_2,C_20_1-C_2_3-C_8_3+C_20_3],[-C_3_2-C_9_2+C_21_2,C_21_1-C_3_3-C_9_3+C_21_3],[-C_4_2-C_10_2+C_22_2,C_22_1-C_4_3-C_10_3+C_22_3],[-C_5_2-C_11_2+C_23_2,C_23_1-C_5_3-C_11_3+C_23_3],[-C_6_2-C_12_2+C_24_2,C_24_1-C_6_3-C_12_3+C_24_3]])))+Trace(Mul(Matrix(2, 6, [[-A_2_1-A_2_7+A_2_19,-A_2_2-A_2_8+A_2_20,-A_2_3-A_2_9+A_2_21,-A_2_4-A_2_10+A_2_22,-A_2_5-A_2_11+A_2_23,-A_2_6-A_2_12+A_2_24],[A_1_1-A_3_1-A_3_7+A_1_7-A_1_19+A_3_19,A_1_2-A_3_2-A_3_8+A_1_8-A_1_20+A_3_20,A_1_3-A_3_3-A_3_9+A_1_9-A_1_21+A_3_21,A_1_4-A_3_4+A_1_10-A_3_10-A_1_22+A_3_22,A_1_5-A_3_5+A_1_11-A_3_11-A_1_23+A_3_23,A_1_6-A_3_6+A_1_12-A_3_12-A_1_24+A_3_24]]),Matrix(6, 6, [[B_1_19,B_1_20,B_1_21,B_1_22,B_1_23,B_1_24],[B_2_19,B_2_20,B_2_21,B_2_22,B_2_23,B_2_24],[B_3_19,B_3_20,B_3_21,B_3_22,B_3_23,B_3_24],[B_4_19,B_4_20,B_4_21,B_4_22,B_4_23,B_4_24],[B_5_19,B_5_20,B_5_21,B_5_22,B_5_23,B_5_24],[B_6_19,B_6_20,B_6_21,B_6_22,B_6_23,B_6_24]]),Matrix(6, 2, [[C_1_2+C_7_2-C_19_2,C_1_3+C_7_3-C_19_3],[C_2_2+C_8_2-C_20_2,C_2_3+C_8_3-C_20_3],[C_3_2+C_9_2-C_21_2,C_3_3+C_9_3-C_21_3],[C_4_2+C_10_2-C_22_2,C_4_3+C_10_3-C_22_3],[C_11_2+C_5_2-C_23_2,C_11_3+C_5_3-C_23_3],[C_6_2+C_12_2-C_24_2,C_6_3+C_12_3-C_24_3]])))+Trace(Mul(Matrix(1, 6, [[-A_1_1-A_1_7+A_1_19,-A_1_2-A_1_8+A_1_20,-A_1_3-A_1_9+A_1_21,-A_1_4-A_1_10+A_1_22,-A_1_5-A_1_11+A_1_23,-A_1_6-A_1_12+A_1_24]]),Matrix(6, 6, [[B_19_1,B_19_2,B_19_3,B_19_4,B_19_5,B_19_6],[B_20_1,B_20_2,B_20_3,B_20_4,B_20_5,B_20_6],[B_21_1,B_21_2,B_21_3,B_21_4,B_21_5,B_21_6],[B_22_1,B_22_2,B_22_3,B_22_4,B_22_5,B_22_6],[B_23_1,B_23_2,B_23_3,B_23_4,B_23_5,B_23_6],[B_24_1,B_24_2,B_24_3,B_24_4,B_24_5,B_24_6]]),Matrix(6, 1, [[C_1_1+C_7_1-C_19_1+C_1_3+C_7_3-C_19_3],[C_2_1+C_8_1-C_20_1+C_2_3+C_8_3-C_20_3],[C_3_1+C_9_1-C_21_1+C_3_3+C_9_3-C_21_3],[C_4_1+C_10_1-C_22_1+C_4_3+C_10_3-C_22_3],[C_11_1+C_5_1-C_23_1+C_5_3+C_11_3-C_23_3],[C_6_1+C_12_1-C_24_1+C_6_3+C_12_3-C_24_3]])))+Trace(Mul(Matrix(2, 6, [[A_2_1+A_2_13,A_2_2+A_2_14,A_2_3+A_2_15,A_2_4+A_2_16,A_2_5+A_2_17,A_2_6+A_2_18],[-A_1_1+A_3_1-A_1_13+A_3_13,-A_1_2+A_3_2-A_1_14+A_3_14,-A_1_3+A_3_3-A_1_15+A_3_15,-A_1_4+A_3_4-A_1_16+A_3_16,-A_1_5+A_3_5-A_1_17+A_3_17,-A_1_6+A_3_6-A_1_18+A_3_18]]),Matrix(6, 6, [[B_13_1,B_13_2,B_13_3,B_13_4,B_13_5,B_13_6],[B_14_1,B_14_2,B_14_3,B_14_4,B_14_5,B_14_6],[B_15_1,B_15_2,B_15_3,B_15_4,B_15_5,B_15_6],[B_16_1,B_16_2,B_16_3,B_16_4,B_16_5,B_16_6],[B_17_1,B_17_2,B_17_3,B_17_4,B_17_5,B_17_6],[B_18_1,B_18_2,B_18_3,B_18_4,B_18_5,B_18_6]]),Matrix(6, 2, [[C_1_2+C_13_2,C_1_3+C_13_3],[C_2_2+C_14_2,C_2_3+C_14_3],[C_3_2+C_15_2,C_3_3+C_15_3],[C_4_2+C_16_2,C_4_3+C_16_3],[C_5_2+C_17_2,C_5_3+C_17_3],[C_6_2+C_18_2,C_6_3+C_18_3]])))+Trace(Mul(Matrix(2, 6, [[A_2_13+A_2_19,A_2_14+A_2_20,A_2_15+A_2_21,A_2_16+A_2_22,A_2_17+A_2_23,A_2_18+A_2_24],[-A_1_13+A_3_13-A_1_19+A_3_19,-A_1_14+A_3_14-A_1_20+A_3_20,-A_1_15+A_3_15-A_1_21+A_3_21,-A_1_16+A_3_16-A_1_22+A_3_22,-A_1_17+A_3_17-A_1_23+A_3_23,A_3_18-A_1_18-A_1_24+A_3_24]]),Matrix(6, 6, [[B_13_19,B_13_20,B_13_21,B_13_22,B_13_23,B_13_24],[B_14_19,B_14_20,B_14_21,B_14_22,B_14_23,B_14_24],[B_15_19,B_15_20,B_15_21,B_15_22,B_15_23,B_15_24],[B_16_19,B_16_20,B_16_21,B_16_22,B_16_23,B_16_24],[B_17_19,B_17_20,B_17_21,B_17_22,B_17_23,B_17_24],[B_18_19,B_18_20,B_18_21,B_18_22,B_18_23,B_18_24]]),Matrix(6, 2, [[C_13_2+C_19_2,C_13_3+C_19_3],[C_14_2+C_20_2,C_14_3+C_20_3],[C_15_2+C_21_2,C_15_3+C_21_3],[C_16_2+C_22_2,C_16_3+C_22_3],[C_17_2+C_23_2,C_17_3+C_23_3],[C_18_2+C_24_2,C_18_3+C_24_3]])))

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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