Description of fast matrix multiplication algorithm: ⟨10×19×26:3075⟩

Algorithm type

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Algorithm definition

The algorithm ⟨10×19×26:3075⟩ could be constructed using the following decomposition:

⟨10×19×26:3075⟩ = ⟨6×9×12:435⟩ + ⟨6×10×14:569⟩ + ⟨4×10×12:336⟩ + ⟨4×10×14:392⟩ + ⟨6×9×14:500⟩ + ⟨4×9×14:355⟩ + ⟨6×10×12:488⟩.

This decomposition is defined by the following equality:

Trace⁡Mul⁡A_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_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_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_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_4_7A_4_8A_4_9A_4_10A_4_11A_4_12A_4_13A_4_14A_4_15A_4_16A_4_17A_4_18A_4_19A_5_1A_5_2A_5_3A_5_4A_5_5A_5_6A_5_7A_5_8A_5_9A_5_10A_5_11A_5_12A_5_13A_5_14A_5_15A_5_16A_5_17A_5_18A_5_19A_6_1A_6_2A_6_3A_6_4A_6_5A_6_6A_6_7A_6_8A_6_9A_6_10A_6_11A_6_12A_6_13A_6_14A_6_15A_6_16A_6_17A_6_18A_6_19A_7_1A_7_2A_7_3A_7_4A_7_5A_7_6A_7_7A_7_8A_7_9A_7_10A_7_11A_7_12A_7_13A_7_14A_7_15A_7_16A_7_17A_7_18A_7_19A_8_1A_8_2A_8_3A_8_4A_8_5A_8_6A_8_7A_8_8A_8_9A_8_10A_8_11A_8_12A_8_13A_8_14A_8_15A_8_16A_8_17A_8_18A_8_19A_9_1A_9_2A_9_3A_9_4A_9_5A_9_6A_9_7A_9_8A_9_9A_9_10A_9_11A_9_12A_9_13A_9_14A_9_15A_9_16A_9_17A_9_18A_9_19A_10_1A_10_2A_10_3A_10_4A_10_5A_10_6A_10_7A_10_8A_10_9A_10_10A_10_11A_10_12A_10_13A_10_14A_10_15A_10_16A_10_17A_10_18A_10_19B_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_1_25B_1_26B_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_2_25B_2_26B_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_3_25B_3_26B_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_4_25B_4_26B_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_5_25B_5_26B_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_6_25B_6_26B_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_7_25B_7_26B_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_8_25B_8_26B_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_9_25B_9_26B_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_10_25B_10_26B_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_11_25B_11_26B_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_12_25B_12_26B_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_13_25B_13_26B_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_14_25B_14_26B_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_15_25B_15_26B_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_16_25B_16_26B_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_17_25B_17_26B_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_18_25B_18_26B_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_19_25B_19_26C_1_1C_1_2C_1_3C_1_4C_1_5C_1_6C_1_7C_1_8C_1_9C_1_10C_2_1C_2_2C_2_3C_2_4C_2_5C_2_6C_2_7C_2_8C_2_9C_2_10C_3_1C_3_2C_3_3C_3_4C_3_5C_3_6C_3_7C_3_8C_3_9C_3_10C_4_1C_4_2C_4_3C_4_4C_4_5C_4_6C_4_7C_4_8C_4_9C_4_10C_5_1C_5_2C_5_3C_5_4C_5_5C_5_6C_5_7C_5_8C_5_9C_5_10C_6_1C_6_2C_6_3C_6_4C_6_5C_6_6C_6_7C_6_8C_6_9C_6_10C_7_1C_7_2C_7_3C_7_4C_7_5C_7_6C_7_7C_7_8C_7_9C_7_10C_8_1C_8_2C_8_3C_8_4C_8_5C_8_6C_8_7C_8_8C_8_9C_8_10C_9_1C_9_2C_9_3C_9_4C_9_5C_9_6C_9_7C_9_8C_9_9C_9_10C_10_1C_10_2C_10_3C_10_4C_10_5C_10_6C_10_7C_10_8C_10_9C_10_10C_11_1C_11_2C_11_3C_11_4C_11_5C_11_6C_11_7C_11_8C_11_9C_11_10C_12_1C_12_2C_12_3C_12_4C_12_5C_12_6C_12_7C_12_8C_12_9C_12_10C_13_1C_13_2C_13_3C_13_4C_13_5C_13_6C_13_7C_13_8C_13_9C_13_10C_14_1C_14_2C_14_3C_14_4C_14_5C_14_6C_14_7C_14_8C_14_9C_14_10C_15_1C_15_2C_15_3C_15_4C_15_5C_15_6C_15_7C_15_8C_15_9C_15_10C_16_1C_16_2C_16_3C_16_4C_16_5C_16_6C_16_7C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C_25_5C_25_6C_25_7C_25_8C_25_9C_25_10C_26_5C_26_6C_26_7C_26_8C_26_9C_26_10C_1_5C_1_6C_1_7C_1_8C_1_9C_1_10C_2_5C_2_6C_2_7C_2_8C_2_9C_2_10C_3_5C_3_6C_3_7C_3_8C_3_9C_3_10C_4_5C_4_6C_4_7C_4_8C_4_9C_4_10C_5_5C_5_6C_5_7C_5_8C_5_9C_5_10C_6_5C_6_6C_6_7C_6_8C_6_9C_6_10C_7_5C_7_6C_7_7C_7_8C_7_9C_7_10C_8_5C_8_6C_8_7C_8_8C_8_9C_8_10C_9_5C_9_6C_9_7C_9_8C_9_9C_9_10C_10_5C_10_6C_10_7C_10_8C_10_9C_10_10C_11_5C_11_6C_11_7C_11_8C_11_9C_11_10C_12_5C_12_6C_12_7C_12_8C_12_9C_12_10TraceMulA_3_9A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_3_7A_3_8A_4_9A_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_4_7A_4_8A_1_9A_1_1A_1_2A_1_3A_1_4A_1_5A_1_6A_1_7A_1_8A_2_9A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_2_7A_2_8B_9_25B_9_26B_9_1B_9_2B_9_3B_9_4B_9_5B_9_6B_9_7B_9_8B_9_9B_9_10B_9_11B_9_12B_1_25B_1_26B_1_1B_1_2B_1_3B_1_4B_1_5B_1_6B_1_7B_1_8B_1_9B_1_10B_1_11B_1_12B_2_25B_2_26B_2_1B_2_2B_2_3B_2_4B_2_5B_2_6B_2_7B_2_8B_2_9B_2_10B_2_11B_2_12B_3_25B_3_26B_3_1B_3_2B_3_3B_3_4B_3_5B_3_6B_3_7B_3_8B_3_9B_3_10B_3_11B_3_12B_4_25B_4_26B_4_1B_4_2B_4_3B_4_4B_4_5B_4_6B_4_7B_4_8B_4_9B_4_10B_4_11B_4_12B_5_25B_5_26B_5_1B_5_2B_5_3B_5_4B_5_5B_5_6B_5_7B_5_8B_5_9B_5_10B_5_11B_5_12B_6_25B_6_26B_6_1B_6_2B_6_3B_6_4B_6_5B_6_6B_6_7B_6_8B_6_9B_6_10B_6_11B_6_12B_7_25B_7_26B_7_1B_7_2B_7_3B_7_4B_7_5B_7_6B_7_7B_7_8B_7_9B_7_10B_7_11B_7_12B_8_25B_8_26B_8_1B_8_2B_8_3B_8_4B_8_5B_8_6B_8_7B_8_8B_8_9B_8_10B_8_11B_8_12C_25_3C_25_5C_25_4C_25_6C_25_1C_25_7C_25_2C_25_8C_26_3C_26_5C_26_4C_26_6C_26_1C_26_7C_26_2C_26_8C_1_3C_1_5C_1_4C_1_6C_1_1C_1_7C_1_2C_1_8C_2_3C_2_5C_2_4C_2_6C_2_1C_2_7C_2_2C_2_8C_3_3C_3_5C_3_4C_3_6C_3_1C_3_7C_3_2C_3_8C_4_3C_4_5C_4_4C_4_6C_4_1C_4_7C_4_2C_4_8C_5_3C_5_5C_5_4C_5_6C_5_1C_5_7C_5_2C_5_8C_6_3C_6_5C_6_4C_6_6C_6_1C_6_7C_6_2C_6_8C_7_3C_7_5C_7_4C_7_6C_7_1C_7_7C_7_2C_7_8C_8_3C_8_5C_8_4C_8_6C_8_1C_8_7C_8_2C_8_8C_9_3C_9_5C_9_4C_9_6C_9_1C_9_7C_9_2C_9_8C_10_3C_10_5C_10_4C_10_6C_10_1C_10_7C_10_2C_10_8C_11_3C_11_5C_11_4C_11_6C_11_1C_11_7C_11_2C_11_8C_12_3C_12_5C_12_4C_12_6C_12_1C_12_7C_12_2C_12_8TraceMulA_5_10A_5_11A_5_12A_5_13A_5_14A_5_15A_5_16A_5_17A_5_18A_5_19A_6_10A_6_11A_6_12A_6_13A_6_14A_6_15A_6_16A_6_17A_6_18A_6_19A_7_10A_7_11A_7_12A_7_13A_7_14A_7_15A_7_16A_7_17A_7_18A_7_19A_8_10A_8_11A_8_12A_8_13A_8_14A_8_15A_8_16A_8_17A_8_18A_8_19A_9_10A_9_11A_9_12A_9_13A_9_14A_9_15A_9_16A_9_17A_9_18A_9_19A_10_10A_10_11A_10_12A_10_13A_10_14A_10_15A_10_16A_10_17A_10_18A_10_19B_9_13B_10_13B_9_14B_10_14B_9_15B_10_15B_9_16B_10_16B_9_17B_10_17B_9_18B_10_18B_9_19B_10_19B_9_20B_10_20B_9_21B_10_21B_9_22B_10_22B_9_23B_10_23B_9_24B_10_24B_1_13B_11_13B_1_14B_11_14B_1_15B_11_15B_1_16B_11_16B_1_17B_11_17B_1_18B_11_18B_1_19B_11_19B_1_20B_11_20B_1_21B_11_21B_1_22B_11_22B_1_23B_11_23B_1_24B_11_24B_2_13B_12_13B_2_14B_12_14B_2_15B_12_15B_2_16B_12_16B_2_17B_12_17B_2_18B_12_18B_2_19B_12_19B_2_20B_12_20B_2_21B_12_21B_2_22B_12_22B_2_23B_12_23B_2_24B_12_24B_3_13B_13_13B_3_14B_13_14B_3_15B_13_15B_3_16B_13_16B_3_17B_13_17B_3_18B_13_18B_3_19B_13_19B_3_20B_13_20B_3_21B_13_21B_3_22B_13_22B_3_23B_13_23B_3_24B_13_24B_4_13B_14_13B_4_14B_14_14B_4_15B_14_15B_4_16B_14_16B_4_17B_14_17B_4_18B_14_18B_4_19B_14_19B_4_20B_14_20B_4_21B_14_21B_4_22B_14_22B_4_23B_14_23B_4_24B_14_24B_5_13B_15_13B_5_14B_15_14B_5_15B_15_15B_5_16B_15_16B_5_17B_15_17B_5_18B_15_18B_5_19B_15_19B_5_20B_15_20B_5_21B_15_21B_5_22B_15_22B_5_23B_15_23B_5_24B_15_24B_6_13B_16_13B_6_14B_16_14B_6_15B_16_15B_6_16B_16_16B_6_17B_16_17B_6_18B_16_18B_6_19B_16_19B_6_20B_16_20B_6_21B_16_21B_6_22B_16_22B_6_23B_16_23B_6_24B_16_24B_7_13B_17_13B_7_14B_17_14B_7_15B_17_15B_7_16B_17_16B_7_17B_17_17B_7_18B_17_18B_7_19B_17_19B_7_20B_17_20B_7_21B_17_21B_7_22B_17_22B_7_23B_17_23B_7_24B_17_24B_8_13B_18_13B_8_14B_18_14B_8_15B_18_15B_8_16B_18_16B_8_17B_18_17B_8_18B_18_18B_8_19B_18_19B_8_20B_18_20B_8_21B_18_21B_8_22B_18_22B_8_23B_18_23B_8_24B_18_24B_19_13B_19_14B_19_15B_19_16B_19_17B_19_18B_19_19B_19_20B_19_21B_19_22B_19_23B_19_24C_13_5C_25_5C_13_6C_25_6C_13_7C_25_7C_13_8C_25_8C_13_9C_25_9C_13_10C_25_10C_14_5C_26_5C_14_6C_26_6C_14_7C_26_7C_14_8C_26_8C_14_9C_26_9C_14_10C_26_10C_1_5C_15_5C_1_6C_15_6C_1_7C_15_7C_1_8C_15_8C_1_9C_15_9C_1_10C_15_10C_2_5C_16_5C_2_6C_16_6C_2_7C_16_7C_2_8C_16_8C_2_9C_16_9C_2_10C_16_10C_3_5C_17_5C_3_6C_17_6C_3_7C_17_7C_3_8C_17_8C_3_9C_17_9C_3_10C_17_10C_4_5C_18_5C_4_6C_18_6C_4_7C_18_7C_4_8C_18_8C_4_9C_18_9C_4_10C_18_10C_5_5C_19_5C_5_6C_19_6C_5_7C_19_7C_5_8C_19_8C_5_9C_19_9C_5_10C_19_10C_6_5C_20_5C_6_6C_20_6C_6_7C_20_7C_6_8C_20_8C_6_9C_20_9C_6_10C_20_10C_7_5C_21_5C_7_6C_21_6C_7_7C_21_7C_7_8C_21_8C_7_9C_21_9C_7_10C_21_10C_8_5C_22_5C_8_6C_22_6C_8_7C_22_7C_8_8C_22_8C_8_9C_22_9C_8_10C_22_10C_9_5C_23_5C_9_6C_23_6C_9_7C_23_7C_9_8C_23_8C_9_9C_23_9C_9_10C_23_10C_10_5C_24_5C_10_6C_24_6C_10_7C_24_7C_10_8C_24_8C_10_9C_24_9C_10_10C_24_10Trace(Mul(Matrix(10, 19, [[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]]),Matrix(19, 26, [[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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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]]),Matrix(26, 10, [[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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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]]))) = Trace(Mul(Matrix(6, 9, [[A_5_9-A_5_10,A_5_1-A_5_11,A_5_2-A_5_12,A_5_3-A_5_13,A_5_4-A_5_14,A_5_5-A_5_15,A_5_6-A_5_16,A_5_7-A_5_17,A_5_8-A_5_18],[A_6_9-A_6_10,A_6_1-A_6_11,A_6_2-A_6_12,A_6_3-A_6_13,A_6_4-A_6_14,A_6_5-A_6_15,A_6_6-A_6_16,A_6_7-A_6_17,A_6_8-A_6_18],[A_7_9-A_7_10,A_7_1-A_7_11,A_7_2-A_7_12,A_7_3-A_7_13,A_7_4-A_7_14,A_7_5-A_7_15,A_7_6-A_7_16,A_7_7-A_7_17,A_7_8-A_7_18],[A_8_9-A_8_10,A_8_1-A_8_11,A_8_2-A_8_12,A_8_3-A_8_13,A_8_4-A_8_14,A_8_5-A_8_15,A_8_6-A_8_16,A_8_7-A_8_17,A_8_8-A_8_18],[A_9_9-A_9_10,A_9_1-A_9_11,A_9_2-A_9_12,A_9_3-A_9_13,A_9_4-A_9_14,A_9_5-A_9_15,A_9_6-A_9_16,A_9_7-A_9_17,A_9_8-A_9_18],[A_10_9-A_10_10,A_10_1-A_10_11,A_10_2-A_10_12,A_10_3-A_10_13,A_10_4-A_10_14,A_10_5-A_10_15,A_10_6-A_10_16,A_10_7-A_10_17,A_10_8-A_10_18]]),Matrix(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_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_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_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_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_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_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_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_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]]),Matrix(12, 6, [[C_13_5-C_13_3,-C_13_4+C_13_6,-C_13_1+C_13_7,-C_13_2+C_13_8,C_13_9,C_13_10],[C_14_5-C_14_3,-C_14_4+C_14_6,-C_14_1+C_14_7,-C_14_2+C_14_8,C_14_9,C_14_10],[C_15_5-C_15_3,-C_15_4+C_15_6,-C_15_1+C_15_7,-C_15_2+C_15_8,C_15_9,C_15_10],[C_16_5-C_16_3,-C_16_4+C_16_6,-C_16_1+C_16_7,-C_16_2+C_16_8,C_16_9,C_16_10],[C_17_5-C_17_3,-C_17_4+C_17_6,-C_17_1+C_17_7,-C_17_2+C_17_8,C_17_9,C_17_10],[-C_18_3+C_18_5,-C_18_4+C_18_6,-C_18_1+C_18_7,-C_18_2+C_18_8,C_18_9,C_18_10],[-C_19_3+C_19_5,-C_19_4+C_19_6,-C_19_1+C_19_7,-C_19_2+C_19_8,C_19_9,C_19_10],[-C_20_3+C_20_5,-C_20_4+C_20_6,-C_20_1+C_20_7,-C_20_2+C_20_8,C_20_9,C_20_10],[-C_21_3+C_21_5,-C_21_4+C_21_6,-C_21_1+C_21_7,-C_21_2+C_21_8,C_21_9,C_21_10],[-C_22_3+C_22_5,-C_22_4+C_22_6,-C_22_1+C_22_7,-C_22_2+C_22_8,C_22_9,C_22_10],[-C_23_3+C_23_5,-C_23_4+C_23_6,-C_23_1+C_23_7,-C_23_2+C_23_8,C_23_9,C_23_10],[C_24_5-C_24_3,-C_24_4+C_24_6,-C_24_1+C_24_7,-C_24_2+C_24_8,C_24_9,C_24_10]])))+Trace(Mul(Matrix(6, 10, [[A_3_9+A_5_9-A_5_10,A_3_1+A_5_1-A_5_11,A_3_2+A_5_2-A_5_12,A_3_3+A_5_3-A_5_13,A_3_4+A_5_4-A_5_14,A_3_5+A_5_5-A_5_15,A_3_6+A_5_6-A_5_16,A_3_7+A_5_7-A_5_17,A_3_8+A_5_8-A_5_18,-A_5_19],[A_4_9+A_6_9-A_6_10,A_4_1+A_6_1-A_6_11,A_4_2+A_6_2-A_6_12,A_4_3+A_6_3-A_6_13,A_4_4+A_6_4-A_6_14,A_4_5+A_6_5-A_6_15,A_4_6+A_6_6-A_6_16,A_4_7+A_6_7-A_6_17,A_4_8+A_6_8-A_6_18,-A_6_19],[A_1_9+A_7_9-A_7_10,A_1_1+A_7_1-A_7_11,A_1_2+A_7_2-A_7_12,A_1_3+A_7_3-A_7_13,A_1_4+A_7_4-A_7_14,A_1_5+A_7_5-A_7_15,A_1_6+A_7_6-A_7_16,A_1_7+A_7_7-A_7_17,A_1_8+A_7_8-A_7_18,-A_7_19],[A_2_9+A_8_9-A_8_10,A_2_1+A_8_1-A_8_11,A_2_2+A_8_2-A_8_12,A_2_3+A_8_3-A_8_13,A_2_4+A_8_4-A_8_14,A_2_5+A_8_5-A_8_15,A_2_6+A_8_6-A_8_16,A_2_7+A_8_7-A_8_17,A_2_8+A_8_8-A_8_18,-A_8_19],[A_9_9-A_9_10,A_9_1-A_9_11,A_9_2-A_9_12,A_9_3-A_9_13,A_9_4-A_9_14,A_9_5-A_9_15,A_9_6-A_9_16,A_9_7-A_9_17,A_9_8-A_9_18,-A_9_19],[A_10_9-A_10_10,A_10_1-A_10_11,A_10_2-A_10_12,A_10_3-A_10_13,A_10_4-A_10_14,A_10_5-A_10_15,A_10_6-A_10_16,A_10_7-A_10_17,A_10_8-A_10_18,-A_10_19]]),Matrix(10, 14, [[B_10_25+B_9_13+B_10_13,B_10_26+B_9_14+B_10_14,B_10_1+B_9_15+B_10_15,B_10_2+B_9_16+B_10_16,B_10_3+B_9_17+B_10_17,B_10_4+B_9_18+B_10_18,B_10_5+B_9_19+B_10_19,B_10_6+B_9_20+B_10_20,B_10_7+B_9_21+B_10_21,B_10_8+B_9_22+B_10_22,B_10_9+B_9_23+B_10_23,B_10_10+B_9_24+B_10_24,B_10_11,B_10_12],[B_1_13+B_11_25+B_11_13,B_1_14+B_11_26+B_11_14,B_11_1+B_1_15+B_11_15,B_11_2+B_1_16+B_11_16,B_11_3+B_1_17+B_11_17,B_11_4+B_1_18+B_11_18,B_11_5+B_1_19+B_11_19,B_11_6+B_1_20+B_11_20,B_11_7+B_1_21+B_11_21,B_11_8+B_1_22+B_11_22,B_11_9+B_1_23+B_11_23,B_11_10+B_1_24+B_11_24,B_11_11,B_11_12],[B_2_13+B_12_25+B_12_13,B_2_14+B_12_26+B_12_14,B_12_1+B_2_15+B_12_15,B_12_2+B_2_16+B_12_16,B_12_3+B_2_17+B_12_17,B_12_4+B_2_18+B_12_18,B_12_5+B_2_19+B_12_19,B_12_6+B_2_20+B_12_20,B_12_7+B_2_21+B_12_21,B_12_8+B_2_22+B_12_22,B_12_9+B_2_23+B_12_23,B_12_10+B_2_24+B_12_24,B_12_11,B_12_12],[B_3_13+B_13_25+B_13_13,B_3_14+B_13_26+B_13_14,B_13_1+B_3_15+B_13_15,B_13_2+B_3_16+B_13_16,B_13_3+B_3_17+B_13_17,B_13_4+B_3_18+B_13_18,B_13_5+B_3_19+B_13_19,B_13_6+B_3_20+B_13_20,B_13_7+B_3_21+B_13_21,B_13_8+B_3_22+B_13_22,B_13_9+B_3_23+B_13_23,B_13_10+B_3_24+B_13_24,B_13_11,B_13_12],[B_4_13+B_14_25+B_14_13,B_4_14+B_14_26+B_14_14,B_14_1+B_4_15+B_14_15,B_14_2+B_4_16+B_14_16,B_14_3+B_4_17+B_14_17,B_14_4+B_4_18+B_14_18,B_14_5+B_4_19+B_14_19,B_14_6+B_4_20+B_14_20,B_14_7+B_4_21+B_14_21,B_14_8+B_4_22+B_14_22,B_14_9+B_4_23+B_14_23,B_14_10+B_4_24+B_14_24,B_14_11,B_14_12],[B_5_13+B_15_25+B_15_13,B_5_14+B_15_26+B_15_14,B_15_1+B_5_15+B_15_15,B_15_2+B_5_16+B_15_16,B_15_3+B_5_17+B_15_17,B_15_4+B_5_18+B_15_18,B_15_5+B_5_19+B_15_19,B_15_6+B_5_20+B_15_20,B_15_7+B_5_21+B_15_21,B_15_8+B_5_22+B_15_22,B_15_9+B_5_23+B_15_23,B_15_10+B_5_24+B_15_24,B_15_11,B_15_12],[B_6_13+B_16_25+B_16_13,B_6_14+B_16_26+B_16_14,B_16_1+B_6_15+B_16_15,B_16_2+B_6_16+B_16_16,B_16_3+B_6_17+B_16_17,B_16_4+B_6_18+B_16_18,B_16_5+B_6_19+B_16_19,B_16_6+B_6_20+B_16_20,B_16_7+B_6_21+B_16_21,B_16_8+B_6_22+B_16_22,B_16_9+B_6_23+B_16_23,B_16_10+B_6_24+B_16_24,B_16_11,B_16_12],[B_7_13+B_17_25+B_17_13,B_7_14+B_17_26+B_17_14,B_17_1+B_7_15+B_17_15,B_17_2+B_7_16+B_17_16,B_17_3+B_7_17+B_17_17,B_17_4+B_7_18+B_17_18,B_17_5+B_7_19+B_17_19,B_17_6+B_7_20+B_17_20,B_17_7+B_7_21+B_17_21,B_17_8+B_7_22+B_17_22,B_17_9+B_7_23+B_17_23,B_17_10+B_7_24+B_17_24,B_17_11,B_17_12],[B_8_13+B_18_25+B_18_13,B_8_14+B_18_26+B_18_14,B_18_1+B_8_15+B_18_15,B_18_2+B_8_16+B_18_16,B_18_3+B_8_17+B_18_17,B_18_4+B_8_18+B_18_18,B_18_5+B_8_19+B_18_19,B_18_6+B_8_20+B_18_20,B_18_7+B_8_21+B_18_21,B_18_8+B_8_22+B_18_22,B_18_9+B_8_23+B_18_23,B_18_10+B_8_24+B_18_24,B_18_11,B_18_12],[B_19_13+B_19_25,B_19_14+B_19_26,B_19_1+B_19_15,B_19_2+B_19_16,B_19_3+B_19_17,B_19_4+B_19_18,B_19_5+B_19_19,B_19_6+B_19_20,B_19_7+B_19_21,B_19_8+B_19_22,B_19_9+B_19_23,B_19_10+B_19_24,B_19_11,B_19_12]]),Matrix(14, 6, [[C_13_3-C_25_5,C_13_4-C_25_6,C_13_1-C_25_7,C_13_2-C_25_8,-C_25_9,-C_25_10],[C_14_3-C_26_5,C_14_4-C_26_6,C_14_1-C_26_7,C_14_2-C_26_8,-C_26_9,-C_26_10],[C_15_3-C_1_5,C_15_4-C_1_6,C_15_1-C_1_7,C_15_2-C_1_8,-C_1_9,-C_1_10],[C_16_3-C_2_5,C_16_4-C_2_6,C_16_1-C_2_7,C_16_2-C_2_8,-C_2_9,-C_2_10],[C_17_3-C_3_5,C_17_4-C_3_6,C_17_1-C_3_7,C_17_2-C_3_8,-C_3_9,-C_3_10],[C_18_3-C_4_5,C_18_4-C_4_6,C_18_1-C_4_7,C_18_2-C_4_8,-C_4_9,-C_4_10],[C_19_3-C_5_5,C_19_4-C_5_6,C_19_1-C_5_7,C_19_2-C_5_8,-C_5_9,-C_5_10],[C_20_3-C_6_5,C_20_4-C_6_6,C_20_1-C_6_7,C_20_2-C_6_8,-C_6_9,-C_6_10],[C_21_3-C_7_5,C_21_4-C_7_6,C_21_1-C_7_7,C_21_2-C_7_8,-C_7_9,-C_7_10],[C_22_3-C_8_5,C_22_4-C_8_6,C_22_1-C_8_7,C_22_2-C_8_8,-C_8_9,-C_8_10],[C_23_3-C_9_5,C_23_4-C_9_6,C_23_1-C_9_7,C_23_2-C_9_8,-C_9_9,-C_9_10],[C_24_3-C_10_5,C_24_4-C_10_6,C_24_1-C_10_7,C_24_2-C_10_8,-C_10_9,-C_10_10],[-C_11_5,-C_11_6,-C_11_7,-C_11_8,-C_11_9,-C_11_10],[-C_12_5,-C_12_6,-C_12_7,-C_12_8,-C_12_9,-C_12_10]])))+Trace(Mul(Matrix(4, 10, [[A_3_9+A_5_9-A_3_10-A_5_10,A_3_1+A_5_1-A_3_11-A_5_11,A_3_2+A_5_2-A_3_12-A_5_12,A_3_3+A_5_3-A_3_13-A_5_13,A_3_4+A_5_4-A_3_14-A_5_14,A_3_5+A_5_5-A_3_15-A_5_15,A_3_6+A_5_6-A_3_16-A_5_16,A_3_7+A_5_7-A_3_17-A_5_17,A_3_8+A_5_8-A_3_18-A_5_18,-A_3_19-A_5_19],[A_4_9+A_6_9-A_4_10-A_6_10,A_4_1+A_6_1-A_4_11-A_6_11,A_4_2+A_6_2-A_4_12-A_6_12,A_4_3+A_6_3-A_4_13-A_6_13,A_4_4+A_6_4-A_4_14-A_6_14,A_4_5+A_6_5-A_4_15-A_6_15,A_4_6+A_6_6-A_4_16-A_6_16,A_4_7+A_6_7-A_4_17-A_6_17,A_4_8+A_6_8-A_4_18-A_6_18,-A_4_19-A_6_19],[A_1_9+A_7_9-A_1_10-A_7_10,A_1_1+A_7_1-A_1_11-A_7_11,A_1_2+A_7_2-A_1_12-A_7_12,A_1_3+A_7_3-A_1_13-A_7_13,A_1_4+A_7_4-A_1_14-A_7_14,A_1_5+A_7_5-A_1_15-A_7_15,A_1_6+A_7_6-A_1_16-A_7_16,A_1_7+A_7_7-A_1_17-A_7_17,A_1_8+A_7_8-A_1_18-A_7_18,-A_1_19-A_7_19],[A_2_9+A_8_9-A_2_10-A_8_10,A_2_1+A_8_1-A_2_11-A_8_11,A_2_2+A_8_2-A_2_12-A_8_12,A_2_3+A_8_3-A_2_13-A_8_13,A_2_4+A_8_4-A_2_14-A_8_14,A_2_5+A_8_5-A_2_15-A_8_15,A_2_6+A_8_6-A_2_16-A_8_16,A_2_7+A_8_7-A_2_17-A_8_17,A_2_8+A_8_8-A_2_18-A_8_18,-A_2_19-A_8_19]]),Matrix(10, 12, [[B_10_13+B_10_25,B_10_14+B_10_26,B_10_1+B_10_15,B_10_2+B_10_16,B_10_3+B_10_17,B_10_4+B_10_18,B_10_5+B_10_19,B_10_6+B_10_20,B_10_7+B_10_21,B_10_8+B_10_22,B_10_9+B_10_23,B_10_10+B_10_24],[B_11_13+B_11_25,B_11_14+B_11_26,B_11_1+B_11_15,B_11_2+B_11_16,B_11_3+B_11_17,B_11_4+B_11_18,B_11_5+B_11_19,B_11_6+B_11_20,B_11_7+B_11_21,B_11_8+B_11_22,B_11_9+B_11_23,B_11_10+B_11_24],[B_12_13+B_12_25,B_12_14+B_12_26,B_12_1+B_12_15,B_12_2+B_12_16,B_12_3+B_12_17,B_12_4+B_12_18,B_12_5+B_12_19,B_12_6+B_12_20,B_12_7+B_12_21,B_12_8+B_12_22,B_12_9+B_12_23,B_12_10+B_12_24],[B_13_13+B_13_25,B_13_14+B_13_26,B_13_1+B_13_15,B_13_2+B_13_16,B_13_3+B_13_17,B_13_4+B_13_18,B_13_5+B_13_19,B_13_6+B_13_20,B_13_7+B_13_21,B_13_8+B_13_22,B_13_9+B_13_23,B_13_10+B_13_24],[B_14_13+B_14_25,B_14_14+B_14_26,B_14_1+B_14_15,B_14_2+B_14_16,B_14_3+B_14_17,B_14_4+B_14_18,B_14_5+B_14_19,B_14_6+B_14_20,B_14_7+B_14_21,B_14_8+B_14_22,B_14_9+B_14_23,B_14_10+B_14_24],[B_15_13+B_15_25,B_15_14+B_15_26,B_15_1+B_15_15,B_15_2+B_15_16,B_15_3+B_15_17,B_15_4+B_15_18,B_15_5+B_15_19,B_15_6+B_15_20,B_15_7+B_15_21,B_15_8+B_15_22,B_15_9+B_15_23,B_15_10+B_15_24],[B_16_13+B_16_25,B_16_14+B_16_26,B_16_1+B_16_15,B_16_2+B_16_16,B_16_3+B_16_17,B_16_4+B_16_18,B_16_5+B_16_19,B_16_6+B_16_20,B_16_7+B_16_21,B_16_8+B_16_22,B_16_9+B_16_23,B_16_10+B_16_24],[B_17_13+B_17_25,B_17_14+B_17_26,B_17_1+B_17_15,B_17_2+B_17_16,B_17_3+B_17_17,B_17_4+B_17_18,B_17_5+B_17_19,B_17_6+B_17_20,B_17_7+B_17_21,B_17_8+B_17_22,B_17_9+B_17_23,B_17_10+B_17_24],[B_18_13+B_18_25,B_18_14+B_18_26,B_18_1+B_18_15,B_18_2+B_18_16,B_18_3+B_18_17,B_18_4+B_18_18,B_18_5+B_18_19,B_18_6+B_18_20,B_18_7+B_18_21,B_18_8+B_18_22,B_18_9+B_18_23,B_18_10+B_18_24],[B_19_13+B_19_25,B_19_14+B_19_26,B_19_1+B_19_15,B_19_2+B_19_16,B_19_3+B_19_17,B_19_4+B_19_18,B_19_5+B_19_19,B_19_6+B_19_20,B_19_7+B_19_21,B_19_8+B_19_22,B_19_9+B_19_23,B_19_10+B_19_24]]),Matrix(12, 4, [[-C_13_3,-C_13_4,-C_13_1,-C_13_2],[-C_14_3,-C_14_4,-C_14_1,-C_14_2],[-C_15_3,-C_15_4,-C_15_1,-C_15_2],[-C_16_3,-C_16_4,-C_16_1,-C_16_2],[-C_17_3,-C_17_4,-C_17_1,-C_17_2],[-C_18_3,-C_18_4,-C_18_1,-C_18_2],[-C_19_3,-C_19_4,-C_19_1,-C_19_2],[-C_20_3,-C_20_4,-C_20_1,-C_20_2],[-C_21_3,-C_21_4,-C_21_1,-C_21_2],[-C_22_3,-C_22_4,-C_22_1,-C_22_2],[-C_23_3,-C_23_4,-C_23_1,-C_23_2],[-C_24_3,-C_24_4,-C_24_1,-C_24_2]])))+Trace(Mul(Matrix(4, 10, [[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_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_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_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]]),Matrix(10, 14, [[B_10_25,B_10_26,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_11_25,B_11_26,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_25,B_12_26,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_25,B_13_26,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_25,B_14_26,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_25,B_15_26,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_25,B_16_26,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_25,B_17_26,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_25,B_18_26,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_25,B_19_26,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]]),Matrix(14, 4, [[-C_13_3+C_25_3,-C_13_4+C_25_4,-C_13_1+C_25_1,-C_13_2+C_25_2],[-C_14_3+C_26_3,-C_14_4+C_26_4,-C_14_1+C_26_1,-C_14_2+C_26_2],[C_1_3-C_15_3,C_1_4-C_15_4,C_1_1-C_15_1,C_1_2-C_15_2],[C_2_3-C_16_3,C_2_4-C_16_4,C_2_1-C_16_1,C_2_2-C_16_2],[C_3_3-C_17_3,C_3_4-C_17_4,C_3_1-C_17_1,C_3_2-C_17_2],[C_4_3-C_18_3,C_4_4-C_18_4,C_4_1-C_18_1,C_4_2-C_18_2],[C_5_3-C_19_3,C_5_4-C_19_4,C_5_1-C_19_1,C_5_2-C_19_2],[C_6_3-C_20_3,C_6_4-C_20_4,C_6_1-C_20_1,C_6_2-C_20_2],[C_7_3-C_21_3,C_7_4-C_21_4,C_7_1-C_21_1,C_7_2-C_21_2],[C_8_3-C_22_3,C_8_4-C_22_4,C_8_1-C_22_1,C_8_2-C_22_2],[C_9_3-C_23_3,C_9_4-C_23_4,C_9_1-C_23_1,C_9_2-C_23_2],[C_10_3-C_24_3,C_10_4-C_24_4,C_10_1-C_24_1,C_10_2-C_24_2],[C_11_3,C_11_4,C_11_1,C_11_2],[C_12_3,C_12_4,C_12_1,C_12_2]])))+Trace(Mul(Matrix(6, 9, [[A_3_9+A_5_9,A_3_1+A_5_1,A_3_2+A_5_2,A_3_3+A_5_3,A_3_4+A_5_4,A_3_5+A_5_5,A_3_6+A_5_6,A_3_7+A_5_7,A_3_8+A_5_8],[A_4_9+A_6_9,A_4_1+A_6_1,A_4_2+A_6_2,A_4_3+A_6_3,A_4_4+A_6_4,A_4_5+A_6_5,A_4_6+A_6_6,A_4_7+A_6_7,A_4_8+A_6_8],[A_1_9+A_7_9,A_1_1+A_7_1,A_1_2+A_7_2,A_1_3+A_7_3,A_1_4+A_7_4,A_1_5+A_7_5,A_1_6+A_7_6,A_1_7+A_7_7,A_1_8+A_7_8],[A_2_9+A_8_9,A_2_1+A_8_1,A_2_2+A_8_2,A_2_3+A_8_3,A_2_4+A_8_4,A_2_5+A_8_5,A_2_6+A_8_6,A_2_7+A_8_7,A_2_8+A_8_8],[A_9_9,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_10_9,A_10_1,A_10_2,A_10_3,A_10_4,A_10_5,A_10_6,A_10_7,A_10_8]]),Matrix(9, 14, [[B_9_25+B_10_25+B_9_13+B_10_13,B_9_26+B_10_26+B_9_14+B_10_14,B_9_1+B_10_1+B_9_15+B_10_15,B_9_2+B_10_2+B_9_16+B_10_16,B_9_3+B_10_3+B_9_17+B_10_17,B_9_4+B_10_4+B_9_18+B_10_18,B_9_5+B_10_5+B_9_19+B_10_19,B_9_6+B_10_6+B_9_20+B_10_20,B_9_7+B_10_7+B_9_21+B_10_21,B_9_8+B_10_8+B_9_22+B_10_22,B_9_9+B_10_9+B_9_23+B_10_23,B_9_10+B_10_10+B_9_24+B_10_24,B_9_11+B_10_11,B_9_12+B_10_12],[B_1_25+B_11_25+B_1_13+B_11_13,B_1_26+B_11_26+B_1_14+B_11_14,B_1_1+B_11_1+B_1_15+B_11_15,B_1_2+B_11_2+B_1_16+B_11_16,B_1_3+B_11_3+B_1_17+B_11_17,B_1_4+B_11_4+B_1_18+B_11_18,B_1_5+B_11_5+B_1_19+B_11_19,B_1_6+B_11_6+B_1_20+B_11_20,B_1_7+B_11_7+B_1_21+B_11_21,B_1_8+B_11_8+B_1_22+B_11_22,B_1_9+B_11_9+B_1_23+B_11_23,B_1_10+B_11_10+B_1_24+B_11_24,B_1_11+B_11_11,B_1_12+B_11_12],[B_2_25+B_12_25+B_2_13+B_12_13,B_2_26+B_12_26+B_2_14+B_12_14,B_2_1+B_12_1+B_2_15+B_12_15,B_2_2+B_12_2+B_2_16+B_12_16,B_2_3+B_12_3+B_2_17+B_12_17,B_2_4+B_12_4+B_2_18+B_12_18,B_2_5+B_12_5+B_2_19+B_12_19,B_2_6+B_12_6+B_2_20+B_12_20,B_2_7+B_12_7+B_2_21+B_12_21,B_2_8+B_12_8+B_2_22+B_12_22,B_2_9+B_12_9+B_2_23+B_12_23,B_2_10+B_12_10+B_2_24+B_12_24,B_2_11+B_12_11,B_2_12+B_12_12],[B_3_25+B_13_25+B_3_13+B_13_13,B_3_26+B_13_26+B_3_14+B_13_14,B_3_1+B_13_1+B_3_15+B_13_15,B_3_2+B_13_2+B_3_16+B_13_16,B_3_3+B_13_3+B_3_17+B_13_17,B_3_4+B_13_4+B_3_18+B_13_18,B_3_5+B_13_5+B_3_19+B_13_19,B_3_6+B_13_6+B_3_20+B_13_20,B_3_7+B_13_7+B_3_21+B_13_21,B_3_8+B_13_8+B_3_22+B_13_22,B_3_9+B_13_9+B_3_23+B_13_23,B_3_10+B_13_10+B_3_24+B_13_24,B_3_11+B_13_11,B_3_12+B_13_12],[B_4_25+B_14_25+B_4_13+B_14_13,B_4_26+B_14_26+B_4_14+B_14_14,B_4_1+B_14_1+B_4_15+B_14_15,B_4_2+B_14_2+B_4_16+B_14_16,B_4_3+B_14_3+B_4_17+B_14_17,B_4_4+B_14_4+B_4_18+B_14_18,B_4_5+B_14_5+B_4_19+B_14_19,B_4_6+B_14_6+B_4_20+B_14_20,B_4_7+B_14_7+B_4_21+B_14_21,B_4_8+B_14_8+B_4_22+B_14_22,B_4_9+B_14_9+B_4_23+B_14_23,B_4_10+B_14_10+B_4_24+B_14_24,B_4_11+B_14_11,B_4_12+B_14_12],[B_5_25+B_15_25+B_5_13+B_15_13,B_5_26+B_15_26+B_5_14+B_15_14,B_5_1+B_15_1+B_5_15+B_15_15,B_5_2+B_15_2+B_5_16+B_15_16,B_5_3+B_15_3+B_5_17+B_15_17,B_5_4+B_15_4+B_5_18+B_15_18,B_5_5+B_15_5+B_5_19+B_15_19,B_5_6+B_15_6+B_5_20+B_15_20,B_5_7+B_15_7+B_5_21+B_15_21,B_5_8+B_15_8+B_5_22+B_15_22,B_5_9+B_15_9+B_5_23+B_15_23,B_5_10+B_15_10+B_5_24+B_15_24,B_5_11+B_15_11,B_5_12+B_15_12],[B_6_25+B_16_25+B_6_13+B_16_13,B_6_26+B_16_26+B_6_14+B_16_14,B_6_1+B_16_1+B_6_15+B_16_15,B_6_2+B_16_2+B_6_16+B_16_16,B_6_3+B_16_3+B_6_17+B_16_17,B_6_4+B_16_4+B_6_18+B_16_18,B_6_5+B_16_5+B_6_19+B_16_19,B_6_6+B_16_6+B_6_20+B_16_20,B_6_7+B_16_7+B_6_21+B_16_21,B_6_8+B_16_8+B_6_22+B_16_22,B_6_9+B_16_9+B_6_23+B_16_23,B_6_10+B_16_10+B_6_24+B_16_24,B_6_11+B_16_11,B_6_12+B_16_12],[B_7_25+B_17_25+B_7_13+B_17_13,B_7_26+B_17_26+B_7_14+B_17_14,B_7_1+B_17_1+B_7_15+B_17_15,B_7_2+B_17_2+B_7_16+B_17_16,B_7_3+B_17_3+B_7_17+B_17_17,B_7_4+B_17_4+B_7_18+B_17_18,B_7_5+B_17_5+B_7_19+B_17_19,B_7_6+B_17_6+B_7_20+B_17_20,B_7_7+B_17_7+B_7_21+B_17_21,B_7_8+B_17_8+B_7_22+B_17_22,B_7_9+B_17_9+B_7_23+B_17_23,B_7_10+B_17_10+B_7_24+B_17_24,B_7_11+B_17_11,B_7_12+B_17_12],[B_8_25+B_18_25+B_8_13+B_18_13,B_8_26+B_18_26+B_8_14+B_18_14,B_8_1+B_18_1+B_8_15+B_18_15,B_8_2+B_18_2+B_8_16+B_18_16,B_8_3+B_18_3+B_8_17+B_18_17,B_8_4+B_18_4+B_8_18+B_18_18,B_8_5+B_18_5+B_8_19+B_18_19,B_8_6+B_18_6+B_8_20+B_18_20,B_8_7+B_18_7+B_8_21+B_18_21,B_8_8+B_18_8+B_8_22+B_18_22,B_8_9+B_18_9+B_8_23+B_18_23,B_8_10+B_18_10+B_8_24+B_18_24,B_8_11+B_18_11,B_8_12+B_18_12]]),Matrix(14, 6, [[C_25_5,C_25_6,C_25_7,C_25_8,C_25_9,C_25_10],[C_26_5,C_26_6,C_26_7,C_26_8,C_26_9,C_26_10],[C_1_5,C_1_6,C_1_7,C_1_8,C_1_9,C_1_10],[C_2_5,C_2_6,C_2_7,C_2_8,C_2_9,C_2_10],[C_3_5,C_3_6,C_3_7,C_3_8,C_3_9,C_3_10],[C_4_5,C_4_6,C_4_7,C_4_8,C_4_9,C_4_10],[C_5_5,C_5_6,C_5_7,C_5_8,C_5_9,C_5_10],[C_6_5,C_6_6,C_6_7,C_6_8,C_6_9,C_6_10],[C_7_5,C_7_6,C_7_7,C_7_8,C_7_9,C_7_10],[C_8_5,C_8_6,C_8_7,C_8_8,C_8_9,C_8_10],[C_9_5,C_9_6,C_9_7,C_9_8,C_9_9,C_9_10],[C_10_5,C_10_6,C_10_7,C_10_8,C_10_9,C_10_10],[C_11_5,C_11_6,C_11_7,C_11_8,C_11_9,C_11_10],[C_12_5,C_12_6,C_12_7,C_12_8,C_12_9,C_12_10]])))+Trace(Mul(Matrix(4, 9, [[A_3_9,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_4_9,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_1_9,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_2_9,A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6,A_2_7,A_2_8]]),Matrix(9, 14, [[B_9_25,B_9_26,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_1_25,B_1_26,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_25,B_2_26,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_25,B_3_26,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_25,B_4_26,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_5_25,B_5_26,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_6_25,B_6_26,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_25,B_7_26,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_25,B_8_26,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]]),Matrix(14, 4, [[C_25_3-C_25_5,C_25_4-C_25_6,C_25_1-C_25_7,C_25_2-C_25_8],[C_26_3-C_26_5,C_26_4-C_26_6,C_26_1-C_26_7,C_26_2-C_26_8],[C_1_3-C_1_5,C_1_4-C_1_6,C_1_1-C_1_7,C_1_2-C_1_8],[C_2_3-C_2_5,C_2_4-C_2_6,C_2_1-C_2_7,C_2_2-C_2_8],[C_3_3-C_3_5,C_3_4-C_3_6,C_3_1-C_3_7,C_3_2-C_3_8],[C_4_3-C_4_5,C_4_4-C_4_6,C_4_1-C_4_7,C_4_2-C_4_8],[C_5_3-C_5_5,C_5_4-C_5_6,C_5_1-C_5_7,C_5_2-C_5_8],[C_6_3-C_6_5,C_6_4-C_6_6,C_6_1-C_6_7,C_6_2-C_6_8],[C_7_3-C_7_5,C_7_4-C_7_6,C_7_1-C_7_7,C_7_2-C_7_8],[C_8_3-C_8_5,C_8_4-C_8_6,C_8_1-C_8_7,C_8_2-C_8_8],[C_9_3-C_9_5,C_9_4-C_9_6,C_9_1-C_9_7,C_9_2-C_9_8],[C_10_3-C_10_5,C_10_4-C_10_6,C_10_1-C_10_7,C_10_2-C_10_8],[C_11_3-C_11_5,C_11_4-C_11_6,C_11_1-C_11_7,C_11_2-C_11_8],[C_12_3-C_12_5,C_12_4-C_12_6,C_12_1-C_12_7,C_12_2-C_12_8]])))+Trace(Mul(Matrix(6, 10, [[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_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_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_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_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_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]]),Matrix(10, 12, [[B_9_13+B_10_13,B_9_14+B_10_14,B_9_15+B_10_15,B_9_16+B_10_16,B_9_17+B_10_17,B_9_18+B_10_18,B_9_19+B_10_19,B_9_20+B_10_20,B_9_21+B_10_21,B_9_22+B_10_22,B_9_23+B_10_23,B_9_24+B_10_24],[B_1_13+B_11_13,B_1_14+B_11_14,B_1_15+B_11_15,B_1_16+B_11_16,B_1_17+B_11_17,B_1_18+B_11_18,B_1_19+B_11_19,B_1_20+B_11_20,B_1_21+B_11_21,B_1_22+B_11_22,B_1_23+B_11_23,B_1_24+B_11_24],[B_2_13+B_12_13,B_2_14+B_12_14,B_2_15+B_12_15,B_2_16+B_12_16,B_2_17+B_12_17,B_2_18+B_12_18,B_2_19+B_12_19,B_2_20+B_12_20,B_2_21+B_12_21,B_2_22+B_12_22,B_2_23+B_12_23,B_2_24+B_12_24],[B_3_13+B_13_13,B_3_14+B_13_14,B_3_15+B_13_15,B_3_16+B_13_16,B_3_17+B_13_17,B_3_18+B_13_18,B_3_19+B_13_19,B_3_20+B_13_20,B_3_21+B_13_21,B_3_22+B_13_22,B_3_23+B_13_23,B_3_24+B_13_24],[B_4_13+B_14_13,B_4_14+B_14_14,B_4_15+B_14_15,B_4_16+B_14_16,B_4_17+B_14_17,B_4_18+B_14_18,B_4_19+B_14_19,B_4_20+B_14_20,B_4_21+B_14_21,B_4_22+B_14_22,B_4_23+B_14_23,B_4_24+B_14_24],[B_5_13+B_15_13,B_5_14+B_15_14,B_5_15+B_15_15,B_5_16+B_15_16,B_5_17+B_15_17,B_5_18+B_15_18,B_5_19+B_15_19,B_5_20+B_15_20,B_5_21+B_15_21,B_5_22+B_15_22,B_5_23+B_15_23,B_5_24+B_15_24],[B_6_13+B_16_13,B_6_14+B_16_14,B_6_15+B_16_15,B_6_16+B_16_16,B_6_17+B_16_17,B_6_18+B_16_18,B_6_19+B_16_19,B_6_20+B_16_20,B_6_21+B_16_21,B_6_22+B_16_22,B_6_23+B_16_23,B_6_24+B_16_24],[B_7_13+B_17_13,B_7_14+B_17_14,B_7_15+B_17_15,B_7_16+B_17_16,B_7_17+B_17_17,B_7_18+B_17_18,B_7_19+B_17_19,B_7_20+B_17_20,B_7_21+B_17_21,B_7_22+B_17_22,B_7_23+B_17_23,B_7_24+B_17_24],[B_8_13+B_18_13,B_8_14+B_18_14,B_8_15+B_18_15,B_8_16+B_18_16,B_8_17+B_18_17,B_8_18+B_18_18,B_8_19+B_18_19,B_8_20+B_18_20,B_8_21+B_18_21,B_8_22+B_18_22,B_8_23+B_18_23,B_8_24+B_18_24],[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]]),Matrix(12, 6, [[C_13_5-C_25_5,C_13_6-C_25_6,C_13_7-C_25_7,C_13_8-C_25_8,C_13_9-C_25_9,C_13_10-C_25_10],[C_14_5-C_26_5,C_14_6-C_26_6,C_14_7-C_26_7,C_14_8-C_26_8,C_14_9-C_26_9,C_14_10-C_26_10],[-C_1_5+C_15_5,-C_1_6+C_15_6,-C_1_7+C_15_7,-C_1_8+C_15_8,-C_1_9+C_15_9,-C_1_10+C_15_10],[-C_2_5+C_16_5,-C_2_6+C_16_6,-C_2_7+C_16_7,-C_2_8+C_16_8,-C_2_9+C_16_9,-C_2_10+C_16_10],[-C_3_5+C_17_5,-C_3_6+C_17_6,-C_3_7+C_17_7,-C_3_8+C_17_8,-C_3_9+C_17_9,-C_3_10+C_17_10],[-C_4_5+C_18_5,-C_4_6+C_18_6,-C_4_7+C_18_7,-C_4_8+C_18_8,-C_4_9+C_18_9,-C_4_10+C_18_10],[-C_5_5+C_19_5,-C_5_6+C_19_6,-C_5_7+C_19_7,-C_5_8+C_19_8,-C_5_9+C_19_9,-C_5_10+C_19_10],[-C_6_5+C_20_5,-C_6_6+C_20_6,-C_6_7+C_20_7,-C_6_8+C_20_8,-C_6_9+C_20_9,-C_6_10+C_20_10],[-C_7_5+C_21_5,-C_7_6+C_21_6,-C_7_7+C_21_7,-C_7_8+C_21_8,-C_7_9+C_21_9,-C_7_10+C_21_10],[-C_8_5+C_22_5,-C_8_6+C_22_6,-C_8_7+C_22_7,-C_8_8+C_22_8,-C_8_9+C_22_9,-C_8_10+C_22_10],[-C_9_5+C_23_5,-C_9_6+C_23_6,-C_9_7+C_23_7,-C_9_8+C_23_8,-C_9_9+C_23_9,-C_9_10+C_23_10],[-C_10_5+C_24_5,-C_10_6+C_24_6,-C_10_7+C_24_7,-C_10_8+C_24_8,-C_10_9+C_24_9,-C_10_10+C_24_10]])))

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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