Description of fast matrix multiplication algorithm: ⟨13×27×29:6000⟩

Algorithm type

64X6Y12Z9+96X3Y12Z9+64X2Y12Z3+512X4Y6Z6+96XY12Z3+48X6Y5Z4+16X9Y3Z2+768X2Y6Z6+24X9Y3Z+72X6Y5Z2+6X6Y3Z3+9X4Y4Z4+X7Y2Z2+48X6Y3Z2+6X4Y4Z3+72X6Y3Z+10X6Y2Z2+15X4Y3Z3+3X3Y4Z3+4X7YZ+2X5Y2Z2+9X3Y3Z3+15X6YZ+40X4Y2Z2+80X3Y3Z2+9X2Y4Z2+1024X2Y3Z3+5X5YZ+120X3Y3Z+17X3Y2Z2+6X2Y4Z+15X2Y3Z2+1536XY3Z3+55X4YZ+6X3Y2Z+8X3YZ2+12X2Y3Z+100X2Y2Z2+2XY3Z2+4XYZ4+51X3YZ+14X2Y2Z+16X2YZ2+12XY3Z+7XY2Z2+2XYZ3+117X2YZ+8XY2Z+32XYZ2+742XYZ64X6Y12Z996X3Y12Z964X2Y12Z3512X4Y6Z696XY12Z348X6Y5Z416X9Y3Z2768X2Y6Z624X9Y3Z72X6Y5Z26X6Y3Z39X4Y4Z4X7Y2Z248X6Y3Z26X4Y4Z372X6Y3Z10X6Y2Z215X4Y3Z33X3Y4Z34X7YZ2X5Y2Z29X3Y3Z315X6YZ40X4Y2Z280X3Y3Z29X2Y4Z21024X2Y3Z35X5YZ120X3Y3Z17X3Y2Z26X2Y4Z15X2Y3Z21536XY3Z355X4YZ6X3Y2Z8X3YZ212X2Y3Z100X2Y2Z22XY3Z24XYZ451X3YZ14X2Y2Z16X2YZ212XY3Z7XY2Z22XYZ3117X2YZ8XY2Z32XYZ2742XYZ64*X^6*Y^12*Z^9+96*X^3*Y^12*Z^9+64*X^2*Y^12*Z^3+512*X^4*Y^6*Z^6+96*X*Y^12*Z^3+48*X^6*Y^5*Z^4+16*X^9*Y^3*Z^2+768*X^2*Y^6*Z^6+24*X^9*Y^3*Z+72*X^6*Y^5*Z^2+6*X^6*Y^3*Z^3+9*X^4*Y^4*Z^4+X^7*Y^2*Z^2+48*X^6*Y^3*Z^2+6*X^4*Y^4*Z^3+72*X^6*Y^3*Z+10*X^6*Y^2*Z^2+15*X^4*Y^3*Z^3+3*X^3*Y^4*Z^3+4*X^7*Y*Z+2*X^5*Y^2*Z^2+9*X^3*Y^3*Z^3+15*X^6*Y*Z+40*X^4*Y^2*Z^2+80*X^3*Y^3*Z^2+9*X^2*Y^4*Z^2+1024*X^2*Y^3*Z^3+5*X^5*Y*Z+120*X^3*Y^3*Z+17*X^3*Y^2*Z^2+6*X^2*Y^4*Z+15*X^2*Y^3*Z^2+1536*X*Y^3*Z^3+55*X^4*Y*Z+6*X^3*Y^2*Z+8*X^3*Y*Z^2+12*X^2*Y^3*Z+100*X^2*Y^2*Z^2+2*X*Y^3*Z^2+4*X*Y*Z^4+51*X^3*Y*Z+14*X^2*Y^2*Z+16*X^2*Y*Z^2+12*X*Y^3*Z+7*X*Y^2*Z^2+2*X*Y*Z^3+117*X^2*Y*Z+8*X*Y^2*Z+32*X*Y*Z^2+742*X*Y*Z

Algorithm definition

The algorithm ⟨13×27×29:6000⟩ could be constructed using the following decomposition:

⟨13×27×29:6000⟩ = ⟨13×27×5:1192⟩ + ⟨13×27×24:4808⟩.

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_1_25A_1_26A_1_27A_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_2_25A_2_26A_2_27A_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_24A_3_25A_3_26A_3_27A_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_4_20A_4_21A_4_22A_4_23A_4_24A_4_25A_4_26A_4_27A_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_5_20A_5_21A_5_22A_5_23A_5_24A_5_25A_5_26A_5_27A_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_6_20A_6_21A_6_22A_6_23A_6_24A_6_25A_6_26A_6_27A_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_7_20A_7_21A_7_22A_7_23A_7_24A_7_25A_7_26A_7_27A_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_8_20A_8_21A_8_22A_8_23A_8_24A_8_25A_8_26A_8_27A_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_9_20A_9_21A_9_22A_9_23A_9_24A_9_25A_9_26A_9_27A_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_19A_10_20A_10_21A_10_22A_10_23A_10_24A_10_25A_10_26A_10_27A_11_1A_11_2A_11_3A_11_4A_11_5A_11_6A_11_7A_11_8A_11_9A_11_10A_11_11A_11_12A_11_13A_11_14A_11_15A_11_16A_11_17A_11_18A_11_19A_11_20A_11_21A_11_22A_11_23A_11_24A_11_25A_11_26A_11_27A_12_1A_12_2A_12_3A_12_4A_12_5A_12_6A_12_7A_12_8A_12_9A_12_10A_12_11A_12_12A_12_13A_12_14A_12_15A_12_16A_12_17A_12_18A_12_19A_12_20A_12_21A_12_22A_12_23A_12_24A_12_25A_12_26A_12_27A_13_1A_13_2A_13_3A_13_4A_13_5A_13_6A_13_7A_13_8A_13_9A_13_10A_13_11A_13_12A_13_13A_13_14A_13_15A_13_16A_13_17A_13_18A_13_19A_13_20A_13_21A_13_22A_13_23A_13_24A_13_25A_13_26A_13_27B_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_1_27B_1_28B_1_29B_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_2_27B_2_28B_2_29B_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_3_27B_3_28B_3_29B_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_4_27B_4_28B_4_29B_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_5_27B_5_28B_5_29B_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_6_27B_6_28B_6_29B_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_7_27B_7_28B_7_29B_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_8_27B_8_28B_8_29B_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_9_27B_9_28B_9_29B_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_10_27B_10_28B_10_29B_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_11_27B_11_28B_11_29B_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_12_27B_12_28B_12_29B_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_13_27B_13_28B_13_29B_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_14_27B_14_28B_14_29B_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_15_27B_15_28B_15_29B_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_16_27B_16_28B_16_29B_17_1B_17_2B_17_3B_17_4B_17_5B_17_6B_17_7B_17_8B_17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10_10C_10_11C_10_12C_10_13C_11_1C_11_2C_11_3C_11_4C_11_5C_11_6C_11_7C_11_8C_11_9C_11_10C_11_11C_11_12C_11_13C_12_1C_12_2C_12_3C_12_4C_12_5C_12_6C_12_7C_12_8C_12_9C_12_10C_12_11C_12_12C_12_13C_13_1C_13_2C_13_3C_13_4C_13_5C_13_6C_13_7C_13_8C_13_9C_13_10C_13_11C_13_12C_13_13C_14_1C_14_2C_14_3C_14_4C_14_5C_14_6C_14_7C_14_8C_14_9C_14_10C_14_11C_14_12C_14_13C_15_1C_15_2C_15_3C_15_4C_15_5C_15_6C_15_7C_15_8C_15_9C_15_10C_15_11C_15_12C_15_13C_16_1C_16_2C_16_3C_16_4C_16_5C_16_6C_16_7C_16_8C_16_9C_16_10C_16_11C_16_12C_16_13C_17_1C_17_2C_17_3C_17_4C_17_5C_17_6C_17_7C_17_8C_17_9C_17_10C_17_11C_17_12C_17_13C_18_1C_18_2C_18_3C_18_4C_18_5C_18_6C_18_7C_18_8C_18_9C_18_10C_18_11C_18_12C_18_13C_19_1C_19_2C_19_3C_19_4C_19_5C_19_6C_19_7C_19_8C_19_9C_19_10C_19_11C_19_12C_19_13C_20_1C_20_2C_20_3C_20_4C_20_5C_20_6C_20_7C_20_8C_20_9C_20_10C_20_11C_20_12C_20_13C_21_1C_21_2C_21_3C_21_4C_21_5C_21_6C_21_7C_21_8C_21_9C_21_10C_21_11C_21_12C_21_13C_22_1C_22_2C_22_3C_22_4C_22_5C_22_6C_22_7C_22_8C_22_9C_22_10C_22_11C_22_12C_22_13C_23_1C_23_2C_23_3C_23_4C_23_5C_23_6C_23_7C_23_8C_23_9C_23_10C_23_11C_23_12C_23_13C_24_1C_24_2C_24_3C_24_4C_24_5C_24_6C_24_7C_24_8C_24_9C_24_10C_24_11C_24_12C_24_13C_25_1C_25_2C_25_3C_25_4C_25_5C_25_6C_25_7C_25_8C_25_9C_25_10C_25_11C_25_12C_25_13C_26_1C_26_2C_26_3C_26_4C_26_5C_26_6C_26_7C_26_8C_26_9C_26_10C_26_11C_26_12C_26_13C_27_1C_27_2C_27_3C_27_4C_27_5C_27_6C_27_7C_27_8C_27_9C_27_10C_27_11C_27_12C_27_13C_28_1C_28_2C_28_3C_28_4C_28_5C_28_6C_28_7C_28_8C_28_9C_28_10C_28_11C_28_12C_28_13C_29_1C_29_2C_29_3C_29_4C_29_5C_29_6C_29_7C_29_8C_29_9C_29_10C_29_11C_29_12C_29_13Trace(Mul(Matrix(13, 27, [[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_1_25,A_1_26,A_1_27],[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_2_25,A_2_26,A_2_27],[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,A_3_25,A_3_26,A_3_27],[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_4_20,A_4_21,A_4_22,A_4_23,A_4_24,A_4_25,A_4_26,A_4_27],[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_5_20,A_5_21,A_5_22,A_5_23,A_5_24,A_5_25,A_5_26,A_5_27],[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_6_20,A_6_21,A_6_22,A_6_23,A_6_24,A_6_25,A_6_26,A_6_27],[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_7_20,A_7_21,A_7_22,A_7_23,A_7_24,A_7_25,A_7_26,A_7_27],[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_8_20,A_8_21,A_8_22,A_8_23,A_8_24,A_8_25,A_8_26,A_8_27],[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_9_20,A_9_21,A_9_22,A_9_23,A_9_24,A_9_25,A_9_26,A_9_27],[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_10_20,A_10_21,A_10_22,A_10_23,A_10_24,A_10_25,A_10_26,A_10_27],[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_11_20,A_11_21,A_11_22,A_11_23,A_11_24,A_11_25,A_11_26,A_11_27],[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_12_20,A_12_21,A_12_22,A_12_23,A_12_24,A_12_25,A_12_26,A_12_27],[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_13_20,A_13_21,A_13_22,A_13_23,A_13_24,A_13_25,A_13_26,A_13_27]]),Matrix(27, 29, [[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_1_28,B_1_29],[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_2_28,B_2_29],[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_3_28,B_3_29],[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_4_28,B_4_29],[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_5_28,B_5_29],[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_6_28,B_6_29],[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_7_28,B_7_29],[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_8_28,B_8_29],[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_9_28,B_9_29],[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_10_28,B_10_29],[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_11_28,B_11_29],[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_12_28,B_12_29],[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_13_28,B_13_29],[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_14_28,B_14_29],[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_15_28,B_15_29],[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_16_28,B_16_29],[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_17_28,B_17_29],[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_18_28,B_18_29],[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,B_19_28,B_19_29],[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_20_25,B_20_26,B_20_27,B_20_28,B_20_29],[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_21_25,B_21_26,B_21_27,B_21_28,B_21_29],[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_22_25,B_22_26,B_22_27,B_22_28,B_22_29],[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_23_25,B_23_26,B_23_27,B_23_28,B_23_29],[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,B_24_25,B_24_26,B_24_27,B_24_28,B_24_29],[B_25_1,B_25_2,B_25_3,B_25_4,B_25_5,B_25_6,B_25_7,B_25_8,B_25_9,B_25_10,B_25_11,B_25_12,B_25_13,B_25_14,B_25_15,B_25_16,B_25_17,B_25_18,B_25_19,B_25_20,B_25_21,B_25_22,B_25_23,B_25_24,B_25_25,B_25_26,B_25_27,B_25_28,B_25_29],[B_26_1,B_26_2,B_26_3,B_26_4,B_26_5,B_26_6,B_26_7,B_26_8,B_26_9,B_26_10,B_26_11,B_26_12,B_26_13,B_26_14,B_26_15,B_26_16,B_26_17,B_26_18,B_26_19,B_26_20,B_26_21,B_26_22,B_26_23,B_26_24,B_26_25,B_26_26,B_26_27,B_26_28,B_26_29],[B_27_1,B_27_2,B_27_3,B_27_4,B_27_5,B_27_6,B_27_7,B_27_8,B_27_9,B_27_10,B_27_11,B_27_12,B_27_13,B_27_14,B_27_15,B_27_16,B_27_17,B_27_18,B_27_19,B_27_20,B_27_21,B_27_22,B_27_23,B_27_24,B_27_25,B_27_26,B_27_27,B_27_28,B_27_29]]),Matrix(29, 13, [[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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_28_1,C_28_2,C_28_3,C_28_4,C_28_5,C_28_6,C_28_7,C_28_8,C_28_9,C_28_10,C_28_11,C_28_12,C_28_13],[C_29_1,C_29_2,C_29_3,C_29_4,C_29_5,C_29_6,C_29_7,C_29_8,C_29_9,C_29_10,C_29_11,C_29_12,C_29_13]]))) = Trace(Mul(Matrix(13, 27, [[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_1_25,A_1_26,A_1_27],[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_2_25,A_2_26,A_2_27],[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,A_3_25,A_3_26,A_3_27],[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_4_20,A_4_21,A_4_22,A_4_23,A_4_24,A_4_25,A_4_26,A_4_27],[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_5_20,A_5_21,A_5_22,A_5_23,A_5_24,A_5_25,A_5_26,A_5_27],[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_6_20,A_6_21,A_6_22,A_6_23,A_6_24,A_6_25,A_6_26,A_6_27],[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_7_20,A_7_21,A_7_22,A_7_23,A_7_24,A_7_25,A_7_26,A_7_27],[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_8_20,A_8_21,A_8_22,A_8_23,A_8_24,A_8_25,A_8_26,A_8_27],[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_9_20,A_9_21,A_9_22,A_9_23,A_9_24,A_9_25,A_9_26,A_9_27],[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_10_20,A_10_21,A_10_22,A_10_23,A_10_24,A_10_25,A_10_26,A_10_27],[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_11_20,A_11_21,A_11_22,A_11_23,A_11_24,A_11_25,A_11_26,A_11_27],[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_12_20,A_12_21,A_12_22,A_12_23,A_12_24,A_12_25,A_12_26,A_12_27],[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_13_20,A_13_21,A_13_22,A_13_23,A_13_24,A_13_25,A_13_26,A_13_27]]),Matrix(27, 5, [[B_1_1,B_1_2,B_1_3,B_1_4,B_1_5],[B_2_1,B_2_2,B_2_3,B_2_4,B_2_5],[B_3_1,B_3_2,B_3_3,B_3_4,B_3_5],[B_4_1,B_4_2,B_4_3,B_4_4,B_4_5],[B_5_1,B_5_2,B_5_3,B_5_4,B_5_5],[B_6_1,B_6_2,B_6_3,B_6_4,B_6_5],[B_7_1,B_7_2,B_7_3,B_7_4,B_7_5],[B_8_1,B_8_2,B_8_3,B_8_4,B_8_5],[B_9_1,B_9_2,B_9_3,B_9_4,B_9_5],[B_10_1,B_10_2,B_10_3,B_10_4,B_10_5],[B_11_1,B_11_2,B_11_3,B_11_4,B_11_5],[B_12_1,B_12_2,B_12_3,B_12_4,B_12_5],[B_13_1,B_13_2,B_13_3,B_13_4,B_13_5],[B_14_1,B_14_2,B_14_3,B_14_4,B_14_5],[B_15_1,B_15_2,B_15_3,B_15_4,B_15_5],[B_16_1,B_16_2,B_16_3,B_16_4,B_16_5],[B_17_1,B_17_2,B_17_3,B_17_4,B_17_5],[B_18_1,B_18_2,B_18_3,B_18_4,B_18_5],[B_19_1,B_19_2,B_19_3,B_19_4,B_19_5],[B_20_1,B_20_2,B_20_3,B_20_4,B_20_5],[B_21_1,B_21_2,B_21_3,B_21_4,B_21_5],[B_22_1,B_22_2,B_22_3,B_22_4,B_22_5],[B_23_1,B_23_2,B_23_3,B_23_4,B_23_5],[B_24_1,B_24_2,B_24_3,B_24_4,B_24_5],[B_25_1,B_25_2,B_25_3,B_25_4,B_25_5],[B_26_1,B_26_2,B_26_3,B_26_4,B_26_5],[B_27_1,B_27_2,B_27_3,B_27_4,B_27_5]]),Matrix(5, 13, [[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_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_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_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_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]])))+Trace(Mul(Matrix(13, 27, [[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_1_25,A_1_26,A_1_27],[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_2_25,A_2_26,A_2_27],[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,A_3_25,A_3_26,A_3_27],[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_4_20,A_4_21,A_4_22,A_4_23,A_4_24,A_4_25,A_4_26,A_4_27],[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_5_20,A_5_21,A_5_22,A_5_23,A_5_24,A_5_25,A_5_26,A_5_27],[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_6_20,A_6_21,A_6_22,A_6_23,A_6_24,A_6_25,A_6_26,A_6_27],[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_7_20,A_7_21,A_7_22,A_7_23,A_7_24,A_7_25,A_7_26,A_7_27],[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_8_20,A_8_21,A_8_22,A_8_23,A_8_24,A_8_25,A_8_26,A_8_27],[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_9_20,A_9_21,A_9_22,A_9_23,A_9_24,A_9_25,A_9_26,A_9_27],[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_10_20,A_10_21,A_10_22,A_10_23,A_10_24,A_10_25,A_10_26,A_10_27],[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_11_20,A_11_21,A_11_22,A_11_23,A_11_24,A_11_25,A_11_26,A_11_27],[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_12_20,A_12_21,A_12_22,A_12_23,A_12_24,A_12_25,A_12_26,A_12_27],[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_13_20,A_13_21,A_13_22,A_13_23,A_13_24,A_13_25,A_13_26,A_13_27]]),Matrix(27, 24, [[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_1_28,B_1_29],[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_2_28,B_2_29],[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_3_28,B_3_29],[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_4_28,B_4_29],[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_5_28,B_5_29],[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_6_28,B_6_29],[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_7_28,B_7_29],[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_8_28,B_8_29],[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_9_28,B_9_29],[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_10_28,B_10_29],[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_11_28,B_11_29],[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_12_28,B_12_29],[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_13_28,B_13_29],[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_14_28,B_14_29],[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_15_28,B_15_29],[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_16_28,B_16_29],[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_17_28,B_17_29],[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_18_28,B_18_29],[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,B_19_28,B_19_29],[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_20_25,B_20_26,B_20_27,B_20_28,B_20_29],[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_21_25,B_21_26,B_21_27,B_21_28,B_21_29],[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_22_25,B_22_26,B_22_27,B_22_28,B_22_29],[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_23_25,B_23_26,B_23_27,B_23_28,B_23_29],[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,B_24_25,B_24_26,B_24_27,B_24_28,B_24_29],[B_25_6,B_25_7,B_25_8,B_25_9,B_25_10,B_25_11,B_25_12,B_25_13,B_25_14,B_25_15,B_25_16,B_25_17,B_25_18,B_25_19,B_25_20,B_25_21,B_25_22,B_25_23,B_25_24,B_25_25,B_25_26,B_25_27,B_25_28,B_25_29],[B_26_6,B_26_7,B_26_8,B_26_9,B_26_10,B_26_11,B_26_12,B_26_13,B_26_14,B_26_15,B_26_16,B_26_17,B_26_18,B_26_19,B_26_20,B_26_21,B_26_22,B_26_23,B_26_24,B_26_25,B_26_26,B_26_27,B_26_28,B_26_29],[B_27_6,B_27_7,B_27_8,B_27_9,B_27_10,B_27_11,B_27_12,B_27_13,B_27_14,B_27_15,B_27_16,B_27_17,B_27_18,B_27_19,B_27_20,B_27_21,B_27_22,B_27_23,B_27_24,B_27_25,B_27_26,B_27_27,B_27_28,B_27_29]]),Matrix(24, 13, [[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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_28_1,C_28_2,C_28_3,C_28_4,C_28_5,C_28_6,C_28_7,C_28_8,C_28_9,C_28_10,C_28_11,C_28_12,C_28_13],[C_29_1,C_29_2,C_29_3,C_29_4,C_29_5,C_29_6,C_29_7,C_29_8,C_29_9,C_29_10,C_29_11,C_29_12,C_29_13]])))

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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