Description of fast matrix multiplication algorithm: ⟨13×21×24:3880⟩

Algorithm type

16X10Y12Z7+16X9Y12Z7+16X10Y12Z5+4X10Y12Z3+8X9Y12Z4+12X10Y11Z3+24X9Y11Z4+16X7Y12Z5+4X10Y11Z2+16X9Y11Z3+4X9Y11Z2+4X7Y12Z3+12X7Y11Z3+32X6Y6Z9+8X7Y11Z2+16X4Y6Z9+16X3Y6Z9+20X6Y6Z5+136X6Y6Z4+12X6Y5Z5+96X4Y6Z6+32X6Y6Z3+8X6Y5Z4+4X4Y6Z5+160X6Y6Z2+12X4Y5Z5+16X3Y6Z5+144X2Y6Z6+12X6Y6Z+8X6Y5Z2+24X5Y6Z2+48X4Y6Z3+8X4Y5Z4+8X3Y6Z4+4X5Y6Z+32X5Y5Z2+68X4Y6Z2+48X4Y4Z4+16X3Y6Z3+64X3Y3Z6+44X4Y6Z+8X4Y5Z2+16X3Y6Z2+16X4Y5Z+192X4Y3Z3+8X3Y6Z+4X3Y5Z2+24X2Y6Z2+12X3Y5Z+96X3Y3Z3+192X3Y3Z2+144X2Y4Z2+480X2Y3Z3+48XY6Z+288X3Y3Z+288XY3Z3+192X2Y2Z2+96XY4Z+48XY3Z+288XY2Z+192XYZ16X10Y12Z716X9Y12Z716X10Y12Z54X10Y12Z38X9Y12Z412X10Y11Z324X9Y11Z416X7Y12Z54X10Y11Z216X9Y11Z34X9Y11Z24X7Y12Z312X7Y11Z332X6Y6Z98X7Y11Z216X4Y6Z916X3Y6Z920X6Y6Z5136X6Y6Z412X6Y5Z596X4Y6Z632X6Y6Z38X6Y5Z44X4Y6Z5160X6Y6Z212X4Y5Z516X3Y6Z5144X2Y6Z612X6Y6Z8X6Y5Z224X5Y6Z248X4Y6Z38X4Y5Z48X3Y6Z44X5Y6Z32X5Y5Z268X4Y6Z248X4Y4Z416X3Y6Z364X3Y3Z644X4Y6Z8X4Y5Z216X3Y6Z216X4Y5Z192X4Y3Z38X3Y6Z4X3Y5Z224X2Y6Z212X3Y5Z96X3Y3Z3192X3Y3Z2144X2Y4Z2480X2Y3Z348XY6Z288X3Y3Z288XY3Z3192X2Y2Z296XY4Z48XY3Z288XY2Z192XYZ16*X^10*Y^12*Z^7+16*X^9*Y^12*Z^7+16*X^10*Y^12*Z^5+4*X^10*Y^12*Z^3+8*X^9*Y^12*Z^4+12*X^10*Y^11*Z^3+24*X^9*Y^11*Z^4+16*X^7*Y^12*Z^5+4*X^10*Y^11*Z^2+16*X^9*Y^11*Z^3+4*X^9*Y^11*Z^2+4*X^7*Y^12*Z^3+12*X^7*Y^11*Z^3+32*X^6*Y^6*Z^9+8*X^7*Y^11*Z^2+16*X^4*Y^6*Z^9+16*X^3*Y^6*Z^9+20*X^6*Y^6*Z^5+136*X^6*Y^6*Z^4+12*X^6*Y^5*Z^5+96*X^4*Y^6*Z^6+32*X^6*Y^6*Z^3+8*X^6*Y^5*Z^4+4*X^4*Y^6*Z^5+160*X^6*Y^6*Z^2+12*X^4*Y^5*Z^5+16*X^3*Y^6*Z^5+144*X^2*Y^6*Z^6+12*X^6*Y^6*Z+8*X^6*Y^5*Z^2+24*X^5*Y^6*Z^2+48*X^4*Y^6*Z^3+8*X^4*Y^5*Z^4+8*X^3*Y^6*Z^4+4*X^5*Y^6*Z+32*X^5*Y^5*Z^2+68*X^4*Y^6*Z^2+48*X^4*Y^4*Z^4+16*X^3*Y^6*Z^3+64*X^3*Y^3*Z^6+44*X^4*Y^6*Z+8*X^4*Y^5*Z^2+16*X^3*Y^6*Z^2+16*X^4*Y^5*Z+192*X^4*Y^3*Z^3+8*X^3*Y^6*Z+4*X^3*Y^5*Z^2+24*X^2*Y^6*Z^2+12*X^3*Y^5*Z+96*X^3*Y^3*Z^3+192*X^3*Y^3*Z^2+144*X^2*Y^4*Z^2+480*X^2*Y^3*Z^3+48*X*Y^6*Z+288*X^3*Y^3*Z+288*X*Y^3*Z^3+192*X^2*Y^2*Z^2+96*X*Y^4*Z+48*X*Y^3*Z+288*X*Y^2*Z+192*X*Y*Z

Algorithm definition

The algorithm ⟨13×21×24:3880⟩ could be constructed using the following decomposition:

⟨13×21×24:3880⟩ = ⟨9×12×12:800⟩ + ⟨4×12×12:390⟩ + ⟨9×9×12:600⟩ + ⟨4×12×12:390⟩ + ⟨4×9×12:300⟩ + ⟨9×12×12:800⟩ + ⟨9×9×12:600⟩.

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_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_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_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_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_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_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_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_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_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_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_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_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_21B_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_24C_1_1C_1_2C_1_3C_1_4C_1_5C_1_6C_1_7C_1_8C_1_9C_1_10C_1_11C_1_12C_1_13C_2_1C_2_2C_2_3C_2_4C_2_5C_2_6C_2_7C_2_8C_2_9C_2_10C_2_11C_2_12C_2_13C_3_1C_3_2C_3_3C_3_4C_3_5C_3_6C_3_7C_3_8C_3_9C_3_10C_3_11C_3_12C_3_13C_4_1C_4_2C_4_3C_4_4C_4_5C_4_6C_4_7C_4_8C_4_9C_4_10C_4_11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20A_10_9A_10_21A_11_1A_11_13A_11_2A_11_14A_11_3A_11_15A_11_4A_11_16A_11_5A_11_17A_11_10A_11_18A_11_11A_11_19A_11_12A_11_20A_11_9A_11_21A_12_1A_12_13A_12_2A_12_14A_12_3A_12_15A_12_4A_12_16A_12_5A_12_17A_12_10A_12_18A_12_11A_12_19A_12_12A_12_20A_12_9A_12_21A_13_1A_13_13A_13_2A_13_14A_13_3A_13_15A_13_4A_13_16A_13_5A_13_17A_13_10A_13_18A_13_11A_13_19A_13_12A_13_20A_13_9A_13_21B_1_1B_1_2B_1_3B_1_4B_1_5B_1_6B_1_7B_1_8B_1_13B_1_14B_1_15B_1_12B_2_1B_2_2B_2_3B_2_4B_2_5B_2_6B_2_7B_2_8B_2_13B_2_14B_2_15B_2_12B_3_1B_3_2B_3_3B_3_4B_3_5B_3_6B_3_7B_3_8B_3_13B_3_14B_3_15B_3_12B_4_1B_4_2B_4_3B_4_4B_4_5B_4_6B_4_7B_4_8B_4_13B_4_14B_4_15B_4_12B_5_1B_5_2B_5_3B_5_4B_5_5B_5_6B_5_7B_5_8B_5_13B_5_14B_5_15B_5_12B_10_1B_10_2B_10_3B_10_4B_10_5B_10_6B_10_7B_10_8B_10_13B_10_14B_10_15B_10_12B_11_1B_11_2B_11_3B_11_4B_11_5B_11_6B_11_7B_11_8B_11_13B_11_14B_11_15B_11_12B_12_1B_12_2B_12_3B_12_4B_12_5B_12_6B_12_7B_12_8B_12_13B_12_14B_12_15B_12_12B_9_1B_9_2B_9_3B_9_4B_9_5B_9_6B_9_7B_9_8B_9_13B_9_14B_9_15B_9_12C_1_5C_9_5C_1_6C_9_6C_1_7C_9_7C_1_8C_9_8C_1_9C_9_9C_1_10C_9_10C_1_11C_9_11C_1_12C_9_12C_1_13C_9_13C_2_5C_10_5C_2_6C_10_6C_2_7C_10_7C_2_8C_10_8C_2_9C_10_9C_2_10C_10_10C_2_11C_10_11C_2_12C_10_12C_2_13C_10_13C_3_5C_11_5C_3_6C_11_6C_3_7C_11_7C_3_8C_11_8C_3_9C_11_9C_3_10C_11_10C_3_11C_11_11C_3_12C_11_12C_3_13C_11_13C_4_5C_16_5C_4_6C_16_6C_4_7C_16_7C_4_8C_16_8C_4_9C_16_9C_4_10C_16_10C_4_11C_16_11C_4_12C_16_12C_4_13C_16_13C_5_5C_17_5C_5_6C_17_6C_5_7C_17_7C_5_8C_17_8C_5_9C_17_9C_5_10C_17_10C_5_11C_17_11C_5_12C_17_12C_5_13C_17_13C_6_5C_18_5C_6_6C_18_6C_6_7C_18_7C_6_8C_18_8C_6_9C_18_9C_6_10C_18_10C_6_11C_18_11C_6_12C_18_12C_6_13C_18_13C_7_5C_19_5C_7_6C_19_6C_7_7C_19_7C_7_8C_19_8C_7_9C_19_9C_7_10C_19_10C_7_11C_19_11C_7_12C_19_12C_7_13C_19_13C_8_5C_20_5C_8_6C_20_6C_8_7C_20_7C_8_8C_20_8C_8_9C_20_9C_8_10C_20_10C_8_11C_20_11C_8_12C_20_12C_8_13C_20_13C_13_5C_21_5C_13_6C_21_6C_13_7C_21_7C_13_8C_21_8C_13_9C_21_9C_13_10C_21_10C_13_11C_21_11C_13_12C_21_12C_13_13C_21_13C_14_5C_22_5C_14_6C_22_6C_14_7C_22_7C_14_8C_22_8C_14_9C_22_9C_14_10C_22_10C_14_11C_22_11C_14_12C_22_12C_14_13C_22_13C_15_5C_23_5C_15_6C_23_6C_15_7C_23_7C_15_8C_23_8C_15_9C_23_9C_15_10C_23_10C_15_11C_23_11C_15_12C_23_12C_15_13C_23_13C_12_5C_24_5C_12_6C_24_6C_12_7C_24_7C_12_8C_24_8C_12_9C_24_9C_12_10C_24_10C_12_11C_24_11C_12_12C_24_12C_12_13C_24_13Trace(Mul(Matrix(13, 21, [[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_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_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_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_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_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_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_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_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_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_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_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_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]]),Matrix(21, 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]]),Matrix(24, 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]]))) = Trace(Mul(Matrix(9, 12, [[A_5_6,A_5_7,A_5_8,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_6_6,A_6_7,A_6_8,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_7_6,A_7_7,A_7_8,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_8_6,A_8_7,A_8_8,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_9_6,A_9_7,A_9_8,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_10_6,A_10_7,A_10_8,A_2_1+A_10_13,A_2_2+A_10_14,A_2_3+A_10_15,A_2_4+A_10_16,A_2_5+A_10_17,A_2_10+A_10_18,A_2_11+A_10_19,A_2_12+A_10_20,A_2_9+A_10_21],[A_11_6,A_11_7,A_11_8,A_3_1+A_11_13,A_3_2+A_11_14,A_3_3+A_11_15,A_3_4+A_11_16,A_3_5+A_11_17,A_3_10+A_11_18,A_3_11+A_11_19,A_3_12+A_11_20,A_3_9+A_11_21],[A_12_6,A_12_7,A_12_8,A_4_1+A_12_13,A_4_2+A_12_14,A_4_3+A_12_15,A_4_4+A_12_16,A_4_5+A_12_17,A_4_10+A_12_18,A_4_11+A_12_19,A_4_12+A_12_20,A_4_9+A_12_21],[A_13_6,A_13_7,A_13_8,A_1_1+A_13_13,A_1_2+A_13_14,A_1_3+A_13_15,A_1_4+A_13_16,A_1_5+A_13_17,A_1_10+A_13_18,A_1_11+A_13_19,A_1_12+A_13_20,A_1_9+A_13_21]]),Matrix(12, 12, [[B_6_9,B_6_10,B_6_11,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_9,B_7_10,B_7_11,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_9,B_8_10,B_8_11,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_1_1+B_13_9,B_1_2+B_13_10,B_1_3+B_13_11,B_1_4+B_13_16,B_1_5+B_13_17,B_1_6+B_13_18,B_1_7+B_13_19,B_1_8+B_13_20,B_1_13+B_13_21,B_1_14+B_13_22,B_1_15+B_13_23,B_1_12+B_13_24],[B_2_1+B_14_9,B_2_2+B_14_10,B_2_3+B_14_11,B_2_4+B_14_16,B_2_5+B_14_17,B_2_6+B_14_18,B_2_7+B_14_19,B_2_8+B_14_20,B_2_13+B_14_21,B_2_14+B_14_22,B_2_15+B_14_23,B_2_12+B_14_24],[B_3_1+B_15_9,B_3_2+B_15_10,B_3_3+B_15_11,B_3_4+B_15_16,B_3_5+B_15_17,B_3_6+B_15_18,B_3_7+B_15_19,B_3_8+B_15_20,B_3_13+B_15_21,B_3_14+B_15_22,B_3_15+B_15_23,B_3_12+B_15_24],[B_4_1+B_16_9,B_4_2+B_16_10,B_4_3+B_16_11,B_4_4+B_16_16,B_4_5+B_16_17,B_4_6+B_16_18,B_4_7+B_16_19,B_4_8+B_16_20,B_4_13+B_16_21,B_4_14+B_16_22,B_4_15+B_16_23,B_4_12+B_16_24],[B_5_1+B_17_9,B_5_2+B_17_10,B_5_3+B_17_11,B_5_4+B_17_16,B_5_5+B_17_17,B_5_6+B_17_18,B_5_7+B_17_19,B_5_8+B_17_20,B_5_13+B_17_21,B_5_14+B_17_22,B_5_15+B_17_23,B_5_12+B_17_24],[B_10_1+B_18_9,B_10_2+B_18_10,B_10_3+B_18_11,B_10_4+B_18_16,B_10_5+B_18_17,B_10_6+B_18_18,B_10_7+B_18_19,B_10_8+B_18_20,B_10_13+B_18_21,B_10_14+B_18_22,B_10_15+B_18_23,B_10_12+B_18_24],[B_11_1+B_19_9,B_11_2+B_19_10,B_11_3+B_19_11,B_11_4+B_19_16,B_11_5+B_19_17,B_11_6+B_19_18,B_11_7+B_19_19,B_11_8+B_19_20,B_11_13+B_19_21,B_11_14+B_19_22,B_11_15+B_19_23,B_11_12+B_19_24],[B_12_1+B_20_9,B_12_2+B_20_10,B_12_3+B_20_11,B_12_4+B_20_16,B_12_5+B_20_17,B_12_6+B_20_18,B_12_7+B_20_19,B_12_8+B_20_20,B_12_13+B_20_21,B_12_14+B_20_22,B_12_15+B_20_23,B_12_12+B_20_24],[B_9_1+B_21_9,B_9_2+B_21_10,B_9_3+B_21_11,B_9_4+B_21_16,B_9_5+B_21_17,B_9_6+B_21_18,B_9_7+B_21_19,B_9_8+B_21_20,B_9_13+B_21_21,B_9_14+B_21_22,B_9_15+B_21_23,B_9_12+B_21_24]]),Matrix(12, 9, [[C_9_5,C_9_6,C_9_7,C_9_8,C_9_9,C_1_2+C_9_10,C_1_3+C_9_11,C_1_4+C_9_12,C_1_1+C_9_13],[C_10_5,C_10_6,C_10_7,C_10_8,C_10_9,C_2_2+C_10_10,C_2_3+C_10_11,C_2_4+C_10_12,C_2_1+C_10_13],[C_11_5,C_11_6,C_11_7,C_11_8,C_11_9,C_3_2+C_11_10,C_3_3+C_11_11,C_3_4+C_11_12,C_3_1+C_11_13],[C_16_5,C_16_6,C_16_7,C_16_8,C_16_9,C_4_2+C_16_10,C_4_3+C_16_11,C_4_4+C_16_12,C_4_1+C_16_13],[C_17_5,C_17_6,C_17_7,C_17_8,C_17_9,C_5_2+C_17_10,C_5_3+C_17_11,C_5_4+C_17_12,C_5_1+C_17_13],[C_18_5,C_18_6,C_18_7,C_18_8,C_18_9,C_6_2+C_18_10,C_6_3+C_18_11,C_6_4+C_18_12,C_6_1+C_18_13],[C_19_5,C_19_6,C_19_7,C_19_8,C_19_9,C_7_2+C_19_10,C_7_3+C_19_11,C_7_4+C_19_12,C_7_1+C_19_13],[C_20_5,C_20_6,C_20_7,C_20_8,C_20_9,C_8_2+C_20_10,C_8_3+C_20_11,C_8_4+C_20_12,C_8_1+C_20_13],[C_21_5,C_21_6,C_21_7,C_21_8,C_21_9,C_13_2+C_21_10,C_13_3+C_21_11,C_13_4+C_21_12,C_13_1+C_21_13],[C_22_5,C_22_6,C_22_7,C_22_8,C_22_9,C_14_2+C_22_10,C_14_3+C_22_11,C_14_4+C_22_12,C_14_1+C_22_13],[C_23_5,C_23_6,C_23_7,C_23_8,C_23_9,C_15_2+C_23_10,C_15_3+C_23_11,C_15_4+C_23_12,C_15_1+C_23_13],[C_24_5,C_24_6,C_24_7,C_24_8,C_24_9,C_12_2+C_24_10,C_12_3+C_24_11,C_12_4+C_24_12,C_12_1+C_24_13]])))+Trace(Mul(Matrix(4, 12, [[A_2_6-A_10_6,A_2_7-A_10_7,A_2_8-A_10_8,A_2_13-A_10_13,A_2_14-A_10_14,A_2_15-A_10_15,A_2_16-A_10_16,A_2_17-A_10_17,A_2_18-A_10_18,A_2_19-A_10_19,A_2_20-A_10_20,A_2_21-A_10_21],[A_3_6-A_11_6,A_3_7-A_11_7,A_3_8-A_11_8,A_3_13-A_11_13,A_3_14-A_11_14,A_3_15-A_11_15,A_3_16-A_11_16,A_3_17-A_11_17,A_3_18-A_11_18,A_3_19-A_11_19,A_3_20-A_11_20,A_3_21-A_11_21],[A_4_6-A_12_6,A_4_7-A_12_7,A_4_8-A_12_8,A_4_13-A_12_13,A_4_14-A_12_14,A_4_15-A_12_15,A_4_16-A_12_16,A_4_17-A_12_17,A_4_18-A_12_18,A_4_19-A_12_19,A_4_20-A_12_20,A_4_21-A_12_21],[A_1_6-A_13_6,A_1_7-A_13_7,A_1_8-A_13_8,A_1_13-A_13_13,A_1_14-A_13_14,A_1_15-A_13_15,A_1_16-A_13_16,A_1_17-A_13_17,A_1_18-A_13_18,A_1_19-A_13_19,A_1_20-A_13_20,A_1_21-A_13_21]]),Matrix(12, 12, [[B_6_1+B_6_9,B_6_2+B_6_10,B_6_3+B_6_11,B_6_4+B_6_16,B_6_5+B_6_17,B_6_6+B_6_18,B_6_7+B_6_19,B_6_8+B_6_20,B_6_13+B_6_21,B_6_14+B_6_22,B_6_15+B_6_23,B_6_12+B_6_24],[B_7_1+B_7_9,B_7_2+B_7_10,B_7_3+B_7_11,B_7_4+B_7_16,B_7_5+B_7_17,B_7_6+B_7_18,B_7_7+B_7_19,B_7_8+B_7_20,B_7_13+B_7_21,B_7_14+B_7_22,B_7_15+B_7_23,B_7_12+B_7_24],[B_8_1+B_8_9,B_8_2+B_8_10,B_8_3+B_8_11,B_8_4+B_8_16,B_8_5+B_8_17,B_8_6+B_8_18,B_8_7+B_8_19,B_8_8+B_8_20,B_8_13+B_8_21,B_8_14+B_8_22,B_8_15+B_8_23,B_8_12+B_8_24],[B_13_1+B_13_9,B_13_2+B_13_10,B_13_3+B_13_11,B_13_4+B_13_16,B_13_5+B_13_17,B_13_6+B_13_18,B_13_7+B_13_19,B_13_8+B_13_20,B_13_13+B_13_21,B_13_14+B_13_22,B_13_15+B_13_23,B_13_12+B_13_24],[B_14_1+B_14_9,B_14_2+B_14_10,B_14_3+B_14_11,B_14_4+B_14_16,B_14_5+B_14_17,B_14_6+B_14_18,B_14_7+B_14_19,B_14_8+B_14_20,B_14_13+B_14_21,B_14_14+B_14_22,B_14_15+B_14_23,B_14_12+B_14_24],[B_15_1+B_15_9,B_15_2+B_15_10,B_15_3+B_15_11,B_15_4+B_15_16,B_15_5+B_15_17,B_15_6+B_15_18,B_15_7+B_15_19,B_15_8+B_15_20,B_15_13+B_15_21,B_15_14+B_15_22,B_15_15+B_15_23,B_15_12+B_15_24],[B_16_1+B_16_9,B_16_2+B_16_10,B_16_3+B_16_11,B_16_4+B_16_16,B_16_5+B_16_17,B_16_6+B_16_18,B_16_7+B_16_19,B_16_8+B_16_20,B_16_13+B_16_21,B_16_14+B_16_22,B_16_15+B_16_23,B_16_12+B_16_24],[B_17_1+B_17_9,B_17_2+B_17_10,B_17_3+B_17_11,B_17_4+B_17_16,B_17_5+B_17_17,B_17_6+B_17_18,B_17_7+B_17_19,B_17_8+B_17_20,B_17_13+B_17_21,B_17_14+B_17_22,B_17_15+B_17_23,B_17_12+B_17_24],[B_18_1+B_18_9,B_18_2+B_18_10,B_18_3+B_18_11,B_18_4+B_18_16,B_18_5+B_18_17,B_18_6+B_18_18,B_18_7+B_18_19,B_18_8+B_18_20,B_18_13+B_18_21,B_18_14+B_18_22,B_18_15+B_18_23,B_18_12+B_18_24],[B_19_1+B_19_9,B_19_2+B_19_10,B_19_3+B_19_11,B_19_4+B_19_16,B_19_5+B_19_17,B_19_6+B_19_18,B_19_7+B_19_19,B_19_8+B_19_20,B_19_13+B_19_21,B_19_14+B_19_22,B_19_15+B_19_23,B_19_12+B_19_24],[B_20_1+B_20_9,B_20_2+B_20_10,B_20_3+B_20_11,B_20_4+B_20_16,B_20_5+B_20_17,B_20_6+B_20_18,B_20_7+B_20_19,B_20_8+B_20_20,B_20_13+B_20_21,B_20_14+B_20_22,B_20_15+B_20_23,B_20_12+B_20_24],[B_21_1+B_21_9,B_21_2+B_21_10,B_21_3+B_21_11,B_21_4+B_21_16,B_21_5+B_21_17,B_21_6+B_21_18,B_21_7+B_21_19,B_21_8+B_21_20,B_21_13+B_21_21,B_21_14+B_21_22,B_21_15+B_21_23,B_21_12+B_21_24]]),Matrix(12, 4, [[C_1_2,C_1_3,C_1_4,C_1_1],[C_2_2,C_2_3,C_2_4,C_2_1],[C_3_2,C_3_3,C_3_4,C_3_1],[C_4_2,C_4_3,C_4_4,C_4_1],[C_5_2,C_5_3,C_5_4,C_5_1],[C_6_2,C_6_3,C_6_4,C_6_1],[C_7_2,C_7_3,C_7_4,C_7_1],[C_8_2,C_8_3,C_8_4,C_8_1],[C_13_2,C_13_3,C_13_4,C_13_1],[C_14_2,C_14_3,C_14_4,C_14_1],[C_15_2,C_15_3,C_15_4,C_15_1],[C_12_2,C_12_3,C_12_4,C_12_1]])))+Trace(Mul(Matrix(9, 9, [[A_5_1,A_5_2,A_5_3,A_5_4,A_5_5,A_5_10,A_5_11,A_5_12,A_5_9],[A_6_1,A_6_2,A_6_3,A_6_4,A_6_5,A_6_10,A_6_11,A_6_12,A_6_9],[A_7_1,A_7_2,A_7_3,A_7_4,A_7_5,A_7_10,A_7_11,A_7_12,A_7_9],[A_8_1,A_8_2,A_8_3,A_8_4,A_8_5,A_8_10,A_8_11,A_8_12,A_8_9],[A_9_1,A_9_2,A_9_3,A_9_4,A_9_5,A_9_10,A_9_11,A_9_12,A_9_9],[-A_2_1+A_10_1,-A_2_2+A_10_2,-A_2_3+A_10_3,-A_2_4+A_10_4,-A_2_5+A_10_5,-A_2_10+A_10_10,-A_2_11+A_10_11,-A_2_12+A_10_12,-A_2_9+A_10_9],[-A_3_1+A_11_1,-A_3_2+A_11_2,-A_3_3+A_11_3,-A_3_4+A_11_4,-A_3_5+A_11_5,-A_3_10+A_11_10,-A_3_11+A_11_11,-A_3_12+A_11_12,-A_3_9+A_11_9],[-A_4_1+A_12_1,-A_4_2+A_12_2,-A_4_3+A_12_3,-A_4_4+A_12_4,-A_4_5+A_12_5,-A_4_10+A_12_10,-A_4_11+A_12_11,-A_4_12+A_12_12,-A_4_9+A_12_9],[-A_1_1+A_13_1,-A_1_2+A_13_2,-A_1_3+A_13_3,-A_1_4+A_13_4,-A_1_5+A_13_5,-A_1_10+A_13_10,-A_1_11+A_13_11,-A_1_12+A_13_12,-A_1_9+A_13_9]]),Matrix(9, 12, [[B_1_1+B_1_9,B_1_2+B_1_10,B_1_3+B_1_11,B_1_4+B_1_16,B_1_5+B_1_17,B_1_6+B_1_18,B_1_7+B_1_19,B_1_8+B_1_20,B_1_13+B_1_21,B_1_14+B_1_22,B_1_15+B_1_23,B_1_12+B_1_24],[B_2_1+B_2_9,B_2_2+B_2_10,B_2_3+B_2_11,B_2_4+B_2_16,B_2_5+B_2_17,B_2_6+B_2_18,B_2_7+B_2_19,B_2_8+B_2_20,B_2_13+B_2_21,B_2_14+B_2_22,B_2_15+B_2_23,B_2_12+B_2_24],[B_3_1+B_3_9,B_3_2+B_3_10,B_3_3+B_3_11,B_3_4+B_3_16,B_3_5+B_3_17,B_3_6+B_3_18,B_3_7+B_3_19,B_3_8+B_3_20,B_3_13+B_3_21,B_3_14+B_3_22,B_3_15+B_3_23,B_3_12+B_3_24],[B_4_1+B_4_9,B_4_2+B_4_10,B_4_3+B_4_11,B_4_4+B_4_16,B_4_5+B_4_17,B_4_6+B_4_18,B_4_7+B_4_19,B_4_8+B_4_20,B_4_13+B_4_21,B_4_14+B_4_22,B_4_15+B_4_23,B_4_12+B_4_24],[B_5_1+B_5_9,B_5_2+B_5_10,B_5_3+B_5_11,B_5_4+B_5_16,B_5_5+B_5_17,B_5_6+B_5_18,B_5_7+B_5_19,B_5_8+B_5_20,B_5_13+B_5_21,B_5_14+B_5_22,B_5_15+B_5_23,B_5_12+B_5_24],[B_10_1+B_10_9,B_10_2+B_10_10,B_10_3+B_10_11,B_10_4+B_10_16,B_10_5+B_10_17,B_10_6+B_10_18,B_10_7+B_10_19,B_10_8+B_10_20,B_10_13+B_10_21,B_10_14+B_10_22,B_10_15+B_10_23,B_10_12+B_10_24],[B_11_1+B_11_9,B_11_2+B_11_10,B_11_3+B_11_11,B_11_4+B_11_16,B_11_5+B_11_17,B_11_6+B_11_18,B_11_7+B_11_19,B_11_8+B_11_20,B_11_13+B_11_21,B_11_14+B_11_22,B_11_15+B_11_23,B_11_12+B_11_24],[B_12_1+B_12_9,B_12_2+B_12_10,B_12_3+B_12_11,B_12_4+B_12_16,B_12_5+B_12_17,B_12_6+B_12_18,B_12_7+B_12_19,B_12_8+B_12_20,B_12_13+B_12_21,B_12_14+B_12_22,B_12_15+B_12_23,B_12_12+B_12_24],[B_9_1+B_9_9,B_9_2+B_9_10,B_9_3+B_9_11,B_9_4+B_9_16,B_9_5+B_9_17,B_9_6+B_9_18,B_9_7+B_9_19,B_9_8+B_9_20,B_9_13+B_9_21,B_9_14+B_9_22,B_9_15+B_9_23,B_9_12+B_9_24]]),Matrix(12, 9, [[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_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_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_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_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_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_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_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_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_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_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_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]])))+Trace(Mul(Matrix(4, 12, [[A_2_6,A_2_7,A_2_8,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_10+A_2_18,A_2_11+A_2_19,A_2_12+A_2_20,A_2_9+A_2_21],[A_3_6,A_3_7,A_3_8,A_3_1+A_3_13,A_3_2+A_3_14,A_3_3+A_3_15,A_3_4+A_3_16,A_3_5+A_3_17,A_3_10+A_3_18,A_3_11+A_3_19,A_3_12+A_3_20,A_3_9+A_3_21],[A_4_6,A_4_7,A_4_8,A_4_1+A_4_13,A_4_2+A_4_14,A_4_3+A_4_15,A_4_4+A_4_16,A_4_5+A_4_17,A_4_10+A_4_18,A_4_11+A_4_19,A_4_12+A_4_20,A_4_9+A_4_21],[A_1_6,A_1_7,A_1_8,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_10+A_1_18,A_1_11+A_1_19,A_1_12+A_1_20,A_1_9+A_1_21]]),Matrix(12, 12, [[B_6_9,B_6_10,B_6_11,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_9,B_7_10,B_7_11,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_9,B_8_10,B_8_11,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_13_9,B_13_10,B_13_11,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_9,B_14_10,B_14_11,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_9,B_15_10,B_15_11,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_9,B_16_10,B_16_11,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_9,B_17_10,B_17_11,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_9,B_18_10,B_18_11,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_9,B_19_10,B_19_11,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_9,B_20_10,B_20_11,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_9,B_21_10,B_21_11,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]]),Matrix(12, 4, [[-C_1_2+C_9_2,-C_1_3+C_9_3,-C_1_4+C_9_4,-C_1_1+C_9_1],[-C_2_2+C_10_2,-C_2_3+C_10_3,-C_2_4+C_10_4,-C_2_1+C_10_1],[-C_3_2+C_11_2,-C_3_3+C_11_3,-C_3_4+C_11_4,-C_3_1+C_11_1],[-C_4_2+C_16_2,-C_4_3+C_16_3,-C_4_4+C_16_4,-C_4_1+C_16_1],[-C_5_2+C_17_2,-C_5_3+C_17_3,-C_5_4+C_17_4,-C_5_1+C_17_1],[-C_6_2+C_18_2,-C_6_3+C_18_3,-C_6_4+C_18_4,-C_6_1+C_18_1],[-C_7_2+C_19_2,-C_7_3+C_19_3,-C_7_4+C_19_4,-C_7_1+C_19_1],[-C_8_2+C_20_2,-C_8_3+C_20_3,-C_8_4+C_20_4,-C_8_1+C_20_1],[-C_13_2+C_21_2,-C_13_3+C_21_3,-C_13_4+C_21_4,-C_13_1+C_21_1],[-C_14_2+C_22_2,-C_14_3+C_22_3,-C_14_4+C_22_4,-C_14_1+C_22_1],[-C_15_2+C_23_2,-C_15_3+C_23_3,-C_15_4+C_23_4,-C_15_1+C_23_1],[-C_12_2+C_24_2,-C_12_3+C_24_3,-C_12_4+C_24_4,-C_12_1+C_24_1]])))+Trace(Mul(Matrix(4, 9, [[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_10,A_2_11,A_2_12,A_2_9],[A_3_1,A_3_2,A_3_3,A_3_4,A_3_5,A_3_10,A_3_11,A_3_12,A_3_9],[A_4_1,A_4_2,A_4_3,A_4_4,A_4_5,A_4_10,A_4_11,A_4_12,A_4_9],[A_1_1,A_1_2,A_1_3,A_1_4,A_1_5,A_1_10,A_1_11,A_1_12,A_1_9]]),Matrix(9, 12, [[B_1_9-B_13_9,B_1_10-B_13_10,B_1_11-B_13_11,B_1_16-B_13_16,B_1_17-B_13_17,B_1_18-B_13_18,B_1_19-B_13_19,B_1_20-B_13_20,B_1_21-B_13_21,B_1_22-B_13_22,B_1_23-B_13_23,B_1_24-B_13_24],[B_2_9-B_14_9,B_2_10-B_14_10,B_2_11-B_14_11,B_2_16-B_14_16,B_2_17-B_14_17,B_2_18-B_14_18,B_2_19-B_14_19,B_2_20-B_14_20,B_2_21-B_14_21,B_2_22-B_14_22,B_2_23-B_14_23,B_2_24-B_14_24],[B_3_9-B_15_9,B_3_10-B_15_10,B_3_11-B_15_11,B_3_16-B_15_16,B_3_17-B_15_17,B_3_18-B_15_18,B_3_19-B_15_19,B_3_20-B_15_20,B_3_21-B_15_21,B_3_22-B_15_22,B_3_23-B_15_23,B_3_24-B_15_24],[B_4_9-B_16_9,B_4_10-B_16_10,B_4_11-B_16_11,B_4_16-B_16_16,B_4_17-B_16_17,B_4_18-B_16_18,B_4_19-B_16_19,B_4_20-B_16_20,B_4_21-B_16_21,B_4_22-B_16_22,B_4_23-B_16_23,B_4_24-B_16_24],[B_5_9-B_17_9,B_5_10-B_17_10,B_5_11-B_17_11,B_5_16-B_17_16,B_5_17-B_17_17,B_5_18-B_17_18,B_5_19-B_17_19,B_5_20-B_17_20,B_5_21-B_17_21,B_5_22-B_17_22,B_5_23-B_17_23,B_5_24-B_17_24],[B_10_9-B_18_9,B_10_10-B_18_10,B_10_11-B_18_11,B_10_16-B_18_16,B_10_17-B_18_17,B_10_18-B_18_18,B_10_19-B_18_19,B_10_20-B_18_20,B_10_21-B_18_21,B_10_22-B_18_22,B_10_23-B_18_23,B_10_24-B_18_24],[B_11_9-B_19_9,B_11_10-B_19_10,B_11_11-B_19_11,B_11_16-B_19_16,B_11_17-B_19_17,B_11_18-B_19_18,B_11_19-B_19_19,B_11_20-B_19_20,B_11_21-B_19_21,B_11_22-B_19_22,B_11_23-B_19_23,B_11_24-B_19_24],[B_12_9-B_20_9,B_12_10-B_20_10,B_12_11-B_20_11,B_12_16-B_20_16,B_12_17-B_20_17,B_12_18-B_20_18,B_12_19-B_20_19,B_12_20-B_20_20,B_12_21-B_20_21,B_12_22-B_20_22,B_12_23-B_20_23,B_12_24-B_20_24],[B_9_9-B_21_9,B_9_10-B_21_10,B_9_11-B_21_11,B_9_16-B_21_16,B_9_17-B_21_17,B_9_18-B_21_18,B_9_19-B_21_19,B_9_20-B_21_20,B_9_21-B_21_21,B_9_22-B_21_22,B_9_23-B_21_23,B_9_24-B_21_24]]),Matrix(12, 4, [[C_9_2+C_9_10,C_9_3+C_9_11,C_9_4+C_9_12,C_9_1+C_9_13],[C_10_2+C_10_10,C_10_3+C_10_11,C_10_4+C_10_12,C_10_1+C_10_13],[C_11_2+C_11_10,C_11_3+C_11_11,C_11_4+C_11_12,C_11_1+C_11_13],[C_16_2+C_16_10,C_16_3+C_16_11,C_16_4+C_16_12,C_16_1+C_16_13],[C_17_2+C_17_10,C_17_3+C_17_11,C_17_4+C_17_12,C_17_1+C_17_13],[C_18_2+C_18_10,C_18_3+C_18_11,C_18_4+C_18_12,C_18_1+C_18_13],[C_19_2+C_19_10,C_19_3+C_19_11,C_19_4+C_19_12,C_19_1+C_19_13],[C_20_2+C_20_10,C_20_3+C_20_11,C_20_4+C_20_12,C_20_1+C_20_13],[C_21_2+C_21_10,C_21_3+C_21_11,C_21_4+C_21_12,C_21_1+C_21_13],[C_22_2+C_22_10,C_22_3+C_22_11,C_22_4+C_22_12,C_22_1+C_22_13],[C_23_2+C_23_10,C_23_3+C_23_11,C_23_4+C_23_12,C_23_1+C_23_13],[C_24_2+C_24_10,C_24_3+C_24_11,C_24_4+C_24_12,C_24_1+C_24_13]])))+Trace(Mul(Matrix(9, 12, [[A_5_6,A_5_7,A_5_8,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_6_6,A_6_7,A_6_8,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_7_6,A_7_7,A_7_8,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_8_6,A_8_7,A_8_8,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_9_6,A_9_7,A_9_8,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_10_6,A_10_7,A_10_8,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_11_6,A_11_7,A_11_8,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_12_6,A_12_7,A_12_8,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_13_6,A_13_7,A_13_8,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]]),Matrix(12, 12, [[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_13,B_6_14,B_6_15,B_6_12],[B_7_1,B_7_2,B_7_3,B_7_4,B_7_5,B_7_6,B_7_7,B_7_8,B_7_13,B_7_14,B_7_15,B_7_12],[B_8_1,B_8_2,B_8_3,B_8_4,B_8_5,B_8_6,B_8_7,B_8_8,B_8_13,B_8_14,B_8_15,B_8_12],[-B_1_1+B_13_1,-B_1_2+B_13_2,-B_1_3+B_13_3,-B_1_4+B_13_4,-B_1_5+B_13_5,-B_1_6+B_13_6,-B_1_7+B_13_7,-B_1_8+B_13_8,-B_1_13+B_13_13,-B_1_14+B_13_14,-B_1_15+B_13_15,-B_1_12+B_13_12],[-B_2_1+B_14_1,-B_2_2+B_14_2,-B_2_3+B_14_3,-B_2_4+B_14_4,-B_2_5+B_14_5,-B_2_6+B_14_6,-B_2_7+B_14_7,-B_2_8+B_14_8,-B_2_13+B_14_13,-B_2_14+B_14_14,-B_2_15+B_14_15,-B_2_12+B_14_12],[-B_3_1+B_15_1,-B_3_2+B_15_2,-B_3_3+B_15_3,-B_3_4+B_15_4,-B_3_5+B_15_5,-B_3_6+B_15_6,-B_3_7+B_15_7,-B_3_8+B_15_8,-B_3_13+B_15_13,-B_3_14+B_15_14,-B_3_15+B_15_15,-B_3_12+B_15_12],[-B_4_1+B_16_1,-B_4_2+B_16_2,-B_4_3+B_16_3,-B_4_4+B_16_4,-B_4_5+B_16_5,-B_4_6+B_16_6,-B_4_7+B_16_7,-B_4_8+B_16_8,-B_4_13+B_16_13,-B_4_14+B_16_14,-B_4_15+B_16_15,-B_4_12+B_16_12],[-B_5_1+B_17_1,-B_5_2+B_17_2,-B_5_3+B_17_3,-B_5_4+B_17_4,-B_5_5+B_17_5,-B_5_6+B_17_6,-B_5_7+B_17_7,-B_5_8+B_17_8,-B_5_13+B_17_13,-B_5_14+B_17_14,-B_5_15+B_17_15,-B_5_12+B_17_12],[-B_10_1+B_18_1,-B_10_2+B_18_2,-B_10_3+B_18_3,-B_10_4+B_18_4,-B_10_5+B_18_5,-B_10_6+B_18_6,-B_10_7+B_18_7,-B_10_8+B_18_8,-B_10_13+B_18_13,-B_10_14+B_18_14,-B_10_15+B_18_15,-B_10_12+B_18_12],[-B_11_1+B_19_1,-B_11_2+B_19_2,-B_11_3+B_19_3,-B_11_4+B_19_4,-B_11_5+B_19_5,-B_11_6+B_19_6,-B_11_7+B_19_7,-B_11_8+B_19_8,-B_11_13+B_19_13,-B_11_14+B_19_14,-B_11_15+B_19_15,-B_11_12+B_19_12],[-B_12_1+B_20_1,-B_12_2+B_20_2,-B_12_3+B_20_3,-B_12_4+B_20_4,-B_12_5+B_20_5,-B_12_6+B_20_6,-B_12_7+B_20_7,-B_12_8+B_20_8,-B_12_13+B_20_13,-B_12_14+B_20_14,-B_12_15+B_20_15,-B_12_12+B_20_12],[-B_9_1+B_21_1,-B_9_2+B_21_2,-B_9_3+B_21_3,-B_9_4+B_21_4,-B_9_5+B_21_5,-B_9_6+B_21_6,-B_9_7+B_21_7,-B_9_8+B_21_8,-B_9_13+B_21_13,-B_9_14+B_21_14,-B_9_15+B_21_15,-B_9_12+B_21_12]]),Matrix(12, 9, [[C_1_5,C_1_6,C_1_7,C_1_8,C_1_9,C_1_2+C_1_10,C_1_3+C_1_11,C_1_4+C_1_12,C_1_1+C_1_13],[C_2_5,C_2_6,C_2_7,C_2_8,C_2_9,C_2_2+C_2_10,C_2_3+C_2_11,C_2_4+C_2_12,C_2_1+C_2_13],[C_3_5,C_3_6,C_3_7,C_3_8,C_3_9,C_3_2+C_3_10,C_3_3+C_3_11,C_3_4+C_3_12,C_3_1+C_3_13],[C_4_5,C_4_6,C_4_7,C_4_8,C_4_9,C_4_2+C_4_10,C_4_3+C_4_11,C_4_4+C_4_12,C_4_1+C_4_13],[C_5_5,C_5_6,C_5_7,C_5_8,C_5_9,C_5_2+C_5_10,C_5_3+C_5_11,C_5_4+C_5_12,C_5_1+C_5_13],[C_6_5,C_6_6,C_6_7,C_6_8,C_6_9,C_6_2+C_6_10,C_6_3+C_6_11,C_6_4+C_6_12,C_6_1+C_6_13],[C_7_5,C_7_6,C_7_7,C_7_8,C_7_9,C_7_2+C_7_10,C_7_3+C_7_11,C_7_4+C_7_12,C_7_1+C_7_13],[C_8_5,C_8_6,C_8_7,C_8_8,C_8_9,C_8_2+C_8_10,C_8_3+C_8_11,C_8_4+C_8_12,C_8_1+C_8_13],[C_13_5,C_13_6,C_13_7,C_13_8,C_13_9,C_13_2+C_13_10,C_13_3+C_13_11,C_13_4+C_13_12,C_13_1+C_13_13],[C_14_5,C_14_6,C_14_7,C_14_8,C_14_9,C_14_2+C_14_10,C_14_3+C_14_11,C_14_4+C_14_12,C_14_1+C_14_13],[C_15_5,C_15_6,C_15_7,C_15_8,C_15_9,C_15_2+C_15_10,C_15_3+C_15_11,C_15_4+C_15_12,C_15_1+C_15_13],[C_12_5,C_12_6,C_12_7,C_12_8,C_12_9,C_12_2+C_12_10,C_12_3+C_12_11,C_12_4+C_12_12,C_12_1+C_12_13]])))+Trace(Mul(Matrix(9, 9, [[A_5_1+A_5_13,A_5_2+A_5_14,A_5_3+A_5_15,A_5_4+A_5_16,A_5_5+A_5_17,A_5_10+A_5_18,A_5_11+A_5_19,A_5_12+A_5_20,A_5_9+A_5_21],[A_6_1+A_6_13,A_6_2+A_6_14,A_6_3+A_6_15,A_6_4+A_6_16,A_6_5+A_6_17,A_6_10+A_6_18,A_6_11+A_6_19,A_6_12+A_6_20,A_6_9+A_6_21],[A_7_1+A_7_13,A_7_2+A_7_14,A_7_3+A_7_15,A_7_4+A_7_16,A_7_5+A_7_17,A_7_10+A_7_18,A_7_11+A_7_19,A_7_12+A_7_20,A_7_9+A_7_21],[A_8_1+A_8_13,A_8_2+A_8_14,A_8_3+A_8_15,A_8_4+A_8_16,A_8_5+A_8_17,A_8_10+A_8_18,A_8_11+A_8_19,A_8_12+A_8_20,A_8_9+A_8_21],[A_9_1+A_9_13,A_9_2+A_9_14,A_9_3+A_9_15,A_9_4+A_9_16,A_9_5+A_9_17,A_9_10+A_9_18,A_9_11+A_9_19,A_9_12+A_9_20,A_9_9+A_9_21],[A_10_1+A_10_13,A_10_2+A_10_14,A_10_3+A_10_15,A_10_4+A_10_16,A_10_5+A_10_17,A_10_10+A_10_18,A_10_11+A_10_19,A_10_12+A_10_20,A_10_9+A_10_21],[A_11_1+A_11_13,A_11_2+A_11_14,A_11_3+A_11_15,A_11_4+A_11_16,A_11_5+A_11_17,A_11_10+A_11_18,A_11_11+A_11_19,A_11_12+A_11_20,A_11_9+A_11_21],[A_12_1+A_12_13,A_12_2+A_12_14,A_12_3+A_12_15,A_12_4+A_12_16,A_12_5+A_12_17,A_12_10+A_12_18,A_12_11+A_12_19,A_12_12+A_12_20,A_12_9+A_12_21],[A_13_1+A_13_13,A_13_2+A_13_14,A_13_3+A_13_15,A_13_4+A_13_16,A_13_5+A_13_17,A_13_10+A_13_18,A_13_11+A_13_19,A_13_12+A_13_20,A_13_9+A_13_21]]),Matrix(9, 12, [[B_1_1,B_1_2,B_1_3,B_1_4,B_1_5,B_1_6,B_1_7,B_1_8,B_1_13,B_1_14,B_1_15,B_1_12],[B_2_1,B_2_2,B_2_3,B_2_4,B_2_5,B_2_6,B_2_7,B_2_8,B_2_13,B_2_14,B_2_15,B_2_12],[B_3_1,B_3_2,B_3_3,B_3_4,B_3_5,B_3_6,B_3_7,B_3_8,B_3_13,B_3_14,B_3_15,B_3_12],[B_4_1,B_4_2,B_4_3,B_4_4,B_4_5,B_4_6,B_4_7,B_4_8,B_4_13,B_4_14,B_4_15,B_4_12],[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_13,B_5_14,B_5_15,B_5_12],[B_10_1,B_10_2,B_10_3,B_10_4,B_10_5,B_10_6,B_10_7,B_10_8,B_10_13,B_10_14,B_10_15,B_10_12],[B_11_1,B_11_2,B_11_3,B_11_4,B_11_5,B_11_6,B_11_7,B_11_8,B_11_13,B_11_14,B_11_15,B_11_12],[B_12_1,B_12_2,B_12_3,B_12_4,B_12_5,B_12_6,B_12_7,B_12_8,B_12_13,B_12_14,B_12_15,B_12_12],[B_9_1,B_9_2,B_9_3,B_9_4,B_9_5,B_9_6,B_9_7,B_9_8,B_9_13,B_9_14,B_9_15,B_9_12]]),Matrix(12, 9, [[C_1_5-C_9_5,C_1_6-C_9_6,C_1_7-C_9_7,C_1_8-C_9_8,C_1_9-C_9_9,C_1_10-C_9_10,C_1_11-C_9_11,C_1_12-C_9_12,C_1_13-C_9_13],[C_2_5-C_10_5,C_2_6-C_10_6,C_2_7-C_10_7,C_2_8-C_10_8,C_2_9-C_10_9,C_2_10-C_10_10,C_2_11-C_10_11,C_2_12-C_10_12,C_2_13-C_10_13],[C_3_5-C_11_5,C_3_6-C_11_6,C_3_7-C_11_7,C_3_8-C_11_8,C_3_9-C_11_9,C_3_10-C_11_10,C_3_11-C_11_11,C_3_12-C_11_12,C_3_13-C_11_13],[C_4_5-C_16_5,C_4_6-C_16_6,C_4_7-C_16_7,C_4_8-C_16_8,C_4_9-C_16_9,C_4_10-C_16_10,C_4_11-C_16_11,C_4_12-C_16_12,C_4_13-C_16_13],[C_5_5-C_17_5,C_5_6-C_17_6,C_5_7-C_17_7,C_5_8-C_17_8,C_5_9-C_17_9,C_5_10-C_17_10,C_5_11-C_17_11,C_5_12-C_17_12,C_5_13-C_17_13],[C_6_5-C_18_5,C_6_6-C_18_6,C_6_7-C_18_7,C_6_8-C_18_8,C_6_9-C_18_9,C_6_10-C_18_10,C_6_11-C_18_11,C_6_12-C_18_12,C_6_13-C_18_13],[C_7_5-C_19_5,C_7_6-C_19_6,C_7_7-C_19_7,C_7_8-C_19_8,C_7_9-C_19_9,C_7_10-C_19_10,C_7_11-C_19_11,C_7_12-C_19_12,C_7_13-C_19_13],[C_8_5-C_20_5,C_8_6-C_20_6,C_8_7-C_20_7,C_8_8-C_20_8,C_8_9-C_20_9,C_8_10-C_20_10,C_8_11-C_20_11,C_8_12-C_20_12,C_8_13-C_20_13],[C_13_5-C_21_5,C_13_6-C_21_6,C_13_7-C_21_7,C_13_8-C_21_8,C_13_9-C_21_9,C_13_10-C_21_10,C_13_11-C_21_11,C_13_12-C_21_12,C_13_13-C_21_13],[C_14_5-C_22_5,C_14_6-C_22_6,C_14_7-C_22_7,C_14_8-C_22_8,C_14_9-C_22_9,C_14_10-C_22_10,C_14_11-C_22_11,C_14_12-C_22_12,C_14_13-C_22_13],[C_15_5-C_23_5,C_15_6-C_23_6,C_15_7-C_23_7,C_15_8-C_23_8,C_15_9-C_23_9,C_15_10-C_23_10,C_15_11-C_23_11,C_15_12-C_23_12,C_15_13-C_23_13],[C_12_5-C_24_5,C_12_6-C_24_6,C_12_7-C_24_7,C_12_8-C_24_8,C_12_9-C_24_9,C_12_10-C_24_10,C_12_11-C_24_11,C_12_12-C_24_12,C_12_13-C_24_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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