Description of fast matrix multiplication algorithm: ⟨5×18×19:1140⟩

Algorithm type

32X4Y6Z5+32X5Y5Z4+2X4Y6Z4+48X2Y6Z5+48X5Y5Z2+8X4Y4Z4+2X3Y6Z3+64X2Y6Z3+XY9Z+16X3Y5Z2+20X3Y4Z3+3X2Y6Z2+2XY8Z+96XY6Z3+24X3Y5Z+2X2Y5Z2+5XY7Z+10X4Y2Z2+59X2Y4Z2+96X2Y3Z3+14XY6Z+10X3Y2Z2+11X2Y3Z2+6XY5Z+6XY4Z2+144XY3Z3+8X3Y2Z+71X2Y2Z2+49XY4Z+16X2Y2Z+22XY3Z+4XY2Z2+127XY2Z+82XYZ32X4Y6Z532X5Y5Z42X4Y6Z448X2Y6Z548X5Y5Z28X4Y4Z42X3Y6Z364X2Y6Z3XY9Z16X3Y5Z220X3Y4Z33X2Y6Z22XY8Z96XY6Z324X3Y5Z2X2Y5Z25XY7Z10X4Y2Z259X2Y4Z296X2Y3Z314XY6Z10X3Y2Z211X2Y3Z26XY5Z6XY4Z2144XY3Z38X3Y2Z71X2Y2Z249XY4Z16X2Y2Z22XY3Z4XY2Z2127XY2Z82XYZ32*X^4*Y^6*Z^5+32*X^5*Y^5*Z^4+2*X^4*Y^6*Z^4+48*X^2*Y^6*Z^5+48*X^5*Y^5*Z^2+8*X^4*Y^4*Z^4+2*X^3*Y^6*Z^3+64*X^2*Y^6*Z^3+X*Y^9*Z+16*X^3*Y^5*Z^2+20*X^3*Y^4*Z^3+3*X^2*Y^6*Z^2+2*X*Y^8*Z+96*X*Y^6*Z^3+24*X^3*Y^5*Z+2*X^2*Y^5*Z^2+5*X*Y^7*Z+10*X^4*Y^2*Z^2+59*X^2*Y^4*Z^2+96*X^2*Y^3*Z^3+14*X*Y^6*Z+10*X^3*Y^2*Z^2+11*X^2*Y^3*Z^2+6*X*Y^5*Z+6*X*Y^4*Z^2+144*X*Y^3*Z^3+8*X^3*Y^2*Z+71*X^2*Y^2*Z^2+49*X*Y^4*Z+16*X^2*Y^2*Z+22*X*Y^3*Z+4*X*Y^2*Z^2+127*X*Y^2*Z+82*X*Y*Z

Algorithm definition

The algorithm ⟨5×18×19:1140⟩ could be constructed using the following decomposition:

⟨5×18×19:1140⟩ = ⟨3×6×6:80⟩ + ⟨3×6×7:96⟩ + ⟨2×6×7:67⟩ + ⟨2×6×7:67⟩ + ⟨2×6×6:57⟩ + ⟨2×6×6:57⟩ + ⟨3×6×6:80⟩ + ⟨3×6×7:96⟩ + ⟨3×6×6:80⟩ + ⟨3×6×6:80⟩ + ⟨2×6×6:57⟩ + ⟨3×6×6:80⟩ + ⟨2×6×7:67⟩ + ⟨3×6×6:80⟩ + ⟨3×6×7:96⟩.

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_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_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_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_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_18B_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_19C_1_1C_1_2C_1_3C_1_4C_1_5C_2_1C_2_2C_2_3C_2_4C_2_5C_3_1C_3_2C_3_3C_3_4C_3_5C_4_1C_4_2C_4_3C_4_4C_4_5C_5_1C_5_2C_5_3C_5_4C_5_5C_6_1C_6_2C_6_3C_6_4C_6_5C_7_1C_7_2C_7_3C_7_4C_7_5C_8_1C_8_2C_8_3C_8_4C_8_5C_9_1C_9_2C_9_3C_9_4C_9_5C_10_1C_10_2C_10_3C_10_4C_10_5C_11_1C_11_2C_11_3C_11_4C_11_5C_12_1C_12_2C_12_3C_12_4C_12_5C_13_1C_13_2C_13_3C_13_4C_13_5C_14_1C_14_2C_14_3C_14_4C_14_5C_15_1C_15_2C_15_3C_15_4C_15_5C_16_1C_16_2C_16_3C_16_4C_16_5C_17_1C_17_2C_17_3C_17_4C_17_5C_18_1C_18_2C_18_3C_18_4C_18_5C_19_1C_19_2C_19_3C_19_4C_19_5=TraceMulA_3_13A_3_14A_3_15A_3_16A_3_17A_3_18A_4_13A_4_14A_4_15A_4_16A_4_17A_4_18A_5_13A_5_14A_5_15A_5_16A_5_17A_5_18B_1_6+B_13_6+B_13_7B_1_1+B_13_1+B_13_8B_1_2+B_13_2+B_13_9B_1_3+B_13_3+B_13_10B_1_4+B_13_4+B_13_11B_1_5+B_13_5+B_13_12B_2_6+B_14_6+B_14_7B_2_1+B_14_1+B_14_8B_2_2+B_14_2+B_14_9B_2_3+B_14_3+B_14_10B_2_4+B_14_4+B_14_11B_2_5+B_14_5+B_14_12B_3_6+B_15_6+B_15_7B_3_1+B_15_1+B_15_8B_3_2+B_15_2+B_15_9B_3_3+B_15_3+B_15_10B_3_4+B_15_4+B_15_11B_3_5+B_15_5+B_15_12B_4_6+B_16_6+B_16_7B_4_1+B_16_1+B_16_8B_4_2+B_16_2+B_16_9B_4_3+B_16_3+B_16_10B_4_4+B_16_4+B_16_11B_4_5+B_16_5+B_16_12B_5_6+B_17_6+B_17_7B_5_1+B_17_1+B_17_8B_5_2+B_17_2+B_17_9B_5_3+B_17_3+B_17_10B_5_4+B_17_4+B_17_11B_5_5+B_17_5+B_17_12B_6_6+B_18_6+B_18_7B_6_1+B_18_1+B_18_8B_6_2+B_18_2+B_18_9B_6_3+B_18_3+B_18_10B_6_4+B_18_4+B_18_11B_6_5+B_18_5+B_18_12C_6_3C_6_1+C_6_4C_6_2+C_6_5C_1_3C_1_1+C_1_4C_1_2+C_1_5C_2_3C_2_1+C_2_4C_2_2+C_2_5C_3_3C_3_1+C_3_4C_3_2+C_3_5C_4_3C_4_1+C_4_4C_4_2+C_4_5C_5_3C_5_1+C_5_4C_5_2+C_5_5+TraceMul-A_3_13-A_3_14-A_3_15-A_3_16-A_3_17-A_3_18A_1_1-A_4_13A_1_2-A_4_14A_1_3-A_4_15A_1_4-A_4_16A_1_5-A_4_17A_1_6-A_4_18A_2_1-A_5_13A_2_2-A_5_14A_2_3-A_5_15A_2_4-A_5_16A_2_5-A_5_17A_2_6-A_5_18B_13_13B_1_6+B_13_14B_1_1+B_13_15B_1_2+B_13_16B_1_3+B_13_17B_1_4+B_13_18B_1_5+B_13_19B_14_13B_2_6+B_14_14B_2_1+B_14_15B_2_2+B_14_16B_2_3+B_14_17B_2_4+B_14_18B_2_5+B_14_19B_15_13B_3_6+B_15_14B_3_1+B_15_15B_3_2+B_15_16B_3_3+B_15_17B_3_4+B_15_18B_3_5+B_15_19B_16_13B_4_6+B_16_14B_4_1+B_16_15B_4_2+B_16_16B_4_3+B_16_17B_4_4+B_16_18B_4_5+B_16_19B_17_13B_5_6+B_17_14B_5_1+B_17_15B_5_2+B_17_16B_5_3+B_17_17B_5_4+B_17_18B_5_5+B_17_19B_18_13B_6_6+B_18_14B_6_1+B_18_15B_6_2+B_18_16B_6_3+B_18_17B_6_4+B_18_18B_6_5+B_18_19-C_13_3-C_13_4-C_13_5-C_14_3C_6_1-C_14_4C_6_2-C_14_5-C_15_3C_1_1-C_15_4C_1_2-C_15_5-C_16_3C_2_1-C_16_4C_2_2-C_16_5-C_17_3C_3_1-C_17_4C_3_2-C_17_5-C_18_3C_4_1-C_18_4C_4_2-C_18_5-C_19_3C_5_1-C_19_4C_5_2-C_19_5+TraceMulA_1_1A_1_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A_3_3A_3_15A_3_4A_3_16A_3_5A_3_17A_3_6A_3_18A_4_1A_4_13A_4_2A_4_14A_4_3A_4_15A_4_4A_4_16A_4_5A_4_17A_4_6A_4_18A_5_1A_5_13A_5_2A_5_14A_5_3A_5_15A_5_4A_5_16A_5_5A_5_17A_5_6A_5_18B_1_6B_1_1B_1_2B_1_3B_1_4B_1_5B_2_6B_2_1B_2_2B_2_3B_2_4B_2_5B_3_6B_3_1B_3_2B_3_3B_3_4B_3_5B_4_6B_4_1B_4_2B_4_3B_4_4B_4_5B_5_6B_5_1B_5_2B_5_3B_5_4B_5_5B_6_6B_6_1B_6_2B_6_3B_6_4B_6_5C_6_3C_14_3C_6_4C_14_4C_6_5C_14_5C_1_3C_15_3C_1_4C_15_4C_1_5C_15_5C_2_3C_16_3C_2_4C_16_4C_2_5C_16_5C_3_3C_17_3C_3_4C_17_4C_3_5C_17_5C_4_3C_18_3C_4_4C_18_4C_4_5C_18_5C_5_3C_19_3C_5_4C_19_4C_5_5C_19_5TraceMulA_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_1_1A_4_1A_1_2A_4_2A_1_3A_4_3A_1_4A_4_4A_1_5A_4_5A_1_6A_4_6A_2_1A_5_1A_2_2A_5_2A_2_3A_5_3A_2_4A_5_4A_2_5A_5_5A_2_6A_5_6B_1_13B_7_13B_1_6B_1_14B_7_14B_1_1B_1_15B_7_15B_1_2B_1_16B_7_16B_1_3B_1_17B_7_17B_1_4B_1_18B_7_18B_1_5B_1_19B_7_19B_2_13B_8_13B_2_6B_2_14B_8_14B_2_1B_2_15B_8_15B_2_2B_2_16B_8_16B_2_3B_2_17B_8_17B_2_4B_2_18B_8_18B_2_5B_2_19B_8_19B_3_13B_9_13B_3_6B_3_14B_9_14B_3_1B_3_15B_9_15B_3_2B_3_16B_9_16B_3_3B_3_17B_9_17B_3_4B_3_18B_9_18B_3_5B_3_19B_9_19B_4_13B_10_13B_4_6B_4_14B_10_14B_4_1B_4_15B_10_15B_4_2B_4_16B_10_16B_4_3B_4_17B_10_17B_4_4B_4_18B_10_18B_4_5B_4_19B_10_19B_5_13B_11_13B_5_6B_5_14B_11_14B_5_1B_5_15B_11_15B_5_2B_5_16B_11_16B_5_3B_5_17B_11_17B_5_4B_5_18B_11_18B_5_5B_5_19B_11_19B_6_13B_12_13B_6_6B_6_14B_12_14B_6_1B_6_15B_12_15B_6_2B_6_16B_12_16B_6_3B_6_17B_12_17B_6_4B_6_18B_12_18B_6_5B_6_19B_12_19C_13_3C_13_4C_13_5C_14_3C_14_4C_14_5C_15_3C_15_4C_15_5C_16_3C_16_4C_16_5C_17_3C_17_4C_17_5C_18_3C_18_4C_18_5C_19_3C_19_4C_19_5Trace(Mul(Matrix(5, 18, [[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_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_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_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_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]]),Matrix(18, 19, [[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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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]]),Matrix(19, 5, [[C_1_1,C_1_2,C_1_3,C_1_4,C_1_5],[C_2_1,C_2_2,C_2_3,C_2_4,C_2_5],[C_3_1,C_3_2,C_3_3,C_3_4,C_3_5],[C_4_1,C_4_2,C_4_3,C_4_4,C_4_5],[C_5_1,C_5_2,C_5_3,C_5_4,C_5_5],[C_6_1,C_6_2,C_6_3,C_6_4,C_6_5],[C_7_1,C_7_2,C_7_3,C_7_4,C_7_5],[C_8_1,C_8_2,C_8_3,C_8_4,C_8_5],[C_9_1,C_9_2,C_9_3,C_9_4,C_9_5],[C_10_1,C_10_2,C_10_3,C_10_4,C_10_5],[C_11_1,C_11_2,C_11_3,C_11_4,C_11_5],[C_12_1,C_12_2,C_12_3,C_12_4,C_12_5],[C_13_1,C_13_2,C_13_3,C_13_4,C_13_5],[C_14_1,C_14_2,C_14_3,C_14_4,C_14_5],[C_15_1,C_15_2,C_15_3,C_15_4,C_15_5],[C_16_1,C_16_2,C_16_3,C_16_4,C_16_5],[C_17_1,C_17_2,C_17_3,C_17_4,C_17_5],[C_18_1,C_18_2,C_18_3,C_18_4,C_18_5],[C_19_1,C_19_2,C_19_3,C_19_4,C_19_5]]))) = Trace(Mul(Matrix(3, 6, [[A_3_13,A_3_14,A_3_15,A_3_16,A_3_17,A_3_18],[A_4_13,A_4_14,A_4_15,A_4_16,A_4_17,A_4_18],[A_5_13,A_5_14,A_5_15,A_5_16,A_5_17,A_5_18]]),Matrix(6, 6, [[B_1_6+B_13_6+B_13_7,B_1_1+B_13_1+B_13_8,B_1_2+B_13_2+B_13_9,B_1_3+B_13_3+B_13_10,B_1_4+B_13_4+B_13_11,B_1_5+B_13_5+B_13_12],[B_2_6+B_14_6+B_14_7,B_2_1+B_14_1+B_14_8,B_2_2+B_14_2+B_14_9,B_2_3+B_14_3+B_14_10,B_2_4+B_14_4+B_14_11,B_2_5+B_14_5+B_14_12],[B_3_6+B_15_6+B_15_7,B_3_1+B_15_1+B_15_8,B_3_2+B_15_2+B_15_9,B_3_3+B_15_3+B_15_10,B_3_4+B_15_4+B_15_11,B_3_5+B_15_5+B_15_12],[B_4_6+B_16_6+B_16_7,B_4_1+B_16_1+B_16_8,B_4_2+B_16_2+B_16_9,B_4_3+B_16_3+B_16_10,B_4_4+B_16_4+B_16_11,B_4_5+B_16_5+B_16_12],[B_5_6+B_17_6+B_17_7,B_5_1+B_17_1+B_17_8,B_5_2+B_17_2+B_17_9,B_5_3+B_17_3+B_17_10,B_5_4+B_17_4+B_17_11,B_5_5+B_17_5+B_17_12],[B_6_6+B_18_6+B_18_7,B_6_1+B_18_1+B_18_8,B_6_2+B_18_2+B_18_9,B_6_3+B_18_3+B_18_10,B_6_4+B_18_4+B_18_11,B_6_5+B_18_5+B_18_12]]),Matrix(6, 3, [[C_6_3,C_6_1+C_6_4,C_6_2+C_6_5],[C_1_3,C_1_1+C_1_4,C_1_2+C_1_5],[C_2_3,C_2_1+C_2_4,C_2_2+C_2_5],[C_3_3,C_3_1+C_3_4,C_3_2+C_3_5],[C_4_3,C_4_1+C_4_4,C_4_2+C_4_5],[C_5_3,C_5_1+C_5_4,C_5_2+C_5_5]])))+Trace(Mul(Matrix(3, 6, [[-A_3_13,-A_3_14,-A_3_15,-A_3_16,-A_3_17,-A_3_18],[A_1_1-A_4_13,A_1_2-A_4_14,A_1_3-A_4_15,A_1_4-A_4_16,A_1_5-A_4_17,A_1_6-A_4_18],[A_2_1-A_5_13,A_2_2-A_5_14,A_2_3-A_5_15,A_2_4-A_5_16,A_2_5-A_5_17,A_2_6-A_5_18]]),Matrix(6, 7, [[B_13_13,B_1_6+B_13_14,B_1_1+B_13_15,B_1_2+B_13_16,B_1_3+B_13_17,B_1_4+B_13_18,B_1_5+B_13_19],[B_14_13,B_2_6+B_14_14,B_2_1+B_14_15,B_2_2+B_14_16,B_2_3+B_14_17,B_2_4+B_14_18,B_2_5+B_14_19],[B_15_13,B_3_6+B_15_14,B_3_1+B_15_15,B_3_2+B_15_16,B_3_3+B_15_17,B_3_4+B_15_18,B_3_5+B_15_19],[B_16_13,B_4_6+B_16_14,B_4_1+B_16_15,B_4_2+B_16_16,B_4_3+B_16_17,B_4_4+B_16_18,B_4_5+B_16_19],[B_17_13,B_5_6+B_17_14,B_5_1+B_17_15,B_5_2+B_17_16,B_5_3+B_17_17,B_5_4+B_17_18,B_5_5+B_17_19],[B_18_13,B_6_6+B_18_14,B_6_1+B_18_15,B_6_2+B_18_16,B_6_3+B_18_17,B_6_4+B_18_18,B_6_5+B_18_19]]),Matrix(7, 3, [[-C_13_3,-C_13_4,-C_13_5],[-C_14_3,C_6_1-C_14_4,C_6_2-C_14_5],[-C_15_3,C_1_1-C_15_4,C_1_2-C_15_5],[-C_16_3,C_2_1-C_16_4,C_2_2-C_16_5],[-C_17_3,C_3_1-C_17_4,C_3_2-C_17_5],[-C_18_3,C_4_1-C_18_4,C_4_2-C_18_5],[-C_19_3,C_5_1-C_19_4,C_5_2-C_19_5]])))+Trace(Mul(Matrix(2, 6, [[A_1_1,A_1_2,A_1_3,A_1_4,A_1_5,A_1_6],[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6]]),Matrix(6, 7, [[-B_1_13-B_13_13,B_1_7-B_1_14-B_13_14,B_1_8-B_1_15-B_13_15,B_1_9-B_1_16-B_13_16,B_1_10-B_1_17-B_13_17,B_1_11-B_1_18-B_13_18,B_1_12-B_1_19-B_13_19],[-B_2_13-B_14_13,B_2_7-B_2_14-B_14_14,B_2_8-B_2_15-B_14_15,B_2_9-B_2_16-B_14_16,B_2_10-B_2_17-B_14_17,B_2_11-B_2_18-B_14_18,B_2_12-B_2_19-B_14_19],[-B_3_13-B_15_13,B_3_7-B_3_14-B_15_14,B_3_8-B_3_15-B_15_15,B_3_9-B_3_16-B_15_16,B_3_10-B_3_17-B_15_17,B_3_11-B_3_18-B_15_18,B_3_12-B_3_19-B_15_19],[-B_4_13-B_16_13,B_4_7-B_4_14-B_16_14,B_4_8-B_4_15-B_16_15,B_4_9-B_4_16-B_16_16,B_4_10-B_4_17-B_16_17,B_4_11-B_4_18-B_16_18,B_4_12-B_4_19-B_16_19],[-B_5_13-B_17_13,B_5_7-B_5_14-B_17_14,B_5_8-B_5_15-B_17_15,B_5_9-B_5_16-B_17_16,B_5_10-B_5_17-B_17_17,B_5_11-B_5_18-B_17_18,B_5_12-B_5_19-B_17_19],[-B_6_13-B_18_13,B_6_7-B_6_14-B_18_14,B_6_8-B_6_15-B_18_15,B_6_9-B_6_16-B_18_16,B_6_10-B_6_17-B_18_17,B_6_11-B_6_18-B_18_18,B_6_12-B_6_19-B_18_19]]),Matrix(7, 2, [[-C_13_1-C_13_4,-C_13_2-C_13_5],[-C_14_1-C_14_4,-C_14_2-C_14_5],[-C_15_1-C_15_4,-C_15_2-C_15_5],[-C_16_1-C_16_4,-C_16_2-C_16_5],[-C_17_1-C_17_4,-C_17_2-C_17_5],[-C_18_1-C_18_4,-C_18_2-C_18_5],[-C_19_1-C_19_4,-C_19_2-C_19_5]])))+Trace(Mul(Matrix(2, 6, [[A_1_1-A_1_13,A_1_2-A_1_14,A_1_3-A_1_15,A_1_4-A_1_16,A_1_5-A_1_17,A_1_6-A_1_18],[A_2_1-A_2_13,A_2_2-A_2_14,A_2_3-A_2_15,A_2_4-A_2_16,A_2_5-A_2_17,A_2_6-A_2_18]]),Matrix(6, 7, [[B_13_13,B_13_14,B_13_15,B_13_16,B_13_17,B_13_18,B_13_19],[B_14_13,B_14_14,B_14_15,B_14_16,B_14_17,B_14_18,B_14_19],[B_15_13,B_15_14,B_15_15,B_15_16,B_15_17,B_15_18,B_15_19],[B_16_13,B_16_14,B_16_15,B_16_16,B_16_17,B_16_18,B_16_19],[B_17_13,B_17_14,B_17_15,B_17_16,B_17_17,B_17_18,B_17_19],[B_18_13,B_18_14,B_18_15,B_18_16,B_18_17,B_18_18,B_18_19]]),Matrix(7, 2, [[-C_13_1,-C_13_2],[-C_6_1-C_14_1,-C_6_2-C_14_2],[-C_1_1-C_15_1,-C_1_2-C_15_2],[-C_2_1-C_16_1,-C_2_2-C_16_2],[-C_3_1-C_17_1,-C_3_2-C_17_2],[-C_4_1-C_18_1,-C_4_2-C_18_2],[-C_5_1-C_19_1,-C_5_2-C_19_2]])))+Trace(Mul(Matrix(2, 6, [[A_1_13-A_4_13,A_1_14-A_4_14,A_1_15-A_4_15,A_1_16-A_4_16,A_1_17-A_4_17,A_1_18-A_4_18],[A_2_13-A_5_13,A_2_14-A_5_14,A_2_15-A_5_15,A_2_16-A_5_16,A_2_17-A_5_17,A_2_18-A_5_18]]),Matrix(6, 6, [[B_7_6+B_13_6-B_13_14,B_7_1+B_13_1-B_13_15,B_7_2+B_13_2-B_13_16,B_7_3+B_13_3-B_13_17,B_7_4+B_13_4-B_13_18,B_7_5+B_13_5-B_13_19],[B_8_6+B_14_6-B_14_14,B_8_1+B_14_1-B_14_15,B_8_2+B_14_2-B_14_16,B_8_3+B_14_3-B_14_17,B_8_4+B_14_4-B_14_18,B_8_5+B_14_5-B_14_19],[B_9_6+B_15_6-B_15_14,B_9_1+B_15_1-B_15_15,B_9_2+B_15_2-B_15_16,B_9_3+B_15_3-B_15_17,B_9_4+B_15_4-B_15_18,B_9_5+B_15_5-B_15_19],[B_10_6+B_16_6-B_16_14,B_10_1+B_16_1-B_16_15,B_10_2+B_16_2-B_16_16,B_10_3+B_16_3-B_16_17,B_10_4+B_16_4-B_16_18,B_10_5+B_16_5-B_16_19],[B_11_6+B_17_6-B_17_14,B_11_1+B_17_1-B_17_15,B_11_2+B_17_2-B_17_16,B_11_3+B_17_3-B_17_17,B_11_4+B_17_4-B_17_18,B_11_5+B_17_5-B_17_19],[B_12_6+B_18_6-B_18_14,B_12_1+B_18_1-B_18_15,B_12_2+B_18_2-B_18_16,B_12_3+B_18_3-B_18_17,B_12_4+B_18_4-B_18_18,B_12_5+B_18_5-B_18_19]]),Matrix(6, 2, [[C_6_1,C_6_2],[C_1_1,C_1_2],[C_2_1,C_2_2],[C_3_1,C_3_2],[C_4_1,C_4_2],[C_5_1,C_5_2]])))+Trace(Mul(Matrix(2, 6, [[A_1_7,A_1_8,A_1_9,A_1_10,A_1_11,A_1_12],[A_2_7,A_2_8,A_2_9,A_2_10,A_2_11,A_2_12]]),Matrix(6, 6, [[B_7_7+B_13_7-B_7_14,B_7_8+B_13_8-B_7_15,B_7_9+B_13_9-B_7_16,B_7_10+B_13_10-B_7_17,B_7_11+B_13_11-B_7_18,B_7_12+B_13_12-B_7_19],[B_8_7+B_14_7-B_8_14,B_8_8+B_14_8-B_8_15,B_8_9+B_14_9-B_8_16,B_8_10+B_14_10-B_8_17,B_8_11+B_14_11-B_8_18,B_8_12+B_14_12-B_8_19],[B_9_7+B_15_7-B_9_14,B_9_8+B_15_8-B_9_15,B_9_9+B_15_9-B_9_16,B_9_10+B_15_10-B_9_17,B_9_11+B_15_11-B_9_18,B_9_12+B_15_12-B_9_19],[B_10_7+B_16_7-B_10_14,B_10_8+B_16_8-B_10_15,B_10_9+B_16_9-B_10_16,B_10_10+B_16_10-B_10_17,B_10_11+B_16_11-B_10_18,B_10_12+B_16_12-B_10_19],[B_11_7+B_17_7-B_11_14,B_11_8+B_17_8-B_11_15,B_11_9+B_17_9-B_11_16,B_11_10+B_17_10-B_11_17,B_11_11+B_17_11-B_11_18,B_11_12+B_17_12-B_11_19],[B_12_7+B_18_7-B_12_14,B_12_8+B_18_8-B_12_15,B_12_9+B_18_9-B_12_16,B_12_10+B_18_10-B_12_17,B_12_11+B_18_11-B_12_18,B_12_12+B_18_12-B_12_19]]),Matrix(6, 2, [[C_7_1,C_7_2],[C_8_1,C_8_2],[C_9_1,C_9_2],[C_10_1,C_10_2],[C_11_1,C_11_2],[C_12_1,C_12_2]])))+Trace(Mul(Matrix(3, 6, [[A_3_13,A_3_14,A_3_15,A_3_16,A_3_17,A_3_18],[A_1_7-A_1_13+A_4_13,A_1_8-A_1_14+A_4_14,A_1_9-A_1_15+A_4_15,A_1_10-A_1_16+A_4_16,A_1_11-A_1_17+A_4_17,A_1_12-A_1_18+A_4_18],[A_2_7-A_2_13+A_5_13,A_2_8-A_2_14+A_5_14,A_2_9-A_2_15+A_5_15,A_2_10-A_2_16+A_5_16,A_2_11-A_2_17+A_5_17,A_2_12-A_2_18+A_5_18]]),Matrix(6, 6, [[B_7_6-B_13_7,B_7_1-B_13_8,B_7_2-B_13_9,B_7_3-B_13_10,B_7_4-B_13_11,B_7_5-B_13_12],[B_8_6-B_14_7,B_8_1-B_14_8,B_8_2-B_14_9,B_8_3-B_14_10,B_8_4-B_14_11,B_8_5-B_14_12],[B_9_6-B_15_7,B_9_1-B_15_8,B_9_2-B_15_9,B_9_3-B_15_10,B_9_4-B_15_11,B_9_5-B_15_12],[B_10_6-B_16_7,B_10_1-B_16_8,B_10_2-B_16_9,B_10_3-B_16_10,B_10_4-B_16_11,B_10_5-B_16_12],[B_11_6-B_17_7,B_11_1-B_17_8,B_11_2-B_17_9,B_11_3-B_17_10,B_11_4-B_17_11,B_11_5-B_17_12],[B_12_6-B_18_7,B_12_1-B_18_8,B_12_2-B_18_9,B_12_3-B_18_10,B_12_4-B_18_11,B_12_5-B_18_12]]),Matrix(6, 3, [[C_6_3-C_7_3,C_6_1+C_6_4-C_7_4,C_6_2+C_6_5-C_7_5],[C_1_3-C_8_3,C_1_1+C_1_4-C_8_4,C_1_2+C_1_5-C_8_5],[C_2_3-C_9_3,C_2_1+C_2_4-C_9_4,C_2_2+C_2_5-C_9_5],[C_3_3-C_10_3,C_3_1+C_3_4-C_10_4,C_3_2+C_3_5-C_10_5],[C_4_3-C_11_3,C_4_1+C_4_4-C_11_4,C_4_2+C_4_5-C_11_5],[C_5_3-C_12_3,C_5_1+C_5_4-C_12_4,C_5_2+C_5_5-C_12_5]])))+Trace(Mul(Matrix(3, 6, [[-A_3_1+A_3_7,-A_3_2+A_3_8,-A_3_3+A_3_9,-A_3_4+A_3_10,-A_3_5+A_3_11,-A_3_6+A_3_12],[A_1_1-A_4_1+A_4_7,A_1_2-A_4_2+A_4_8,A_1_3-A_4_3+A_4_9,A_1_4-A_4_4+A_4_10,A_1_5-A_4_5+A_4_11,A_1_6-A_4_6+A_4_12],[A_2_1-A_5_1+A_5_7,A_2_2-A_5_2+A_5_8,A_2_3-A_5_3+A_5_9,A_2_4-A_5_4+A_5_10,A_2_5-A_5_5+A_5_11,A_2_6-A_5_6+A_5_12]]),Matrix(6, 7, [[B_7_13,B_1_7+B_7_14,B_1_8+B_7_15,B_1_9+B_7_16,B_1_10+B_7_17,B_1_11+B_7_18,B_1_12+B_7_19],[B_8_13,B_2_7+B_8_14,B_2_8+B_8_15,B_2_9+B_8_16,B_2_10+B_8_17,B_2_11+B_8_18,B_2_12+B_8_19],[B_9_13,B_3_7+B_9_14,B_3_8+B_9_15,B_3_9+B_9_16,B_3_10+B_9_17,B_3_11+B_9_18,B_3_12+B_9_19],[B_10_13,B_4_7+B_10_14,B_4_8+B_10_15,B_4_9+B_10_16,B_4_10+B_10_17,B_4_11+B_10_18,B_4_12+B_10_19],[B_11_13,B_5_7+B_11_14,B_5_8+B_11_15,B_5_9+B_11_16,B_5_10+B_11_17,B_5_11+B_11_18,B_5_12+B_11_19],[B_12_13,B_6_7+B_12_14,B_6_8+B_12_15,B_6_9+B_12_16,B_6_10+B_12_17,B_6_11+B_12_18,B_6_12+B_12_19]]),Matrix(7, 3, [[C_13_3,C_13_1+C_13_4,C_13_2+C_13_5],[C_14_3,C_7_1+C_14_1+C_14_4,C_7_2+C_14_2+C_14_5],[C_15_3,C_8_1+C_15_1+C_15_4,C_8_2+C_15_2+C_15_5],[C_16_3,C_9_1+C_16_1+C_16_4,C_9_2+C_16_2+C_16_5],[C_17_3,C_10_1+C_17_1+C_17_4,C_10_2+C_17_2+C_17_5],[C_18_3,C_11_1+C_18_1+C_18_4,C_11_2+C_18_2+C_18_5],[C_19_3,C_12_1+C_19_1+C_19_4,C_12_2+C_19_2+C_19_5]])))+Trace(Mul(Matrix(3, 6, [[A_3_1-A_3_7,A_3_2-A_3_8,A_3_3-A_3_9,A_3_4-A_3_10,A_3_5-A_3_11,A_3_6-A_3_12],[A_4_1-A_4_7,A_4_2-A_4_8,A_4_3-A_4_9,A_4_4-A_4_10,A_4_5-A_4_11,A_4_6-A_4_12],[A_5_1-A_5_7,A_5_2-A_5_8,A_5_3-A_5_9,A_5_4-A_5_10,A_5_5-A_5_11,A_5_6-A_5_12]]),Matrix(6, 6, [[B_1_7,B_1_8,B_1_9,B_1_10,B_1_11,B_1_12],[B_2_7,B_2_8,B_2_9,B_2_10,B_2_11,B_2_12],[B_3_7,B_3_8,B_3_9,B_3_10,B_3_11,B_3_12],[B_4_7,B_4_8,B_4_9,B_4_10,B_4_11,B_4_12],[B_5_7,B_5_8,B_5_9,B_5_10,B_5_11,B_5_12],[B_6_7,B_6_8,B_6_9,B_6_10,B_6_11,B_6_12]]),Matrix(6, 3, [[C_7_3+C_14_3,C_7_1+C_14_1+C_7_4+C_14_4,C_7_2+C_14_2+C_7_5+C_14_5],[C_8_3+C_15_3,C_8_1+C_15_1+C_8_4+C_15_4,C_8_2+C_15_2+C_8_5+C_15_5],[C_9_3+C_16_3,C_9_1+C_16_1+C_9_4+C_16_4,C_9_2+C_16_2+C_9_5+C_16_5],[C_10_3+C_17_3,C_10_1+C_17_1+C_10_4+C_17_4,C_10_2+C_17_2+C_10_5+C_17_5],[C_11_3+C_18_3,C_11_1+C_18_1+C_11_4+C_18_4,C_11_2+C_18_2+C_11_5+C_18_5],[C_12_3+C_19_3,C_12_1+C_19_1+C_12_4+C_19_4,C_12_2+C_19_2+C_12_5+C_19_5]])))+Trace(Mul(Matrix(3, 6, [[-A_3_7+A_3_13,-A_3_8+A_3_14,-A_3_9+A_3_15,-A_3_10+A_3_16,-A_3_11+A_3_17,-A_3_12+A_3_18],[A_1_7-A_4_7-A_1_13+A_4_13,A_1_8-A_4_8-A_1_14+A_4_14,A_1_9-A_4_9-A_1_15+A_4_15,A_1_10-A_4_10-A_1_16+A_4_16,A_1_11-A_4_11-A_1_17+A_4_17,A_1_12-A_4_12-A_1_18+A_4_18],[A_2_7-A_5_7-A_2_13+A_5_13,A_2_8-A_5_8-A_2_14+A_5_14,A_2_9-A_5_9-A_2_15+A_5_15,A_2_10-A_5_10-A_2_16+A_5_16,A_2_11-A_5_11-A_2_17+A_5_17,A_2_12-A_5_12-A_2_18+A_5_18]]),Matrix(6, 6, [[B_7_6,B_7_1,B_7_2,B_7_3,B_7_4,B_7_5],[B_8_6,B_8_1,B_8_2,B_8_3,B_8_4,B_8_5],[B_9_6,B_9_1,B_9_2,B_9_3,B_9_4,B_9_5],[B_10_6,B_10_1,B_10_2,B_10_3,B_10_4,B_10_5],[B_11_6,B_11_1,B_11_2,B_11_3,B_11_4,B_11_5],[B_12_6,B_12_1,B_12_2,B_12_3,B_12_4,B_12_5]]),Matrix(6, 3, [[C_7_3-C_6_3,-C_6_4+C_7_4,-C_6_5+C_7_5],[-C_1_3+C_8_3,-C_1_4+C_8_4,-C_1_5+C_8_5],[-C_2_3+C_9_3,-C_2_4+C_9_4,-C_2_5+C_9_5],[-C_3_3+C_10_3,-C_3_4+C_10_4,-C_3_5+C_10_5],[-C_4_3+C_11_3,-C_4_4+C_11_4,-C_4_5+C_11_5],[-C_5_3+C_12_3,-C_5_4+C_12_4,-C_5_5+C_12_5]])))+Trace(Mul(Matrix(2, 6, [[A_1_7-A_1_13,A_1_8-A_1_14,A_1_9-A_1_15,A_1_10-A_1_16,A_1_11-A_1_17,A_1_12-A_1_18],[A_2_7-A_2_13,A_2_8-A_2_14,A_2_9-A_2_15,A_2_10-A_2_16,A_2_11-A_2_17,A_2_12-A_2_18]]),Matrix(6, 6, [[B_13_7,B_13_8,B_13_9,B_13_10,B_13_11,B_13_12],[B_14_7,B_14_8,B_14_9,B_14_10,B_14_11,B_14_12],[B_15_7,B_15_8,B_15_9,B_15_10,B_15_11,B_15_12],[B_16_7,B_16_8,B_16_9,B_16_10,B_16_11,B_16_12],[B_17_7,B_17_8,B_17_9,B_17_10,B_17_11,B_17_12],[B_18_7,B_18_8,B_18_9,B_18_10,B_18_11,B_18_12]]),Matrix(6, 2, [[C_6_1-C_7_1+C_6_4-C_7_4,C_6_2-C_7_2+C_6_5-C_7_5],[C_1_1-C_8_1+C_1_4-C_8_4,C_1_2-C_8_2+C_1_5-C_8_5],[C_2_1-C_9_1+C_2_4-C_9_4,C_2_2-C_9_2+C_2_5-C_9_5],[C_3_1-C_10_1+C_3_4-C_10_4,C_3_2-C_10_2+C_3_5-C_10_5],[C_4_1-C_11_1+C_4_4-C_11_4,C_4_2-C_11_2+C_4_5-C_11_5],[C_5_1-C_12_1+C_5_4-C_12_4,C_5_2-C_12_2+C_5_5-C_12_5]])))+Trace(Mul(Matrix(3, 6, [[A_3_7,A_3_8,A_3_9,A_3_10,A_3_11,A_3_12],[A_4_7,A_4_8,A_4_9,A_4_10,A_4_11,A_4_12],[A_5_7,A_5_8,A_5_9,A_5_10,A_5_11,A_5_12]]),Matrix(6, 6, [[B_7_6+B_1_7+B_7_7,B_7_1+B_1_8+B_7_8,B_7_2+B_1_9+B_7_9,B_7_3+B_1_10+B_7_10,B_7_4+B_1_11+B_7_11,B_7_5+B_1_12+B_7_12],[B_8_6+B_2_7+B_8_7,B_8_1+B_2_8+B_8_8,B_8_2+B_2_9+B_8_9,B_8_3+B_2_10+B_8_10,B_8_4+B_2_11+B_8_11,B_8_5+B_2_12+B_8_12],[B_9_6+B_3_7+B_9_7,B_9_1+B_3_8+B_9_8,B_9_2+B_3_9+B_9_9,B_9_3+B_3_10+B_9_10,B_9_4+B_3_11+B_9_11,B_9_5+B_3_12+B_9_12],[B_10_6+B_4_7+B_10_7,B_10_1+B_4_8+B_10_8,B_10_2+B_4_9+B_10_9,B_10_3+B_4_10+B_10_10,B_10_4+B_4_11+B_10_11,B_10_5+B_4_12+B_10_12],[B_11_6+B_5_7+B_11_7,B_11_1+B_5_8+B_11_8,B_11_2+B_5_9+B_11_9,B_11_3+B_5_10+B_11_10,B_11_4+B_5_11+B_11_11,B_11_5+B_5_12+B_11_12],[B_12_6+B_6_7+B_12_7,B_12_1+B_6_8+B_12_8,B_12_2+B_6_9+B_12_9,B_12_3+B_6_10+B_12_10,B_12_4+B_6_11+B_12_11,B_12_5+B_6_12+B_12_12]]),Matrix(6, 3, [[C_7_3,C_7_4,C_7_5],[C_8_3,C_8_4,C_8_5],[C_9_3,C_9_4,C_9_5],[C_10_3,C_10_4,C_10_5],[C_11_3,C_11_4,C_11_5],[C_12_3,C_12_4,C_12_5]])))+Trace(Mul(Matrix(2, 6, [[A_1_1-A_4_1-A_1_7+A_4_7,A_1_2-A_4_2-A_1_8+A_4_8,A_1_3-A_4_3-A_1_9+A_4_9,A_1_4-A_4_4-A_1_10+A_4_10,A_1_5-A_4_5-A_1_11+A_4_11,A_1_6-A_4_6-A_1_12+A_4_12],[A_2_1-A_5_1-A_2_7+A_5_7,A_2_2-A_5_2-A_2_8+A_5_8,A_2_3-A_5_3-A_2_9+A_5_9,A_2_4-A_5_4-A_2_10+A_5_10,A_2_5-A_5_5-A_2_11+A_5_11,A_2_6-A_5_6-A_2_12+A_5_12]]),Matrix(6, 7, [[B_7_13,B_7_14,B_7_15,B_7_16,B_7_17,B_7_18,B_7_19],[B_8_13,B_8_14,B_8_15,B_8_16,B_8_17,B_8_18,B_8_19],[B_9_13,B_9_14,B_9_15,B_9_16,B_9_17,B_9_18,B_9_19],[B_10_13,B_10_14,B_10_15,B_10_16,B_10_17,B_10_18,B_10_19],[B_11_13,B_11_14,B_11_15,B_11_16,B_11_17,B_11_18,B_11_19],[B_12_13,B_12_14,B_12_15,B_12_16,B_12_17,B_12_18,B_12_19]]),Matrix(7, 2, [[-C_13_1,-C_13_2],[-C_7_1-C_14_1,-C_7_2-C_14_2],[-C_8_1-C_15_1,-C_8_2-C_15_2],[-C_9_1-C_16_1,-C_9_2-C_16_2],[-C_10_1-C_17_1,-C_10_2-C_17_2],[-C_11_1-C_18_1,-C_11_2-C_18_2],[-C_12_1-C_19_1,-C_12_2-C_19_2]])))+Trace(Mul(Matrix(3, 6, [[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_6-A_3_18],[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_6-A_4_18],[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_6-A_5_18]]),Matrix(6, 6, [[B_1_6,B_1_1,B_1_2,B_1_3,B_1_4,B_1_5],[B_2_6,B_2_1,B_2_2,B_2_3,B_2_4,B_2_5],[B_3_6,B_3_1,B_3_2,B_3_3,B_3_4,B_3_5],[B_4_6,B_4_1,B_4_2,B_4_3,B_4_4,B_4_5],[B_5_6,B_5_1,B_5_2,B_5_3,B_5_4,B_5_5],[B_6_6,B_6_1,B_6_2,B_6_3,B_6_4,B_6_5]]),Matrix(6, 3, [[C_6_3+C_14_3,C_6_4+C_14_4,C_6_5+C_14_5],[C_1_3+C_15_3,C_1_4+C_15_4,C_1_5+C_15_5],[C_2_3+C_16_3,C_2_4+C_16_4,C_2_5+C_16_5],[C_3_3+C_17_3,C_3_4+C_17_4,C_3_5+C_17_5],[C_4_3+C_18_3,C_4_4+C_18_4,C_4_5+C_18_5],[C_5_3+C_19_3,C_5_4+C_19_4,C_5_5+C_19_5]])))+Trace(Mul(Matrix(3, 6, [[-A_3_1,-A_3_2,-A_3_3,-A_3_4,-A_3_5,-A_3_6],[A_1_1-A_4_1,A_1_2-A_4_2,A_1_3-A_4_3,A_1_4-A_4_4,A_1_5-A_4_5,A_1_6-A_4_6],[A_2_1-A_5_1,A_2_2-A_5_2,A_2_3-A_5_3,A_2_4-A_5_4,A_2_5-A_5_5,A_2_6-A_5_6]]),Matrix(6, 7, [[-B_1_13-B_7_13,B_1_6-B_1_14-B_7_14,B_1_1-B_1_15-B_7_15,B_1_2-B_1_16-B_7_16,B_1_3-B_1_17-B_7_17,B_1_4-B_1_18-B_7_18,B_1_5-B_1_19-B_7_19],[-B_2_13-B_8_13,B_2_6-B_2_14-B_8_14,B_2_1-B_2_15-B_8_15,B_2_2-B_2_16-B_8_16,B_2_3-B_2_17-B_8_17,B_2_4-B_2_18-B_8_18,B_2_5-B_2_19-B_8_19],[-B_3_13-B_9_13,B_3_6-B_3_14-B_9_14,B_3_1-B_3_15-B_9_15,B_3_2-B_3_16-B_9_16,B_3_3-B_3_17-B_9_17,B_3_4-B_3_18-B_9_18,B_3_5-B_3_19-B_9_19],[-B_4_13-B_10_13,B_4_6-B_4_14-B_10_14,B_4_1-B_4_15-B_10_15,B_4_2-B_4_16-B_10_16,B_4_3-B_4_17-B_10_17,B_4_4-B_4_18-B_10_18,B_4_5-B_4_19-B_10_19],[-B_5_13-B_11_13,B_5_6-B_5_14-B_11_14,B_5_1-B_5_15-B_11_15,B_5_2-B_5_16-B_11_16,B_5_3-B_5_17-B_11_17,B_5_4-B_5_18-B_11_18,B_5_5-B_5_19-B_11_19],[-B_6_13-B_12_13,B_6_6-B_6_14-B_12_14,B_6_1-B_6_15-B_12_15,B_6_2-B_6_16-B_12_16,B_6_3-B_6_17-B_12_17,B_6_4-B_6_18-B_12_18,B_6_5-B_6_19-B_12_19]]),Matrix(7, 3, [[C_13_3,C_13_4,C_13_5],[C_14_3,C_14_4,C_14_5],[C_15_3,C_15_4,C_15_5],[C_16_3,C_16_4,C_16_5],[C_17_3,C_17_4,C_17_5],[C_18_3,C_18_4,C_18_5],[C_19_3,C_19_4,C_19_5]])))

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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