Description of fast matrix multiplication algorithm: ⟨11×15×18:1848⟩

Algorithm type

16X6Y8Z6+80X6Y6Z6+120X6Y4Z6+120X6Y3Z6+144X6Y2Z6+48X3Y8Z3+9X2Y10Z2+80X3Y6Z3+27X2Y8Z2+136X3Y4Z3+27X2Y6Z2+2X3Y5Z+120X3Y3Z3+6X3Y4Z+192X3Y2Z3+6X2Y5Z+36X2Y4Z2+6XY5Z2+6X3Y3Z+144X3YZ3+18X2Y4Z+13XY5Z+18XY4Z2+8X3Y2Z+18X2Y3Z+63X2Y2Z2+39XY4Z+18XY3Z2+14X3YZ+24X2Y2Z+39XY3Z+24XY2Z2+42X2YZ+52XY2Z+42XYZ2+91XYZ16X6Y8Z680X6Y6Z6120X6Y4Z6120X6Y3Z6144X6Y2Z648X3Y8Z39X2Y10Z280X3Y6Z327X2Y8Z2136X3Y4Z327X2Y6Z22X3Y5Z120X3Y3Z36X3Y4Z192X3Y2Z36X2Y5Z36X2Y4Z26XY5Z26X3Y3Z144X3YZ318X2Y4Z13XY5Z18XY4Z28X3Y2Z18X2Y3Z63X2Y2Z239XY4Z18XY3Z214X3YZ24X2Y2Z39XY3Z24XY2Z242X2YZ52XY2Z42XYZ291XYZ16*X^6*Y^8*Z^6+80*X^6*Y^6*Z^6+120*X^6*Y^4*Z^6+120*X^6*Y^3*Z^6+144*X^6*Y^2*Z^6+48*X^3*Y^8*Z^3+9*X^2*Y^10*Z^2+80*X^3*Y^6*Z^3+27*X^2*Y^8*Z^2+136*X^3*Y^4*Z^3+27*X^2*Y^6*Z^2+2*X^3*Y^5*Z+120*X^3*Y^3*Z^3+6*X^3*Y^4*Z+192*X^3*Y^2*Z^3+6*X^2*Y^5*Z+36*X^2*Y^4*Z^2+6*X*Y^5*Z^2+6*X^3*Y^3*Z+144*X^3*Y*Z^3+18*X^2*Y^4*Z+13*X*Y^5*Z+18*X*Y^4*Z^2+8*X^3*Y^2*Z+18*X^2*Y^3*Z+63*X^2*Y^2*Z^2+39*X*Y^4*Z+18*X*Y^3*Z^2+14*X^3*Y*Z+24*X^2*Y^2*Z+39*X*Y^3*Z+24*X*Y^2*Z^2+42*X^2*Y*Z+52*X*Y^2*Z+42*X*Y*Z^2+91*X*Y*Z

Algorithm definition

The algorithm ⟨11×15×18:1848⟩ could be constructed using the following decomposition:

⟨11×15×18:1848⟩ = ⟨6×3×3:40⟩ + ⟨5×3×3:36⟩ + ⟨6×3×3:40⟩ + ⟨5×3×3:36⟩ + ⟨6×3×3:40⟩ + ⟨5×3×3:36⟩ + ⟨5×3×3:36⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨5×3×3:36⟩ + ⟨5×3×3:36⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨5×3×3:36⟩ + ⟨6×3×3:40⟩ + ⟨5×3×3:36⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨5×3×3:36⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨5×3×3:36⟩ + ⟨5×3×3:36⟩ + ⟨5×3×3:36⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨5×3×3:36⟩ + ⟨5×3×3:36⟩ + ⟨6×3×3:40⟩ + ⟨5×3×3:36⟩ + ⟨5×3×3:36⟩ + ⟨6×3×3:40⟩ + ⟨6×3×3:40⟩ + ⟨5×3×3:36⟩ + ⟨5×3×3:36⟩.

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_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_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_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_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_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_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_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_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_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_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_15B_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_18C_1_1C_1_2C_1_3C_1_4C_1_5C_1_6C_1_7C_1_8C_1_9C_1_10C_1_11C_2_1C_2_2C_2_3C_2_4C_2_5C_2_6C_2_7C_2_8C_2_9C_2_10C_2_11C_3_1C_3_2C_3_3C_3_4C_3_5C_3_6C_3_7C_3_8C_3_9C_3_10C_3_11C_4_1C_4_2C_4_3C_4_4C_4_5C_4_6C_4_7C_4_8C_4_9C_4_10C_4_11C_5_1C_5_2C_5_3C_5_4C_5_5C_5_6C_5_7C_5_8C_5_9C_5_10C_5_11C_6_1C_6_2C_6_3C_6_4C_6_5C_6_6C_6_7C_6_8C_6_9C_6_10C_6_11C_7_1C_7_2C_7_3C_7_4C_7_5C_7_6C_7_7C_7_8C_7_9C_7_10C_7_11C_8_1C_8_2C_8_3C_8_4C_8_5C_8_6C_8_7C_8_8C_8_9C_8_10C_8_11C_9_1C_9_2C_9_3C_9_4C_9_5C_9_6C_9_7C_9_8C_9_9C_9_10C_9_11C_10_1C_10_2C_10_3C_10_4C_10_5C_10_6C_10_7C_10_8C_10_9C_10_10C_10_11C_11_1C_11_2C_11_3C_11_4C_11_5C_11_6C_11_7C_11_8C_11_9C_11_10C_11_11C_12_1C_12_2C_12_3C_12_4C_12_5C_12_6C_12_7C_12_8C_12_9C_12_10C_12_11C_13_1C_13_2C_13_3C_13_4C_13_5C_13_6C_13_7C_13_8C_13_9C_13_10C_13_11C_14_1C_14_2C_14_3C_14_4C_14_5C_14_6C_14_7C_14_8C_14_9C_14_10C_14_11C_15_1C_15_2C_15_3C_15_4C_15_5C_15_6C_15_7C_15_8C_15_9C_15_10C_15_11C_16_1C_16_2C_16_3C_16_4C_16_5C_16_6C_16_7C_16_8C_16_9C_16_10C_16_11C_17_1C_17_2C_17_3C_17_4C_17_5C_17_6C_17_7C_17_8C_17_9C_17_10C_17_11C_18_1C_18_2C_18_3C_18_4C_18_5C_18_6C_18_7C_18_8C_18_9C_18_10C_18_11=TraceMulA_6_4+A_6_7A_6_5+A_6_8A_6_6+A_6_9A_7_4+A_7_7A_7_5+A_7_8A_7_6+A_7_9A_8_4+A_8_7A_8_5+A_8_8A_8_6+A_8_9A_9_4+A_9_7A_9_5+A_9_8A_9_6+A_9_9A_10_4+A_10_7A_10_5+A_10_8A_10_6+A_10_9A_11_4+A_11_7A_11_5+A_11_8A_11_6+A_11_9-a21+a11+a41+1B_10_1a41-a21+a11+a41+1B_13_1a51+B_10_4+a21+a11+a41+1B_13_4a51-B_1_7+B_4_7-a21+a11+a41+1B_10_2a41-a21+a11+a41+1B_13_2a51+B_10_5+a21+a11+a41+1B_13_5a51-B_1_8+B_4_8-a21+a11+a41+1B_10_3a41-a21+a11+a41+1B_13_3a51+B_10_6+a21+a11+a41+1B_13_6a51-B_1_9+B_4_9-a21+a11+a41+1B_11_1a41-a21+a11+a41+1B_14_1a51+B_11_4+a21+a11+a41+1B_14_4a51-B_2_7+B_5_7-a21+a11+a41+1B_11_2a41-a21+a11+a41+1B_14_2a51+B_11_5+a21+a11+a41+1B_14_5a51-B_2_8+B_5_8-a21+a11+a41+1B_11_3a41-a21+a11+a41+1B_14_3a51+B_11_6+a21+a11+a41+1B_14_6a51-B_2_9+B_5_9-a21+a11+a41+1B_12_1a41-a21+a11+a41+1B_15_1a51+B_12_4+a21+a11+a41+1B_15_4a51-B_3_7+B_6_7-a21+a11+a41+1B_12_2a41-a21+a11+a41+1B_15_2a51+B_12_5+a21+a11+a41+1B_15_5a51-B_3_8+B_6_8-a21+a11+a41+1B_12_3a41-a21+a11+a41+1B_15_3a51+B_12_6+a21+a11+a41+1B_15_6a51-B_3_9+B_6_9C_4_6+C_7_6C_4_7+C_7_7C_4_8+C_7_8C_4_9+C_7_9C_4_10+C_7_10C_4_11+C_7_11C_5_6+C_8_6C_5_7+C_8_7C_5_8+C_8_8C_5_9+C_8_9C_5_10+C_8_10C_5_11+C_8_11C_6_6+C_9_6C_6_7+C_9_7C_6_8+C_9_8C_6_9+C_9_9C_6_10+C_9_10C_6_11+C_9_11+TraceMulA_1_4+A_1_7A_1_5+A_1_8A_1_6+A_1_9A_2_4+A_2_7A_2_5+A_2_8A_2_6+A_2_9A_3_4+A_3_7A_3_5+A_3_8A_3_6+A_3_9A_4_4+A_4_7A_4_5+A_4_8A_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[[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_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_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_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_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_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_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_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_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_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_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]]),Matrix(15, 18, [[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_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_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_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_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_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_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_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_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_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_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_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_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_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_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]]),Matrix(18, 11, [[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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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]]))) = Trace(Mul(Matrix(6, 3, [[A_6_4+A_6_7,A_6_5+A_6_8,A_6_6+A_6_9],[A_7_4+A_7_7,A_7_5+A_7_8,A_7_6+A_7_9],[A_8_4+A_8_7,A_8_5+A_8_8,A_8_6+A_8_9],[A_9_4+A_9_7,A_9_5+A_9_8,A_9_6+A_9_9],[A_10_4+A_10_7,A_10_5+A_10_8,A_10_6+A_10_9],[A_11_4+A_11_7,A_11_5+A_11_8,A_11_6+A_11_9]]),Matrix(3, 3, [[-(a21+a11+a41+1)/a41*B_10_1-(a21+a11+a41+1)/a51*B_13_1+B_10_4+(a21+a11+a41+1)/a51*B_13_4-B_1_7+B_4_7,-(a21+a11+a41+1)/a41*B_10_2-(a21+a11+a41+1)/a51*B_13_2+B_10_5+(a21+a11+a41+1)/a51*B_13_5-B_1_8+B_4_8,-(a21+a11+a41+1)/a41*B_10_3-(a21+a11+a41+1)/a51*B_13_3+B_10_6+(a21+a11+a41+1)/a51*B_13_6-B_1_9+B_4_9],[-(a21+a11+a41+1)/a41*B_11_1-(a21+a11+a41+1)/a51*B_14_1+B_11_4+(a21+a11+a41+1)/a51*B_14_4-B_2_7+B_5_7,-(a21+a11+a41+1)/a41*B_11_2-(a21+a11+a41+1)/a51*B_14_2+B_11_5+(a21+a11+a41+1)/a51*B_14_5-B_2_8+B_5_8,-(a21+a11+a41+1)/a41*B_11_3-(a21+a11+a41+1)/a51*B_14_3+B_11_6+(a21+a11+a41+1)/a51*B_14_6-B_2_9+B_5_9],[-(a21+a11+a41+1)/a41*B_12_1-(a21+a11+a41+1)/a51*B_15_1+B_12_4+(a21+a11+a41+1)/a51*B_15_4-B_3_7+B_6_7,-(a21+a11+a41+1)/a41*B_12_2-(a21+a11+a41+1)/a51*B_15_2+B_12_5+(a21+a11+a41+1)/a51*B_15_5-B_3_8+B_6_8,-(a21+a11+a41+1)/a41*B_12_3-(a21+a11+a41+1)/a51*B_15_3+B_12_6+(a21+a11+a41+1)/a51*B_15_6-B_3_9+B_6_9]]),Matrix(3, 6, [[C_4_6+C_7_6,C_4_7+C_7_7,C_4_8+C_7_8,C_4_9+C_7_9,C_4_10+C_7_10,C_4_11+C_7_11],[C_5_6+C_8_6,C_5_7+C_8_7,C_5_8+C_8_8,C_5_9+C_8_9,C_5_10+C_8_10,C_5_11+C_8_11],[C_6_6+C_9_6,C_6_7+C_9_7,C_6_8+C_9_8,C_6_9+C_9_9,C_6_10+C_9_10,C_6_11+C_9_11]])))+Trace(Mul(Matrix(5, 3, [[A_1_4+A_1_7,A_1_5+A_1_8,A_1_6+A_1_9],[A_2_4+A_2_7,A_2_5+A_2_8,A_2_6+A_2_9],[A_3_4+A_3_7,A_3_5+A_3_8,A_3_6+A_3_9],[A_4_4+A_4_7,A_4_5+A_4_8,A_4_6+A_4_9],[A_5_4+A_5_7,A_5_5+A_5_8,A_5_6+A_5_9]]),Matrix(3, 3, [[-B_7_1+a31/a51*B_13_1+B_7_4-a31/a51*B_13_4+a21/a11*B_1_10+B_4_10+a31/(a21+a31)*B_4_16+1/(a21+a31)*a21*B_7_16,-B_7_2+a31/a51*B_13_2+B_7_5-a31/a51*B_13_5+a21/a11*B_1_11+B_4_11+a31/(a21+a31)*B_4_17+1/(a21+a31)*a21*B_7_17,-B_7_3+a31/a51*B_13_3+B_7_6-a31/a51*B_13_6+a21/a11*B_1_12+B_4_12+a31/(a21+a31)*B_4_18+1/(a21+a31)*a21*B_7_18],[-B_8_1+a31/a51*B_14_1+B_8_4-a31/a51*B_14_4+a21/a11*B_2_10+B_5_10+a31/(a21+a31)*B_5_16+1/(a21+a31)*a21*B_8_16,-B_8_2+a31/a51*B_14_2+B_8_5-a31/a51*B_14_5+a21/a11*B_2_11+B_5_11+a31/(a21+a31)*B_5_17+1/(a21+a31)*a21*B_8_17,-B_8_3+a31/a51*B_14_3+B_8_6-a31/a51*B_14_6+a21/a11*B_2_12+B_5_12+a31/(a21+a31)*B_5_18+1/(a21+a31)*a21*B_8_18],[-B_9_1+a31/a51*B_15_1+B_9_4-a31/a51*B_15_4+a21/a11*B_3_10+B_6_10+a31/(a21+a31)*B_6_16+1/(a21+a31)*a21*B_9_16,-B_9_2+a31/a51*B_15_2+B_9_5-a31/a51*B_15_5+a21/a11*B_3_11+B_6_11+a31/(a21+a31)*B_6_17+1/(a21+a31)*a21*B_9_17,-B_9_3+a31/a51*B_15_3+B_9_6-a31/a51*B_15_6+a21/a11*B_3_12+B_6_12+a31/(a21+a31)*B_6_18+1/(a21+a31)*a21*B_9_18]]),Matrix(3, 5, [[C_4_1+C_7_1,C_4_2+C_7_2,C_4_3+C_7_3,C_4_4+C_7_4,C_4_5+C_7_5],[C_5_1+C_8_1,C_5_2+C_8_2,C_5_3+C_8_3,C_5_4+C_8_4,C_5_5+C_8_5],[C_9_1+C_6_1,C_9_2+C_6_2,C_6_3+C_9_3,C_6_4+C_9_4,C_6_5+C_9_5]])))+Trace(Mul(Matrix(5, 3, [[A_1_7-A_7_7,A_1_8-A_7_8,A_1_9-A_7_9],[A_2_7-A_8_7,A_2_8-A_8_8,A_2_9-A_8_9],[A_3_7-A_9_7,A_3_8-A_9_8,A_3_9-A_9_9],[A_4_7-A_10_7,A_4_8-A_10_8,A_4_9-A_10_9],[A_5_7-A_11_7,A_5_8-A_11_8,A_5_9-A_11_9]]),Matrix(3, 3, [[B_7_1+(a31+a11)/a41*B_10_1+a11/a51*B_13_1-B_7_4-a11/a51*B_13_4+B_1_7+B_7_7+(a21+a31)/a11*B_1_10+B_4_10-B_7_10,B_7_2+(a31+a11)/a41*B_10_2+a11/a51*B_13_2-B_7_5-a11/a51*B_13_5+B_1_8+B_7_8+(a21+a31)/a11*B_1_11+B_4_11-B_7_11,B_7_3+(a31+a11)/a41*B_10_3+a11/a51*B_13_3-B_7_6-a11/a51*B_13_6+B_1_9+B_7_9+(a21+a31)/a11*B_1_12+B_4_12-B_7_12],[B_8_1+(a31+a11)/a41*B_11_1+a11/a51*B_14_1-B_8_4-a11/a51*B_14_4+B_2_7+B_8_7+(a21+a31)/a11*B_2_10+B_5_10-B_8_10,B_8_2+(a31+a11)/a41*B_11_2+a11/a51*B_14_2-B_8_5-a11/a51*B_14_5+B_2_8+B_8_8+(a21+a31)/a11*B_2_11+B_5_11-B_8_11,B_8_3+(a31+a11)/a41*B_11_3+a11/a51*B_14_3-B_8_6-a11/a51*B_14_6+B_2_9+B_8_9+(a21+a31)/a11*B_2_12+B_5_12-B_8_12],[B_9_1+(a31+a11)/a41*B_12_1+a11/a51*B_15_1-B_9_4-a11/a51*B_15_4+B_3_7+B_9_7+(a21+a31)/a11*B_3_10+B_6_10-B_9_10,B_9_2+(a31+a11)/a41*B_12_2+a11/a51*B_15_2-B_9_5-a11/a51*B_15_5+B_3_8+B_9_8+(a21+a31)/a11*B_3_11+B_6_11-B_9_11,B_9_3+(a31+a11)/a41*B_12_3+a11/a51*B_15_3-B_9_6-a11/a51*B_15_6+B_3_9+B_9_9+(a21+a31)/a11*B_3_12+B_6_12-B_9_12]]),Matrix(3, 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]])))+Trace(Mul(Matrix(6, 3, [[A_6_7,A_6_8,A_6_9],[A_1_4+A_7_7,A_1_5+A_7_8,A_1_6+A_7_9],[A_2_4+A_8_7,A_2_5+A_8_8,A_2_6+A_8_9],[A_3_4+A_9_7,A_3_5+A_9_8,A_3_6+A_9_9],[A_4_4+A_10_7,A_4_5+A_10_8,A_4_6+A_10_9],[A_5_4+A_11_7,A_5_5+A_11_8,A_5_6+A_11_9]]),Matrix(3, 3, [[B_7_1-(a21+a11)/a41*B_10_1-(a21+a11+a31)/a51*B_13_1-B_7_4+(a21+a11+a31)/a51*B_13_4-B_1_7+B_4_7,B_7_2-(a21+a11)/a41*B_10_2-(a21+a11+a31)/a51*B_13_2-B_7_5+(a21+a11+a31)/a51*B_13_5-B_1_8+B_4_8,B_7_3-(a21+a11)/a41*B_10_3-(a21+a11+a31)/a51*B_13_3-B_7_6+(a21+a11+a31)/a51*B_13_6-B_1_9+B_4_9],[B_8_1-(a21+a11)/a41*B_11_1-(a21+a11+a31)/a51*B_14_1-B_8_4+(a21+a11+a31)/a51*B_14_4-B_2_7+B_5_7,B_8_2-(a21+a11)/a41*B_11_2-(a21+a11+a31)/a51*B_14_2-B_8_5+(a21+a11+a31)/a51*B_14_5-B_2_8+B_5_8,B_8_3-(a21+a11)/a41*B_11_3-(a21+a11+a31)/a51*B_14_3-B_8_6+(a21+a11+a31)/a51*B_14_6-B_2_9+B_5_9],[B_9_1-(a21+a11)/a41*B_12_1-(a21+a11+a31)/a51*B_15_1-B_9_4+(a21+a11+a31)/a51*B_15_4-B_3_7+B_6_7,B_9_2-(a21+a11)/a41*B_12_2-(a21+a11+a31)/a51*B_15_2-B_9_5+(a21+a11+a31)/a51*B_15_5-B_3_8+B_6_8,B_9_3-(a21+a11)/a41*B_12_3-(a21+a11+a31)/a51*B_15_3-B_9_6+(a21+a11+a31)/a51*B_15_6-B_3_9+B_6_9]]),Matrix(3, 6, [[-C_4_6,C_7_1-C_4_7,C_7_2-C_4_8,C_7_3-C_4_9,C_7_4-C_4_10,C_7_5-C_4_11],[-C_5_6,C_8_1-C_5_7,C_8_2-C_5_8,C_8_3-C_5_9,C_8_4-C_5_10,C_8_5-C_5_11],[-C_6_6,C_9_1-C_6_7,C_9_2-C_6_8,C_9_3-C_6_9,C_9_4-C_6_10,C_9_5-C_6_11]])))+Trace(Mul(Matrix(6, 3, [[A_6_7,A_6_8,A_6_9],[A_7_7+A_1_10,A_7_8+A_1_11,A_7_9+A_1_12],[A_8_7+A_2_10,A_8_8+A_2_11,A_8_9+A_2_12],[A_9_7+A_3_10,A_9_8+A_3_11,A_9_9+A_3_12],[A_10_7+A_4_10,A_10_8+A_4_11,A_10_9+A_4_12],[A_11_7+A_5_10,A_11_8+A_5_11,A_11_9+A_5_12]]),Matrix(3, 3, [[-B_10_4+B_10_7+(a21+a31)/a11*B_1_10+B_4_10-B_7_10,-B_10_5+B_10_8+(a21+a31)/a11*B_1_11+B_4_11-B_7_11,-B_10_6+B_10_9+(a21+a31)/a11*B_1_12+B_4_12-B_7_12],[-B_11_4+B_11_7+(a21+a31)/a11*B_2_10+B_5_10-B_8_10,-B_11_5+B_11_8+(a21+a31)/a11*B_2_11+B_5_11-B_8_11,-B_11_6+B_11_9+(a21+a31)/a11*B_2_12+B_5_12-B_8_12],[-B_12_4+B_12_7+(a21+a31)/a11*B_3_10+B_6_10-B_9_10,-B_12_5+B_12_8+(a21+a31)/a11*B_3_11+B_6_11-B_9_11,-B_12_6+B_12_9+(a21+a31)/a11*B_3_12+B_6_12-B_9_12]]),Matrix(3, 6, [[-C_10_6,C_7_1-C_10_7,C_7_2-C_10_8,C_7_3-C_10_9,C_7_4-C_10_10,C_7_5-C_10_11],[-C_11_6,C_8_1-C_11_7,C_8_2-C_11_8,C_8_3-C_11_9,C_8_4-C_11_10,C_8_5-C_11_11],[-C_12_6,C_9_1-C_12_7,C_9_2-C_12_8,C_9_3-C_12_9,C_9_4-C_12_10,C_9_5-C_12_11]])))+Trace(Mul(Matrix(5, 3, [[A_1_7+A_1_10,A_1_8+A_1_11,A_1_9+A_1_12],[A_2_7+A_2_10,A_2_8+A_2_11,A_2_9+A_2_12],[A_3_7+A_3_10,A_3_8+A_3_11,A_3_9+A_3_12],[A_4_7+A_4_10,A_4_8+A_4_11,A_4_9+A_4_12],[A_5_7+A_5_10,A_5_8+A_5_11,A_5_9+A_5_12]]),Matrix(3, 3, [[a51/a41*B_10_1+B_13_1-B_13_4+B_13_7-(a21+a31)/a11*B_1_10-B_4_10+B_7_10,a51/a41*B_10_2+B_13_2-B_13_5+B_13_8-(a21+a31)/a11*B_1_11-B_4_11+B_7_11,a51/a41*B_10_3+B_13_3-B_13_6+B_13_9-(a21+a31)/a11*B_1_12-B_4_12+B_7_12],[a51/a41*B_11_1+B_14_1-B_14_4+B_14_7-(a21+a31)/a11*B_2_10-B_5_10+B_8_10,a51/a41*B_11_2+B_14_2-B_14_5+B_14_8-(a21+a31)/a11*B_2_11-B_5_11+B_8_11,a51/a41*B_11_3+B_14_3-B_14_6+B_14_9-(a21+a31)/a11*B_2_12-B_5_12+B_8_12],[a51/a41*B_12_1+B_15_1-B_15_4+B_15_7-(a21+a31)/a11*B_3_10-B_6_10+B_9_10,a51/a41*B_12_2+B_15_2-B_15_5+B_15_8-(a21+a31)/a11*B_3_11-B_6_11+B_9_11,a51/a41*B_12_3+B_15_3-B_15_6+B_15_9-(a21+a31)/a11*B_3_12-B_6_12+B_9_12]]),Matrix(3, 5, [[C_7_1+C_10_1,C_7_2+C_10_2,C_7_3+C_10_3,C_7_4+C_10_4,C_7_5+C_10_5],[C_8_1+C_11_1,C_8_2+C_11_2,C_8_3+C_11_3,C_8_4+C_11_4,C_8_5+C_11_5],[C_9_1+C_12_1,C_9_2+C_12_2,C_9_3+C_12_3,C_9_4+C_12_4,C_9_5+C_12_5]])))+Trace(Mul(Matrix(6, 3, [[-A_6_10,-A_6_11,-A_6_12],[A_1_10-A_7_10,A_1_11-A_7_11,A_1_12-A_7_12],[A_2_10-A_8_10,A_2_11-A_8_11,A_2_12-A_8_12],[A_3_10-A_9_10,A_3_11-A_9_11,A_3_12-A_9_12],[A_4_10-A_10_10,A_4_11-A_10_11,A_4_12-A_10_12],[A_5_10-A_11_10,A_5_11-A_11_11,A_5_12-A_11_12]]),Matrix(3, 3, [[-B_10_4+B_10_7-(a41+a21)/a11*B_1_10-B_4_10-B_10_10+(a31+a41)/(a21+a11)*B_1_13-(a31+a41)/(a21+a11)*B_4_13-B_7_13+B_10_13,-B_10_5+B_10_8-(a41+a21)/a11*B_1_11-B_4_11-B_10_11+(a31+a41)/(a21+a11)*B_1_14-(a31+a41)/(a21+a11)*B_4_14-B_7_14+B_10_14,-B_10_6+B_10_9-(a41+a21)/a11*B_1_12-B_4_12-B_10_12+(a31+a41)/(a21+a11)*B_1_15-(a31+a41)/(a21+a11)*B_4_15-B_7_15+B_10_15],[-B_11_4+B_11_7-(a41+a21)/a11*B_2_10-B_5_10-B_11_10+(a31+a41)/(a21+a11)*B_2_13-(a31+a41)/(a21+a11)*B_5_13-B_8_13+B_11_13,-B_11_5+B_11_8-(a41+a21)/a11*B_2_11-B_5_11-B_11_11+(a31+a41)/(a21+a11)*B_2_14-(a31+a41)/(a21+a11)*B_5_14-B_8_14+B_11_14,-B_11_6+B_11_9-(a41+a21)/a11*B_2_12-B_5_12-B_11_12+(a31+a41)/(a21+a11)*B_2_15-(a31+a41)/(a21+a11)*B_5_15-B_8_15+B_11_15],[-B_12_4+B_12_7-(a41+a21)/a11*B_3_10-B_6_10-B_12_10+(a31+a41)/(a21+a11)*B_3_13-(a31+a41)/(a21+a11)*B_6_13-B_9_13+B_12_13,-B_12_5+B_12_8-(a41+a21)/a11*B_3_11-B_6_11-B_12_11+(a31+a41)/(a21+a11)*B_3_14-(a31+a41)/(a21+a11)*B_6_14-B_9_14+B_12_14,-B_12_6+B_12_9-(a41+a21)/a11*B_3_12-B_6_12-B_12_12+(a31+a41)/(a21+a11)*B_3_15-(a31+a41)/(a21+a11)*B_6_15-B_9_15+B_12_15]]),Matrix(3, 6, [[C_10_6,C_10_7,C_10_8,C_10_9,C_10_10,C_10_11],[C_11_6,C_11_7,C_11_8,C_11_9,C_11_10,C_11_11],[C_12_6,C_12_7,C_12_8,C_12_9,C_12_10,C_12_11]])))+Trace(Mul(Matrix(5, 3, [[A_1_10+A_1_13,A_1_11+A_1_14,A_1_12+A_1_15],[A_2_10+A_2_13,A_2_11+A_2_14,A_2_12+A_2_15],[A_3_10+A_3_13,A_3_11+A_3_14,A_3_12+A_3_15],[A_4_10+A_4_13,A_4_11+A_4_14,A_4_12+A_4_15],[A_5_10+A_5_13,A_5_11+A_5_14,A_5_12+A_5_15]]),Matrix(3, 3, [[-a51/a41*B_10_1-B_13_1+B_13_4-B_13_7-a51/a11*B_1_10+B_13_10-a41/(a21+a31)*B_4_16+a41/(a21+a31)*B_7_16+B_10_16,-a51/a41*B_10_2-B_13_2+B_13_5-B_13_8-a51/a11*B_1_11+B_13_11-a41/(a21+a31)*B_4_17+a41/(a21+a31)*B_7_17+B_10_17,-a51/a41*B_10_3-B_13_3+B_13_6-B_13_9-a51/a11*B_1_12+B_13_12-a41/(a21+a31)*B_4_18+a41/(a21+a31)*B_7_18+B_10_18],[-a51/a41*B_11_1-B_14_1+B_14_4-B_14_7-a51/a11*B_2_10+B_14_10-a41/(a21+a31)*B_5_16+a41/(a21+a31)*B_8_16+B_11_16,-a51/a41*B_11_2-B_14_2+B_14_5-B_14_8-a51/a11*B_2_11+B_14_11-a41/(a21+a31)*B_5_17+a41/(a21+a31)*B_8_17+B_11_17,-a51/a41*B_11_3-B_14_3+B_14_6-B_14_9-a51/a11*B_2_12+B_14_12-a41/(a21+a31)*B_5_18+a41/(a21+a31)*B_8_18+B_11_18],[-a51/a41*B_12_1-B_15_1+B_15_4-B_15_7-a51/a11*B_3_10+B_15_10-a41/(a21+a31)*B_6_16+a41/(a21+a31)*B_9_16+B_12_16,-a51/a41*B_12_2-B_15_2+B_15_5-B_15_8-a51/a11*B_3_11+B_15_11-a41/(a21+a31)*B_6_17+a41/(a21+a31)*B_9_17+B_12_17,-a51/a41*B_12_3-B_15_3+B_15_6-B_15_9-a51/a11*B_3_12+B_15_12-a41/(a21+a31)*B_6_18+a41/(a21+a31)*B_9_18+B_12_18]]),Matrix(3, 5, [[C_10_1+C_13_1,C_10_2+C_13_2,C_10_3+C_13_3,C_10_4+C_13_4,C_10_5+C_13_5],[C_11_1+C_14_1,C_11_2+C_14_2,C_11_3+C_14_3,C_11_4+C_14_4,C_11_5+C_14_5],[C_12_1+C_15_1,C_12_2+C_15_2,C_12_3+C_15_3,C_12_4+C_15_4,C_12_5+C_15_5]])))+Trace(Mul(Matrix(6, 3, [[A_6_7+A_6_10,A_6_8+A_6_11,A_6_9+A_6_12],[A_7_7+A_7_10,A_7_8+A_7_11,A_7_9+A_7_12],[A_8_7+A_8_10,A_8_8+A_8_11,A_8_9+A_8_12],[A_9_7+A_9_10,A_9_8+A_9_11,A_9_9+A_9_12],[A_10_7+A_10_10,A_10_8+A_10_11,A_10_9+A_10_12],[A_11_7+A_11_10,A_11_8+A_11_11,A_11_9+A_11_12]]),Matrix(3, 3, [[-B_10_4+B_10_7-a31/(a21+a11)*B_1_13+a31/(a21+a11)*B_4_13+B_7_13,-B_10_5+B_10_8-a31/(a21+a11)*B_1_14+a31/(a21+a11)*B_4_14+B_7_14,-B_10_6+B_10_9-a31/(a21+a11)*B_1_15+a31/(a21+a11)*B_4_15+B_7_15],[-B_11_4+B_11_7-a31/(a21+a11)*B_2_13+a31/(a21+a11)*B_5_13+B_8_13,-B_11_5+B_11_8-a31/(a21+a11)*B_2_14+a31/(a21+a11)*B_5_14+B_8_14,-B_11_6+B_11_9-a31/(a21+a11)*B_2_15+a31/(a21+a11)*B_5_15+B_8_15],[-B_12_4+B_12_7-a31/(a21+a11)*B_3_13+a31/(a21+a11)*B_6_13+B_9_13,-B_12_5+B_12_8-a31/(a21+a11)*B_3_14+a31/(a21+a11)*B_6_14+B_9_14,-B_12_6+B_12_9-a31/(a21+a11)*B_3_15+a31/(a21+a11)*B_6_15+B_9_15]]),Matrix(3, 6, [[C_7_6+C_10_6,C_7_7+C_10_7,C_10_8+C_7_8,C_10_9+C_7_9,C_10_10+C_7_10,C_7_11+C_10_11],[C_8_6+C_11_6,C_8_7+C_11_7,C_8_8+C_11_8,C_8_9+C_11_9,C_8_10+C_11_10,C_8_11+C_11_11],[C_9_6+C_12_6,C_9_7+C_12_7,C_9_8+C_12_8,C_9_9+C_12_9,C_9_10+C_12_10,C_9_11+C_12_11]])))+Trace(Mul(Matrix(6, 3, [[A_6_10+A_6_13,A_6_11+A_6_14,A_6_12+A_6_15],[A_7_10+A_7_13,A_7_11+A_7_14,A_7_12+A_7_15],[A_8_10+A_8_13,A_8_11+A_8_14,A_8_12+A_8_15],[A_9_10+A_9_13,A_9_11+A_9_14,A_9_12+A_9_15],[A_10_10+A_10_13,A_10_11+A_10_14,A_10_12+A_10_15],[A_11_10+A_11_13,A_11_11+A_11_14,A_11_12+A_11_15]]),Matrix(3, 3, [[1/a11*B_1_10+(a31+a41)/(a21+a11)*B_1_13-(a31+a41)/(a21+a11)*B_4_13-B_7_13+B_10_13,1/a11*B_1_11+(a31+a41)/(a21+a11)*B_1_14-(a31+a41)/(a21+a11)*B_4_14-B_7_14+B_10_14,1/a11*B_1_12+(a31+a41)/(a21+a11)*B_1_15-(a31+a41)/(a21+a11)*B_4_15-B_7_15+B_10_15],[1/a11*B_2_10+(a31+a41)/(a21+a11)*B_2_13-(a31+a41)/(a21+a11)*B_5_13-B_8_13+B_11_13,1/a11*B_2_11+(a31+a41)/(a21+a11)*B_2_14-(a31+a41)/(a21+a11)*B_5_14-B_8_14+B_11_14,1/a11*B_2_12+(a31+a41)/(a21+a11)*B_2_15-(a31+a41)/(a21+a11)*B_5_15-B_8_15+B_11_15],[1/a11*B_3_10+(a31+a41)/(a21+a11)*B_3_13-(a31+a41)/(a21+a11)*B_6_13-B_9_13+B_12_13,1/a11*B_3_11+(a31+a41)/(a21+a11)*B_3_14-(a31+a41)/(a21+a11)*B_6_14-B_9_14+B_12_14,1/a11*B_3_12+(a31+a41)/(a21+a11)*B_3_15-(a31+a41)/(a21+a11)*B_6_15-B_9_15+B_12_15]]),Matrix(3, 6, [[C_10_6+C_13_6,C_10_7+C_13_7,C_10_8+C_13_8,C_10_9+C_13_9,C_10_10+C_13_10,C_10_11+C_13_11],[C_11_6+C_14_6,C_11_7+C_14_7,C_11_8+C_14_8,C_11_9+C_14_9,C_11_10+C_14_10,C_11_11+C_14_11],[C_12_6+C_15_6,C_12_7+C_15_7,C_12_8+C_15_8,C_12_9+C_15_9,C_12_10+C_15_10,C_12_11+C_15_11]])))+Trace(Mul(Matrix(5, 3, [[A_1_13-A_7_13,A_1_14-A_7_14,A_1_15-A_7_15],[A_2_13-A_8_13,A_2_14-A_8_14,A_2_15-A_8_15],[A_3_13-A_9_13,A_3_14-A_9_14,A_3_15-A_9_15],[A_4_13-A_10_13,A_4_14-A_10_14,A_4_15-A_10_15],[A_5_13-A_11_13,A_5_14-A_11_14,A_5_15-A_11_15]]),Matrix(3, 3, [[a51/a41*B_10_1+B_13_1-B_13_4+B_13_7+a51/a11*B_1_10-B_13_10+(-a51+a21-a31)/(a21+a11)*B_1_13+(a51+a11+a31)/(a21+a11)*B_4_13+B_7_13+B_13_13-(a41+a51)/(a21+a31)*B_4_16+(a41+a51)/(a21+a31)*B_7_16+B_10_16-B_13_16,a51/a41*B_10_2+B_13_2-B_13_5+B_13_8+a51/a11*B_1_11-B_13_11+(-a51+a21-a31)/(a21+a11)*B_1_14+(a51+a11+a31)/(a21+a11)*B_4_14+B_7_14+B_13_14-(a41+a51)/(a21+a31)*B_4_17+(a41+a51)/(a21+a31)*B_7_17+B_10_17-B_13_17,a51/a41*B_10_3+B_13_3-B_13_6+B_13_9+a51/a11*B_1_12-B_13_12+(-a51+a21-a31)/(a21+a11)*B_1_15+(a51+a11+a31)/(a21+a11)*B_4_15+B_7_15+B_13_15-(a41+a51)/(a21+a31)*B_4_18+(a41+a51)/(a21+a31)*B_7_18+B_10_18-B_13_18],[a51/a41*B_11_1+B_14_1-B_14_4+B_14_7+a51/a11*B_2_10-B_14_10+(-a51+a21-a31)/(a21+a11)*B_2_13+(a51+a11+a31)/(a21+a11)*B_5_13+B_8_13+B_14_13-(a41+a51)/(a21+a31)*B_5_16+(a41+a51)/(a21+a31)*B_8_16+B_11_16-B_14_16,a51/a41*B_11_2+B_14_2-B_14_5+B_14_8+a51/a11*B_2_11-B_14_11+(-a51+a21-a31)/(a21+a11)*B_2_14+(a51+a11+a31)/(a21+a11)*B_5_14+B_8_14+B_14_14-(a41+a51)/(a21+a31)*B_5_17+(a41+a51)/(a21+a31)*B_8_17+B_11_17-B_14_17,a51/a41*B_11_3+B_14_3-B_14_6+B_14_9+a51/a11*B_2_12-B_14_12+(-a51+a21-a31)/(a21+a11)*B_2_15+(a51+a11+a31)/(a21+a11)*B_5_15+B_8_15+B_14_15-(a41+a51)/(a21+a31)*B_5_18+(a41+a51)/(a21+a31)*B_8_18+B_11_18-B_14_18],[a51/a41*B_12_1+B_15_1-B_15_4+B_15_7+a51/a11*B_3_10-B_15_10+(-a51+a21-a31)/(a21+a11)*B_3_13+(a51+a11+a31)/(a21+a11)*B_6_13+B_9_13+B_15_13-(a41+a51)/(a21+a31)*B_6_16+(a41+a51)/(a21+a31)*B_9_16+B_12_16-B_15_16,a51/a41*B_12_2+B_15_2-B_15_5+B_15_8+a51/a11*B_3_11-B_15_11+(-a51+a21-a31)/(a21+a11)*B_3_14+(a51+a11+a31)/(a21+a11)*B_6_14+B_9_14+B_15_14-(a41+a51)/(a21+a31)*B_6_17+(a41+a51)/(a21+a31)*B_9_17+B_12_17-B_15_17,a51/a41*B_12_3+B_15_3-B_15_6+B_15_9+a51/a11*B_3_12-B_15_12+(-a51+a21-a31)/(a21+a11)*B_3_15+(a51+a11+a31)/(a21+a11)*B_6_15+B_9_15+B_15_15-(a41+a51)/(a21+a31)*B_6_18+(a41+a51)/(a21+a31)*B_9_18+B_12_18-B_15_18]]),Matrix(3, 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]])))+Trace(Mul(Matrix(6, 3, [[A_6_13,A_6_14,A_6_15],[A_1_10+A_7_13,A_1_11+A_7_14,A_1_12+A_7_15],[A_2_10+A_8_13,A_2_11+A_8_14,A_2_12+A_8_15],[A_3_10+A_9_13,A_3_11+A_9_14,A_3_12+A_9_15],[A_4_10+A_10_13,A_4_11+A_10_14,A_4_12+A_10_15],[A_5_10+A_11_13,A_5_11+A_11_14,A_5_12+A_11_15]]),Matrix(3, 3, [[a51/a41*B_10_1+B_13_1-B_13_4+B_13_7+a51/a11*B_1_10-B_13_10+(a31+a41)/(a21+a11)*B_1_13-(a31+a41)/(a21+a11)*B_4_13-B_7_13+B_10_13,a51/a41*B_10_2+B_13_2-B_13_5+B_13_8+a51/a11*B_1_11-B_13_11+(a31+a41)/(a21+a11)*B_1_14-(a31+a41)/(a21+a11)*B_4_14-B_7_14+B_10_14,a51/a41*B_10_3+B_13_3-B_13_6+B_13_9+a51/a11*B_1_12-B_13_12+(a31+a41)/(a21+a11)*B_1_15-(a31+a41)/(a21+a11)*B_4_15-B_7_15+B_10_15],[a51/a41*B_11_1+B_14_1-B_14_4+B_14_7+a51/a11*B_2_10-B_14_10+(a31+a41)/(a21+a11)*B_2_13-(a31+a41)/(a21+a11)*B_5_13-B_8_13+B_11_13,a51/a41*B_11_2+B_14_2-B_14_5+B_14_8+a51/a11*B_2_11-B_14_11+(a31+a41)/(a21+a11)*B_2_14-(a31+a41)/(a21+a11)*B_5_14-B_8_14+B_11_14,a51/a41*B_11_3+B_14_3-B_14_6+B_14_9+a51/a11*B_2_12-B_14_12+(a31+a41)/(a21+a11)*B_2_15-(a31+a41)/(a21+a11)*B_5_15-B_8_15+B_11_15],[a51/a41*B_12_1+B_15_1-B_15_4+B_15_7+a51/a11*B_3_10-B_15_10+(a31+a41)/(a21+a11)*B_3_13-(a31+a41)/(a21+a11)*B_6_13-B_9_13+B_12_13,a51/a41*B_12_2+B_15_2-B_15_5+B_15_8+a51/a11*B_3_11-B_15_11+(a31+a41)/(a21+a11)*B_3_14-(a31+a41)/(a21+a11)*B_6_14-B_9_14+B_12_14,a51/a41*B_12_3+B_15_3-B_15_6+B_15_9+a51/a11*B_3_12-B_15_12+(a31+a41)/(a21+a11)*B_3_15-(a31+a41)/(a21+a11)*B_6_15-B_9_15+B_12_15]]),Matrix(3, 6, [[-C_10_6,C_13_1-C_10_7,C_13_2-C_10_8,C_13_3-C_10_9,C_13_4-C_10_10,C_13_5-C_10_11],[-C_11_6,C_14_1-C_11_7,C_14_2-C_11_8,C_14_3-C_11_9,C_14_4-C_11_10,C_14_5-C_11_11],[-C_12_6,C_15_1-C_12_7,C_15_2-C_12_8,C_15_3-C_12_9,C_15_4-C_12_10,C_15_5-C_12_11]])))+Trace(Mul(Matrix(6, 3, [[A_6_4+A_6_7-A_6_10,A_6_5+A_6_8-A_6_11,A_6_6+A_6_9-A_6_12],[A_7_4+A_7_7+A_1_10-A_7_10,A_7_5+A_7_8+A_1_11-A_7_11,A_7_6+A_7_9+A_1_12-A_7_12],[A_8_4+A_8_7+A_2_10-A_8_10,A_8_5+A_8_8+A_2_11-A_8_11,A_8_6+A_8_9+A_2_12-A_8_12],[A_9_4+A_9_7+A_3_10-A_9_10,A_9_5+A_9_8+A_3_11-A_9_11,A_9_6+A_9_9+A_3_12-A_9_12],[A_10_4+A_10_7+A_4_10-A_10_10,A_10_5+A_10_8+A_4_11-A_10_11,A_10_6+A_10_9+A_4_12-A_10_12],[A_11_4+A_11_7+A_5_10-A_11_10,A_11_5+A_11_8+A_5_11-A_11_11,A_11_6+A_11_9+A_5_12-A_11_12]]),Matrix(3, 3, [[-B_10_1-a41/a51*B_13_1+B_10_4+a41/a51*B_13_4-a21/a11*B_1_10-B_4_10,-B_10_2-a41/a51*B_13_2+B_10_5+a41/a51*B_13_5-a21/a11*B_1_11-B_4_11,-B_10_3-a41/a51*B_13_3+B_10_6+a41/a51*B_13_6-a21/a11*B_1_12-B_4_12],[-B_11_1-a41/a51*B_14_1+B_11_4+a41/a51*B_14_4-a21/a11*B_2_10-B_5_10,-B_11_2-a41/a51*B_14_2+B_11_5+a41/a51*B_14_5-a21/a11*B_2_11-B_5_11,-B_11_3-a41/a51*B_14_3+B_11_6+a41/a51*B_14_6-a21/a11*B_2_12-B_5_12],[-B_12_1-a41/a51*B_15_1+B_12_4+a41/a51*B_15_4-a21/a11*B_3_10-B_6_10,-B_12_2-a41/a51*B_15_2+B_12_5+a41/a51*B_15_5-a21/a11*B_3_11-B_6_11,-B_12_3-a41/a51*B_15_3+B_12_6+a41/a51*B_15_6-a21/a11*B_3_12-B_6_12]]),Matrix(3, 6, [[-C_10_6,C_4_1+C_7_1-C_10_1-C_10_7,C_4_2+C_7_2-C_10_2-C_10_8,C_4_3+C_7_3-C_10_3-C_10_9,C_4_4+C_7_4-C_10_4-C_10_10,C_4_5+C_7_5-C_10_5-C_10_11],[-C_11_6,C_5_1+C_8_1-C_11_1-C_11_7,C_5_2+C_8_2-C_11_2-C_11_8,C_5_3+C_8_3-C_11_3-C_11_9,C_5_4+C_8_4-C_11_4-C_11_10,C_5_5+C_8_5-C_11_5-C_11_11],[-C_12_6,C_9_1+C_6_1-C_12_1-C_12_7,C_9_2+C_6_2-C_12_2-C_12_8,C_6_3+C_9_3-C_12_3-C_12_9,C_6_4+C_9_4-C_12_4-C_12_10,C_6_5+C_9_5-C_12_5-C_12_11]])))+Trace(Mul(Matrix(6, 3, [[A_6_7,A_6_8,A_6_9],[A_1_1+A_1_4-A_1_7+A_7_7,A_1_2+A_1_5-A_1_8+A_7_8,A_1_3+A_1_6-A_1_9+A_7_9],[A_2_1+A_2_4-A_2_7+A_8_7,A_2_2+A_2_5-A_2_8+A_8_8,A_2_3+A_2_6-A_2_9+A_8_9],[A_3_1+A_3_4-A_3_7+A_9_7,A_3_2+A_3_5-A_3_8+A_9_8,A_3_3+A_3_6-A_3_9+A_9_9],[A_4_1+A_4_4-A_4_7+A_10_7,A_4_2+A_4_5-A_4_8+A_10_8,A_4_3+A_4_6-A_4_9+A_10_9],[A_5_1+A_5_4-A_5_7+A_11_7,A_5_2+A_5_5-A_5_8+A_11_8,A_5_3+A_5_6-A_5_9+A_11_9]]),Matrix(3, 3, [[-B_7_1+(-a31+a11)/a41*B_10_1+a11/a51*B_13_1-a11/a51*B_13_4+B_1_7,-B_7_2+(-a31+a11)/a41*B_10_2+a11/a51*B_13_2-a11/a51*B_13_5+B_1_8,-B_7_3+(-a31+a11)/a41*B_10_3+a11/a51*B_13_3-a11/a51*B_13_6+B_1_9],[-B_8_1+(-a31+a11)/a41*B_11_1+a11/a51*B_14_1-a11/a51*B_14_4+B_2_7,-B_8_2+(-a31+a11)/a41*B_11_2+a11/a51*B_14_2-a11/a51*B_14_5+B_2_8,-B_8_3+(-a31+a11)/a41*B_11_3+a11/a51*B_14_3-a11/a51*B_14_6+B_2_9],[-B_9_1+(-a31+a11)/a41*B_12_1+a11/a51*B_15_1-a11/a51*B_15_4+B_3_7,-B_9_2+(-a31+a11)/a41*B_12_2+a11/a51*B_15_2-a11/a51*B_15_5+B_3_8,-B_9_3+(-a31+a11)/a41*B_12_3+a11/a51*B_15_3-a11/a51*B_15_6+B_3_9]]),Matrix(3, 6, [[-C_1_6-C_4_6+C_7_6,C_7_1-C_1_7-C_4_7+C_7_7,C_7_2-C_1_8-C_4_8+C_7_8,C_7_3-C_1_9-C_4_9+C_7_9,C_7_4-C_1_10-C_4_10+C_7_10,C_7_5-C_1_11-C_4_11+C_7_11],[-C_2_6-C_5_6+C_8_6,C_8_1-C_2_7-C_5_7+C_8_7,C_8_2-C_2_8-C_5_8+C_8_8,C_8_3-C_2_9-C_5_9+C_8_9,C_8_4-C_2_10-C_5_10+C_8_10,C_8_5-C_2_11-C_5_11+C_8_11],[-C_3_6-C_6_6+C_9_6,C_9_1-C_3_7-C_6_7+C_9_7,C_9_2-C_3_8-C_6_8+C_9_8,C_9_3-C_3_9-C_6_9+C_9_9,C_9_4-C_3_10-C_6_10+C_9_10,C_9_5-C_3_11-C_6_11+C_9_11]])))+Trace(Mul(Matrix(6, 3, [[A_6_13,A_6_14,A_6_15],[A_1_1+A_1_4-A_1_13+A_7_13,A_1_2+A_1_5-A_1_14+A_7_14,A_1_3+A_1_6-A_1_15+A_7_15],[A_2_1+A_2_4-A_2_13+A_8_13,A_2_2+A_2_5-A_2_14+A_8_14,A_2_3+A_2_6-A_2_15+A_8_15],[A_3_1+A_3_4-A_3_13+A_9_13,A_3_2+A_3_5-A_3_14+A_9_14,A_3_3+A_3_6-A_3_15+A_9_15],[A_4_1+A_4_4-A_4_13+A_10_13,A_4_2+A_4_5-A_4_14+A_10_14,A_4_3+A_4_6-A_4_15+A_10_15],[A_5_1+A_5_4-A_5_13+A_11_13,A_5_2+A_5_5-A_5_14+A_11_14,A_5_3+A_5_6-A_5_15+A_11_15]]),Matrix(3, 3, [[-a51/a41*B_10_1-B_13_1+a21/(a21+a11)*B_1_13+a11/(a21+a11)*B_4_13,-a51/a41*B_10_2-B_13_2+a21/(a21+a11)*B_1_14+a11/(a21+a11)*B_4_14,-a51/a41*B_10_3-B_13_3+a21/(a21+a11)*B_1_15+a11/(a21+a11)*B_4_15],[-a51/a41*B_11_1-B_14_1+a21/(a21+a11)*B_2_13+a11/(a21+a11)*B_5_13,-a51/a41*B_11_2-B_14_2+a21/(a21+a11)*B_2_14+a11/(a21+a11)*B_5_14,-a51/a41*B_11_3-B_14_3+a21/(a21+a11)*B_2_15+a11/(a21+a11)*B_5_15],[-a51/a41*B_12_1-B_15_1+a21/(a21+a11)*B_3_13+a11/(a21+a11)*B_6_13,-a51/a41*B_12_2-B_15_2+a21/(a21+a11)*B_3_14+a11/(a21+a11)*B_6_14,-a51/a41*B_12_3-B_15_3+a21/(a21+a11)*B_3_15+a11/(a21+a11)*B_6_15]]),Matrix(3, 6, [[-C_1_6-C_4_6+C_13_6,C_13_1-C_1_7-C_4_7+C_13_7,C_13_2-C_1_8-C_4_8+C_13_8,C_13_3-C_1_9-C_4_9+C_13_9,C_13_4-C_1_10-C_4_10+C_13_10,C_13_5-C_1_11-C_4_11+C_13_11],[-C_2_6-C_5_6+C_14_6,C_14_1-C_2_7-C_5_7+C_14_7,C_14_2-C_2_8-C_5_8+C_14_8,C_14_3-C_2_9-C_5_9+C_14_9,C_14_4-C_2_10-C_5_10+C_14_10,C_14_5-C_2_11-C_5_11+C_14_11],[-C_3_6-C_6_6+C_15_6,C_15_1-C_3_7-C_6_7+C_15_7,C_15_2-C_3_8-C_6_8+C_15_8,C_15_3-C_3_9-C_6_9+C_15_9,C_15_4-C_3_10-C_6_10+C_15_10,C_15_5-C_3_11-C_6_11+C_15_11]])))+Trace(Mul(Matrix(6, 3, [[A_6_13,A_6_14,A_6_15],[A_1_7+A_1_10-A_1_13+A_7_13,A_1_8+A_1_11-A_1_14+A_7_14,A_1_9+A_1_12-A_1_15+A_7_15],[A_2_7+A_2_10-A_2_13+A_8_13,A_2_8+A_2_11-A_2_14+A_8_14,A_2_9+A_2_12-A_2_15+A_8_15],[A_3_7+A_3_10-A_3_13+A_9_13,A_3_8+A_3_11-A_3_14+A_9_14,A_3_9+A_3_12-A_3_15+A_9_15],[A_4_7+A_4_10-A_4_13+A_10_13,A_4_8+A_4_11-A_4_14+A_10_14,A_4_9+A_4_12-A_4_15+A_10_15],[A_5_7+A_5_10-A_5_13+A_11_13,A_5_8+A_5_11-A_5_14+A_11_14,A_5_9+A_5_12-A_5_15+A_11_15]]),Matrix(3, 3, [[-a51/a41*B_10_1-B_13_1+B_13_4-B_13_7-a31/(a21+a11)*B_1_13+a31/(a21+a11)*B_4_13+B_7_13,-a51/a41*B_10_2-B_13_2+B_13_5-B_13_8-a31/(a21+a11)*B_1_14+a31/(a21+a11)*B_4_14+B_7_14,-a51/a41*B_10_3-B_13_3+B_13_6-B_13_9-a31/(a21+a11)*B_1_15+a31/(a21+a11)*B_4_15+B_7_15],[-a51/a41*B_11_1-B_14_1+B_14_4-B_14_7-a31/(a21+a11)*B_2_13+a31/(a21+a11)*B_5_13+B_8_13,-a51/a41*B_11_2-B_14_2+B_14_5-B_14_8-a31/(a21+a11)*B_2_14+a31/(a21+a11)*B_5_14+B_8_14,-a51/a41*B_11_3-B_14_3+B_14_6-B_14_9-a31/(a21+a11)*B_2_15+a31/(a21+a11)*B_5_15+B_8_15],[-a51/a41*B_12_1-B_15_1+B_15_4-B_15_7-a31/(a21+a11)*B_3_13+a31/(a21+a11)*B_6_13+B_9_13,-a51/a41*B_12_2-B_15_2+B_15_5-B_15_8-a31/(a21+a11)*B_3_14+a31/(a21+a11)*B_6_14+B_9_14,-a51/a41*B_12_3-B_15_3+B_15_6-B_15_9-a31/(a21+a11)*B_3_15+a31/(a21+a11)*B_6_15+B_9_15]]),Matrix(3, 6, [[-C_7_6-C_10_6+C_13_6,C_13_1-C_7_7-C_10_7+C_13_7,C_13_2-C_7_8-C_10_8+C_13_8,C_13_3-C_7_9-C_10_9+C_13_9,C_13_4-C_7_10-C_10_10+C_13_10,C_13_5-C_7_11-C_10_11+C_13_11],[-C_8_6-C_11_6+C_14_6,C_14_1-C_8_7-C_11_7+C_14_7,C_14_2-C_8_8-C_11_8+C_14_8,C_14_3-C_8_9-C_11_9+C_14_9,C_14_4-C_8_10-C_11_10+C_14_10,C_14_5-C_8_11-C_11_11+C_14_11],[-C_9_6-C_12_6+C_15_6,C_15_1-C_9_7-C_12_7+C_15_7,C_15_2-C_9_8-C_12_8+C_15_8,C_15_3-C_9_9-C_12_9+C_15_9,C_15_4-C_9_10-C_12_10+C_15_10,C_15_5-C_9_11-C_12_11+C_15_11]])))+Trace(Mul(Matrix(6, 3, [[-A_6_1-A_6_4+A_6_7,-A_6_2-A_6_5+A_6_8,-A_6_3-A_6_6+A_6_9],[A_1_1-A_7_1+A_1_4-A_7_4-A_1_7+A_7_7,A_1_2-A_7_2+A_1_5-A_7_5-A_1_8+A_7_8,A_1_3-A_7_3+A_1_6-A_7_6-A_1_9+A_7_9],[A_2_1-A_8_1+A_2_4-A_8_4-A_2_7+A_8_7,A_2_2-A_8_2+A_2_5-A_8_5-A_2_8+A_8_8,A_2_3-A_8_3+A_2_6-A_8_6-A_2_9+A_8_9],[A_3_1-A_9_1+A_3_4-A_9_4-A_3_7+A_9_7,A_3_2-A_9_2+A_3_5-A_9_5-A_3_8+A_9_8,A_3_3-A_9_3+A_3_6-A_9_6-A_3_9+A_9_9],[A_4_1-A_10_1+A_4_4-A_10_4-A_4_7+A_10_7,A_4_2-A_10_2+A_4_5-A_10_5-A_4_8+A_10_8,A_4_3-A_10_3+A_4_6-A_10_6-A_4_9+A_10_9],[A_5_1-A_11_1+A_5_4-A_11_4-A_5_7+A_11_7,A_5_2-A_11_2+A_5_5-A_11_5-A_5_8+A_11_8,A_5_3-A_11_3+A_5_6-A_11_6-A_5_9+A_11_9]]),Matrix(3, 3, [[a11/a41*B_10_1+a11/a51*B_13_1-a11/a51*B_13_4+B_1_7,a11/a41*B_10_2+a11/a51*B_13_2-a11/a51*B_13_5+B_1_8,a11/a41*B_10_3+a11/a51*B_13_3-a11/a51*B_13_6+B_1_9],[a11/a41*B_11_1+a11/a51*B_14_1-a11/a51*B_14_4+B_2_7,a11/a41*B_11_2+a11/a51*B_14_2-a11/a51*B_14_5+B_2_8,a11/a41*B_11_3+a11/a51*B_14_3-a11/a51*B_14_6+B_2_9],[a11/a41*B_12_1+a11/a51*B_15_1-a11/a51*B_15_4+B_3_7,a11/a41*B_12_2+a11/a51*B_15_2-a11/a51*B_15_5+B_3_8,a11/a41*B_12_3+a11/a51*B_15_3-a11/a51*B_15_6+B_3_9]]),Matrix(3, 6, [[C_1_6+C_4_6-C_7_6,C_1_7+C_4_7-C_7_7,C_1_8+C_4_8-C_7_8,C_1_9+C_4_9-C_7_9,C_1_10+C_4_10-C_7_10,C_1_11+C_4_11-C_7_11],[C_2_6+C_5_6-C_8_6,C_2_7+C_5_7-C_8_7,C_2_8+C_5_8-C_8_8,C_2_9+C_5_9-C_8_9,C_2_10+C_5_10-C_8_10,C_2_11+C_5_11-C_8_11],[C_3_6+C_6_6-C_9_6,C_3_7+C_6_7-C_9_7,C_3_8+C_6_8-C_9_8,C_3_9+C_6_9-C_9_9,C_3_10+C_6_10-C_9_10,C_3_11+C_6_11-C_9_11]])))+Trace(Mul(Matrix(6, 3, [[-A_6_1-A_6_4+A_6_13,-A_6_2-A_6_5+A_6_14,-A_6_3-A_6_6+A_6_15],[A_1_1-A_7_1+A_1_4-A_7_4-A_1_13+A_7_13,A_1_2-A_7_2+A_1_5-A_7_5-A_1_14+A_7_14,A_1_3-A_7_3+A_1_6-A_7_6-A_1_15+A_7_15],[A_2_1-A_8_1+A_2_4-A_8_4-A_2_13+A_8_13,A_2_2-A_8_2+A_2_5-A_8_5-A_2_14+A_8_14,A_2_3-A_8_3+A_2_6-A_8_6-A_2_15+A_8_15],[A_3_1-A_9_1+A_3_4-A_9_4-A_3_13+A_9_13,A_3_2-A_9_2+A_3_5-A_9_5-A_3_14+A_9_14,A_3_3-A_9_3+A_3_6-A_9_6-A_3_15+A_9_15],[A_4_1-A_10_1+A_4_4-A_10_4-A_4_13+A_10_13,A_4_2-A_10_2+A_4_5-A_10_5-A_4_14+A_10_14,A_4_3-A_10_3+A_4_6-A_10_6-A_4_15+A_10_15],[A_5_1-A_11_1+A_5_4-A_11_4-A_5_13+A_11_13,A_5_2-A_11_2+A_5_5-A_11_5-A_5_14+A_11_14,A_5_3-A_11_3+A_5_6-A_11_6-A_5_15+A_11_15]]),Matrix(3, 3, [[a21/(a21+a11)*B_1_13+a11/(a21+a11)*B_4_13,a21/(a21+a11)*B_1_14+a11/(a21+a11)*B_4_14,a21/(a21+a11)*B_1_15+a11/(a21+a11)*B_4_15],[a21/(a21+a11)*B_2_13+a11/(a21+a11)*B_5_13,a21/(a21+a11)*B_2_14+a11/(a21+a11)*B_5_14,a21/(a21+a11)*B_2_15+a11/(a21+a11)*B_5_15],[a21/(a21+a11)*B_3_13+a11/(a21+a11)*B_6_13,a21/(a21+a11)*B_3_14+a11/(a21+a11)*B_6_14,a21/(a21+a11)*B_3_15+a11/(a21+a11)*B_6_15]]),Matrix(3, 6, [[C_1_6+C_4_6-C_13_6,C_1_7+C_4_7-C_13_7,C_1_8+C_4_8-C_13_8,C_1_9+C_4_9-C_13_9,C_1_10+C_4_10-C_13_10,C_1_11+C_4_11-C_13_11],[C_2_6+C_5_6-C_14_6,C_2_7+C_5_7-C_14_7,C_2_8+C_5_8-C_14_8,C_2_9+C_5_9-C_14_9,C_2_10+C_5_10-C_14_10,C_2_11+C_5_11-C_14_11],[C_3_6+C_6_6-C_15_6,C_3_7+C_6_7-C_15_7,C_3_8+C_6_8-C_15_8,C_3_9+C_6_9-C_15_9,C_3_10+C_6_10-C_15_10,C_3_11+C_6_11-C_15_11]])))+Trace(Mul(Matrix(6, 3, [[-A_6_7-A_6_10+A_6_13,-A_6_8-A_6_11+A_6_14,-A_6_9-A_6_12+A_6_15],[A_1_7-A_7_7+A_1_10-A_7_10-A_1_13+A_7_13,A_1_8-A_7_8+A_1_11-A_7_11-A_1_14+A_7_14,A_1_9-A_7_9+A_1_12-A_7_12-A_1_15+A_7_15],[A_2_7-A_8_7+A_2_10-A_8_10-A_2_13+A_8_13,A_2_8-A_8_8+A_2_11-A_8_11-A_2_14+A_8_14,A_2_9-A_8_9+A_2_12-A_8_12-A_2_15+A_8_15],[A_3_7-A_9_7+A_3_10-A_9_10-A_3_13+A_9_13,A_3_8-A_9_8+A_3_11-A_9_11-A_3_14+A_9_14,A_3_9-A_9_9+A_3_12-A_9_12-A_3_15+A_9_15],[A_4_7-A_10_7+A_4_10-A_10_10-A_4_13+A_10_13,A_4_8-A_10_8+A_4_11-A_10_11-A_4_14+A_10_14,A_4_9-A_10_9+A_4_12-A_10_12-A_4_15+A_10_15],[A_5_7-A_11_7+A_5_10-A_11_10-A_5_13+A_11_13,A_5_8-A_11_8+A_5_11-A_11_11-A_5_14+A_11_14,A_5_9-A_11_9+A_5_12-A_11_12-A_5_15+A_11_15]]),Matrix(3, 3, [[-a31/(a21+a11)*B_1_13+a31/(a21+a11)*B_4_13+B_7_13,-a31/(a21+a11)*B_1_14+a31/(a21+a11)*B_4_14+B_7_14,-a31/(a21+a11)*B_1_15+a31/(a21+a11)*B_4_15+B_7_15],[-a31/(a21+a11)*B_2_13+a31/(a21+a11)*B_5_13+B_8_13,-a31/(a21+a11)*B_2_14+a31/(a21+a11)*B_5_14+B_8_14,-a31/(a21+a11)*B_2_15+a31/(a21+a11)*B_5_15+B_8_15],[-a31/(a21+a11)*B_3_13+a31/(a21+a11)*B_6_13+B_9_13,-a31/(a21+a11)*B_3_14+a31/(a21+a11)*B_6_14+B_9_14,-a31/(a21+a11)*B_3_15+a31/(a21+a11)*B_6_15+B_9_15]]),Matrix(3, 6, [[C_7_6+C_10_6-C_13_6,C_7_7+C_10_7-C_13_7,C_10_8+C_7_8-C_13_8,C_10_9+C_7_9-C_13_9,C_10_10+C_7_10-C_13_10,C_7_11+C_10_11-C_13_11],[C_8_6+C_11_6-C_14_6,C_8_7+C_11_7-C_14_7,C_8_8+C_11_8-C_14_8,C_8_9+C_11_9-C_14_9,C_8_10+C_11_10-C_14_10,C_8_11+C_11_11-C_14_11],[C_9_6+C_12_6-C_15_6,C_9_7+C_12_7-C_15_7,C_9_8+C_12_8-C_15_8,C_9_9+C_12_9-C_15_9,C_9_10+C_12_10-C_15_10,C_9_11+C_12_11-C_15_11]])))+Trace(Mul(Matrix(5, 3, [[A_1_1*a11-A_1_10*a41+A_1_13*a51-A_1_4*a21+A_1_7*a31,-A_1_11*a41+A_1_14*a51+A_1_2*a11-A_1_5*a21+A_1_8*a31,-A_1_12*a41+A_1_15*a51+A_1_3*a11-A_1_6*a21+A_1_9*a31],[A_2_1*a11-A_2_10*a41+A_2_13*a51-A_2_4*a21+A_2_7*a31,-A_2_11*a41+A_2_14*a51+A_2_2*a11-A_2_5*a21+A_2_8*a31,-A_2_12*a41+A_2_15*a51+A_2_3*a11-A_2_6*a21+A_2_9*a31],[A_3_1*a11-A_3_10*a41+A_3_13*a51-A_3_4*a21+A_3_7*a31,-A_3_11*a41+A_3_14*a51+A_3_2*a11-A_3_5*a21+A_3_8*a31,-A_3_12*a41+A_3_15*a51+A_3_3*a11-A_3_6*a21+A_3_9*a31],[A_4_1*a11-A_4_10*a41+A_4_13*a51-A_4_4*a21+A_4_7*a31,-A_4_11*a41+A_4_14*a51+A_4_2*a11-A_4_5*a21+A_4_8*a31,-A_4_12*a41+A_4_15*a51+A_4_3*a11-A_4_6*a21+A_4_9*a31],[A_5_1*a11-A_5_10*a41+A_5_13*a51-A_5_4*a21+A_5_7*a31,-A_5_11*a41+A_5_14*a51+A_5_2*a11-A_5_5*a21+A_5_8*a31,-A_5_12*a41+A_5_15*a51+A_5_3*a11-A_5_6*a21+A_5_9*a31]]),Matrix(3, 3, [[-1/a41*B_10_1-1/a51*B_13_1+1/a51*B_13_4+1/a11*B_1_10-B_1_16-(a11+a41+a51+1)/(a21+a31)*B_4_16+(a11+a41+a51+1)/(a21+a31)*B_7_16+B_10_16-B_13_16,-1/a41*B_10_2-1/a51*B_13_2+1/a51*B_13_5+1/a11*B_1_11-B_1_17-(a11+a41+a51+1)/(a21+a31)*B_4_17+(a11+a41+a51+1)/(a21+a31)*B_7_17+B_10_17-B_13_17,-1/a41*B_10_3-1/a51*B_13_3+1/a51*B_13_6+1/a11*B_1_12-B_1_18-(a11+a41+a51+1)/(a21+a31)*B_4_18+(a11+a41+a51+1)/(a21+a31)*B_7_18+B_10_18-B_13_18],[-1/a41*B_11_1-1/a51*B_14_1+1/a51*B_14_4+1/a11*B_2_10-B_2_16-(a11+a41+a51+1)/(a21+a31)*B_5_16+(a11+a41+a51+1)/(a21+a31)*B_8_16+B_11_16-B_14_16,-1/a41*B_11_2-1/a51*B_14_2+1/a51*B_14_5+1/a11*B_2_11-B_2_17-(a11+a41+a51+1)/(a21+a31)*B_5_17+(a11+a41+a51+1)/(a21+a31)*B_8_17+B_11_17-B_14_17,-1/a41*B_11_3-1/a51*B_14_3+1/a51*B_14_6+1/a11*B_2_12-B_2_18-(a11+a41+a51+1)/(a21+a31)*B_5_18+(a11+a41+a51+1)/(a21+a31)*B_8_18+B_11_18-B_14_18],[-1/a41*B_12_1-1/a51*B_15_1+1/a51*B_15_4+1/a11*B_3_10-B_3_16-(a11+a41+a51+1)/(a21+a31)*B_6_16+(a11+a41+a51+1)/(a21+a31)*B_9_16+B_12_16-B_15_16,-1/a41*B_12_2-1/a51*B_15_2+1/a51*B_15_5+1/a11*B_3_11-B_3_17-(a11+a41+a51+1)/(a21+a31)*B_6_17+(a11+a41+a51+1)/(a21+a31)*B_9_17+B_12_17-B_15_17,-1/a41*B_12_3-1/a51*B_15_3+1/a51*B_15_6+1/a11*B_3_12-B_3_18-(a11+a41+a51+1)/(a21+a31)*B_6_18+(a11+a41+a51+1)/(a21+a31)*B_9_18+B_12_18-B_15_18]]),Matrix(3, 5, [[C_16_1+C_16_7,C_16_2+C_16_8,C_16_3+C_16_9,C_16_4+C_16_10,C_16_5+C_16_11],[C_17_1+C_17_7,C_17_2+C_17_8,C_17_3+C_17_9,C_17_4+C_17_10,C_17_5+C_17_11],[C_18_1+C_18_7,C_18_2+C_18_8,C_18_3+C_18_9,C_18_4+C_18_10,C_18_5+C_18_11]])))+Trace(Mul(Matrix(5, 3, [[A_1_1*a11-A_1_10*a41-A_1_4*a21+A_1_7*a31+(a51+1)*A_1_13,-A_1_11*a41+A_1_2*a11-A_1_5*a21+A_1_8*a31+(a51+1)*A_1_14,-A_1_12*a41+A_1_3*a11-A_1_6*a21+A_1_9*a31+(a51+1)*A_1_15],[A_2_1*a11-A_2_10*a41-A_2_4*a21+A_2_7*a31+(a51+1)*A_2_13,-A_2_11*a41+A_2_2*a11-A_2_5*a21+A_2_8*a31+(a51+1)*A_2_14,-A_2_12*a41+A_2_3*a11-A_2_6*a21+A_2_9*a31+(a51+1)*A_2_15],[A_3_1*a11-A_3_10*a41-A_3_4*a21+A_3_7*a31+(a51+1)*A_3_13,-A_3_11*a41+A_3_2*a11-A_3_5*a21+A_3_8*a31+(a51+1)*A_3_14,-A_3_12*a41+A_3_3*a11-A_3_6*a21+A_3_9*a31+(a51+1)*A_3_15],[A_4_1*a11-A_4_10*a41-A_4_4*a21+A_4_7*a31+(a51+1)*A_4_13,-A_4_11*a41+A_4_2*a11-A_4_5*a21+A_4_8*a31+(a51+1)*A_4_14,-A_4_12*a41+A_4_3*a11-A_4_6*a21+A_4_9*a31+(a51+1)*A_4_15],[A_5_1*a11-A_5_10*a41-A_5_4*a21+A_5_7*a31+(a51+1)*A_5_13,-A_5_11*a41+A_5_2*a11-A_5_5*a21+A_5_8*a31+(a51+1)*A_5_14,-A_5_12*a41+A_5_3*a11-A_5_6*a21+A_5_9*a31+(a51+1)*A_5_15]]),Matrix(3, 3, [[(a41+a51)/(a21+a31)*B_4_16-(a41+a51)/(a21+a31)*B_7_16-B_10_16+B_13_16,(a41+a51)/(a21+a31)*B_4_17-(a41+a51)/(a21+a31)*B_7_17-B_10_17+B_13_17,(a41+a51)/(a21+a31)*B_4_18-(a41+a51)/(a21+a31)*B_7_18-B_10_18+B_13_18],[(a41+a51)/(a21+a31)*B_5_16-(a41+a51)/(a21+a31)*B_8_16-B_11_16+B_14_16,(a41+a51)/(a21+a31)*B_5_17-(a41+a51)/(a21+a31)*B_8_17-B_11_17+B_14_17,(a41+a51)/(a21+a31)*B_5_18-(a41+a51)/(a21+a31)*B_8_18-B_11_18+B_14_18],[(a41+a51)/(a21+a31)*B_6_16-(a41+a51)/(a21+a31)*B_9_16-B_12_16+B_15_16,(a41+a51)/(a21+a31)*B_6_17-(a41+a51)/(a21+a31)*B_9_17-B_12_17+B_15_17,(a41+a51)/(a21+a31)*B_6_18-(a41+a51)/(a21+a31)*B_9_18-B_12_18+B_15_18]]),Matrix(3, 5, [[C_13_1+C_16_1,C_13_2+C_16_2,C_13_3+C_16_3,C_13_4+C_16_4,C_13_5+C_16_5],[C_14_1+C_17_1,C_14_2+C_17_2,C_14_3+C_17_3,C_14_4+C_17_4,C_14_5+C_17_5],[C_15_1+C_18_1,C_15_2+C_18_2,C_15_3+C_18_3,C_15_4+C_18_4,C_15_5+C_18_5]])))+Trace(Mul(Matrix(5, 3, [[(a11+1)*A_1_1-A_1_4*a21+A_1_7*a31-A_1_10*a41+A_1_13*a51,(a11+1)*A_1_2-A_1_5*a21+A_1_8*a31-A_1_11*a41+A_1_14*a51,(a11+1)*A_1_3-A_1_6*a21+A_1_9*a31-A_1_12*a41+A_1_15*a51],[(a11+1)*A_2_1-A_2_4*a21+A_2_7*a31-A_2_10*a41+A_2_13*a51,(a11+1)*A_2_2-A_2_5*a21+A_2_8*a31-A_2_11*a41+A_2_14*a51,(a11+1)*A_2_3-A_2_6*a21+A_2_9*a31-A_2_12*a41+A_2_15*a51],[(a11+1)*A_3_1-A_3_4*a21+A_3_7*a31-A_3_10*a41+A_3_13*a51,(a11+1)*A_3_2-A_3_5*a21+A_3_8*a31-A_3_11*a41+A_3_14*a51,(a11+1)*A_3_3-A_3_6*a21+A_3_9*a31-A_3_12*a41+A_3_15*a51],[(a11+1)*A_4_1-A_4_4*a21+A_4_7*a31-A_4_10*a41+A_4_13*a51,(a11+1)*A_4_2-A_4_5*a21+A_4_8*a31-A_4_11*a41+A_4_14*a51,(a11+1)*A_4_3-A_4_6*a21+A_4_9*a31-A_4_12*a41+A_4_15*a51],[(a11+1)*A_5_1-A_5_4*a21+A_5_7*a31-A_5_10*a41+A_5_13*a51,(a11+1)*A_5_2-A_5_5*a21+A_5_8*a31-A_5_11*a41+A_5_14*a51,(a11+1)*A_5_3-A_5_6*a21+A_5_9*a31-A_5_12*a41+A_5_15*a51]]),Matrix(3, 3, [[B_1_16+a11/(a21+a31)*B_4_16-a11/(a21+a31)*B_7_16,B_1_17+a11/(a21+a31)*B_4_17-a11/(a21+a31)*B_7_17,B_1_18+a11/(a21+a31)*B_4_18-a11/(a21+a31)*B_7_18],[B_2_16+a11/(a21+a31)*B_5_16-a11/(a21+a31)*B_8_16,B_2_17+a11/(a21+a31)*B_5_17-a11/(a21+a31)*B_8_17,B_2_18+a11/(a21+a31)*B_5_18-a11/(a21+a31)*B_8_18],[B_3_16+a11/(a21+a31)*B_6_16-a11/(a21+a31)*B_9_16,B_3_17+a11/(a21+a31)*B_6_17-a11/(a21+a31)*B_9_17,B_3_18+a11/(a21+a31)*B_6_18-a11/(a21+a31)*B_9_18]]),Matrix(3, 5, [[C_1_1+C_16_1,C_1_2+C_16_2,C_1_3+C_16_3,C_1_4+C_16_4,C_1_5+C_16_5],[C_2_1+C_17_1,C_2_2+C_17_2,C_2_3+C_17_3,C_2_4+C_17_4,C_2_5+C_17_5],[C_3_1+C_18_1,C_3_2+C_18_2,C_3_3+C_18_3,C_3_4+C_18_4,C_3_5+C_18_5]])))+Trace(Mul(Matrix(6, 3, [[A_6_1*a11-A_6_10*a41-A_6_4*a21+A_6_7*a31+(a51+1)*A_6_13,-A_6_11*a41+A_6_2*a11-A_6_5*a21+A_6_8*a31+(a51+1)*A_6_14,-A_6_12*a41+A_6_3*a11-A_6_6*a21+A_6_9*a31+(a51+1)*A_6_15],[A_7_1*a11-A_7_10*a41-A_7_4*a21+A_7_7*a31+(a51+1)*A_7_13,-A_7_11*a41+A_7_2*a11-A_7_5*a21+A_7_8*a31+(a51+1)*A_7_14,-A_7_12*a41+A_7_3*a11-A_7_6*a21+A_7_9*a31+(a51+1)*A_7_15],[A_8_1*a11-A_8_10*a41-A_8_4*a21+A_8_7*a31+(a51+1)*A_8_13,-A_8_11*a41+A_8_2*a11-A_8_5*a21+A_8_8*a31+(a51+1)*A_8_14,-A_8_12*a41+A_8_3*a11-A_8_6*a21+A_8_9*a31+(a51+1)*A_8_15],[A_9_1*a11-A_9_10*a41-A_9_4*a21+A_9_7*a31+(a51+1)*A_9_13,-A_9_11*a41+A_9_2*a11-A_9_5*a21+A_9_8*a31+(a51+1)*A_9_14,-A_9_12*a41+A_9_3*a11-A_9_6*a21+A_9_9*a31+(a51+1)*A_9_15],[A_10_1*a11-A_10_10*a41-A_10_4*a21+A_10_7*a31+(a51+1)*A_10_13,-A_10_11*a41+A_10_2*a11-A_10_5*a21+A_10_8*a31+(a51+1)*A_10_14,-A_10_12*a41+A_10_3*a11-A_10_6*a21+A_10_9*a31+(a51+1)*A_10_15],[A_11_1*a11-A_11_10*a41-A_11_4*a21+A_11_7*a31+(a51+1)*A_11_13,-A_11_11*a41+A_11_2*a11-A_11_5*a21+A_11_8*a31+(a51+1)*A_11_14,-A_11_12*a41+A_11_3*a11-A_11_6*a21+A_11_9*a31+(a51+1)*A_11_15]]),Matrix(3, 3, [[-1/a11*B_1_10+1/(a21+a11)*B_1_13-1/(a21+a11)*B_4_13,-1/a11*B_1_11+1/(a21+a11)*B_1_14-1/(a21+a11)*B_4_14,-1/a11*B_1_12+1/(a21+a11)*B_1_15-1/(a21+a11)*B_4_15],[-1/a11*B_2_10+1/(a21+a11)*B_2_13-1/(a21+a11)*B_5_13,-1/a11*B_2_11+1/(a21+a11)*B_2_14-1/(a21+a11)*B_5_14,-1/a11*B_2_12+1/(a21+a11)*B_2_15-1/(a21+a11)*B_5_15],[-1/a11*B_3_10+1/(a21+a11)*B_3_13-1/(a21+a11)*B_6_13,-1/a11*B_3_11+1/(a21+a11)*B_3_14-1/(a21+a11)*B_6_14,-1/a11*B_3_12+1/(a21+a11)*B_3_15-1/(a21+a11)*B_6_15]]),Matrix(3, 6, [[C_13_6+C_16_6,C_13_7+C_16_7,C_13_8+C_16_8,C_13_9+C_16_9,C_13_10+C_16_10,C_13_11+C_16_11],[C_14_6+C_17_6,C_14_7+C_17_7,C_14_8+C_17_8,C_14_9+C_17_9,C_14_10+C_17_10,C_14_11+C_17_11],[C_15_6+C_18_6,C_15_7+C_18_7,C_15_8+C_18_8,C_15_9+C_18_9,C_15_10+C_18_10,C_15_11+C_18_11]])))+Trace(Mul(Matrix(6, 3, [[-1/a41*(a11+1)*A_6_1+a21/a41*A_6_4-a31/a41*A_6_7+A_6_10-a51/a41*A_6_13,-1/a41*(a11+1)*A_6_2+a21/a41*A_6_5-a31/a41*A_6_8+A_6_11-a51/a41*A_6_14,-1/a41*(a11+1)*A_6_3+a21/a41*A_6_6-a31/a41*A_6_9+A_6_12-a51/a41*A_6_15],[-1/a41*(a11+1)*A_7_1+a21/a41*A_7_4-a31/a41*A_7_7+A_7_10-a51/a41*A_7_13,-1/a41*(a11+1)*A_7_2+a21/a41*A_7_5-a31/a41*A_7_8+A_7_11-a51/a41*A_7_14,-1/a41*(a11+1)*A_7_3+a21/a41*A_7_6-a31/a41*A_7_9+A_7_12-a51/a41*A_7_15],[-1/a41*(a11+1)*A_8_1+a21/a41*A_8_4-a31/a41*A_8_7+A_8_10-a51/a41*A_8_13,-1/a41*(a11+1)*A_8_2+a21/a41*A_8_5-a31/a41*A_8_8+A_8_11-a51/a41*A_8_14,-1/a41*(a11+1)*A_8_3+a21/a41*A_8_6-a31/a41*A_8_9+A_8_12-a51/a41*A_8_15],[-1/a41*(a11+1)*A_9_1+a21/a41*A_9_4-a31/a41*A_9_7+A_9_10-a51/a41*A_9_13,-1/a41*(a11+1)*A_9_2+a21/a41*A_9_5-a31/a41*A_9_8+A_9_11-a51/a41*A_9_14,-1/a41*(a11+1)*A_9_3+a21/a41*A_9_6-a31/a41*A_9_9+A_9_12-a51/a41*A_9_15],[-1/a41*(a11+1)*A_10_1+a21/a41*A_10_4-a31/a41*A_10_7+A_10_10-a51/a41*A_10_13,-1/a41*(a11+1)*A_10_2+a21/a41*A_10_5-a31/a41*A_10_8+A_10_11-a51/a41*A_10_14,-1/a41*(a11+1)*A_10_3+a21/a41*A_10_6-a31/a41*A_10_9+A_10_12-a51/a41*A_10_15],[-1/a41*(a11+1)*A_11_1+a21/a41*A_11_4-a31/a41*A_11_7+A_11_10-a51/a41*A_11_13,-1/a41*(a11+1)*A_11_2+a21/a41*A_11_5-a31/a41*A_11_8+A_11_11-a51/a41*A_11_14,-1/a41*(a11+1)*A_11_3+a21/a41*A_11_6-a31/a41*A_11_9+A_11_12-a51/a41*A_11_15]]),Matrix(3, 3, [[B_10_1,B_10_2,B_10_3],[B_11_1,B_11_2,B_11_3],[B_12_1,B_12_2,B_12_3]]),Matrix(3, 6, [[C_1_6+C_16_6,C_1_7+C_16_7,C_1_8+C_16_8,C_1_9+C_16_9,C_1_10+C_16_10,C_1_11+C_16_11],[C_2_6+C_17_6,C_2_7+C_17_7,C_2_8+C_17_8,C_2_9+C_17_9,C_2_10+C_17_10,C_2_11+C_17_11],[C_3_6+C_18_6,C_3_7+C_18_7,C_3_8+C_18_8,C_3_9+C_18_9,C_3_10+C_18_10,C_3_11+C_18_11]])))+Trace(Mul(Matrix(6, 3, [[A_6_1,A_6_2,A_6_3],[A_1_1*a11-A_1_10*a41+A_1_13*a51-A_1_4*a21+A_1_7*a31+A_7_1,-A_1_11*a41+A_1_14*a51+A_1_2*a11-A_1_5*a21+A_1_8*a31+A_7_2,-A_1_12*a41+A_1_15*a51+A_1_3*a11-A_1_6*a21+A_1_9*a31+A_7_3],[A_2_1*a11-A_2_10*a41+A_2_13*a51-A_2_4*a21+A_2_7*a31+A_8_1,-A_2_11*a41+A_2_14*a51+A_2_2*a11-A_2_5*a21+A_2_8*a31+A_8_2,-A_2_12*a41+A_2_15*a51+A_2_3*a11-A_2_6*a21+A_2_9*a31+A_8_3],[A_3_1*a11-A_3_10*a41+A_3_13*a51-A_3_4*a21+A_3_7*a31+A_9_1,-A_3_11*a41+A_3_14*a51+A_3_2*a11-A_3_5*a21+A_3_8*a31+A_9_2,-A_3_12*a41+A_3_15*a51+A_3_3*a11-A_3_6*a21+A_3_9*a31+A_9_3],[A_4_1*a11-A_4_10*a41+A_4_13*a51-A_4_4*a21+A_4_7*a31+A_10_1,-A_4_11*a41+A_4_14*a51+A_4_2*a11-A_4_5*a21+A_4_8*a31+A_10_2,-A_4_12*a41+A_4_15*a51+A_4_3*a11-A_4_6*a21+A_4_9*a31+A_10_3],[A_5_1*a11-A_5_10*a41+A_5_13*a51-A_5_4*a21+A_5_7*a31+A_11_1,-A_5_11*a41+A_5_14*a51+A_5_2*a11-A_5_5*a21+A_5_8*a31+A_11_2,-A_5_12*a41+A_5_15*a51+A_5_3*a11-A_5_6*a21+A_5_9*a31+A_11_3]]),Matrix(3, 3, [[-1/a41*B_10_1-B_1_16-a11/(a21+a31)*B_4_16+a11/(a21+a31)*B_7_16,-1/a41*B_10_2-B_1_17-a11/(a21+a31)*B_4_17+a11/(a21+a31)*B_7_17,-1/a41*B_10_3-B_1_18-a11/(a21+a31)*B_4_18+a11/(a21+a31)*B_7_18],[-1/a41*B_11_1-B_2_16-a11/(a21+a31)*B_5_16+a11/(a21+a31)*B_8_16,-1/a41*B_11_2-B_2_17-a11/(a21+a31)*B_5_17+a11/(a21+a31)*B_8_17,-1/a41*B_11_3-B_2_18-a11/(a21+a31)*B_5_18+a11/(a21+a31)*B_8_18],[-1/a41*B_12_1-B_3_16-a11/(a21+a31)*B_6_16+a11/(a21+a31)*B_9_16,-1/a41*B_12_2-B_3_17-a11/(a21+a31)*B_6_17+a11/(a21+a31)*B_9_17,-1/a41*B_12_3-B_3_18-a11/(a21+a31)*B_6_18+a11/(a21+a31)*B_9_18]]),Matrix(3, 6, [[-C_16_6,C_1_1-C_16_7,C_1_2-C_16_8,C_1_3-C_16_9,C_1_4-C_16_10,C_1_5-C_16_11],[-C_17_6,C_2_1-C_17_7,C_2_2-C_17_8,C_2_3-C_17_9,C_2_4-C_17_10,C_2_5-C_17_11],[-C_18_6,C_3_1-C_18_7,C_3_2-C_18_8,C_3_3-C_18_9,C_3_4-C_18_10,C_3_5-C_18_11]])))+Trace(Mul(Matrix(6, 3, [[A_6_13,A_6_14,A_6_15],[A_1_1*a11-A_1_10*a41+A_1_13*a51-A_1_4*a21+A_1_7*a31+A_7_13,-A_1_11*a41+A_1_14*a51+A_1_2*a11-A_1_5*a21+A_1_8*a31+A_7_14,-A_1_12*a41+A_1_15*a51+A_1_3*a11-A_1_6*a21+A_1_9*a31+A_7_15],[A_2_1*a11-A_2_10*a41+A_2_13*a51-A_2_4*a21+A_2_7*a31+A_8_13,-A_2_11*a41+A_2_14*a51+A_2_2*a11-A_2_5*a21+A_2_8*a31+A_8_14,-A_2_12*a41+A_2_15*a51+A_2_3*a11-A_2_6*a21+A_2_9*a31+A_8_15],[A_3_1*a11-A_3_10*a41+A_3_13*a51-A_3_4*a21+A_3_7*a31+A_9_13,-A_3_11*a41+A_3_14*a51+A_3_2*a11-A_3_5*a21+A_3_8*a31+A_9_14,-A_3_12*a41+A_3_15*a51+A_3_3*a11-A_3_6*a21+A_3_9*a31+A_9_15],[A_4_1*a11-A_4_10*a41+A_4_13*a51-A_4_4*a21+A_4_7*a31+A_10_13,-A_4_11*a41+A_4_14*a51+A_4_2*a11-A_4_5*a21+A_4_8*a31+A_10_14,-A_4_12*a41+A_4_15*a51+A_4_3*a11-A_4_6*a21+A_4_9*a31+A_10_15],[A_5_1*a11-A_5_10*a41+A_5_13*a51-A_5_4*a21+A_5_7*a31+A_11_13,-A_5_11*a41+A_5_14*a51+A_5_2*a11-A_5_5*a21+A_5_8*a31+A_11_14,-A_5_12*a41+A_5_15*a51+A_5_3*a11-A_5_6*a21+A_5_9*a31+A_11_15]]),Matrix(3, 3, [[-1/a11*B_1_10+1/(a21+a11)*B_1_13-1/(a21+a11)*B_4_13-(a41+a51)/(a21+a31)*B_4_16+(a41+a51)/(a21+a31)*B_7_16+B_10_16-B_13_16,-1/a11*B_1_11+1/(a21+a11)*B_1_14-1/(a21+a11)*B_4_14-(a41+a51)/(a21+a31)*B_4_17+(a41+a51)/(a21+a31)*B_7_17+B_10_17-B_13_17,-1/a11*B_1_12+1/(a21+a11)*B_1_15-1/(a21+a11)*B_4_15-(a41+a51)/(a21+a31)*B_4_18+(a41+a51)/(a21+a31)*B_7_18+B_10_18-B_13_18],[-1/a11*B_2_10+1/(a21+a11)*B_2_13-1/(a21+a11)*B_5_13-(a41+a51)/(a21+a31)*B_5_16+(a41+a51)/(a21+a31)*B_8_16+B_11_16-B_14_16,-1/a11*B_2_11+1/(a21+a11)*B_2_14-1/(a21+a11)*B_5_14-(a41+a51)/(a21+a31)*B_5_17+(a41+a51)/(a21+a31)*B_8_17+B_11_17-B_14_17,-1/a11*B_2_12+1/(a21+a11)*B_2_15-1/(a21+a11)*B_5_15-(a41+a51)/(a21+a31)*B_5_18+(a41+a51)/(a21+a31)*B_8_18+B_11_18-B_14_18],[-1/a11*B_3_10+1/(a21+a11)*B_3_13-1/(a21+a11)*B_6_13-(a41+a51)/(a21+a31)*B_6_16+(a41+a51)/(a21+a31)*B_9_16+B_12_16-B_15_16,-1/a11*B_3_11+1/(a21+a11)*B_3_14-1/(a21+a11)*B_6_14-(a41+a51)/(a21+a31)*B_6_17+(a41+a51)/(a21+a31)*B_9_17+B_12_17-B_15_17,-1/a11*B_3_12+1/(a21+a11)*B_3_15-1/(a21+a11)*B_6_15-(a41+a51)/(a21+a31)*B_6_18+(a41+a51)/(a21+a31)*B_9_18+B_12_18-B_15_18]]),Matrix(3, 6, [[-C_16_6,C_13_1-C_16_7,C_13_2-C_16_8,C_13_3-C_16_9,C_13_4-C_16_10,C_13_5-C_16_11],[-C_17_6,C_14_1-C_17_7,C_14_2-C_17_8,C_14_3-C_17_9,C_14_4-C_17_10,C_14_5-C_17_11],[-C_18_6,C_15_1-C_18_7,C_15_2-C_18_8,C_15_3-C_18_9,C_15_4-C_18_10,C_15_5-C_18_11]])))+Trace(Mul(Matrix(6, 3, [[-A_6_1*a11+A_6_10*a41-A_6_13*a51+A_6_4*a21-A_6_7*a31,A_6_11*a41-A_6_14*a51-A_6_2*a11+A_6_5*a21-A_6_8*a31,A_6_12*a41-A_6_15*a51-A_6_3*a11+A_6_6*a21-A_6_9*a31],[A_1_1*a11-A_1_10*a41+A_1_13*a51-A_1_4*a21+A_1_7*a31-A_7_1*a11+A_7_10*a41-A_7_13*a51+A_7_4*a21-A_7_7*a31,-A_1_11*a41+A_1_14*a51+A_1_2*a11-A_1_5*a21+A_1_8*a31+A_7_11*a41-A_7_14*a51-A_7_2*a11+A_7_5*a21-A_7_8*a31,-A_1_12*a41+A_1_15*a51+A_1_3*a11-A_1_6*a21+A_1_9*a31+A_7_12*a41-A_7_15*a51-A_7_3*a11+A_7_6*a21-A_7_9*a31],[A_2_1*a11-A_2_10*a41+A_2_13*a51-A_2_4*a21+A_2_7*a31-A_8_1*a11+A_8_10*a41-A_8_13*a51+A_8_4*a21-A_8_7*a31,-A_2_11*a41+A_2_14*a51+A_2_2*a11-A_2_5*a21+A_2_8*a31+A_8_11*a41-A_8_14*a51-A_8_2*a11+A_8_5*a21-A_8_8*a31,-A_2_12*a41+A_2_15*a51+A_2_3*a11-A_2_6*a21+A_2_9*a31+A_8_12*a41-A_8_15*a51-A_8_3*a11+A_8_6*a21-A_8_9*a31],[A_3_1*a11-A_3_10*a41+A_3_13*a51-A_3_4*a21+A_3_7*a31-A_9_1*a11+A_9_10*a41-A_9_13*a51+A_9_4*a21-A_9_7*a31,-A_3_11*a41+A_3_14*a51+A_3_2*a11-A_3_5*a21+A_3_8*a31+A_9_11*a41-A_9_14*a51-A_9_2*a11+A_9_5*a21-A_9_8*a31,-A_3_12*a41+A_3_15*a51+A_3_3*a11-A_3_6*a21+A_3_9*a31+A_9_12*a41-A_9_15*a51-A_9_3*a11+A_9_6*a21-A_9_9*a31],[-A_10_1*a11+A_10_10*a41-A_10_13*a51+A_10_4*a21-A_10_7*a31+A_4_1*a11-A_4_10*a41+A_4_13*a51-A_4_4*a21+A_4_7*a31,A_10_11*a41-A_10_14*a51-A_10_2*a11+A_10_5*a21-A_10_8*a31-A_4_11*a41+A_4_14*a51+A_4_2*a11-A_4_5*a21+A_4_8*a31,A_10_12*a41-A_10_15*a51-A_10_3*a11+A_10_6*a21-A_10_9*a31-A_4_12*a41+A_4_15*a51+A_4_3*a11-A_4_6*a21+A_4_9*a31],[-A_11_1*a11+A_11_10*a41-A_11_13*a51+A_11_4*a21-A_11_7*a31+A_5_1*a11-A_5_10*a41+A_5_13*a51-A_5_4*a21+A_5_7*a31,A_11_11*a41-A_11_14*a51-A_11_2*a11+A_11_5*a21-A_11_8*a31-A_5_11*a41+A_5_14*a51+A_5_2*a11-A_5_5*a21+A_5_8*a31,A_11_12*a41-A_11_15*a51-A_11_3*a11+A_11_6*a21-A_11_9*a31-A_5_12*a41+A_5_15*a51+A_5_3*a11-A_5_6*a21+A_5_9*a31]]),Matrix(3, 3, [[-1/a41*B_10_1-1/a11*B_1_10+1/(a21+a11)*B_1_13-1/(a21+a11)*B_4_13-(a31-a41-1)/(a21+a31)*B_4_16-(a21+a41+1)/(a21+a31)*B_7_16-B_10_16,-1/a41*B_10_2-1/a11*B_1_11+1/(a21+a11)*B_1_14-1/(a21+a11)*B_4_14-(a31-a41-1)/(a21+a31)*B_4_17-(a21+a41+1)/(a21+a31)*B_7_17-B_10_17,-1/a41*B_10_3-1/a11*B_1_12+1/(a21+a11)*B_1_15-1/(a21+a11)*B_4_15-(a31-a41-1)/(a21+a31)*B_4_18-(a21+a41+1)/(a21+a31)*B_7_18-B_10_18],[-1/a41*B_11_1-1/a11*B_2_10+1/(a21+a11)*B_2_13-1/(a21+a11)*B_5_13-(a31-a41-1)/(a21+a31)*B_5_16-(a21+a41+1)/(a21+a31)*B_8_16-B_11_16,-1/a41*B_11_2-1/a11*B_2_11+1/(a21+a11)*B_2_14-1/(a21+a11)*B_5_14-(a31-a41-1)/(a21+a31)*B_5_17-(a21+a41+1)/(a21+a31)*B_8_17-B_11_17,-1/a41*B_11_3-1/a11*B_2_12+1/(a21+a11)*B_2_15-1/(a21+a11)*B_5_15-(a31-a41-1)/(a21+a31)*B_5_18-(a21+a41+1)/(a21+a31)*B_8_18-B_11_18],[-1/a41*B_12_1-1/a11*B_3_10+1/(a21+a11)*B_3_13-1/(a21+a11)*B_6_13-(a31-a41-1)/(a21+a31)*B_6_16-(a21+a41+1)/(a21+a31)*B_9_16-B_12_16,-1/a41*B_12_2-1/a11*B_3_11+1/(a21+a11)*B_3_14-1/(a21+a11)*B_6_14-(a31-a41-1)/(a21+a31)*B_6_17-(a21+a41+1)/(a21+a31)*B_9_17-B_12_17,-1/a41*B_12_3-1/a11*B_3_12+1/(a21+a11)*B_3_15-1/(a21+a11)*B_6_15-(a31-a41-1)/(a21+a31)*B_6_18-(a21+a41+1)/(a21+a31)*B_9_18-B_12_18]]),Matrix(3, 6, [[C_16_6,C_16_7,C_16_8,C_16_9,C_16_10,C_16_11],[C_17_6,C_17_7,C_17_8,C_17_9,C_17_10,C_17_11],[C_18_6,C_18_7,C_18_8,C_18_9,C_18_10,C_18_11]])))+Trace(Mul(Matrix(6, 3, [[-A_6_1*a11+A_6_4*a21-A_6_7*a31+(a41+1)*A_6_10+(-a51+1)*A_6_13,-A_6_2*a11+A_6_5*a21-A_6_8*a31+(a41+1)*A_6_11+(-a51+1)*A_6_14,-A_6_3*a11+A_6_6*a21-A_6_9*a31+(a41+1)*A_6_12+(-a51+1)*A_6_15],[A_1_1*a11-A_1_10*a41-A_1_4*a21+A_1_7*a31-A_7_1*a11+A_7_4*a21-A_7_7*a31+(a41+1)*A_7_10+A_1_13*a51+(-a51+1)*A_7_13,-A_1_11*a41+A_1_2*a11-A_1_5*a21+A_1_8*a31-A_7_2*a11+A_7_5*a21-A_7_8*a31+(a41+1)*A_7_11+A_1_14*a51+(-a51+1)*A_7_14,-A_1_12*a41+A_1_3*a11-A_1_6*a21+A_1_9*a31-A_7_3*a11+A_7_6*a21-A_7_9*a31+(a41+1)*A_7_12+A_1_15*a51+(-a51+1)*A_7_15],[A_2_1*a11-A_2_10*a41-A_2_4*a21+A_2_7*a31-A_8_1*a11+A_8_4*a21-A_8_7*a31+(a41+1)*A_8_10+A_2_13*a51+(-a51+1)*A_8_13,-A_2_11*a41+A_2_2*a11-A_2_5*a21+A_2_8*a31-A_8_2*a11+A_8_5*a21-A_8_8*a31+(a41+1)*A_8_11+A_2_14*a51+(-a51+1)*A_8_14,-A_2_12*a41+A_2_3*a11-A_2_6*a21+A_2_9*a31-A_8_3*a11+A_8_6*a21-A_8_9*a31+(a41+1)*A_8_12+A_2_15*a51+(-a51+1)*A_8_15],[A_3_1*a11-A_3_10*a41-A_3_4*a21+A_3_7*a31-A_9_1*a11+A_9_4*a21-A_9_7*a31+(a41+1)*A_9_10+A_3_13*a51+(-a51+1)*A_9_13,-A_3_11*a41+A_3_2*a11-A_3_5*a21+A_3_8*a31-A_9_2*a11+A_9_5*a21-A_9_8*a31+(a41+1)*A_9_11+A_3_14*a51+(-a51+1)*A_9_14,-A_3_12*a41+A_3_3*a11-A_3_6*a21+A_3_9*a31-A_9_3*a11+A_9_6*a21-A_9_9*a31+(a41+1)*A_9_12+A_3_15*a51+(-a51+1)*A_9_15],[-A_10_1*a11+A_10_4*a21-A_10_7*a31+A_4_1*a11-A_4_10*a41-A_4_4*a21+A_4_7*a31+(a41+1)*A_10_10+A_4_13*a51+(-a51+1)*A_10_13,-A_10_2*a11+A_10_5*a21-A_10_8*a31-A_4_11*a41+A_4_2*a11-A_4_5*a21+A_4_8*a31+(a41+1)*A_10_11+A_4_14*a51+(-a51+1)*A_10_14,-A_10_3*a11+A_10_6*a21-A_10_9*a31-A_4_12*a41+A_4_3*a11-A_4_6*a21+A_4_9*a31+(a41+1)*A_10_12+A_4_15*a51+(-a51+1)*A_10_15],[-A_11_1*a11+A_11_4*a21-A_11_7*a31+A_5_1*a11-A_5_10*a41-A_5_4*a21+A_5_7*a31+(a41+1)*A_11_10+A_5_13*a51+(-a51+1)*A_11_13,-A_11_2*a11+A_11_5*a21-A_11_8*a31-A_5_11*a41+A_5_2*a11-A_5_5*a21+A_5_8*a31+(a41+1)*A_11_11+A_5_14*a51+(-a51+1)*A_11_14,-A_11_3*a11+A_11_6*a21-A_11_9*a31-A_5_12*a41+A_5_3*a11-A_5_6*a21+A_5_9*a31+(a41+1)*A_11_12+A_5_15*a51+(-a51+1)*A_11_15]]),Matrix(3, 3, [[1/a11*B_1_10+a41/(a21+a31)*B_4_16-a41/(a21+a31)*B_7_16-B_10_16,1/a11*B_1_11+a41/(a21+a31)*B_4_17-a41/(a21+a31)*B_7_17-B_10_17,1/a11*B_1_12+a41/(a21+a31)*B_4_18-a41/(a21+a31)*B_7_18-B_10_18],[1/a11*B_2_10+a41/(a21+a31)*B_5_16-a41/(a21+a31)*B_8_16-B_11_16,1/a11*B_2_11+a41/(a21+a31)*B_5_17-a41/(a21+a31)*B_8_17-B_11_17,1/a11*B_2_12+a41/(a21+a31)*B_5_18-a41/(a21+a31)*B_8_18-B_11_18],[1/a11*B_3_10+a41/(a21+a31)*B_6_16-a41/(a21+a31)*B_9_16-B_12_16,1/a11*B_3_11+a41/(a21+a31)*B_6_17-a41/(a21+a31)*B_9_17-B_12_17,1/a11*B_3_12+a41/(a21+a31)*B_6_18-a41/(a21+a31)*B_9_18-B_12_18]]),Matrix(3, 6, [[-C_16_6,C_10_1+C_13_1-C_16_1-C_16_7,C_10_2+C_13_2-C_16_2-C_16_8,C_10_3+C_13_3-C_16_3-C_16_9,C_10_4+C_13_4-C_16_4-C_16_10,C_10_5+C_13_5-C_16_5-C_16_11],[-C_17_6,C_11_1+C_14_1-C_17_1-C_17_7,C_11_2+C_14_2-C_17_2-C_17_8,C_11_3+C_14_3-C_17_3-C_17_9,C_11_4+C_14_4-C_17_4-C_17_10,C_11_5+C_14_5-C_17_5-C_17_11],[-C_18_6,C_12_1+C_15_1-C_18_1-C_18_7,C_12_2+C_15_2-C_18_2-C_18_8,C_12_3+C_15_3-C_18_3-C_18_9,C_12_4+C_15_4-C_18_4-C_18_10,C_12_5+C_15_5-C_18_5-C_18_11]])))+Trace(Mul(Matrix(6, 3, [[-A_6_1*a11+(a21+1)*A_6_4+(-a31+1)*A_6_7+A_6_10*a41-A_6_13*a51,-A_6_2*a11+(a21+1)*A_6_5+(-a31+1)*A_6_8+A_6_11*a41-A_6_14*a51,-A_6_3*a11+(a21+1)*A_6_6+(-a31+1)*A_6_9+A_6_12*a41-A_6_15*a51],[A_1_1*a11-A_1_4*a21-A_7_1*a11+(a21+1)*A_7_4+A_1_7*a31+(-a31+1)*A_7_7-A_1_10*a41+A_7_10*a41+A_1_13*a51-A_7_13*a51,A_1_2*a11-A_1_5*a21-A_7_2*a11+(a21+1)*A_7_5+A_1_8*a31+(-a31+1)*A_7_8-A_1_11*a41+A_7_11*a41+A_1_14*a51-A_7_14*a51,A_1_3*a11-A_1_6*a21-A_7_3*a11+(a21+1)*A_7_6+A_1_9*a31+(-a31+1)*A_7_9-A_1_12*a41+A_7_12*a41+A_1_15*a51-A_7_15*a51],[A_2_1*a11-A_2_4*a21-A_8_1*a11+(a21+1)*A_8_4+A_2_7*a31+(-a31+1)*A_8_7-A_2_10*a41+A_8_10*a41+A_2_13*a51-A_8_13*a51,A_2_2*a11-A_2_5*a21-A_8_2*a11+(a21+1)*A_8_5+A_2_8*a31+(-a31+1)*A_8_8-A_2_11*a41+A_8_11*a41+A_2_14*a51-A_8_14*a51,A_2_3*a11-A_2_6*a21-A_8_3*a11+(a21+1)*A_8_6+A_2_9*a31+(-a31+1)*A_8_9-A_2_12*a41+A_8_12*a41+A_2_15*a51-A_8_15*a51],[A_3_1*a11-A_3_4*a21-A_9_1*a11+(a21+1)*A_9_4+A_3_7*a31+(-a31+1)*A_9_7-A_3_10*a41+A_9_10*a41+A_3_13*a51-A_9_13*a51,A_3_2*a11-A_3_5*a21-A_9_2*a11+(a21+1)*A_9_5+A_3_8*a31+(-a31+1)*A_9_8-A_3_11*a41+A_9_11*a41+A_3_14*a51-A_9_14*a51,A_3_3*a11-A_3_6*a21-A_9_3*a11+(a21+1)*A_9_6+A_3_9*a31+(-a31+1)*A_9_9-A_3_12*a41+A_9_12*a41+A_3_15*a51-A_9_15*a51],[-A_10_1*a11+A_4_1*a11-A_4_4*a21+(a21+1)*A_10_4+A_4_7*a31+(-a31+1)*A_10_7-A_4_10*a41+A_10_10*a41+A_4_13*a51-A_10_13*a51,-A_10_2*a11+A_4_2*a11-A_4_5*a21+(a21+1)*A_10_5+A_4_8*a31+(-a31+1)*A_10_8-A_4_11*a41+A_10_11*a41+A_4_14*a51-A_10_14*a51,-A_10_3*a11+A_4_3*a11-A_4_6*a21+(a21+1)*A_10_6+A_4_9*a31+(-a31+1)*A_10_9-A_4_12*a41+A_10_12*a41+A_4_15*a51-A_10_15*a51],[-A_11_1*a11+A_5_1*a11-A_5_4*a21+(a21+1)*A_11_4+A_5_7*a31+(-a31+1)*A_11_7-A_5_10*a41+A_11_10*a41+A_5_13*a51-A_11_13*a51,-A_11_2*a11+A_5_2*a11-A_5_5*a21+(a21+1)*A_11_5+A_5_8*a31+(-a31+1)*A_11_8-A_5_11*a41+A_11_11*a41+A_5_14*a51-A_11_14*a51,-A_11_3*a11+A_5_3*a11-A_5_6*a21+(a21+1)*A_11_6+A_5_9*a31+(-a31+1)*A_11_9-A_5_12*a41+A_11_12*a41+A_5_15*a51-A_11_15*a51]]),Matrix(3, 3, [[-1/a41*B_10_1-1/a51*B_13_1+1/a51*B_13_4-a31/(a21+a31)*B_4_16-1/(a21+a31)*a21*B_7_16,-1/a41*B_10_2-1/a51*B_13_2+1/a51*B_13_5-a31/(a21+a31)*B_4_17-1/(a21+a31)*a21*B_7_17,-1/a41*B_10_3-1/a51*B_13_3+1/a51*B_13_6-a31/(a21+a31)*B_4_18-1/(a21+a31)*a21*B_7_18],[-1/a41*B_11_1-1/a51*B_14_1+1/a51*B_14_4-a31/(a21+a31)*B_5_16-1/(a21+a31)*a21*B_8_16,-1/a41*B_11_2-1/a51*B_14_2+1/a51*B_14_5-a31/(a21+a31)*B_5_17-1/(a21+a31)*a21*B_8_17,-1/a41*B_11_3-1/a51*B_14_3+1/a51*B_14_6-a31/(a21+a31)*B_5_18-1/(a21+a31)*a21*B_8_18],[-1/a41*B_12_1-1/a51*B_15_1+1/a51*B_15_4-a31/(a21+a31)*B_6_16-1/(a21+a31)*a21*B_9_16,-1/a41*B_12_2-1/a51*B_15_2+1/a51*B_15_5-a31/(a21+a31)*B_6_17-1/(a21+a31)*a21*B_9_17,-1/a41*B_12_3-1/a51*B_15_3+1/a51*B_15_6-a31/(a21+a31)*B_6_18-1/(a21+a31)*a21*B_9_18]]),Matrix(3, 6, [[-C_16_6,C_4_1+C_7_1-C_16_1-C_16_7,C_4_2+C_7_2-C_16_2-C_16_8,C_4_3+C_7_3-C_16_3-C_16_9,C_4_4+C_7_4-C_16_4-C_16_10,C_4_5+C_7_5-C_16_5-C_16_11],[-C_17_6,C_5_1+C_8_1-C_17_1-C_17_7,C_5_2+C_8_2-C_17_2-C_17_8,C_5_3+C_8_3-C_17_3-C_17_9,C_5_4+C_8_4-C_17_4-C_17_10,C_5_5+C_8_5-C_17_5-C_17_11],[-C_18_6,C_9_1+C_6_1-C_18_1-C_18_7,C_9_2+C_6_2-C_18_2-C_18_8,C_6_3+C_9_3-C_18_3-C_18_9,C_6_4+C_9_4-C_18_4-C_18_10,C_6_5+C_9_5-C_18_5-C_18_11]])))+Trace(Mul(Matrix(5, 3, [[-A_1_1-A_1_4+A_1_7,-A_1_2-A_1_5+A_1_8,-A_1_3-A_1_6+A_1_9],[-A_2_1-A_2_4+A_2_7,-A_2_2-A_2_5+A_2_8,-A_2_3-A_2_6+A_2_9],[-A_3_1-A_3_4+A_3_7,-A_3_2-A_3_5+A_3_8,-A_3_3-A_3_6+A_3_9],[-A_4_1-A_4_4+A_4_7,-A_4_2-A_4_5+A_4_8,-A_4_3-A_4_6+A_4_9],[-A_5_1-A_5_4+A_5_7,-A_5_2-A_5_5+A_5_8,-A_5_3-A_5_6+A_5_9]]),Matrix(3, 3, [[B_7_1+a31/a41*B_10_1,B_7_2+a31/a41*B_10_2,B_7_3+a31/a41*B_10_3],[B_8_1+a31/a41*B_11_1,B_8_2+a31/a41*B_11_2,B_8_3+a31/a41*B_11_3],[B_9_1+a31/a41*B_12_1,B_9_2+a31/a41*B_12_2,B_9_3+a31/a41*B_12_3]]),Matrix(3, 5, [[C_1_1+C_4_1-C_7_1+C_1_7+C_4_7-C_7_7,C_1_2+C_4_2-C_7_2+C_1_8+C_4_8-C_7_8,C_1_3+C_4_3-C_7_3+C_1_9+C_4_9-C_7_9,C_1_4+C_4_4-C_7_4+C_1_10+C_4_10-C_7_10,C_1_5+C_4_5-C_7_5+C_1_11+C_4_11-C_7_11],[C_2_1+C_5_1-C_8_1+C_2_7+C_5_7-C_8_7,C_2_2+C_5_2-C_8_2+C_2_8+C_5_8-C_8_8,C_2_3+C_5_3-C_8_3+C_2_9+C_5_9-C_8_9,C_2_4+C_5_4-C_8_4+C_2_10+C_5_10-C_8_10,C_2_5+C_5_5-C_8_5+C_2_11+C_5_11-C_8_11],[C_3_1+C_6_1-C_9_1+C_3_7+C_6_7-C_9_7,C_3_2+C_6_2-C_9_2+C_3_8+C_6_8-C_9_8,C_3_3+C_6_3-C_9_3+C_3_9+C_6_9-C_9_9,C_3_4+C_6_4-C_9_4+C_3_10+C_6_10-C_9_10,C_3_5+C_6_5-C_9_5+C_3_11+C_6_11-C_9_11]])))+Trace(Mul(Matrix(5, 3, [[-A_1_1-A_1_4+A_1_13,-A_1_2-A_1_5+A_1_14,-A_1_3-A_1_6+A_1_15],[-A_2_1-A_2_4+A_2_13,-A_2_2-A_2_5+A_2_14,-A_2_3-A_2_6+A_2_15],[-A_3_1-A_3_4+A_3_13,-A_3_2-A_3_5+A_3_14,-A_3_3-A_3_6+A_3_15],[-A_4_1-A_4_4+A_4_13,-A_4_2-A_4_5+A_4_14,-A_4_3-A_4_6+A_4_15],[-A_5_1-A_5_4+A_5_13,-A_5_2-A_5_5+A_5_14,-A_5_3-A_5_6+A_5_15]]),Matrix(3, 3, [[a51/a41*B_10_1+B_13_1,a51/a41*B_10_2+B_13_2,a51/a41*B_10_3+B_13_3],[a51/a41*B_11_1+B_14_1,a51/a41*B_11_2+B_14_2,a51/a41*B_11_3+B_14_3],[a51/a41*B_12_1+B_15_1,a51/a41*B_12_2+B_15_2,a51/a41*B_12_3+B_15_3]]),Matrix(3, 5, [[C_1_1+C_4_1-C_13_1+C_1_7+C_4_7-C_13_7,C_1_2+C_4_2-C_13_2+C_1_8+C_4_8-C_13_8,C_1_3+C_4_3-C_13_3+C_1_9+C_4_9-C_13_9,C_1_4+C_4_4-C_13_4+C_1_10+C_4_10-C_13_10,C_1_5+C_4_5-C_13_5+C_1_11+C_4_11-C_13_11],[C_2_1+C_5_1-C_14_1+C_2_7+C_5_7-C_14_7,C_2_2+C_5_2-C_14_2+C_2_8+C_5_8-C_14_8,C_2_3+C_5_3-C_14_3+C_2_9+C_5_9-C_14_9,C_2_4+C_5_4-C_14_4+C_2_10+C_5_10-C_14_10,C_2_5+C_5_5-C_14_5+C_2_11+C_5_11-C_14_11],[C_3_1+C_6_1-C_15_1+C_3_7+C_6_7-C_15_7,C_3_2+C_6_2-C_15_2+C_3_8+C_6_8-C_15_8,C_3_3+C_6_3-C_15_3+C_3_9+C_6_9-C_15_9,C_3_4+C_6_4-C_15_4+C_3_10+C_6_10-C_15_10,C_3_5+C_6_5-C_15_5+C_3_11+C_6_11-C_15_11]])))+Trace(Mul(Matrix(6, 3, [[-A_6_4-A_6_7+A_6_10,-A_6_5-A_6_8+A_6_11,-A_6_6-A_6_9+A_6_12],[-A_7_4-A_7_7+A_7_10,-A_7_5-A_7_8+A_7_11,-A_7_6-A_7_9+A_7_12],[-A_8_4-A_8_7+A_8_10,-A_8_5-A_8_8+A_8_11,-A_8_6-A_8_9+A_8_12],[-A_9_4-A_9_7+A_9_10,-A_9_5-A_9_8+A_9_11,-A_9_6-A_9_9+A_9_12],[-A_10_4-A_10_7+A_10_10,-A_10_5-A_10_8+A_10_11,-A_10_6-A_10_9+A_10_12],[-A_11_4-A_11_7+A_11_10,-A_11_5-A_11_8+A_11_11,-A_11_6-A_11_9+A_11_12]]),Matrix(3, 3, [[-B_10_1-a41/a51*B_13_1+B_10_4+a41/a51*B_13_4,-B_10_2-a41/a51*B_13_2+B_10_5+a41/a51*B_13_5,-B_10_3-a41/a51*B_13_3+B_10_6+a41/a51*B_13_6],[-B_11_1-a41/a51*B_14_1+B_11_4+a41/a51*B_14_4,-B_11_2-a41/a51*B_14_2+B_11_5+a41/a51*B_14_5,-B_11_3-a41/a51*B_14_3+B_11_6+a41/a51*B_14_6],[-B_12_1-a41/a51*B_15_1+B_12_4+a41/a51*B_15_4,-B_12_2-a41/a51*B_15_2+B_12_5+a41/a51*B_15_5,-B_12_3-a41/a51*B_15_3+B_12_6+a41/a51*B_15_6]]),Matrix(3, 6, [[C_4_6+C_7_6-C_10_6,C_4_1+C_7_1-C_10_1+C_4_7+C_7_7-C_10_7,C_4_2+C_7_2-C_10_2+C_4_8+C_7_8-C_10_8,C_4_3+C_7_3-C_10_3+C_4_9+C_7_9-C_10_9,C_4_4+C_7_4-C_10_4+C_4_10+C_7_10-C_10_10,C_4_5+C_7_5-C_10_5+C_4_11+C_7_11-C_10_11],[C_5_6+C_8_6-C_11_6,C_5_1+C_8_1-C_11_1+C_5_7+C_8_7-C_11_7,C_5_2+C_8_2-C_11_2+C_5_8+C_8_8-C_11_8,C_5_3+C_8_3-C_11_3+C_5_9+C_8_9-C_11_9,C_5_4+C_8_4-C_11_4+C_5_10+C_8_10-C_11_10,C_5_5+C_8_5-C_11_5+C_5_11+C_8_11-C_11_11],[C_6_6+C_9_6-C_12_6,C_9_1+C_6_1-C_12_1+C_6_7+C_9_7-C_12_7,C_9_2+C_6_2-C_12_2+C_6_8+C_9_8-C_12_8,C_6_3+C_9_3-C_12_3+C_6_9+C_9_9-C_12_9,C_6_4+C_9_4-C_12_4+C_6_10+C_9_10-C_12_10,C_6_5+C_9_5-C_12_5+C_6_11+C_9_11-C_12_11]])))+Trace(Mul(Matrix(5, 3, [[-A_1_7-A_1_10+A_1_13,-A_1_8-A_1_11+A_1_14,-A_1_9-A_1_12+A_1_15],[-A_2_7-A_2_10+A_2_13,-A_2_8-A_2_11+A_2_14,-A_2_9-A_2_12+A_2_15],[-A_3_7-A_3_10+A_3_13,-A_3_8-A_3_11+A_3_14,-A_3_9-A_3_12+A_3_15],[-A_4_7-A_4_10+A_4_13,-A_4_8-A_4_11+A_4_14,-A_4_9-A_4_12+A_4_15],[-A_5_7-A_5_10+A_5_13,-A_5_8-A_5_11+A_5_14,-A_5_9-A_5_12+A_5_15]]),Matrix(3, 3, [[a51/a41*B_10_1+B_13_1-B_13_4+B_13_7,a51/a41*B_10_2+B_13_2-B_13_5+B_13_8,a51/a41*B_10_3+B_13_3-B_13_6+B_13_9],[a51/a41*B_11_1+B_14_1-B_14_4+B_14_7,a51/a41*B_11_2+B_14_2-B_14_5+B_14_8,a51/a41*B_11_3+B_14_3-B_14_6+B_14_9],[a51/a41*B_12_1+B_15_1-B_15_4+B_15_7,a51/a41*B_12_2+B_15_2-B_15_5+B_15_8,a51/a41*B_12_3+B_15_3-B_15_6+B_15_9]]),Matrix(3, 5, [[C_7_1+C_10_1-C_13_1+C_7_7+C_10_7-C_13_7,C_7_2+C_10_2-C_13_2+C_7_8+C_10_8-C_13_8,C_7_3+C_10_3-C_13_3+C_7_9+C_10_9-C_13_9,C_7_4+C_10_4-C_13_4+C_7_10+C_10_10-C_13_10,C_7_5+C_10_5-C_13_5+C_7_11+C_10_11-C_13_11],[C_8_1+C_11_1-C_14_1+C_8_7+C_11_7-C_14_7,C_8_2+C_11_2-C_14_2+C_8_8+C_11_8-C_14_8,C_8_3+C_11_3-C_14_3+C_8_9+C_11_9-C_14_9,C_8_4+C_11_4-C_14_4+C_8_10+C_11_10-C_14_10,C_8_5+C_11_5-C_14_5+C_8_11+C_11_11-C_14_11],[C_9_1+C_12_1-C_15_1+C_9_7+C_12_7-C_15_7,C_9_2+C_12_2-C_15_2+C_9_8+C_12_8-C_15_8,C_9_3+C_12_3-C_15_3+C_9_9+C_12_9-C_15_9,C_9_4+C_12_4-C_15_4+C_9_10+C_12_10-C_15_10,C_9_5+C_12_5-C_15_5+C_9_11+C_12_11-C_15_11]])))+Trace(Mul(Matrix(5, 3, [[-A_1_4+A_7_4-A_1_7+A_7_7+A_1_10-A_7_10,-A_1_5+A_7_5-A_1_8+A_7_8+A_1_11-A_7_11,-A_1_6+A_7_6-A_1_9+A_7_9+A_1_12-A_7_12],[-A_2_4+A_8_4-A_2_7+A_8_7+A_2_10-A_8_10,-A_2_5+A_8_5-A_2_8+A_8_8+A_2_11-A_8_11,-A_2_6+A_8_6-A_2_9+A_8_9+A_2_12-A_8_12],[-A_3_4+A_9_4-A_3_7+A_9_7+A_3_10-A_9_10,-A_3_5+A_9_5-A_3_8+A_9_8+A_3_11-A_9_11,-A_3_6+A_9_6-A_3_9+A_9_9+A_3_12-A_9_12],[-A_4_4+A_10_4-A_4_7+A_10_7+A_4_10-A_10_10,-A_4_5+A_10_5-A_4_8+A_10_8+A_4_11-A_10_11,-A_4_6+A_10_6-A_4_9+A_10_9+A_4_12-A_10_12],[-A_5_4+A_11_4-A_5_7+A_11_7+A_5_10-A_11_10,-A_5_5+A_11_5-A_5_8+A_11_8+A_5_11-A_11_11,-A_5_6+A_11_6-A_5_9+A_11_9+A_5_12-A_11_12]]),Matrix(3, 3, [[a21/a11*B_1_10+B_4_10,a21/a11*B_1_11+B_4_11,a21/a11*B_1_12+B_4_12],[a21/a11*B_2_10+B_5_10,a21/a11*B_2_11+B_5_11,a21/a11*B_2_12+B_5_12],[a21/a11*B_3_10+B_6_10,a21/a11*B_3_11+B_6_11,a21/a11*B_3_12+B_6_12]]),Matrix(3, 5, [[C_4_1+C_7_1-C_10_1,C_4_2+C_7_2-C_10_2,C_4_3+C_7_3-C_10_3,C_4_4+C_7_4-C_10_4,C_4_5+C_7_5-C_10_5],[C_5_1+C_8_1-C_11_1,C_5_2+C_8_2-C_11_2,C_5_3+C_8_3-C_11_3,C_5_4+C_8_4-C_11_4,C_5_5+C_8_5-C_11_5],[C_9_1+C_6_1-C_12_1,C_9_2+C_6_2-C_12_2,C_6_3+C_9_3-C_12_3,C_6_4+C_9_4-C_12_4,C_6_5+C_9_5-C_12_5]])))+Trace(Mul(Matrix(6, 3, [[A_6_1-a21/a11*A_6_4+1/a11*a31*A_6_7-1/a11*(a41+1)*A_6_10-1/a11*(-a51+1)*A_6_13,A_6_2-a21/a11*A_6_5+1/a11*a31*A_6_8-1/a11*(a41+1)*A_6_11-1/a11*(-a51+1)*A_6_14,A_6_3-a21/a11*A_6_6+1/a11*a31*A_6_9-1/a11*(a41+1)*A_6_12-1/a11*(-a51+1)*A_6_15],[A_7_1-a21/a11*A_7_4+1/a11*a31*A_7_7-1/a11*(a41+1)*A_7_10-1/a11*(-a51+1)*A_7_13,A_7_2-a21/a11*A_7_5+1/a11*a31*A_7_8-1/a11*(a41+1)*A_7_11-1/a11*(-a51+1)*A_7_14,A_7_3-a21/a11*A_7_6+1/a11*a31*A_7_9-1/a11*(a41+1)*A_7_12-1/a11*(-a51+1)*A_7_15],[A_8_1-a21/a11*A_8_4+1/a11*a31*A_8_7-1/a11*(a41+1)*A_8_10-1/a11*(-a51+1)*A_8_13,A_8_2-a21/a11*A_8_5+1/a11*a31*A_8_8-1/a11*(a41+1)*A_8_11-1/a11*(-a51+1)*A_8_14,A_8_3-a21/a11*A_8_6+1/a11*a31*A_8_9-1/a11*(a41+1)*A_8_12-1/a11*(-a51+1)*A_8_15],[A_9_1-a21/a11*A_9_4+1/a11*a31*A_9_7-1/a11*(a41+1)*A_9_10-1/a11*(-a51+1)*A_9_13,A_9_2-a21/a11*A_9_5+1/a11*a31*A_9_8-1/a11*(a41+1)*A_9_11-1/a11*(-a51+1)*A_9_14,A_9_3-a21/a11*A_9_6+1/a11*a31*A_9_9-1/a11*(a41+1)*A_9_12-1/a11*(-a51+1)*A_9_15],[A_10_1-a21/a11*A_10_4+1/a11*a31*A_10_7-1/a11*(a41+1)*A_10_10-1/a11*(-a51+1)*A_10_13,A_10_2-a21/a11*A_10_5+1/a11*a31*A_10_8-1/a11*(a41+1)*A_10_11-1/a11*(-a51+1)*A_10_14,A_10_3-a21/a11*A_10_6+1/a11*a31*A_10_9-1/a11*(a41+1)*A_10_12-1/a11*(-a51+1)*A_10_15],[A_11_1-a21/a11*A_11_4+1/a11*a31*A_11_7-1/a11*(a41+1)*A_11_10-1/a11*(-a51+1)*A_11_13,A_11_2-a21/a11*A_11_5+1/a11*a31*A_11_8-1/a11*(a41+1)*A_11_11-1/a11*(-a51+1)*A_11_14,A_11_3-a21/a11*A_11_6+1/a11*a31*A_11_9-1/a11*(a41+1)*A_11_12-1/a11*(-a51+1)*A_11_15]]),Matrix(3, 3, [[B_1_10,B_1_11,B_1_12],[B_2_10,B_2_11,B_2_12],[B_3_10,B_3_11,B_3_12]]),Matrix(3, 6, [[C_10_6+C_13_6-C_16_6,C_10_1+C_13_1-C_16_1+C_10_7+C_13_7-C_16_7,C_10_2+C_13_2-C_16_2+C_10_8+C_13_8-C_16_8,C_10_3+C_13_3-C_16_3+C_10_9+C_13_9-C_16_9,C_10_4+C_13_4-C_16_4+C_10_10+C_13_10-C_16_10,C_10_5+C_13_5-C_16_5+C_10_11+C_13_11-C_16_11],[C_11_6+C_14_6-C_17_6,C_11_1+C_14_1-C_17_1+C_11_7+C_14_7-C_17_7,C_11_2+C_14_2-C_17_2+C_11_8+C_14_8-C_17_8,C_11_3+C_14_3-C_17_3+C_11_9+C_14_9-C_17_9,C_11_4+C_14_4-C_17_4+C_11_10+C_14_10-C_17_10,C_11_5+C_14_5-C_17_5+C_11_11+C_14_11-C_17_11],[C_12_6+C_15_6-C_18_6,C_12_1+C_15_1-C_18_1+C_12_7+C_15_7-C_18_7,C_12_2+C_15_2-C_18_2+C_12_8+C_15_8-C_18_8,C_12_3+C_15_3-C_18_3+C_12_9+C_15_9-C_18_9,C_12_4+C_15_4-C_18_4+C_12_10+C_15_10-C_18_10,C_12_5+C_15_5-C_18_5+C_12_11+C_15_11-C_18_11]])))+Trace(Mul(Matrix(6, 3, [[A_6_1*a11+(-a21-1)*A_6_4+(a31-1)*A_6_7-A_6_10*a41+A_6_13*a51,A_6_2*a11+(-a21-1)*A_6_5+(a31-1)*A_6_8-A_6_11*a41+A_6_14*a51,A_6_3*a11+(-a21-1)*A_6_6+(a31-1)*A_6_9-A_6_12*a41+A_6_15*a51],[A_7_1*a11+(-a21-1)*A_7_4+(a31-1)*A_7_7-A_7_10*a41+A_7_13*a51,A_7_2*a11+(-a21-1)*A_7_5+(a31-1)*A_7_8-A_7_11*a41+A_7_14*a51,A_7_3*a11+(-a21-1)*A_7_6+(a31-1)*A_7_9-A_7_12*a41+A_7_15*a51],[A_8_1*a11+(-a21-1)*A_8_4+(a31-1)*A_8_7-A_8_10*a41+A_8_13*a51,A_8_2*a11+(-a21-1)*A_8_5+(a31-1)*A_8_8-A_8_11*a41+A_8_14*a51,A_8_3*a11+(-a21-1)*A_8_6+(a31-1)*A_8_9-A_8_12*a41+A_8_15*a51],[A_9_1*a11+(-a21-1)*A_9_4+(a31-1)*A_9_7-A_9_10*a41+A_9_13*a51,A_9_2*a11+(-a21-1)*A_9_5+(a31-1)*A_9_8-A_9_11*a41+A_9_14*a51,A_9_3*a11+(-a21-1)*A_9_6+(a31-1)*A_9_9-A_9_12*a41+A_9_15*a51],[A_10_1*a11+(-a21-1)*A_10_4+(a31-1)*A_10_7-A_10_10*a41+A_10_13*a51,A_10_2*a11+(-a21-1)*A_10_5+(a31-1)*A_10_8-A_10_11*a41+A_10_14*a51,A_10_3*a11+(-a21-1)*A_10_6+(a31-1)*A_10_9-A_10_12*a41+A_10_15*a51],[A_11_1*a11+(-a21-1)*A_11_4+(a31-1)*A_11_7-A_11_10*a41+A_11_13*a51,A_11_2*a11+(-a21-1)*A_11_5+(a31-1)*A_11_8-A_11_11*a41+A_11_14*a51,A_11_3*a11+(-a21-1)*A_11_6+(a31-1)*A_11_9-A_11_12*a41+A_11_15*a51]]),Matrix(3, 3, [[-1/a41*B_10_1-1/a51*B_13_1+1/a51*B_13_4,-1/a41*B_10_2-1/a51*B_13_2+1/a51*B_13_5,-1/a41*B_10_3-1/a51*B_13_3+1/a51*B_13_6],[-1/a41*B_11_1-1/a51*B_14_1+1/a51*B_14_4,-1/a41*B_11_2-1/a51*B_14_2+1/a51*B_14_5,-1/a41*B_11_3-1/a51*B_14_3+1/a51*B_14_6],[-1/a41*B_12_1-1/a51*B_15_1+1/a51*B_15_4,-1/a41*B_12_2-1/a51*B_15_2+1/a51*B_15_5,-1/a41*B_12_3-1/a51*B_15_3+1/a51*B_15_6]]),Matrix(3, 6, [[C_4_6+C_7_6-C_16_6,C_4_1+C_7_1-C_16_1+C_4_7+C_7_7-C_16_7,C_4_2+C_7_2-C_16_2+C_4_8+C_7_8-C_16_8,C_4_3+C_7_3-C_16_3+C_4_9+C_7_9-C_16_9,C_4_4+C_7_4-C_16_4+C_4_10+C_7_10-C_16_10,C_4_5+C_7_5-C_16_5+C_4_11+C_7_11-C_16_11],[C_5_6+C_8_6-C_17_6,C_5_1+C_8_1-C_17_1+C_5_7+C_8_7-C_17_7,C_5_2+C_8_2-C_17_2+C_5_8+C_8_8-C_17_8,C_5_3+C_8_3-C_17_3+C_5_9+C_8_9-C_17_9,C_5_4+C_8_4-C_17_4+C_5_10+C_8_10-C_17_10,C_5_5+C_8_5-C_17_5+C_5_11+C_8_11-C_17_11],[C_6_6+C_9_6-C_18_6,C_9_1+C_6_1-C_18_1+C_6_7+C_9_7-C_18_7,C_9_2+C_6_2-C_18_2+C_6_8+C_9_8-C_18_8,C_6_3+C_9_3-C_18_3+C_6_9+C_9_9-C_18_9,C_6_4+C_9_4-C_18_4+C_6_10+C_9_10-C_18_10,C_6_5+C_9_5-C_18_5+C_6_11+C_9_11-C_18_11]])))+Trace(Mul(Matrix(5, 3, [[A_1_1*a11-A_1_4*a21+A_1_7*a31-A_7_1*a11+A_7_4*a21-A_7_7*a31+(-a41-1)*A_1_10+(a41+1)*A_7_10+(a51-1)*A_1_13+(-a51+1)*A_7_13,A_1_2*a11-A_1_5*a21+A_1_8*a31-A_7_2*a11+A_7_5*a21-A_7_8*a31+(-a41-1)*A_1_11+(a41+1)*A_7_11+(a51-1)*A_1_14+(-a51+1)*A_7_14,A_1_3*a11-A_1_6*a21+A_1_9*a31-A_7_3*a11+A_7_6*a21-A_7_9*a31+(-a41-1)*A_1_12+(a41+1)*A_7_12+(a51-1)*A_1_15+(-a51+1)*A_7_15],[A_2_1*a11-A_2_4*a21+A_2_7*a31-A_8_1*a11+A_8_4*a21-A_8_7*a31+(-a41-1)*A_2_10+(a41+1)*A_8_10+(a51-1)*A_2_13+(-a51+1)*A_8_13,A_2_2*a11-A_2_5*a21+A_2_8*a31-A_8_2*a11+A_8_5*a21-A_8_8*a31+(-a41-1)*A_2_11+(a41+1)*A_8_11+(a51-1)*A_2_14+(-a51+1)*A_8_14,A_2_3*a11-A_2_6*a21+A_2_9*a31-A_8_3*a11+A_8_6*a21-A_8_9*a31+(-a41-1)*A_2_12+(a41+1)*A_8_12+(a51-1)*A_2_15+(-a51+1)*A_8_15],[A_3_1*a11-A_3_4*a21+A_3_7*a31-A_9_1*a11+A_9_4*a21-A_9_7*a31+(-a41-1)*A_3_10+(a41+1)*A_9_10+(a51-1)*A_3_13+(-a51+1)*A_9_13,A_3_2*a11-A_3_5*a21+A_3_8*a31-A_9_2*a11+A_9_5*a21-A_9_8*a31+(-a41-1)*A_3_11+(a41+1)*A_9_11+(a51-1)*A_3_14+(-a51+1)*A_9_14,A_3_3*a11-A_3_6*a21+A_3_9*a31-A_9_3*a11+A_9_6*a21-A_9_9*a31+(-a41-1)*A_3_12+(a41+1)*A_9_12+(a51-1)*A_3_15+(-a51+1)*A_9_15],[-A_10_1*a11+A_10_4*a21-A_10_7*a31+A_4_1*a11-A_4_4*a21+A_4_7*a31+(-a41-1)*A_4_10+(a41+1)*A_10_10+(a51-1)*A_4_13+(-a51+1)*A_10_13,-A_10_2*a11+A_10_5*a21-A_10_8*a31+A_4_2*a11-A_4_5*a21+A_4_8*a31+(-a41-1)*A_4_11+(a41+1)*A_10_11+(a51-1)*A_4_14+(-a51+1)*A_10_14,-A_10_3*a11+A_10_6*a21-A_10_9*a31+A_4_3*a11-A_4_6*a21+A_4_9*a31+(-a41-1)*A_4_12+(a41+1)*A_10_12+(a51-1)*A_4_15+(-a51+1)*A_10_15],[-A_11_1*a11+A_11_4*a21-A_11_7*a31+A_5_1*a11-A_5_4*a21+A_5_7*a31+(-a41-1)*A_5_10+(a41+1)*A_11_10+(a51-1)*A_5_13+(-a51+1)*A_11_13,-A_11_2*a11+A_11_5*a21-A_11_8*a31+A_5_2*a11-A_5_5*a21+A_5_8*a31+(-a41-1)*A_5_11+(a41+1)*A_11_11+(a51-1)*A_5_14+(-a51+1)*A_11_14,-A_11_3*a11+A_11_6*a21-A_11_9*a31+A_5_3*a11-A_5_6*a21+A_5_9*a31+(-a41-1)*A_5_12+(a41+1)*A_11_12+(a51-1)*A_5_15+(-a51+1)*A_11_15]]),Matrix(3, 3, [[-a41/(a21+a31)*B_4_16+a41/(a21+a31)*B_7_16+B_10_16,-a41/(a21+a31)*B_4_17+a41/(a21+a31)*B_7_17+B_10_17,-a41/(a21+a31)*B_4_18+a41/(a21+a31)*B_7_18+B_10_18],[-a41/(a21+a31)*B_5_16+a41/(a21+a31)*B_8_16+B_11_16,-a41/(a21+a31)*B_5_17+a41/(a21+a31)*B_8_17+B_11_17,-a41/(a21+a31)*B_5_18+a41/(a21+a31)*B_8_18+B_11_18],[-a41/(a21+a31)*B_6_16+a41/(a21+a31)*B_9_16+B_12_16,-a41/(a21+a31)*B_6_17+a41/(a21+a31)*B_9_17+B_12_17,-a41/(a21+a31)*B_6_18+a41/(a21+a31)*B_9_18+B_12_18]]),Matrix(3, 5, [[C_10_1+C_13_1-C_16_1,C_10_2+C_13_2-C_16_2,C_10_3+C_13_3-C_16_3,C_10_4+C_13_4-C_16_4,C_10_5+C_13_5-C_16_5],[C_11_1+C_14_1-C_17_1,C_11_2+C_14_2-C_17_2,C_11_3+C_14_3-C_17_3,C_11_4+C_14_4-C_17_4,C_11_5+C_14_5-C_17_5],[C_12_1+C_15_1-C_18_1,C_12_2+C_15_2-C_18_2,C_12_3+C_15_3-C_18_3,C_12_4+C_15_4-C_18_4,C_12_5+C_15_5-C_18_5]])))+Trace(Mul(Matrix(5, 3, [[A_1_1*a11-A_7_1*a11+(-a21-1)*A_1_4+(a21+1)*A_7_4+(a31-1)*A_1_7+(-a31+1)*A_7_7-A_1_10*a41+A_7_10*a41+A_1_13*a51-A_7_13*a51,A_1_2*a11-A_7_2*a11+(-a21-1)*A_1_5+(a21+1)*A_7_5+(a31-1)*A_1_8+(-a31+1)*A_7_8-A_1_11*a41+A_7_11*a41+A_1_14*a51-A_7_14*a51,A_1_3*a11-A_7_3*a11+(-a21-1)*A_1_6+(a21+1)*A_7_6+(a31-1)*A_1_9+(-a31+1)*A_7_9-A_1_12*a41+A_7_12*a41+A_1_15*a51-A_7_15*a51],[A_2_1*a11-A_8_1*a11+(-a21-1)*A_2_4+(a21+1)*A_8_4+(a31-1)*A_2_7+(-a31+1)*A_8_7-A_2_10*a41+A_8_10*a41+A_2_13*a51-A_8_13*a51,A_2_2*a11-A_8_2*a11+(-a21-1)*A_2_5+(a21+1)*A_8_5+(a31-1)*A_2_8+(-a31+1)*A_8_8-A_2_11*a41+A_8_11*a41+A_2_14*a51-A_8_14*a51,A_2_3*a11-A_8_3*a11+(-a21-1)*A_2_6+(a21+1)*A_8_6+(a31-1)*A_2_9+(-a31+1)*A_8_9-A_2_12*a41+A_8_12*a41+A_2_15*a51-A_8_15*a51],[A_3_1*a11-A_9_1*a11+(-a21-1)*A_3_4+(a21+1)*A_9_4+(a31-1)*A_3_7+(-a31+1)*A_9_7-A_3_10*a41+A_9_10*a41+A_3_13*a51-A_9_13*a51,A_3_2*a11-A_9_2*a11+(-a21-1)*A_3_5+(a21+1)*A_9_5+(a31-1)*A_3_8+(-a31+1)*A_9_8-A_3_11*a41+A_9_11*a41+A_3_14*a51-A_9_14*a51,A_3_3*a11-A_9_3*a11+(-a21-1)*A_3_6+(a21+1)*A_9_6+(a31-1)*A_3_9+(-a31+1)*A_9_9-A_3_12*a41+A_9_12*a41+A_3_15*a51-A_9_15*a51],[-A_10_1*a11+A_4_1*a11+(-a21-1)*A_4_4+(a21+1)*A_10_4+(a31-1)*A_4_7+(-a31+1)*A_10_7-A_4_10*a41+A_10_10*a41+A_4_13*a51-A_10_13*a51,-A_10_2*a11+A_4_2*a11+(-a21-1)*A_4_5+(a21+1)*A_10_5+(a31-1)*A_4_8+(-a31+1)*A_10_8-A_4_11*a41+A_10_11*a41+A_4_14*a51-A_10_14*a51,-A_10_3*a11+A_4_3*a11+(-a21-1)*A_4_6+(a21+1)*A_10_6+(a31-1)*A_4_9+(-a31+1)*A_10_9-A_4_12*a41+A_10_12*a41+A_4_15*a51-A_10_15*a51],[-A_11_1*a11+A_5_1*a11+(-a21-1)*A_5_4+(a21+1)*A_11_4+(a31-1)*A_5_7+(-a31+1)*A_11_7-A_5_10*a41+A_11_10*a41+A_5_13*a51-A_11_13*a51,-A_11_2*a11+A_5_2*a11+(-a21-1)*A_5_5+(a21+1)*A_11_5+(a31-1)*A_5_8+(-a31+1)*A_11_8-A_5_11*a41+A_11_11*a41+A_5_14*a51-A_11_14*a51,-A_11_3*a11+A_5_3*a11+(-a21-1)*A_5_6+(a21+1)*A_11_6+(a31-1)*A_5_9+(-a31+1)*A_11_9-A_5_12*a41+A_11_12*a41+A_5_15*a51-A_11_15*a51]]),Matrix(3, 3, [[a31/(a21+a31)*B_4_16+1/(a21+a31)*a21*B_7_16,a31/(a21+a31)*B_4_17+1/(a21+a31)*a21*B_7_17,a31/(a21+a31)*B_4_18+1/(a21+a31)*a21*B_7_18],[a31/(a21+a31)*B_5_16+1/(a21+a31)*a21*B_8_16,a31/(a21+a31)*B_5_17+1/(a21+a31)*a21*B_8_17,a31/(a21+a31)*B_5_18+1/(a21+a31)*a21*B_8_18],[a31/(a21+a31)*B_6_16+1/(a21+a31)*a21*B_9_16,a31/(a21+a31)*B_6_17+1/(a21+a31)*a21*B_9_17,a31/(a21+a31)*B_6_18+1/(a21+a31)*a21*B_9_18]]),Matrix(3, 5, [[C_4_1+C_7_1-C_16_1,C_4_2+C_7_2-C_16_2,C_4_3+C_7_3-C_16_3,C_4_4+C_7_4-C_16_4,C_4_5+C_7_5-C_16_5],[C_5_1+C_8_1-C_17_1,C_5_2+C_8_2-C_17_2,C_5_3+C_8_3-C_17_3,C_5_4+C_8_4-C_17_4,C_5_5+C_8_5-C_17_5],[C_9_1+C_6_1-C_18_1,C_9_2+C_6_2-C_18_2,C_6_3+C_9_3-C_18_3,C_6_4+C_9_4-C_18_4,C_6_5+C_9_5-C_18_5]])))+Trace(Mul(Matrix(6, 3, [[A_6_1,A_6_2,A_6_3],[A_7_1,A_7_2,A_7_3],[A_8_1,A_8_2,A_8_3],[A_9_1,A_9_2,A_9_3],[A_10_1,A_10_2,A_10_3],[A_11_1,A_11_2,A_11_3]]),Matrix(3, 3, [[B_1_1-B_4_1+(a11+a21+1)/a41*B_10_1,B_1_2-B_4_2+(a11+a21+1)/a41*B_10_2,B_1_3-B_4_3+(a11+a21+1)/a41*B_10_3],[B_2_1-B_5_1+(a11+a21+1)/a41*B_11_1,B_2_2-B_5_2+(a11+a21+1)/a41*B_11_2,B_2_3-B_5_3+(a11+a21+1)/a41*B_11_3],[-B_6_1+B_3_1+(a11+a21+1)/a41*B_12_1,B_3_2-B_6_2+(a11+a21+1)/a41*B_12_2,B_3_3-B_6_3+(a11+a21+1)/a41*B_12_3]]),Matrix(3, 6, [[C_1_6,C_1_1+C_1_7,C_1_2+C_1_8,C_1_3+C_1_9,C_1_4+C_1_10,C_1_5+C_1_11],[C_2_6,C_2_1+C_2_7,C_2_2+C_2_8,C_2_3+C_2_9,C_2_4+C_2_10,C_2_5+C_2_11],[C_3_6,C_3_1+C_3_7,C_3_2+C_3_8,C_3_3+C_3_9,C_3_4+C_3_10,C_3_5+C_3_11]])))+Trace(Mul(Matrix(5, 3, [[A_1_4,A_1_5,A_1_6],[A_2_4,A_2_5,A_2_6],[A_3_4,A_3_5,A_3_6],[A_4_4,A_4_5,A_4_6],[A_5_4,A_5_5,A_5_6]]),Matrix(3, 3, [[B_7_1-(a21+a11)/a41*B_10_1-(a21+a11+a31)/a51*B_13_1-B_1_4+B_4_4-B_7_4+(a21+a11+a31)/a51*B_13_4,B_7_2-(a21+a11)/a41*B_10_2-(a21+a11+a31)/a51*B_13_2-B_1_5+B_4_5-B_7_5+(a21+a11+a31)/a51*B_13_5,B_7_3-(a21+a11)/a41*B_10_3-(a21+a11+a31)/a51*B_13_3-B_1_6+B_4_6-B_7_6+(a21+a11+a31)/a51*B_13_6],[B_8_1-(a21+a11)/a41*B_11_1-(a21+a11+a31)/a51*B_14_1-B_2_4+B_5_4-B_8_4+(a21+a11+a31)/a51*B_14_4,B_8_2-(a21+a11)/a41*B_11_2-(a21+a11+a31)/a51*B_14_2-B_2_5+B_5_5-B_8_5+(a21+a11+a31)/a51*B_14_5,B_8_3-(a21+a11)/a41*B_11_3-(a21+a11+a31)/a51*B_14_3-B_2_6+B_5_6-B_8_6+(a21+a11+a31)/a51*B_14_6],[B_9_1-(a21+a11)/a41*B_12_1-(a21+a11+a31)/a51*B_15_1-B_3_4+B_6_4-B_9_4+(a21+a11+a31)/a51*B_15_4,B_9_2-(a21+a11)/a41*B_12_2-(a21+a11+a31)/a51*B_15_2-B_3_5+B_6_5-B_9_5+(a21+a11+a31)/a51*B_15_5,B_9_3-(a21+a11)/a41*B_12_3-(a21+a11+a31)/a51*B_15_3-B_3_6+B_6_6-B_9_6+(a21+a11+a31)/a51*B_15_6]]),Matrix(3, 5, [[C_4_1+C_4_7,C_4_2+C_4_8,C_4_3+C_4_9,C_4_4+C_4_10,C_4_5+C_4_11],[C_5_1+C_5_7,C_5_2+C_5_8,C_5_3+C_5_9,C_5_4+C_5_10,C_5_5+C_5_11],[C_6_1+C_6_7,C_6_2+C_6_8,C_6_3+C_6_9,C_6_4+C_6_10,C_6_5+C_6_11]])))+Trace(Mul(Matrix(6, 3, [[A_6_7,A_6_8,A_6_9],[A_7_7,A_7_8,A_7_9],[A_8_7,A_8_8,A_8_9],[A_9_7,A_9_8,A_9_9],[A_10_7,A_10_8,A_10_9],[A_11_7,A_11_8,A_11_9]]),Matrix(3, 3, [[B_7_1+(a21+a11+2*a31)/a41*B_10_1+(a21+a11+a31)/a51*B_13_1+B_10_4-(a21+a11+a31)/a51*B_13_4+B_1_7-B_4_7+B_7_7-B_10_7,B_7_2+(a21+a11+2*a31)/a41*B_10_2+(a21+a11+a31)/a51*B_13_2+B_10_5-(a21+a11+a31)/a51*B_13_5+B_1_8-B_4_8+B_7_8-B_10_8,B_7_3+(a21+a11+2*a31)/a41*B_10_3+(a21+a11+a31)/a51*B_13_3+B_10_6-(a21+a11+a31)/a51*B_13_6+B_1_9-B_4_9+B_7_9-B_10_9],[B_8_1+(a21+a11+2*a31)/a41*B_11_1+(a21+a11+a31)/a51*B_14_1+B_11_4-(a21+a11+a31)/a51*B_14_4+B_2_7-B_5_7+B_8_7-B_11_7,B_8_2+(a21+a11+2*a31)/a41*B_11_2+(a21+a11+a31)/a51*B_14_2+B_11_5-(a21+a11+a31)/a51*B_14_5+B_2_8-B_5_8+B_8_8-B_11_8,B_8_3+(a21+a11+2*a31)/a41*B_11_3+(a21+a11+a31)/a51*B_14_3+B_11_6-(a21+a11+a31)/a51*B_14_6+B_2_9-B_5_9+B_8_9-B_11_9],[B_9_1+(a21+a11+2*a31)/a41*B_12_1+(a21+a11+a31)/a51*B_15_1+B_12_4-(a21+a11+a31)/a51*B_15_4+B_3_7-B_6_7+B_9_7-B_12_7,B_9_2+(a21+a11+2*a31)/a41*B_12_2+(a21+a11+a31)/a51*B_15_2+B_12_5-(a21+a11+a31)/a51*B_15_5+B_3_8-B_6_8+B_9_8-B_12_8,B_9_3+(a21+a11+2*a31)/a41*B_12_3+(a21+a11+a31)/a51*B_15_3+B_12_6-(a21+a11+a31)/a51*B_15_6+B_3_9-B_6_9+B_9_9-B_12_9]]),Matrix(3, 6, [[C_7_6,C_7_1+C_7_7,C_7_2+C_7_8,C_7_3+C_7_9,C_7_4+C_7_10,C_7_5+C_7_11],[C_8_6,C_8_1+C_8_7,C_8_2+C_8_8,C_8_3+C_8_9,C_8_4+C_8_10,C_8_5+C_8_11],[C_9_6,C_9_1+C_9_7,C_9_2+C_9_8,C_9_3+C_9_9,C_9_4+C_9_10,C_9_5+C_9_11]])))+Trace(Mul(Matrix(5, 3, [[A_1_10,A_1_11,A_1_12],[A_2_10,A_2_11,A_2_12],[A_3_10,A_3_11,A_3_12],[A_4_10,A_4_11,A_4_12],[A_5_10,A_5_11,A_5_12]]),Matrix(3, 3, [[-(-a51+a41)/a41*B_10_1-(-a51+a41)/a51*B_13_1+B_10_4+(-a51+a41)/a51*B_13_4+B_13_7+(a41+a51+a21+a31)/a11*B_1_10+B_4_10-B_7_10+B_10_10-B_13_10,-(-a51+a41)/a41*B_10_2-(-a51+a41)/a51*B_13_2+B_10_5+(-a51+a41)/a51*B_13_5+B_13_8+(a41+a51+a21+a31)/a11*B_1_11+B_4_11-B_7_11+B_10_11-B_13_11,-(-a51+a41)/a41*B_10_3-(-a51+a41)/a51*B_13_3+B_10_6+(-a51+a41)/a51*B_13_6+B_13_9+(a41+a51+a21+a31)/a11*B_1_12+B_4_12-B_7_12+B_10_12-B_13_12],[-(-a51+a41)/a41*B_11_1-(-a51+a41)/a51*B_14_1+B_11_4+(-a51+a41)/a51*B_14_4+B_14_7+(a41+a51+a21+a31)/a11*B_2_10+B_5_10-B_8_10+B_11_10-B_14_10,-(-a51+a41)/a41*B_11_2-(-a51+a41)/a51*B_14_2+B_11_5+(-a51+a41)/a51*B_14_5+B_14_8+(a41+a51+a21+a31)/a11*B_2_11+B_5_11-B_8_11+B_11_11-B_14_11,-(-a51+a41)/a41*B_11_3-(-a51+a41)/a51*B_14_3+B_11_6+(-a51+a41)/a51*B_14_6+B_14_9+(a41+a51+a21+a31)/a11*B_2_12+B_5_12-B_8_12+B_11_12-B_14_12],[-(-a51+a41)/a41*B_12_1-(-a51+a41)/a51*B_15_1+B_12_4+(-a51+a41)/a51*B_15_4+B_15_7+(a41+a51+a21+a31)/a11*B_3_10+B_6_10-B_9_10+B_12_10-B_15_10,-(-a51+a41)/a41*B_12_2-(-a51+a41)/a51*B_15_2+B_12_5+(-a51+a41)/a51*B_15_5+B_15_8+(a41+a51+a21+a31)/a11*B_3_11+B_6_11-B_9_11+B_12_11-B_15_11,-(-a51+a41)/a41*B_12_3-(-a51+a41)/a51*B_15_3+B_12_6+(-a51+a41)/a51*B_15_6+B_15_9+(a41+a51+a21+a31)/a11*B_3_12+B_6_12-B_9_12+B_12_12-B_15_12]]),Matrix(3, 5, [[C_10_1+C_10_7,C_10_2+C_10_8,C_10_3+C_10_9,C_10_4+C_10_10,C_10_5+C_10_11],[C_11_1+C_11_7,C_11_2+C_11_8,C_11_3+C_11_9,C_11_4+C_11_10,C_11_5+C_11_11],[C_12_1+C_12_7,C_12_2+C_12_8,C_12_3+C_12_9,C_12_4+C_12_10,C_12_5+C_12_11]])))+Trace(Mul(Matrix(6, 3, [[A_6_13,A_6_14,A_6_15],[A_7_13,A_7_14,A_7_15],[A_8_13,A_8_14,A_8_15],[A_9_13,A_9_14,A_9_15],[A_10_13,A_10_14,A_10_15],[A_11_13,A_11_14,A_11_15]]),Matrix(3, 3, [[2*a51/a41*B_10_1+2*B_13_1-B_13_4+B_13_7+1/a11*B_1_10-(a31+a41+a51+1)/(a21+a11)*B_1_13+(a31+a41+a51+1)/(a21+a11)*B_4_13+B_7_13-B_10_13+B_13_13,2*a51/a41*B_10_2+2*B_13_2-B_13_5+B_13_8+1/a11*B_1_11-(a31+a41+a51+1)/(a21+a11)*B_1_14+(a31+a41+a51+1)/(a21+a11)*B_4_14+B_7_14-B_10_14+B_13_14,2*a51/a41*B_10_3+2*B_13_3-B_13_6+B_13_9+1/a11*B_1_12-(a31+a41+a51+1)/(a21+a11)*B_1_15+(a31+a41+a51+1)/(a21+a11)*B_4_15+B_7_15-B_10_15+B_13_15],[2*a51/a41*B_11_1+2*B_14_1-B_14_4+B_14_7+1/a11*B_2_10-(a31+a41+a51+1)/(a21+a11)*B_2_13+(a31+a41+a51+1)/(a21+a11)*B_5_13+B_8_13-B_11_13+B_14_13,2*a51/a41*B_11_2+2*B_14_2-B_14_5+B_14_8+1/a11*B_2_11-(a31+a41+a51+1)/(a21+a11)*B_2_14+(a31+a41+a51+1)/(a21+a11)*B_5_14+B_8_14-B_11_14+B_14_14,2*a51/a41*B_11_3+2*B_14_3-B_14_6+B_14_9+1/a11*B_2_12-(a31+a41+a51+1)/(a21+a11)*B_2_15+(a31+a41+a51+1)/(a21+a11)*B_5_15+B_8_15-B_11_15+B_14_15],[2*a51/a41*B_12_1+2*B_15_1-B_15_4+B_15_7+1/a11*B_3_10-(a31+a41+a51+1)/(a21+a11)*B_3_13+(a31+a41+a51+1)/(a21+a11)*B_6_13+B_9_13-B_12_13+B_15_13,2*a51/a41*B_12_2+2*B_15_2-B_15_5+B_15_8+1/a11*B_3_11-(a31+a41+a51+1)/(a21+a11)*B_3_14+(a31+a41+a51+1)/(a21+a11)*B_6_14+B_9_14-B_12_14+B_15_14,2*a51/a41*B_12_3+2*B_15_3-B_15_6+B_15_9+1/a11*B_3_12-(a31+a41+a51+1)/(a21+a11)*B_3_15+(a31+a41+a51+1)/(a21+a11)*B_6_15+B_9_15-B_12_15+B_15_15]]),Matrix(3, 6, [[C_13_6,C_13_1+C_13_7,C_13_2+C_13_8,C_13_3+C_13_9,C_13_4+C_13_10,C_13_5+C_13_11],[C_14_6,C_14_1+C_14_7,C_14_2+C_14_8,C_14_3+C_14_9,C_14_4+C_14_10,C_14_5+C_14_11],[C_15_6,C_15_1+C_15_7,C_15_2+C_15_8,C_15_3+C_15_9,C_15_4+C_15_10,C_15_5+C_15_11]])))+Trace(Mul(Matrix(5, 3, [[A_1_1+A_1_4,A_1_2+A_1_5,A_1_3+A_1_6],[A_2_1+A_2_4,A_2_2+A_2_5,A_2_3+A_2_6],[A_3_1+A_3_4,A_3_2+A_3_5,A_3_3+A_3_6],[A_4_1+A_4_4,A_4_2+A_4_5,A_4_3+A_4_6],[A_5_1+A_5_4,A_5_2+A_5_5,A_5_3+A_5_6]]),Matrix(3, 3, [[B_7_1+(a51+a11+a31)/a41*B_10_1+(a51+a11)/a51*B_13_1+B_1_4-a11/a51*B_13_4,B_7_2+(a51+a11+a31)/a41*B_10_2+(a51+a11)/a51*B_13_2+B_1_5-a11/a51*B_13_5,B_7_3+(a51+a11+a31)/a41*B_10_3+(a51+a11)/a51*B_13_3+B_1_6-a11/a51*B_13_6],[B_8_1+(a51+a11+a31)/a41*B_11_1+(a51+a11)/a51*B_14_1+B_2_4-a11/a51*B_14_4,B_8_2+(a51+a11+a31)/a41*B_11_2+(a51+a11)/a51*B_14_2+B_2_5-a11/a51*B_14_5,B_8_3+(a51+a11+a31)/a41*B_11_3+(a51+a11)/a51*B_14_3+B_2_6-a11/a51*B_14_6],[B_9_1+(a51+a11+a31)/a41*B_12_1+(a51+a11)/a51*B_15_1+B_3_4-a11/a51*B_15_4,B_9_2+(a51+a11+a31)/a41*B_12_2+(a51+a11)/a51*B_15_2+B_3_5-a11/a51*B_15_5,B_9_3+(a51+a11+a31)/a41*B_12_3+(a51+a11)/a51*B_15_3+B_3_6-a11/a51*B_15_6]]),Matrix(3, 5, [[C_1_1+C_4_1,C_1_2+C_4_2,C_1_3+C_4_3,C_1_4+C_4_4,C_1_5+C_4_5],[C_2_1+C_5_1,C_2_2+C_5_2,C_2_3+C_5_3,C_2_4+C_5_4,C_2_5+C_5_5],[C_3_1+C_6_1,C_3_2+C_6_2,C_3_3+C_6_3,C_3_4+C_6_4,C_3_5+C_6_5]])))+Trace(Mul(Matrix(5, 3, [[A_1_1-A_7_1,A_1_2-A_7_2,A_1_3-A_7_3],[A_2_1-A_8_1,A_2_2-A_8_2,A_2_3-A_8_3],[A_3_1-A_9_1,A_3_2-A_9_2,A_3_3-A_9_3],[A_4_1-A_10_1,A_4_2-A_10_2,A_4_3-A_10_3],[A_5_1-A_11_1,A_5_2-A_11_2,A_5_3-A_11_3]]),Matrix(3, 3, [[B_1_1-a11/a51*B_13_1-B_1_4+a11/a51*B_13_4-B_1_16-a11/(a21+a31)*B_4_16+a11/(a21+a31)*B_7_16,B_1_2-a11/a51*B_13_2-B_1_5+a11/a51*B_13_5-B_1_17-a11/(a21+a31)*B_4_17+a11/(a21+a31)*B_7_17,B_1_3-a11/a51*B_13_3-B_1_6+a11/a51*B_13_6-B_1_18-a11/(a21+a31)*B_4_18+a11/(a21+a31)*B_7_18],[B_2_1-a11/a51*B_14_1-B_2_4+a11/a51*B_14_4-B_2_16-a11/(a21+a31)*B_5_16+a11/(a21+a31)*B_8_16,B_2_2-a11/a51*B_14_2-B_2_5+a11/a51*B_14_5-B_2_17-a11/(a21+a31)*B_5_17+a11/(a21+a31)*B_8_17,B_2_3-a11/a51*B_14_3-B_2_6+a11/a51*B_14_6-B_2_18-a11/(a21+a31)*B_5_18+a11/(a21+a31)*B_8_18],[B_3_1-a11/a51*B_15_1-B_3_4+a11/a51*B_15_4-B_3_16-a11/(a21+a31)*B_6_16+a11/(a21+a31)*B_9_16,B_3_2-a11/a51*B_15_2-B_3_5+a11/a51*B_15_5-B_3_17-a11/(a21+a31)*B_6_17+a11/(a21+a31)*B_9_17,B_3_3-a11/a51*B_15_3-B_3_6+a11/a51*B_15_6-B_3_18-a11/(a21+a31)*B_6_18+a11/(a21+a31)*B_9_18]]),Matrix(3, 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]])))+Trace(Mul(Matrix(6, 3, [[A_6_1,A_6_2,A_6_3],[A_7_1+A_1_4,A_1_5+A_7_2,A_7_3+A_1_6],[A_8_1+A_2_4,A_2_5+A_8_2,A_8_3+A_2_6],[A_9_1+A_3_4,A_3_5+A_9_2,A_9_3+A_3_6],[A_10_1+A_4_4,A_4_5+A_10_2,A_10_3+A_4_6],[A_11_1+A_5_4,A_5_5+A_11_2,A_11_3+A_5_6]]),Matrix(3, 3, [[B_4_1-(a21+a11)/a41*B_10_1-a11/a51*B_13_1-B_1_4+a11/a51*B_13_4,B_4_2-(a21+a11)/a41*B_10_2-a11/a51*B_13_2-B_1_5+a11/a51*B_13_5,B_4_3-(a21+a11)/a41*B_10_3-a11/a51*B_13_3-B_1_6+a11/a51*B_13_6],[B_5_1-(a21+a11)/a41*B_11_1-a11/a51*B_14_1-B_2_4+a11/a51*B_14_4,B_5_2-(a21+a11)/a41*B_11_2-a11/a51*B_14_2-B_2_5+a11/a51*B_14_5,B_5_3-(a21+a11)/a41*B_11_3-a11/a51*B_14_3-B_2_6+a11/a51*B_14_6],[B_6_1-(a21+a11)/a41*B_12_1-a11/a51*B_15_1-B_3_4+a11/a51*B_15_4,B_6_2-(a21+a11)/a41*B_12_2-a11/a51*B_15_2-B_3_5+a11/a51*B_15_5,B_6_3-(a21+a11)/a41*B_12_3-a11/a51*B_15_3-B_3_6+a11/a51*B_15_6]]),Matrix(3, 6, [[-C_4_6,C_1_1-C_4_7,C_1_2-C_4_8,C_1_3-C_4_9,C_1_4-C_4_10,C_1_5-C_4_11],[-C_5_6,C_2_1-C_5_7,C_2_2-C_5_8,C_2_3-C_5_9,C_2_4-C_5_10,C_2_5-C_5_11],[-C_6_6,C_3_1-C_6_7,C_3_2-C_6_8,C_3_3-C_6_9,C_3_4-C_6_10,C_3_5-C_6_11]])))+Trace(Mul(Matrix(6, 3, [[A_6_1+A_6_4,A_6_2+A_6_5,A_6_3+A_6_6],[A_7_1+A_7_4,A_7_2+A_7_5,A_7_3+A_7_6],[A_8_1+A_8_4,A_8_2+A_8_5,A_8_3+A_8_6],[A_9_1+A_9_4,A_9_2+A_9_5,A_9_3+A_9_6],[A_10_1+A_10_4,A_10_2+A_10_5,A_10_3+A_10_6],[A_11_1+A_11_4,A_11_2+A_11_5,A_11_3+A_11_6]]),Matrix(3, 3, [[B_4_1+(-a21+a11)/a41*B_10_1+a11/a51*B_13_1-a11/a51*B_13_4+B_1_7+a21/(a21+a11)*B_1_13+a11/(a21+a11)*B_4_13,B_4_2+(-a21+a11)/a41*B_10_2+a11/a51*B_13_2-a11/a51*B_13_5+B_1_8+a21/(a21+a11)*B_1_14+a11/(a21+a11)*B_4_14,B_4_3+(-a21+a11)/a41*B_10_3+a11/a51*B_13_3-a11/a51*B_13_6+B_1_9+a21/(a21+a11)*B_1_15+a11/(a21+a11)*B_4_15],[B_5_1+(-a21+a11)/a41*B_11_1+a11/a51*B_14_1-a11/a51*B_14_4+B_2_7+a21/(a21+a11)*B_2_13+a11/(a21+a11)*B_5_13,B_5_2+(-a21+a11)/a41*B_11_2+a11/a51*B_14_2-a11/a51*B_14_5+B_2_8+a21/(a21+a11)*B_2_14+a11/(a21+a11)*B_5_14,B_5_3+(-a21+a11)/a41*B_11_3+a11/a51*B_14_3-a11/a51*B_14_6+B_2_9+a21/(a21+a11)*B_2_15+a11/(a21+a11)*B_5_15],[B_6_1+(-a21+a11)/a41*B_12_1+a11/a51*B_15_1-a11/a51*B_15_4+B_3_7+a21/(a21+a11)*B_3_13+a11/(a21+a11)*B_6_13,B_6_2+(-a21+a11)/a41*B_12_2+a11/a51*B_15_2-a11/a51*B_15_5+B_3_8+a21/(a21+a11)*B_3_14+a11/(a21+a11)*B_6_14,B_6_3+(-a21+a11)/a41*B_12_3+a11/a51*B_15_3-a11/a51*B_15_6+B_3_9+a21/(a21+a11)*B_3_15+a11/(a21+a11)*B_6_15]]),Matrix(3, 6, [[C_1_6+C_4_6,C_1_7+C_4_7,C_1_8+C_4_8,C_1_9+C_4_9,C_1_10+C_4_10,C_1_11+C_4_11],[C_2_6+C_5_6,C_2_7+C_5_7,C_2_8+C_5_8,C_2_9+C_5_9,C_2_10+C_5_10,C_2_11+C_5_11],[C_3_6+C_6_6,C_3_7+C_6_7,C_3_8+C_6_8,C_3_9+C_6_9,C_3_10+C_6_10,C_3_11+C_6_11]])))+Trace(Mul(Matrix(6, 3, [[-A_6_4,-A_6_5,-A_6_6],[A_1_4-A_7_4,A_1_5-A_7_5,A_1_6-A_7_6],[A_2_4-A_8_4,A_2_5-A_8_5,A_2_6-A_8_6],[A_3_4-A_9_4,A_3_5-A_9_5,A_3_6-A_9_6],[A_4_4-A_10_4,A_4_5-A_10_5,A_4_6-A_10_6],[A_5_4-A_11_4,A_5_5-A_11_5,A_5_6-A_11_6]]),Matrix(3, 3, [[B_4_1-(a21+a11)/a41*B_10_1-a11/a51*B_13_1-B_4_4+a11/a51*B_13_4-B_1_7+B_4_7,B_4_2-(a21+a11)/a41*B_10_2-a11/a51*B_13_2-B_4_5+a11/a51*B_13_5-B_1_8+B_4_8,B_4_3-(a21+a11)/a41*B_10_3-a11/a51*B_13_3-B_4_6+a11/a51*B_13_6-B_1_9+B_4_9],[B_5_1-(a21+a11)/a41*B_11_1-a11/a51*B_14_1-B_5_4+a11/a51*B_14_4-B_2_7+B_5_7,B_5_2-(a21+a11)/a41*B_11_2-a11/a51*B_14_2-B_5_5+a11/a51*B_14_5-B_2_8+B_5_8,B_5_3-(a21+a11)/a41*B_11_3-a11/a51*B_14_3-B_5_6+a11/a51*B_14_6-B_2_9+B_5_9],[B_6_1-(a21+a11)/a41*B_12_1-a11/a51*B_15_1-B_6_4+a11/a51*B_15_4-B_3_7+B_6_7,B_6_2-(a21+a11)/a41*B_12_2-a11/a51*B_15_2-B_6_5+a11/a51*B_15_5-B_3_8+B_6_8,B_6_3-(a21+a11)/a41*B_12_3-a11/a51*B_15_3-B_6_6+a11/a51*B_15_6-B_3_9+B_6_9]]),Matrix(3, 6, [[C_4_6,C_4_7,C_4_8,C_4_9,C_4_10,C_4_11],[C_5_6,C_5_7,C_5_8,C_5_9,C_5_10,C_5_11],[C_6_6,C_6_7,C_6_8,C_6_9,C_6_10,C_6_11]])))

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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