Description of fast matrix multiplication algorithm: ⟨7×9×30:1240⟩

Algorithm type

5X4Y4Z6+16X2Y9Z3+5X4Y4Z5+24XY9Z3+30X4Y4Z4+5X4Y4Z3+10X3Y4Z4+50X2Y6Z3+25X3Y4Z3+14X2Y6Z2+72XY6Z3+6X2Y4Z3+82X2Y4Z2+96X2Y3Z3+30X2Y2Z4+14XY6Z+20X2Y4Z+12X2Y2Z3+5XY4Z2+144XY3Z3+169X2Y2Z2+47XY4Z+6XY3Z2+5X2Y2Z+20XY3Z+23XY2Z2+149XY2Z+36XYZ2+120XYZ5X4Y4Z616X2Y9Z35X4Y4Z524XY9Z330X4Y4Z45X4Y4Z310X3Y4Z450X2Y6Z325X3Y4Z314X2Y6Z272XY6Z36X2Y4Z382X2Y4Z296X2Y3Z330X2Y2Z414XY6Z20X2Y4Z12X2Y2Z35XY4Z2144XY3Z3169X2Y2Z247XY4Z6XY3Z25X2Y2Z20XY3Z23XY2Z2149XY2Z36XYZ2120XYZ5*X^4*Y^4*Z^6+16*X^2*Y^9*Z^3+5*X^4*Y^4*Z^5+24*X*Y^9*Z^3+30*X^4*Y^4*Z^4+5*X^4*Y^4*Z^3+10*X^3*Y^4*Z^4+50*X^2*Y^6*Z^3+25*X^3*Y^4*Z^3+14*X^2*Y^6*Z^2+72*X*Y^6*Z^3+6*X^2*Y^4*Z^3+82*X^2*Y^4*Z^2+96*X^2*Y^3*Z^3+30*X^2*Y^2*Z^4+14*X*Y^6*Z+20*X^2*Y^4*Z+12*X^2*Y^2*Z^3+5*X*Y^4*Z^2+144*X*Y^3*Z^3+169*X^2*Y^2*Z^2+47*X*Y^4*Z+6*X*Y^3*Z^2+5*X^2*Y^2*Z+20*X*Y^3*Z+23*X*Y^2*Z^2+149*X*Y^2*Z+36*X*Y*Z^2+120*X*Y*Z

Algorithm definition

The algorithm ⟨7×9×30:1240⟩ could be constructed using the following decomposition:

⟨7×9×30:1240⟩ = ⟨4×3×6:56⟩ + ⟨3×3×6:40⟩ + ⟨4×3×6:56⟩ + ⟨3×3×6:40⟩ + ⟨3×3×6:40⟩ + ⟨4×3×6:56⟩ + ⟨4×3×6:56⟩ + ⟨4×3×6:56⟩ + ⟨4×3×6:56⟩ + ⟨3×3×6:40⟩ + ⟨3×3×6:40⟩ + ⟨4×3×6:56⟩ + ⟨3×3×6:40⟩ + ⟨3×3×6:40⟩ + ⟨4×3×6:56⟩ + ⟨3×3×6:40⟩ + ⟨3×3×6:40⟩ + ⟨4×3×6:56⟩ + ⟨4×3×6:56⟩ + ⟨4×3×6:56⟩ + ⟨4×3×6:56⟩ + ⟨4×3×6:56⟩ + ⟨4×3×6:56⟩ + ⟨3×3×6:40⟩ + ⟨4×3×6:56⟩.

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_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_2_7A_2_8A_2_9A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_3_7A_3_8A_3_9A_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_4_7A_4_8A_4_9A_5_1A_5_2A_5_3A_5_4A_5_5A_5_6A_5_7A_5_8A_5_9A_6_1A_6_2A_6_3A_6_4A_6_5A_6_6A_6_7A_6_8A_6_9A_7_1A_7_2A_7_3A_7_4A_7_5A_7_6A_7_7A_7_8A_7_9B_1_1B_1_2B_1_3B_1_4B_1_5B_1_6B_1_7B_1_8B_1_9B_1_10B_1_11B_1_12B_1_13B_1_14B_1_15B_1_16B_1_17B_1_18B_1_19B_1_20B_1_21B_1_22B_1_23B_1_24B_1_25B_1_26B_1_27B_1_28B_1_29B_1_30B_2_1B_2_2B_2_3B_2_4B_2_5B_2_6B_2_7B_2_8B_2_9B_2_10B_2_11B_2_12B_2_13B_2_14B_2_15B_2_16B_2_17B_2_18B_2_19B_2_20B_2_21B_2_22B_2_23B_2_24B_2_25B_2_26B_2_27B_2_28B_2_29B_2_30B_3_1B_3_2B_3_3B_3_4B_3_5B_3_6B_3_7B_3_8B_3_9B_3_10B_3_11B_3_12B_3_13B_3_14B_3_15B_3_16B_3_17B_3_18B_3_19B_3_20B_3_21B_3_22B_3_23B_3_24B_3_25B_3_26B_3_27B_3_28B_3_29B_3_30B_4_1B_4_2B_4_3B_4_4B_4_5B_4_6B_4_7B_4_8B_4_9B_4_10B_4_11B_4_12B_4_13B_4_14B_4_15B_4_16B_4_17B_4_18B_4_19B_4_20B_4_21B_4_22B_4_23B_4_24B_4_25B_4_26B_4_27B_4_28B_4_29B_4_30B_5_1B_5_2B_5_3B_5_4B_5_5B_5_6B_5_7B_5_8B_5_9B_5_10B_5_11B_5_12B_5_13B_5_14B_5_15B_5_16B_5_17B_5_18B_5_19B_5_20B_5_21B_5_22B_5_23B_5_24B_5_25B_5_26B_5_27B_5_28B_5_29B_5_30B_6_1B_6_2B_6_3B_6_4B_6_5B_6_6B_6_7B_6_8B_6_9B_6_10B_6_11B_6_12B_6_13B_6_14B_6_15B_6_16B_6_17B_6_18B_6_19B_6_20B_6_21B_6_22B_6_23B_6_24B_6_25B_6_26B_6_27B_6_28B_6_29B_6_30B_7_1B_7_2B_7_3B_7_4B_7_5B_7_6B_7_7B_7_8B_7_9B_7_10B_7_11B_7_12B_7_13B_7_14B_7_15B_7_16B_7_17B_7_18B_7_19B_7_20B_7_21B_7_22B_7_23B_7_24B_7_25B_7_26B_7_27B_7_28B_7_29B_7_30B_8_1B_8_2B_8_3B_8_4B_8_5B_8_6B_8_7B_8_8B_8_9B_8_10B_8_11B_8_12B_8_13B_8_14B_8_15B_8_16B_8_17B_8_18B_8_19B_8_20B_8_21B_8_22B_8_23B_8_24B_8_25B_8_26B_8_27B_8_28B_8_29B_8_30B_9_1B_9_2B_9_3B_9_4B_9_5B_9_6B_9_7B_9_8B_9_9B_9_10B_9_11B_9_12B_9_13B_9_14B_9_15B_9_16B_9_17B_9_18B_9_19B_9_20B_9_21B_9_22B_9_23B_9_24B_9_25B_9_26B_9_27B_9_28B_9_29B_9_30C_1_1C_1_2C_1_3C_1_4C_1_5C_1_6C_1_7C_2_1C_2_2C_2_3C_2_4C_2_5C_2_6C_2_7C_3_1C_3_2C_3_3C_3_4C_3_5C_3_6C_3_7C_4_1C_4_2C_4_3C_4_4C_4_5C_4_6C_4_7C_5_1C_5_2C_5_3C_5_4C_5_5C_5_6C_5_7C_6_1C_6_2C_6_3C_6_4C_6_5C_6_6C_6_7C_7_1C_7_2C_7_3C_7_4C_7_5C_7_6C_7_7C_8_1C_8_2C_8_3C_8_4C_8_5C_8_6C_8_7C_9_1C_9_2C_9_3C_9_4C_9_5C_9_6C_9_7C_10_1C_10_2C_10_3C_10_4C_10_5C_10_6C_10_7C_11_1C_11_2C_11_3C_11_4C_11_5C_11_6C_11_7C_12_1C_12_2C_12_3C_12_4C_12_5C_12_6C_12_7C_13_1C_13_2C_13_3C_13_4C_13_5C_13_6C_13_7C_14_1C_14_2C_14_3C_14_4C_14_5C_14_6C_14_7C_15_1C_15_2C_15_3C_15_4C_15_5C_15_6C_15_7C_16_1C_16_2C_16_3C_16_4C_16_5C_16_6C_16_7C_17_1C_17_2C_17_3C_17_4C_17_5C_17_6C_17_7C_18_1C_18_2C_18_3C_18_4C_18_5C_18_6C_18_7C_19_1C_19_2C_19_3C_19_4C_19_5C_19_6C_19_7C_20_1C_20_2C_20_3C_20_4C_20_5C_20_6C_20_7C_21_1C_21_2C_21_3C_21_4C_21_5C_21_6C_21_7C_22_1C_22_2C_22_3C_22_4C_22_5C_22_6C_22_7C_23_1C_23_2C_23_3C_23_4C_23_5C_23_6C_23_7C_24_1C_24_2C_24_3C_24_4C_24_5C_24_6C_24_7C_25_1C_25_2C_25_3C_25_4C_25_5C_25_6C_25_7C_26_1C_26_2C_26_3C_26_4C_26_5C_26_6C_26_7C_27_1C_27_2C_27_3C_27_4C_27_5C_27_6C_27_7C_28_1C_28_2C_28_3C_28_4C_28_5C_28_6C_28_7C_29_1C_29_2C_29_3C_29_4C_29_5C_29_6C_29_7C_30_1C_30_2C_30_3C_30_4C_30_5C_30_6C_30_7=TraceMulA_4_1A_4_2A_4_3A_5_1A_5_2A_5_3A_6_1A_6_2A_6_3A_7_1A_7_2A_7_3B_1_1-B_4_1-a12+a22B_7_1a32-B_1_25-a32a11-a31a12B_4_25a21a32-a22a31-a22a11-a21a12B_7_25a21a32-a22a31B_1_2-B_4_2-a12+a22B_7_2a32-B_1_26-a32a11-a31a12B_4_26a21a32-a22a31-a22a11-a21a12B_7_26a21a32-a22a31B_1_3-B_4_3-a12+a22B_7_3a32-B_1_27-a32a11-a31a12B_4_27a21a32-a22a31-a22a11-a21a12B_7_27a21a32-a22a31B_1_4-B_4_4-a12+a22B_7_4a32-B_1_28-a32a11-a31a12B_4_28a21a32-a22a31-a22a11-a21a12B_7_28a21a32-a22a31B_1_5-B_4_5-a12+a22B_7_5a32-B_1_29-a32a11-a31a12B_4_29a21a32-a22a31-a22a11-a21a12B_7_29a21a32-a22a31B_1_6-B_4_6-a12+a22B_7_6a32-B_1_30-a32a11-a31a12B_4_30a21a32-a22a31-a22a11-a21a12B_7_30a21a32-a22a31B_2_1-B_5_1-a12+a22B_8_1a32-B_2_25-a32a11-a31a12B_5_25a21a32-a22a31-a22a11-a21a12B_8_25a21a32-a22a31B_2_2-B_5_2-a12+a22B_8_2a32-B_2_26-a32a11-a31a12B_5_26a21a32-a22a31-a22a11-a21a12B_8_26a21a32-a22a31B_2_3-B_5_3-a12+a22B_8_3a32-B_2_27-a32a11-a31a12B_5_27a21a32-a22a31-a22a11-a21a12B_8_27a21a32-a22a31B_2_4-B_5_4-a12+a22B_8_4a32-B_2_28-a32a11-a31a12B_5_28a21a32-a22a31-a22a11-a21a12B_8_28a21a32-a22a31B_2_5-B_5_5-a12+a22B_8_5a32-B_2_29-a32a11-a31a12B_5_29a21a32-a22a31-a22a11-a21a12B_8_29a21a32-a22a31B_2_6-B_5_6-a12+a22B_8_6a32-B_2_30-a32a11-a31a12B_5_30a21a32-a22a31-a22a11-a21a12B_8_30a21a32-a22a31-B_6_1+B_3_1-a12+a22B_9_1a32-B_3_25-a32a11-a31a12B_6_25a21a32-a22a31-a22a11-a21a12B_9_25a21a32-a22a31B_3_2-B_6_2-a12+a22B_9_2a32-B_3_26-a32a11-a31a12B_6_26a21a32-a22a31-a22a11-a21a12B_9_26a21a32-a22a31B_3_3-B_6_3-a12+a22B_9_3a32-B_3_27-a32a11-a31a12B_6_27a21a32-a22a31-a22a11-a21a12B_9_27a21a32-a22a31B_3_4-B_6_4-a12+a22B_9_4a32-B_3_28-a32a11-a31a12B_6_28a21a32-a22a31-a22a11-a21a12B_9_28a21a32-a22a31B_3_5-B_6_5-a12+a22B_9_5a32-B_3_29-a32a11-a31a12B_6_29a21a32-a22a31-a22a11-a21a12B_9_29a21a32-a22a31B_3_6-B_6_6-a12+a22B_9_6a32-B_3_30-a32a11-a31a12B_6_30a21a32-a22a31-a22a11-a21a12B_9_30a21a32-a22a31C_1_4C_1_1+C_1_5C_1_2+C_1_6C_1_3+C_1_7C_2_4C_2_1+C_2_5C_2_2+C_2_6C_2_3+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A_5_2a32A_1_5a22a32A_5_5a22a32A_1_8A_5_8a121A_1_3a32a12-1A_5_3a32A_1_6a22a32A_5_6a22a32A_1_9A_5_9a121A_2_1a32a12-1A_6_1a32A_2_4a22a32A_6_4a22a32A_2_7A_6_7a121A_2_2a32a12-1A_6_2a32A_2_5a22a32A_6_5a22a32A_2_8A_6_8a121A_2_3a32a12-1A_6_3a32A_2_6a22a32A_6_6a22a32A_2_9A_6_9a121A_3_1a32a12-1A_7_1a32A_3_4a22a32A_7_4a22a32A_3_7A_7_7a121A_3_2a32a12-1A_7_2a32A_3_5a22a32A_7_5a22a32A_3_8A_7_8a121A_3_3a32a12-1A_7_3a32A_3_6a22a32A_7_6a22a32A_3_9A_7_9B_7_1B_7_2B_7_3B_7_4B_7_5B_7_6B_8_1B_8_2B_8_3B_8_4B_8_5B_8_6B_9_1B_9_2B_9_3B_9_4B_9_5B_9_6C_1_4C_25_4C_1_5C_25_5C_1_6C_25_6C_1_7C_25_7C_2_4C_26_4C_2_5C_26_5C_2_6C_26_6C_2_7C_26_7C_3_4C_27_4C_3_5C_27_5C_3_6C_27_6C_3_7C_27_7C_4_4C_28_4C_4_5C_28_5C_4_6C_28_6C_4_7C_28_7C_5_4C_29_4C_5_5C_29_5C_5_6C_29_6C_5_7C_29_7C_6_4C_30_4C_6_5C_30_5C_6_6C_30_6C_6_7C_30_7Trace(Mul(Matrix(7, 9, [[A_1_1,A_1_2,A_1_3,A_1_4,A_1_5,A_1_6,A_1_7,A_1_8,A_1_9],[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6,A_2_7,A_2_8,A_2_9],[A_3_1,A_3_2,A_3_3,A_3_4,A_3_5,A_3_6,A_3_7,A_3_8,A_3_9],[A_4_1,A_4_2,A_4_3,A_4_4,A_4_5,A_4_6,A_4_7,A_4_8,A_4_9],[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_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_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]]),Matrix(9, 30, [[B_1_1,B_1_2,B_1_3,B_1_4,B_1_5,B_1_6,B_1_7,B_1_8,B_1_9,B_1_10,B_1_11,B_1_12,B_1_13,B_1_14,B_1_15,B_1_16,B_1_17,B_1_18,B_1_19,B_1_20,B_1_21,B_1_22,B_1_23,B_1_24,B_1_25,B_1_26,B_1_27,B_1_28,B_1_29,B_1_30],[B_2_1,B_2_2,B_2_3,B_2_4,B_2_5,B_2_6,B_2_7,B_2_8,B_2_9,B_2_10,B_2_11,B_2_12,B_2_13,B_2_14,B_2_15,B_2_16,B_2_17,B_2_18,B_2_19,B_2_20,B_2_21,B_2_22,B_2_23,B_2_24,B_2_25,B_2_26,B_2_27,B_2_28,B_2_29,B_2_30],[B_3_1,B_3_2,B_3_3,B_3_4,B_3_5,B_3_6,B_3_7,B_3_8,B_3_9,B_3_10,B_3_11,B_3_12,B_3_13,B_3_14,B_3_15,B_3_16,B_3_17,B_3_18,B_3_19,B_3_20,B_3_21,B_3_22,B_3_23,B_3_24,B_3_25,B_3_26,B_3_27,B_3_28,B_3_29,B_3_30],[B_4_1,B_4_2,B_4_3,B_4_4,B_4_5,B_4_6,B_4_7,B_4_8,B_4_9,B_4_10,B_4_11,B_4_12,B_4_13,B_4_14,B_4_15,B_4_16,B_4_17,B_4_18,B_4_19,B_4_20,B_4_21,B_4_22,B_4_23,B_4_24,B_4_25,B_4_26,B_4_27,B_4_28,B_4_29,B_4_30],[B_5_1,B_5_2,B_5_3,B_5_4,B_5_5,B_5_6,B_5_7,B_5_8,B_5_9,B_5_10,B_5_11,B_5_12,B_5_13,B_5_14,B_5_15,B_5_16,B_5_17,B_5_18,B_5_19,B_5_20,B_5_21,B_5_22,B_5_23,B_5_24,B_5_25,B_5_26,B_5_27,B_5_28,B_5_29,B_5_30],[B_6_1,B_6_2,B_6_3,B_6_4,B_6_5,B_6_6,B_6_7,B_6_8,B_6_9,B_6_10,B_6_11,B_6_12,B_6_13,B_6_14,B_6_15,B_6_16,B_6_17,B_6_18,B_6_19,B_6_20,B_6_21,B_6_22,B_6_23,B_6_24,B_6_25,B_6_26,B_6_27,B_6_28,B_6_29,B_6_30],[B_7_1,B_7_2,B_7_3,B_7_4,B_7_5,B_7_6,B_7_7,B_7_8,B_7_9,B_7_10,B_7_11,B_7_12,B_7_13,B_7_14,B_7_15,B_7_16,B_7_17,B_7_18,B_7_19,B_7_20,B_7_21,B_7_22,B_7_23,B_7_24,B_7_25,B_7_26,B_7_27,B_7_28,B_7_29,B_7_30],[B_8_1,B_8_2,B_8_3,B_8_4,B_8_5,B_8_6,B_8_7,B_8_8,B_8_9,B_8_10,B_8_11,B_8_12,B_8_13,B_8_14,B_8_15,B_8_16,B_8_17,B_8_18,B_8_19,B_8_20,B_8_21,B_8_22,B_8_23,B_8_24,B_8_25,B_8_26,B_8_27,B_8_28,B_8_29,B_8_30],[B_9_1,B_9_2,B_9_3,B_9_4,B_9_5,B_9_6,B_9_7,B_9_8,B_9_9,B_9_10,B_9_11,B_9_12,B_9_13,B_9_14,B_9_15,B_9_16,B_9_17,B_9_18,B_9_19,B_9_20,B_9_21,B_9_22,B_9_23,B_9_24,B_9_25,B_9_26,B_9_27,B_9_28,B_9_29,B_9_30]]),Matrix(30, 7, [[C_1_1,C_1_2,C_1_3,C_1_4,C_1_5,C_1_6,C_1_7],[C_2_1,C_2_2,C_2_3,C_2_4,C_2_5,C_2_6,C_2_7],[C_3_1,C_3_2,C_3_3,C_3_4,C_3_5,C_3_6,C_3_7],[C_4_1,C_4_2,C_4_3,C_4_4,C_4_5,C_4_6,C_4_7],[C_5_1,C_5_2,C_5_3,C_5_4,C_5_5,C_5_6,C_5_7],[C_6_1,C_6_2,C_6_3,C_6_4,C_6_5,C_6_6,C_6_7],[C_7_1,C_7_2,C_7_3,C_7_4,C_7_5,C_7_6,C_7_7],[C_8_1,C_8_2,C_8_3,C_8_4,C_8_5,C_8_6,C_8_7],[C_9_1,C_9_2,C_9_3,C_9_4,C_9_5,C_9_6,C_9_7],[C_10_1,C_10_2,C_10_3,C_10_4,C_10_5,C_10_6,C_10_7],[C_11_1,C_11_2,C_11_3,C_11_4,C_11_5,C_11_6,C_11_7],[C_12_1,C_12_2,C_12_3,C_12_4,C_12_5,C_12_6,C_12_7],[C_13_1,C_13_2,C_13_3,C_13_4,C_13_5,C_13_6,C_13_7],[C_14_1,C_14_2,C_14_3,C_14_4,C_14_5,C_14_6,C_14_7],[C_15_1,C_15_2,C_15_3,C_15_4,C_15_5,C_15_6,C_15_7],[C_16_1,C_16_2,C_16_3,C_16_4,C_16_5,C_16_6,C_16_7],[C_17_1,C_17_2,C_17_3,C_17_4,C_17_5,C_17_6,C_17_7],[C_18_1,C_18_2,C_18_3,C_18_4,C_18_5,C_18_6,C_18_7],[C_19_1,C_19_2,C_19_3,C_19_4,C_19_5,C_19_6,C_19_7],[C_20_1,C_20_2,C_20_3,C_20_4,C_20_5,C_20_6,C_20_7],[C_21_1,C_21_2,C_21_3,C_21_4,C_21_5,C_21_6,C_21_7],[C_22_1,C_22_2,C_22_3,C_22_4,C_22_5,C_22_6,C_22_7],[C_23_1,C_23_2,C_23_3,C_23_4,C_23_5,C_23_6,C_23_7],[C_24_1,C_24_2,C_24_3,C_24_4,C_24_5,C_24_6,C_24_7],[C_25_1,C_25_2,C_25_3,C_25_4,C_25_5,C_25_6,C_25_7],[C_26_1,C_26_2,C_26_3,C_26_4,C_26_5,C_26_6,C_26_7],[C_27_1,C_27_2,C_27_3,C_27_4,C_27_5,C_27_6,C_27_7],[C_28_1,C_28_2,C_28_3,C_28_4,C_28_5,C_28_6,C_28_7],[C_29_1,C_29_2,C_29_3,C_29_4,C_29_5,C_29_6,C_29_7],[C_30_1,C_30_2,C_30_3,C_30_4,C_30_5,C_30_6,C_30_7]]))) = Trace(Mul(Matrix(4, 3, [[A_4_1,A_4_2,A_4_3],[A_5_1,A_5_2,A_5_3],[A_6_1,A_6_2,A_6_3],[A_7_1,A_7_2,A_7_3]]),Matrix(3, 6, [[B_1_1-B_4_1-(a12+a22)/a32*B_7_1-B_1_25-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_25-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_25,B_1_2-B_4_2-(a12+a22)/a32*B_7_2-B_1_26-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_26-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_26,B_1_3-B_4_3-(a12+a22)/a32*B_7_3-B_1_27-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_27-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_27,B_1_4-B_4_4-(a12+a22)/a32*B_7_4-B_1_28-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_28-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_28,B_1_5-B_4_5-(a12+a22)/a32*B_7_5-B_1_29-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_29-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_29,B_1_6-B_4_6-(a12+a22)/a32*B_7_6-B_1_30-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_30-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_30],[B_2_1-B_5_1-(a12+a22)/a32*B_8_1-B_2_25-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_25-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_25,B_2_2-B_5_2-(a12+a22)/a32*B_8_2-B_2_26-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_26-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_26,B_2_3-B_5_3-(a12+a22)/a32*B_8_3-B_2_27-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_27-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_27,B_2_4-B_5_4-(a12+a22)/a32*B_8_4-B_2_28-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_28-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_28,B_2_5-B_5_5-(a12+a22)/a32*B_8_5-B_2_29-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_29-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_29,B_2_6-B_5_6-(a12+a22)/a32*B_8_6-B_2_30-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_30-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_30],[-B_6_1+B_3_1-(a12+a22)/a32*B_9_1-B_3_25-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_25-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_25,B_3_2-B_6_2-(a12+a22)/a32*B_9_2-B_3_26-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_26-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_26,B_3_3-B_6_3-(a12+a22)/a32*B_9_3-B_3_27-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_27-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_27,B_3_4-B_6_4-(a12+a22)/a32*B_9_4-B_3_28-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_28-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_28,B_3_5-B_6_5-(a12+a22)/a32*B_9_5-B_3_29-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_29-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_29,B_3_6-B_6_6-(a12+a22)/a32*B_9_6-B_3_30-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_30-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_30]]),Matrix(6, 4, [[C_1_4,C_1_1+C_1_5,C_1_2+C_1_6,C_1_3+C_1_7],[C_2_4,C_2_1+C_2_5,C_2_2+C_2_6,C_2_3+C_2_7],[C_3_4,C_3_1+C_3_5,C_3_2+C_3_6,C_3_3+C_3_7],[C_4_4,C_4_1+C_4_5,C_4_2+C_4_6,C_4_3+C_4_7],[C_5_4,C_5_1+C_5_5,C_5_2+C_5_6,C_5_3+C_5_7],[C_6_4,C_6_1+C_6_5,C_6_2+C_6_6,C_6_3+C_6_7]])))+Trace(Mul(Matrix(3, 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]]),Matrix(3, 6, [[-B_1_7+B_4_7-B_7_7,-B_1_8+B_4_8-B_7_8,-B_1_9+B_4_9-B_7_9,-B_1_10+B_4_10-B_7_10,-B_1_11+B_4_11-B_7_11,-B_1_12+B_4_12-B_7_12],[-B_2_7+B_5_7-B_8_7,-B_2_8+B_5_8-B_8_8,-B_2_9+B_5_9-B_8_9,-B_2_10+B_5_10-B_8_10,-B_2_11+B_5_11-B_8_11,-B_2_12+B_5_12-B_8_12],[-B_3_7+B_6_7-B_9_7,-B_3_8+B_6_8-B_9_8,-B_3_9+B_6_9-B_9_9,-B_3_10+B_6_10-B_9_10,-B_3_11+B_6_11-B_9_11,-B_3_12+B_6_12-B_9_12]]),Matrix(6, 3, [[C_7_1+C_7_5,C_7_2+C_7_6,C_7_3+C_7_7],[C_8_1+C_8_5,C_8_2+C_8_6,C_8_3+C_8_7],[C_9_1+C_9_5,C_9_2+C_9_6,C_9_3+C_9_7],[C_10_1+C_10_5,C_10_2+C_10_6,C_10_3+C_10_7],[C_11_1+C_11_5,C_11_2+C_11_6,C_11_3+C_11_7],[C_12_1+C_12_5,C_12_2+C_12_6,C_12_3+C_12_7]])))+Trace(Mul(Matrix(4, 3, [[A_4_7,A_4_8,A_4_9],[A_5_7,A_5_8,A_5_9],[A_6_7,A_6_8,A_6_9],[A_7_7,A_7_8,A_7_9]]),Matrix(3, 6, [[-(a21+a31+1)/a11*B_1_13-B_4_13+B_7_13,-(a21+a31+1)/a11*B_1_14-B_4_14+B_7_14,-(a21+a31+1)/a11*B_1_15-B_4_15+B_7_15,-(a21+a31+1)/a11*B_1_16-B_4_16+B_7_16,-(a21+a31+1)/a11*B_1_17-B_4_17+B_7_17,-(a21+a31+1)/a11*B_1_18-B_4_18+B_7_18],[-(a21+a31+1)/a11*B_2_13-B_5_13+B_8_13,-(a21+a31+1)/a11*B_2_14-B_5_14+B_8_14,-(a21+a31+1)/a11*B_2_15-B_5_15+B_8_15,-(a21+a31+1)/a11*B_2_16-B_5_16+B_8_16,-(a21+a31+1)/a11*B_2_17-B_5_17+B_8_17,-(a21+a31+1)/a11*B_2_18-B_5_18+B_8_18],[-(a21+a31+1)/a11*B_3_13-B_6_13+B_9_13,-(a21+a31+1)/a11*B_3_14-B_6_14+B_9_14,-(a21+a31+1)/a11*B_3_15-B_6_15+B_9_15,-(a21+a31+1)/a11*B_3_16-B_6_16+B_9_16,-(a21+a31+1)/a11*B_3_17-B_6_17+B_9_17,-(a21+a31+1)/a11*B_3_18-B_6_18+B_9_18]]),Matrix(6, 4, [[C_13_4,C_13_1+C_13_5,C_13_2+C_13_6,C_13_3+C_13_7],[C_14_4,C_14_1+C_14_5,C_14_2+C_14_6,C_14_3+C_14_7],[C_15_4,C_15_1+C_15_5,C_15_2+C_15_6,C_15_3+C_15_7],[C_16_4,C_16_1+C_16_5,C_16_2+C_16_6,C_16_3+C_16_7],[C_17_4,C_17_1+C_17_5,C_17_2+C_17_6,C_17_3+C_17_7],[C_18_4,C_18_1+C_18_5,C_18_2+C_18_6,C_18_3+C_18_7]])))+Trace(Mul(Matrix(3, 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]]),Matrix(3, 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]]),Matrix(6, 3, [[C_1_1+C_7_1,C_1_2+C_7_2,C_1_3+C_7_3],[C_2_1+C_8_1,C_2_2+C_8_2,C_2_3+C_8_3],[C_3_1+C_9_1,C_3_2+C_9_2,C_3_3+C_9_3],[C_4_1+C_10_1,C_4_2+C_10_2,C_4_3+C_10_3],[C_11_1+C_5_1,C_11_2+C_5_2,C_11_3+C_5_3],[C_6_1+C_12_1,C_6_2+C_12_2,C_6_3+C_12_3]])))+Trace(Mul(Matrix(3, 3, [[A_1_1-A_5_1,A_1_2-A_5_2,A_1_3-A_5_3],[A_2_1-A_6_1,A_2_2-A_6_2,A_2_3-A_6_3],[A_3_1-A_7_1,A_3_2-A_7_2,A_3_3-A_7_3]]),Matrix(3, 6, [[B_1_1-(a12-1)/a32*B_7_1-B_1_7,B_1_2-(a12-1)/a32*B_7_2-B_1_8,B_1_3-(a12-1)/a32*B_7_3-B_1_9,B_1_4-(a12-1)/a32*B_7_4-B_1_10,B_1_5-(a12-1)/a32*B_7_5-B_1_11,B_1_6-(a12-1)/a32*B_7_6-B_1_12],[B_2_1-(a12-1)/a32*B_8_1-B_2_7,B_2_2-(a12-1)/a32*B_8_2-B_2_8,B_2_3-(a12-1)/a32*B_8_3-B_2_9,B_2_4-(a12-1)/a32*B_8_4-B_2_10,B_2_5-(a12-1)/a32*B_8_5-B_2_11,B_2_6-(a12-1)/a32*B_8_6-B_2_12],[B_3_1-(a12-1)/a32*B_9_1-B_3_7,B_3_2-(a12-1)/a32*B_9_2-B_3_8,B_3_3-(a12-1)/a32*B_9_3-B_3_9,B_3_4-(a12-1)/a32*B_9_4-B_3_10,B_3_5-(a12-1)/a32*B_9_5-B_3_11,B_3_6-(a12-1)/a32*B_9_6-B_3_12]]),Matrix(6, 3, [[C_1_1,C_1_2,C_1_3],[C_2_1,C_2_2,C_2_3],[C_3_1,C_3_2,C_3_3],[C_4_1,C_4_2,C_4_3],[C_5_1,C_5_2,C_5_3],[C_6_1,C_6_2,C_6_3]])))+Trace(Mul(Matrix(4, 3, [[A_4_1,A_4_2,A_4_3],[A_5_1+A_1_4,A_1_5+A_5_2,A_5_3+A_1_6],[A_6_1+A_2_4,A_2_5+A_6_2,A_2_6+A_6_3],[A_7_1+A_3_4,A_3_5+A_7_2,A_3_6+A_7_3]]),Matrix(3, 6, [[B_4_1+a22/a32*B_7_1-B_1_7,B_4_2+a22/a32*B_7_2-B_1_8,B_4_3+a22/a32*B_7_3-B_1_9,B_4_4+a22/a32*B_7_4-B_1_10,B_4_5+a22/a32*B_7_5-B_1_11,B_4_6+a22/a32*B_7_6-B_1_12],[B_5_1+a22/a32*B_8_1-B_2_7,B_5_2+a22/a32*B_8_2-B_2_8,B_5_3+a22/a32*B_8_3-B_2_9,B_5_4+a22/a32*B_8_4-B_2_10,B_5_5+a22/a32*B_8_5-B_2_11,B_5_6+a22/a32*B_8_6-B_2_12],[B_6_1+a22/a32*B_9_1-B_3_7,B_6_2+a22/a32*B_9_2-B_3_8,B_6_3+a22/a32*B_9_3-B_3_9,B_6_4+a22/a32*B_9_4-B_3_10,B_6_5+a22/a32*B_9_5-B_3_11,B_6_6+a22/a32*B_9_6-B_3_12]]),Matrix(6, 4, [[-C_7_4,C_1_1-C_7_5,C_1_2-C_7_6,C_1_3-C_7_7],[-C_8_4,C_2_1-C_8_5,C_2_2-C_8_6,C_2_3-C_8_7],[-C_9_4,C_3_1-C_9_5,C_3_2-C_9_6,C_3_3-C_9_7],[-C_10_4,C_4_1-C_10_5,C_4_2-C_10_6,C_4_3-C_10_7],[-C_11_4,C_5_1-C_11_5,C_5_2-C_11_6,C_5_3-C_11_7],[-C_12_4,C_6_1-C_12_5,C_6_2-C_12_6,C_6_3-C_12_7]])))+Trace(Mul(Matrix(4, 3, [[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],[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]]),Matrix(3, 6, [[B_4_1+a22/a32*B_7_1,B_4_2+a22/a32*B_7_2,B_4_3+a22/a32*B_7_3,B_4_4+a22/a32*B_7_4,B_4_5+a22/a32*B_7_5,B_4_6+a22/a32*B_7_6],[B_5_1+a22/a32*B_8_1,B_5_2+a22/a32*B_8_2,B_5_3+a22/a32*B_8_3,B_5_4+a22/a32*B_8_4,B_5_5+a22/a32*B_8_5,B_5_6+a22/a32*B_8_6],[B_6_1+a22/a32*B_9_1,B_6_2+a22/a32*B_9_2,B_6_3+a22/a32*B_9_3,B_6_4+a22/a32*B_9_4,B_6_5+a22/a32*B_9_5,B_6_6+a22/a32*B_9_6]]),Matrix(6, 4, [[C_1_4+C_7_4,C_1_5+C_7_5,C_1_6+C_7_6,C_1_7+C_7_7],[C_2_4+C_8_4,C_2_5+C_8_5,C_2_6+C_8_6,C_2_7+C_8_7],[C_3_4+C_9_4,C_3_5+C_9_5,C_3_6+C_9_6,C_3_7+C_9_7],[C_4_4+C_10_4,C_4_5+C_10_5,C_4_6+C_10_6,C_4_7+C_10_7],[C_5_4+C_11_4,C_5_5+C_11_5,C_5_6+C_11_6,C_5_7+C_11_7],[C_6_4+C_12_4,C_6_5+C_12_5,C_6_6+C_12_6,C_6_7+C_12_7]])))+Trace(Mul(Matrix(4, 3, [[-A_4_4,-A_4_5,-A_4_6],[A_1_4-A_5_4,A_1_5-A_5_5,A_1_6-A_5_6],[A_2_4-A_6_4,A_2_5-A_6_5,A_2_6-A_6_6],[A_3_4-A_7_4,A_3_5-A_7_5,A_3_6-A_7_6]]),Matrix(3, 6, [[B_4_1+a22/a32*B_7_1-B_4_7+a21/a11*B_1_13+B_4_13,B_4_2+a22/a32*B_7_2-B_4_8+a21/a11*B_1_14+B_4_14,B_4_3+a22/a32*B_7_3-B_4_9+a21/a11*B_1_15+B_4_15,B_4_4+a22/a32*B_7_4-B_4_10+a21/a11*B_1_16+B_4_16,B_4_5+a22/a32*B_7_5-B_4_11+1/a11*a21*B_1_17+B_4_17,B_4_6+a22/a32*B_7_6-B_4_12+1/a11*a21*B_1_18+B_4_18],[B_5_1+a22/a32*B_8_1-B_5_7+a21/a11*B_2_13+B_5_13,B_5_2+a22/a32*B_8_2-B_5_8+a21/a11*B_2_14+B_5_14,B_5_3+a22/a32*B_8_3-B_5_9+a21/a11*B_2_15+B_5_15,B_5_4+a22/a32*B_8_4-B_5_10+a21/a11*B_2_16+B_5_16,B_5_5+a22/a32*B_8_5-B_5_11+1/a11*a21*B_2_17+B_5_17,B_5_6+a22/a32*B_8_6-B_5_12+1/a11*a21*B_2_18+B_5_18],[B_6_1+a22/a32*B_9_1-B_6_7+a21/a11*B_3_13+B_6_13,B_6_2+a22/a32*B_9_2-B_6_8+a21/a11*B_3_14+B_6_14,B_6_3+a22/a32*B_9_3-B_6_9+a21/a11*B_3_15+B_6_15,B_6_4+a22/a32*B_9_4-B_6_10+a21/a11*B_3_16+B_6_16,B_6_5+a22/a32*B_9_5-B_6_11+1/a11*a21*B_3_17+B_6_17,B_6_6+a22/a32*B_9_6-B_6_12+1/a11*a21*B_3_18+B_6_18]]),Matrix(6, 4, [[C_7_4,C_7_5,C_7_6,C_7_7],[C_8_4,C_8_5,C_8_6,C_8_7],[C_9_4,C_9_5,C_9_6,C_9_7],[C_10_4,C_10_5,C_10_6,C_10_7],[C_11_4,C_11_5,C_11_6,C_11_7],[C_12_4,C_12_5,C_12_6,C_12_7]])))+Trace(Mul(Matrix(4, 3, [[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],[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]]),Matrix(3, 6, [[a21/a11*B_1_13+B_4_13,a21/a11*B_1_14+B_4_14,a21/a11*B_1_15+B_4_15,a21/a11*B_1_16+B_4_16,1/a11*a21*B_1_17+B_4_17,1/a11*a21*B_1_18+B_4_18],[a21/a11*B_2_13+B_5_13,a21/a11*B_2_14+B_5_14,a21/a11*B_2_15+B_5_15,a21/a11*B_2_16+B_5_16,1/a11*a21*B_2_17+B_5_17,1/a11*a21*B_2_18+B_5_18],[a21/a11*B_3_13+B_6_13,a21/a11*B_3_14+B_6_14,a21/a11*B_3_15+B_6_15,a21/a11*B_3_16+B_6_16,1/a11*a21*B_3_17+B_6_17,1/a11*a21*B_3_18+B_6_18]]),Matrix(6, 4, [[C_7_4+C_13_4,C_7_5+C_13_5,C_7_6+C_13_6,C_7_7+C_13_7],[C_8_4+C_14_4,C_8_5+C_14_5,C_8_6+C_14_6,C_8_7+C_14_7],[C_9_4+C_15_4,C_9_5+C_15_5,C_9_6+C_15_6,C_9_7+C_15_7],[C_10_4+C_16_4,C_10_5+C_16_5,C_10_6+C_16_6,C_10_7+C_16_7],[C_11_4+C_17_4,C_11_5+C_17_5,C_11_6+C_17_6,C_11_7+C_17_7],[C_12_4+C_18_4,C_12_5+C_18_5,C_12_6+C_18_6,C_12_7+C_18_7]])))+Trace(Mul(Matrix(3, 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]]),Matrix(3, 6, [[B_7_7,B_7_8,B_7_9,B_7_10,B_7_11,B_7_12],[B_8_7,B_8_8,B_8_9,B_8_10,B_8_11,B_8_12],[B_9_7,B_9_8,B_9_9,B_9_10,B_9_11,B_9_12]]),Matrix(6, 3, [[C_7_1+C_13_1,C_7_2+C_13_2,C_7_3+C_13_3],[C_8_1+C_14_1,C_8_2+C_14_2,C_8_3+C_14_3],[C_9_1+C_15_1,C_9_2+C_15_2,C_9_3+C_15_3],[C_10_1+C_16_1,C_10_2+C_16_2,C_10_3+C_16_3],[C_11_1+C_17_1,C_11_2+C_17_2,C_11_3+C_17_3],[C_12_1+C_18_1,C_12_2+C_18_2,C_12_3+C_18_3]])))+Trace(Mul(Matrix(3, 3, [[A_1_7-A_5_7,A_1_8-A_5_8,A_1_9-A_5_9],[A_2_7-A_6_7,A_2_8-A_6_8,A_2_9-A_6_9],[A_3_7-A_7_7,A_3_8-A_7_8,A_3_9-A_7_9]]),Matrix(3, 6, [[-B_7_7-a31/a11*B_1_13+B_7_13-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_19-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_19-B_7_19,-B_7_8-a31/a11*B_1_14+B_7_14-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_20-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_20-B_7_20,-B_7_9-a31/a11*B_1_15+B_7_15-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_21-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_21-B_7_21,-B_7_10-a31/a11*B_1_16+B_7_16-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_22-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_22-B_7_22,-B_7_11-a31/a11*B_1_17+B_7_17-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_23-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_23-B_7_23,-B_7_12-a31/a11*B_1_18+B_7_18-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_24-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_24-B_7_24],[-B_8_7-a31/a11*B_2_13+B_8_13-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_19-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_19-B_8_19,-B_8_8-a31/a11*B_2_14+B_8_14-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_20-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_20-B_8_20,-B_8_9-a31/a11*B_2_15+B_8_15-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_21-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_21-B_8_21,-B_8_10-a31/a11*B_2_16+B_8_16-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_22-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_22-B_8_22,-B_8_11-a31/a11*B_2_17+B_8_17-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_23-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_23-B_8_23,-B_8_12-a31/a11*B_2_18+B_8_18-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_24-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_24-B_8_24],[-B_9_7-a31/a11*B_3_13+B_9_13-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_19-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_19-B_9_19,-B_9_8-a31/a11*B_3_14+B_9_14-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_20-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_20-B_9_20,-B_9_9-a31/a11*B_3_15+B_9_15-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_21-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_21-B_9_21,-B_9_10-a31/a11*B_3_16+B_9_16-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_22-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_22-B_9_22,-B_9_11-a31/a11*B_3_17+B_9_17-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_23-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_23-B_9_23,-B_9_12-a31/a11*B_3_18+B_9_18-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_24-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_24-B_9_24]]),Matrix(6, 3, [[C_13_1,C_13_2,C_13_3],[C_14_1,C_14_2,C_14_3],[C_15_1,C_15_2,C_15_3],[C_16_1,C_16_2,C_16_3],[C_17_1,C_17_2,C_17_3],[C_18_1,C_18_2,C_18_3]])))+Trace(Mul(Matrix(4, 3, [[A_4_7,A_4_8,A_4_9],[A_1_4+A_5_7,A_1_5+A_5_8,A_1_6+A_5_9],[A_2_4+A_6_7,A_2_5+A_6_8,A_2_6+A_6_9],[A_3_4+A_7_7,A_3_5+A_7_8,A_3_6+A_7_9]]),Matrix(3, 6, [[-B_7_7+a21/a11*B_1_13+B_4_13,-B_7_8+a21/a11*B_1_14+B_4_14,-B_7_9+a21/a11*B_1_15+B_4_15,-B_7_10+a21/a11*B_1_16+B_4_16,-B_7_11+1/a11*a21*B_1_17+B_4_17,-B_7_12+1/a11*a21*B_1_18+B_4_18],[-B_8_7+a21/a11*B_2_13+B_5_13,-B_8_8+a21/a11*B_2_14+B_5_14,-B_8_9+a21/a11*B_2_15+B_5_15,-B_8_10+a21/a11*B_2_16+B_5_16,-B_8_11+1/a11*a21*B_2_17+B_5_17,-B_8_12+1/a11*a21*B_2_18+B_5_18],[-B_9_7+a21/a11*B_3_13+B_6_13,-B_9_8+a21/a11*B_3_14+B_6_14,-B_9_9+a21/a11*B_3_15+B_6_15,-B_9_10+a21/a11*B_3_16+B_6_16,-B_9_11+1/a11*a21*B_3_17+B_6_17,-B_9_12+1/a11*a21*B_3_18+B_6_18]]),Matrix(6, 4, [[-C_7_4,C_13_1-C_7_5,C_13_2-C_7_6,C_13_3-C_7_7],[-C_8_4,C_14_1-C_8_5,C_14_2-C_8_6,C_14_3-C_8_7],[-C_9_4,C_15_1-C_9_5,C_15_2-C_9_6,C_15_3-C_9_7],[-C_10_4,C_16_1-C_10_5,C_16_2-C_10_6,C_16_3-C_10_7],[-C_11_4,C_17_1-C_11_5,C_17_2-C_11_6,C_17_3-C_11_7],[-C_12_4,C_18_1-C_12_5,C_18_2-C_12_6,C_18_3-C_12_7]])))+Trace(Mul(Matrix(3, 3, [[A_1_1*a11-A_1_4*a21+A_1_7*a31,A_1_2*a11-A_1_5*a21+A_1_8*a31,A_1_3*a11-A_1_6*a21+A_1_9*a31],[A_2_1*a11-A_2_4*a21+A_2_7*a31,A_2_2*a11-A_2_5*a21+A_2_8*a31,A_2_3*a11-A_2_6*a21+A_2_9*a31],[A_3_1*a11-A_3_4*a21+A_3_7*a31,A_3_2*a11-A_3_5*a21+A_3_8*a31,A_3_3*a11-A_3_6*a21+A_3_9*a31]]),Matrix(3, 6, [[-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_1_19-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_4_19-B_7_19+a32/(a21*a32-a22*a31)*B_4_25+a22/(a21*a32-a22*a31)*B_7_25,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_1_20-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_4_20-B_7_20+a32/(a21*a32-a22*a31)*B_4_26+a22/(a21*a32-a22*a31)*B_7_26,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_1_21-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_4_21-B_7_21+a32/(a21*a32-a22*a31)*B_4_27+a22/(a21*a32-a22*a31)*B_7_27,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_1_22-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_4_22-B_7_22+a32/(a21*a32-a22*a31)*B_4_28+a22/(a21*a32-a22*a31)*B_7_28,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_1_23-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_4_23-B_7_23+a32/(a21*a32-a22*a31)*B_4_29+a22/(a21*a32-a22*a31)*B_7_29,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_1_24-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_4_24-B_7_24+a32/(a21*a32-a22*a31)*B_4_30+a22/(a21*a32-a22*a31)*B_7_30],[-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_2_19-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_5_19-B_8_19+a32/(a21*a32-a22*a31)*B_5_25+a22/(a21*a32-a22*a31)*B_8_25,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_2_20-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_5_20-B_8_20+a32/(a21*a32-a22*a31)*B_5_26+a22/(a21*a32-a22*a31)*B_8_26,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_2_21-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_5_21-B_8_21+a32/(a21*a32-a22*a31)*B_5_27+a22/(a21*a32-a22*a31)*B_8_27,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_2_22-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_5_22-B_8_22+a32/(a21*a32-a22*a31)*B_5_28+a22/(a21*a32-a22*a31)*B_8_28,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_2_23-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_5_23-B_8_23+a32/(a21*a32-a22*a31)*B_5_29+a22/(a21*a32-a22*a31)*B_8_29,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_2_24-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_5_24-B_8_24+a32/(a21*a32-a22*a31)*B_5_30+a22/(a21*a32-a22*a31)*B_8_30],[-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_3_19-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_6_19-B_9_19+a32/(a21*a32-a22*a31)*B_6_25+a22/(a21*a32-a22*a31)*B_9_25,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_3_20-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_6_20-B_9_20+a32/(a21*a32-a22*a31)*B_6_26+a22/(a21*a32-a22*a31)*B_9_26,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_3_21-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_6_21-B_9_21+a32/(a21*a32-a22*a31)*B_6_27+a22/(a21*a32-a22*a31)*B_9_27,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_3_22-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_6_22-B_9_22+a32/(a21*a32-a22*a31)*B_6_28+a22/(a21*a32-a22*a31)*B_9_28,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_3_23-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_6_23-B_9_23+a32/(a21*a32-a22*a31)*B_6_29+a22/(a21*a32-a22*a31)*B_9_29,-(a21*a32-a22*a31-a22)/(a11*a22-a12*a21)*B_3_24-(a11*a32-a12*a31-a12)/(a11*a22-a12*a21)*B_6_24-B_9_24+a32/(a21*a32-a22*a31)*B_6_30+a22/(a21*a32-a22*a31)*B_9_30]]),Matrix(6, 3, [[C_19_1+C_19_5,C_19_2+C_19_6,C_19_3+C_19_7],[C_20_1+C_20_5,C_20_2+C_20_6,C_20_3+C_20_7],[C_21_1+C_21_5,C_21_2+C_21_6,C_21_3+C_21_7],[C_22_1+C_22_5,C_22_2+C_22_6,C_22_3+C_22_7],[C_23_1+C_23_5,C_23_2+C_23_6,C_23_3+C_23_7],[C_24_1+C_24_5,C_24_2+C_24_6,C_24_3+C_24_7]])))+Trace(Mul(Matrix(3, 3, [[-A_1_1*a12+A_1_4*a22-A_1_7*a32,-A_1_2*a12+A_1_5*a22-A_1_8*a32,-A_1_3*a12+A_1_6*a22-A_1_9*a32],[-A_2_1*a12+A_2_4*a22-A_2_7*a32,-A_2_2*a12+A_2_5*a22-A_2_8*a32,-A_2_3*a12+A_2_6*a22-A_2_9*a32],[-A_3_1*a12+A_3_4*a22-A_3_7*a32,-A_3_2*a12+A_3_5*a22-A_3_8*a32,-A_3_3*a12+A_3_6*a22-A_3_9*a32]]),Matrix(3, 6, [[-a21/(a11*a22-a12*a21)*B_1_19-1/(a11*a22-a12*a21)*a11*B_4_19-B_1_25-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_4_25-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_7_25,-a21/(a11*a22-a12*a21)*B_1_20-1/(a11*a22-a12*a21)*a11*B_4_20-B_1_26-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_4_26-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_7_26,-a21/(a11*a22-a12*a21)*B_1_21-1/(a11*a22-a12*a21)*a11*B_4_21-B_1_27-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_4_27-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_7_27,-a21/(a11*a22-a12*a21)*B_1_22-1/(a11*a22-a12*a21)*a11*B_4_22-B_1_28-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_4_28-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_7_28,-a21/(a11*a22-a12*a21)*B_1_23-1/(a11*a22-a12*a21)*a11*B_4_23-B_1_29-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_4_29-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_7_29,-a21/(a11*a22-a12*a21)*B_1_24-1/(a11*a22-a12*a21)*a11*B_4_24-B_1_30-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_4_30-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_7_30],[-a21/(a11*a22-a12*a21)*B_2_19-1/(a11*a22-a12*a21)*a11*B_5_19-B_2_25-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_5_25-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_8_25,-a21/(a11*a22-a12*a21)*B_2_20-1/(a11*a22-a12*a21)*a11*B_5_20-B_2_26-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_5_26-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_8_26,-a21/(a11*a22-a12*a21)*B_2_21-1/(a11*a22-a12*a21)*a11*B_5_21-B_2_27-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_5_27-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_8_27,-a21/(a11*a22-a12*a21)*B_2_22-1/(a11*a22-a12*a21)*a11*B_5_22-B_2_28-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_5_28-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_8_28,-a21/(a11*a22-a12*a21)*B_2_23-1/(a11*a22-a12*a21)*a11*B_5_23-B_2_29-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_5_29-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_8_29,-a21/(a11*a22-a12*a21)*B_2_24-1/(a11*a22-a12*a21)*a11*B_5_24-B_2_30-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_5_30-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_8_30],[-a21/(a11*a22-a12*a21)*B_3_19-1/(a11*a22-a12*a21)*a11*B_6_19-B_3_25-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_6_25-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_9_25,-a21/(a11*a22-a12*a21)*B_3_20-1/(a11*a22-a12*a21)*a11*B_6_20-B_3_26-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_6_26-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_9_26,-a21/(a11*a22-a12*a21)*B_3_21-1/(a11*a22-a12*a21)*a11*B_6_21-B_3_27-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_6_27-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_9_27,-a21/(a11*a22-a12*a21)*B_3_22-1/(a11*a22-a12*a21)*a11*B_6_22-B_3_28-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_6_28-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_9_28,-a21/(a11*a22-a12*a21)*B_3_23-1/(a11*a22-a12*a21)*a11*B_6_23-B_3_29-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_6_29-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_9_29,-a21/(a11*a22-a12*a21)*B_3_24-1/(a11*a22-a12*a21)*a11*B_6_24-B_3_30-(a11*a32-a12*a31+a31)/(a21*a32-a22*a31)*B_6_30-(a11*a22-a12*a21+a21)/(a21*a32-a22*a31)*B_9_30]]),Matrix(6, 3, [[C_25_1,C_25_2,C_25_3],[C_26_1,C_26_2,C_26_3],[C_27_1,C_27_2,C_27_3],[C_28_1,C_28_2,C_28_3],[C_29_1,C_29_2,C_29_3],[C_30_1,C_30_2,C_30_3]])))+Trace(Mul(Matrix(4, 3, [[-A_4_1*a12+A_4_4*a22-A_4_7*a32,-A_4_2*a12+A_4_5*a22-A_4_8*a32,-A_4_3*a12+A_4_6*a22-A_4_9*a32],[-A_5_1*a12+A_5_4*a22-A_5_7*a32,-A_5_2*a12+A_5_5*a22-A_5_8*a32,-A_5_3*a12+A_5_6*a22-A_5_9*a32],[-A_6_1*a12+A_6_4*a22-A_6_7*a32,-A_6_2*a12+A_6_5*a22-A_6_8*a32,-A_6_3*a12+A_6_6*a22-A_6_9*a32],[-A_7_1*a12+A_7_4*a22-A_7_7*a32,-A_7_2*a12+A_7_5*a22-A_7_8*a32,-A_7_3*a12+A_7_6*a22-A_7_9*a32]]),Matrix(3, 6, [[1/a32*B_7_1-(a31-a32)/(a21*a32-a22*a31)*B_4_25-(a21-a22)/(a21*a32-a22*a31)*B_7_25,1/a32*B_7_2-(a31-a32)/(a21*a32-a22*a31)*B_4_26-(a21-a22)/(a21*a32-a22*a31)*B_7_26,1/a32*B_7_3-(a31-a32)/(a21*a32-a22*a31)*B_4_27-(a21-a22)/(a21*a32-a22*a31)*B_7_27,1/a32*B_7_4-(a31-a32)/(a21*a32-a22*a31)*B_4_28-(a21-a22)/(a21*a32-a22*a31)*B_7_28,1/a32*B_7_5-(a31-a32)/(a21*a32-a22*a31)*B_4_29-(a21-a22)/(a21*a32-a22*a31)*B_7_29,1/a32*B_7_6-(a31-a32)/(a21*a32-a22*a31)*B_4_30-(a21-a22)/(a21*a32-a22*a31)*B_7_30],[1/a32*B_8_1-(a31-a32)/(a21*a32-a22*a31)*B_5_25-(a21-a22)/(a21*a32-a22*a31)*B_8_25,1/a32*B_8_2-(a31-a32)/(a21*a32-a22*a31)*B_5_26-(a21-a22)/(a21*a32-a22*a31)*B_8_26,1/a32*B_8_3-(a31-a32)/(a21*a32-a22*a31)*B_5_27-(a21-a22)/(a21*a32-a22*a31)*B_8_27,1/a32*B_8_4-(a31-a32)/(a21*a32-a22*a31)*B_5_28-(a21-a22)/(a21*a32-a22*a31)*B_8_28,1/a32*B_8_5-(a31-a32)/(a21*a32-a22*a31)*B_5_29-(a21-a22)/(a21*a32-a22*a31)*B_8_29,1/a32*B_8_6-(a31-a32)/(a21*a32-a22*a31)*B_5_30-(a21-a22)/(a21*a32-a22*a31)*B_8_30],[1/a32*B_9_1-(a31-a32)/(a21*a32-a22*a31)*B_6_25-(a21-a22)/(a21*a32-a22*a31)*B_9_25,1/a32*B_9_2-(a31-a32)/(a21*a32-a22*a31)*B_6_26-(a21-a22)/(a21*a32-a22*a31)*B_9_26,1/a32*B_9_3-(a31-a32)/(a21*a32-a22*a31)*B_6_27-(a21-a22)/(a21*a32-a22*a31)*B_9_27,1/a32*B_9_4-(a31-a32)/(a21*a32-a22*a31)*B_6_28-(a21-a22)/(a21*a32-a22*a31)*B_9_28,1/a32*B_9_5-(a31-a32)/(a21*a32-a22*a31)*B_6_29-(a21-a22)/(a21*a32-a22*a31)*B_9_29,1/a32*B_9_6-(a31-a32)/(a21*a32-a22*a31)*B_6_30-(a21-a22)/(a21*a32-a22*a31)*B_9_30]]),Matrix(6, 4, [[C_25_4,C_25_5,C_25_6,C_25_7],[C_26_4,C_26_5,C_26_6,C_26_7],[C_27_4,C_27_5,C_27_6,C_27_7],[C_28_4,C_28_5,C_28_6,C_28_7],[C_29_4,C_29_5,C_29_6,C_29_7],[C_30_4,C_30_5,C_30_6,C_30_7]])))+Trace(Mul(Matrix(3, 3, [[A_1_1*a11-A_1_4*a21+(a31+1)*A_1_7,A_1_2*a11-A_1_5*a21+(a31+1)*A_1_8,A_1_3*a11-A_1_6*a21+(a31+1)*A_1_9],[A_2_1*a11-A_2_4*a21+(a31+1)*A_2_7,A_2_2*a11-A_2_5*a21+(a31+1)*A_2_8,A_2_3*a11-A_2_6*a21+(a31+1)*A_2_9],[A_3_1*a11-A_3_4*a21+(a31+1)*A_3_7,A_3_2*a11-A_3_5*a21+(a31+1)*A_3_8,A_3_3*a11-A_3_6*a21+(a31+1)*A_3_9]]),Matrix(3, 6, [[(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_19+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_19+B_7_19,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_20+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_20+B_7_20,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_21+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_21+B_7_21,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_22+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_22+B_7_22,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_23+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_23+B_7_23,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_24+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_24+B_7_24],[(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_19+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_19+B_8_19,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_20+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_20+B_8_20,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_21+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_21+B_8_21,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_22+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_22+B_8_22,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_23+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_23+B_8_23,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_24+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_24+B_8_24],[(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_19+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_19+B_9_19,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_20+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_20+B_9_20,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_21+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_21+B_9_21,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_22+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_22+B_9_22,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_23+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_23+B_9_23,(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_24+(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_24+B_9_24]]),Matrix(6, 3, [[C_13_1+C_19_1,C_13_2+C_19_2,C_13_3+C_19_3],[C_14_1+C_20_1,C_14_2+C_20_2,C_14_3+C_20_3],[C_15_1+C_21_1,C_15_2+C_21_2,C_15_3+C_21_3],[C_16_1+C_22_1,C_16_2+C_22_2,C_16_3+C_22_3],[C_17_1+C_23_1,C_17_2+C_23_2,C_17_3+C_23_3],[C_18_1+C_24_1,C_18_2+C_24_2,C_18_3+C_24_3]])))+Trace(Mul(Matrix(3, 3, [[(-a12+1)*A_1_1+A_1_4*a22-A_1_7*a32,(-a12+1)*A_1_2+A_1_5*a22-A_1_8*a32,(-a12+1)*A_1_3+A_1_6*a22-A_1_9*a32],[(-a12+1)*A_2_1+A_2_4*a22-A_2_7*a32,(-a12+1)*A_2_2+A_2_5*a22-A_2_8*a32,(-a12+1)*A_2_3+A_2_6*a22-A_2_9*a32],[(-a12+1)*A_3_1+A_3_4*a22-A_3_7*a32,(-a12+1)*A_3_2+A_3_5*a22-A_3_8*a32,(-a12+1)*A_3_3+A_3_6*a22-A_3_9*a32]]),Matrix(3, 6, [[B_1_25+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_25+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_25,B_1_26+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_26+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_26,B_1_27+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_27+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_27,B_1_28+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_28+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_28,B_1_29+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_29+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_29,B_1_30+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_30+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_30],[B_2_25+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_25+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_25,B_2_26+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_26+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_26,B_2_27+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_27+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_27,B_2_28+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_28+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_28,B_2_29+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_29+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_29,B_2_30+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_30+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_30],[B_3_25+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_25+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_25,B_3_26+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_26+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_26,B_3_27+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_27+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_27,B_3_28+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_28+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_28,B_3_29+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_29+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_29,B_3_30+(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_30+(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_30]]),Matrix(6, 3, [[C_1_1+C_25_1+C_1_5+C_25_5,C_1_2+C_25_2+C_1_6+C_25_6,C_1_3+C_25_3+C_1_7+C_25_7],[C_2_1+C_26_1+C_2_5+C_26_5,C_2_2+C_26_2+C_2_6+C_26_6,C_2_3+C_26_3+C_2_7+C_26_7],[C_3_1+C_27_1+C_3_5+C_27_5,C_3_2+C_27_2+C_3_6+C_27_6,C_3_3+C_27_3+C_3_7+C_27_7],[C_4_1+C_28_1+C_4_5+C_28_5,C_4_2+C_28_2+C_4_6+C_28_6,C_4_3+C_28_3+C_4_7+C_28_7],[C_5_1+C_29_1+C_5_5+C_29_5,C_5_2+C_29_2+C_5_6+C_29_6,C_5_3+C_29_3+C_5_7+C_29_7],[C_6_1+C_30_1+C_6_5+C_30_5,C_6_2+C_30_2+C_6_6+C_30_6,C_6_3+C_30_3+C_6_7+C_30_7]])))+Trace(Mul(Matrix(4, 3, [[A_4_1-a21/a11*A_4_4+1/a11*(a31+1)*A_4_7,A_4_2-a21/a11*A_4_5+1/a11*(a31+1)*A_4_8,A_4_3-a21/a11*A_4_6+1/a11*(a31+1)*A_4_9],[A_5_1-a21/a11*A_5_4+1/a11*(a31+1)*A_5_7,A_5_2-a21/a11*A_5_5+1/a11*(a31+1)*A_5_8,A_5_3-a21/a11*A_5_6+1/a11*(a31+1)*A_5_9],[A_6_1-a21/a11*A_6_4+1/a11*(a31+1)*A_6_7,A_6_2-a21/a11*A_6_5+1/a11*(a31+1)*A_6_8,A_6_3-a21/a11*A_6_6+1/a11*(a31+1)*A_6_9],[A_7_1-a21/a11*A_7_4+1/a11*(a31+1)*A_7_7,A_7_2-a21/a11*A_7_5+1/a11*(a31+1)*A_7_8,A_7_3-a21/a11*A_7_6+1/a11*(a31+1)*A_7_9]]),Matrix(3, 6, [[B_1_13,B_1_14,B_1_15,B_1_16,B_1_17,B_1_18],[B_2_13,B_2_14,B_2_15,B_2_16,B_2_17,B_2_18],[B_3_13,B_3_14,B_3_15,B_3_16,B_3_17,B_3_18]]),Matrix(6, 4, [[C_13_4+C_19_4,C_13_5+C_19_5,C_13_6+C_19_6,C_13_7+C_19_7],[C_14_4+C_20_4,C_14_5+C_20_5,C_14_6+C_20_6,C_14_7+C_20_7],[C_15_4+C_21_4,C_15_5+C_21_5,C_15_6+C_21_6,C_15_7+C_21_7],[C_16_4+C_22_4,C_16_5+C_22_5,C_16_6+C_22_6,C_16_7+C_22_7],[C_17_4+C_23_4,C_17_5+C_23_5,C_17_6+C_23_6,C_17_7+C_23_7],[C_18_4+C_24_4,C_18_5+C_24_5,C_18_6+C_24_6,C_18_7+C_24_7]])))+Trace(Mul(Matrix(4, 3, [[A_4_7,A_4_8,A_4_9],[A_1_1*a11-A_1_4*a21+A_1_7*a31+A_5_7,A_1_2*a11-A_1_5*a21+A_1_8*a31+A_5_8,A_1_3*a11-A_1_6*a21+A_1_9*a31+A_5_9],[A_2_1*a11-A_2_4*a21+A_2_7*a31+A_6_7,A_2_2*a11-A_2_5*a21+A_2_8*a31+A_6_8,A_2_3*a11-A_2_6*a21+A_2_9*a31+A_6_9],[A_3_1*a11-A_3_4*a21+A_3_7*a31+A_7_7,A_3_2*a11-A_3_5*a21+A_3_8*a31+A_7_8,A_3_3*a11-A_3_6*a21+A_3_9*a31+A_7_9]]),Matrix(3, 6, [[1/a11*B_1_13-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_19-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_19-B_7_19,1/a11*B_1_14-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_20-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_20-B_7_20,1/a11*B_1_15-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_21-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_21-B_7_21,1/a11*B_1_16-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_22-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_22-B_7_22,1/a11*B_1_17-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_23-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_23-B_7_23,1/a11*B_1_18-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_1_24-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_4_24-B_7_24],[1/a11*B_2_13-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_19-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_19-B_8_19,1/a11*B_2_14-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_20-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_20-B_8_20,1/a11*B_2_15-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_21-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_21-B_8_21,1/a11*B_2_16-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_22-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_22-B_8_22,1/a11*B_2_17-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_23-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_23-B_8_23,1/a11*B_2_18-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_2_24-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_5_24-B_8_24],[1/a11*B_3_13-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_19-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_19-B_9_19,1/a11*B_3_14-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_20-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_20-B_9_20,1/a11*B_3_15-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_21-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_21-B_9_21,1/a11*B_3_16-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_22-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_22-B_9_22,1/a11*B_3_17-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_23-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_23-B_9_23,1/a11*B_3_18-(a21*a32-a22*a31)/(a11*a22-a12*a21)*B_3_24-(a11*a32-a12*a31)/(a11*a22-a12*a21)*B_6_24-B_9_24]]),Matrix(6, 4, [[-C_19_4,C_13_1-C_19_5,C_13_2-C_19_6,C_13_3-C_19_7],[-C_20_4,C_14_1-C_20_5,C_14_2-C_20_6,C_14_3-C_20_7],[-C_21_4,C_15_1-C_21_5,C_15_2-C_21_6,C_15_3-C_21_7],[-C_22_4,C_16_1-C_22_5,C_16_2-C_22_6,C_16_3-C_22_7],[-C_23_4,C_17_1-C_23_5,C_17_2-C_23_6,C_17_3-C_23_7],[-C_24_4,C_18_1-C_24_5,C_18_2-C_24_6,C_18_3-C_24_7]])))+Trace(Mul(Matrix(4, 3, [[-A_4_1,-A_4_2,-A_4_3],[(-a12+1)*A_1_1-A_5_1+A_1_4*a22-A_1_7*a32,(-a12+1)*A_1_2-A_5_2+A_1_5*a22-A_1_8*a32,(-a12+1)*A_1_3-A_5_3+A_1_6*a22-A_1_9*a32],[(-a12+1)*A_2_1-A_6_1+A_2_4*a22-A_2_7*a32,(-a12+1)*A_2_2-A_6_2+A_2_5*a22-A_2_8*a32,(-a12+1)*A_2_3-A_6_3+A_2_6*a22-A_2_9*a32],[(-a12+1)*A_3_1-A_7_1+A_3_4*a22-A_3_7*a32,(-a12+1)*A_3_2-A_7_2+A_3_5*a22-A_3_8*a32,(-a12+1)*A_3_3-A_7_3+A_3_6*a22-A_3_9*a32]]),Matrix(3, 6, [[-1/a32*B_7_1-B_1_25-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_25-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_25,-1/a32*B_7_2-B_1_26-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_26-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_26,-1/a32*B_7_3-B_1_27-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_27-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_27,-1/a32*B_7_4-B_1_28-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_28-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_28,-1/a32*B_7_5-B_1_29-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_29-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_29,-1/a32*B_7_6-B_1_30-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_4_30-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_7_30],[-1/a32*B_8_1-B_2_25-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_25-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_25,-1/a32*B_8_2-B_2_26-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_26-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_26,-1/a32*B_8_3-B_2_27-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_27-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_27,-1/a32*B_8_4-B_2_28-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_28-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_28,-1/a32*B_8_5-B_2_29-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_29-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_29,-1/a32*B_8_6-B_2_30-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_5_30-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_8_30],[-1/a32*B_9_1-B_3_25-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_25-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_25,-1/a32*B_9_2-B_3_26-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_26-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_26,-1/a32*B_9_3-B_3_27-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_27-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_27,-1/a32*B_9_4-B_3_28-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_28-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_28,-1/a32*B_9_5-B_3_29-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_29-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_29,-1/a32*B_9_6-B_3_30-(a11*a32-a12*a31)/(a21*a32-a22*a31)*B_6_30-(a11*a22-a12*a21)/(a21*a32-a22*a31)*B_9_30]]),Matrix(6, 4, [[C_1_4+C_25_4,C_1_1+C_1_5+C_25_5,C_1_2+C_1_6+C_25_6,C_1_3+C_1_7+C_25_7],[C_2_4+C_26_4,C_2_1+C_2_5+C_26_5,C_2_2+C_2_6+C_26_6,C_2_3+C_2_7+C_26_7],[C_3_4+C_27_4,C_3_1+C_3_5+C_27_5,C_3_2+C_3_6+C_27_6,C_3_3+C_3_7+C_27_7],[C_4_4+C_28_4,C_4_1+C_4_5+C_28_5,C_4_2+C_4_6+C_28_6,C_4_3+C_4_7+C_28_7],[C_5_4+C_29_4,C_5_1+C_5_5+C_29_5,C_5_2+C_5_6+C_29_6,C_5_3+C_5_7+C_29_7],[C_6_4+C_30_4,C_6_1+C_6_5+C_30_5,C_6_2+C_6_6+C_30_6,C_6_3+C_6_7+C_30_7]])))+Trace(Mul(Matrix(4, 3, [[-A_4_1*a11+A_4_4*a21-A_4_7*a31,-A_4_2*a11+A_4_5*a21-A_4_8*a31,-A_4_3*a11+A_4_6*a21-A_4_9*a31],[A_1_1*a11-A_1_4*a21+A_1_7*a31-A_5_1*a11+A_5_4*a21-A_5_7*a31,A_1_2*a11-A_1_5*a21+A_1_8*a31-A_5_2*a11+A_5_5*a21-A_5_8*a31,A_1_3*a11-A_1_6*a21+A_1_9*a31-A_5_3*a11+A_5_6*a21-A_5_9*a31],[A_2_1*a11-A_2_4*a21+A_2_7*a31-A_6_1*a11+A_6_4*a21-A_6_7*a31,A_2_2*a11-A_2_5*a21+A_2_8*a31-A_6_2*a11+A_6_5*a21-A_6_8*a31,A_2_3*a11-A_2_6*a21+A_2_9*a31-A_6_3*a11+A_6_6*a21-A_6_9*a31],[A_3_1*a11-A_3_4*a21+A_3_7*a31-A_7_1*a11+A_7_4*a21-A_7_7*a31,A_3_2*a11-A_3_5*a21+A_3_8*a31-A_7_2*a11+A_7_5*a21-A_7_8*a31,A_3_3*a11-A_3_6*a21+A_3_9*a31-A_7_3*a11+A_7_6*a21-A_7_9*a31]]),Matrix(3, 6, [[1/a11*B_1_13+(a21-a22)/(a11*a22-a12*a21)*B_1_19+(a11-a12)/(a11*a22-a12*a21)*B_4_19,1/a11*B_1_14+(a21-a22)/(a11*a22-a12*a21)*B_1_20+(a11-a12)/(a11*a22-a12*a21)*B_4_20,1/a11*B_1_15+(a21-a22)/(a11*a22-a12*a21)*B_1_21+(a11-a12)/(a11*a22-a12*a21)*B_4_21,1/a11*B_1_16+(a21-a22)/(a11*a22-a12*a21)*B_1_22+(a11-a12)/(a11*a22-a12*a21)*B_4_22,1/a11*B_1_17+(a21-a22)/(a11*a22-a12*a21)*B_1_23+(a11-a12)/(a11*a22-a12*a21)*B_4_23,1/a11*B_1_18+(a21-a22)/(a11*a22-a12*a21)*B_1_24+(a11-a12)/(a11*a22-a12*a21)*B_4_24],[1/a11*B_2_13+(a21-a22)/(a11*a22-a12*a21)*B_2_19+(a11-a12)/(a11*a22-a12*a21)*B_5_19,1/a11*B_2_14+(a21-a22)/(a11*a22-a12*a21)*B_2_20+(a11-a12)/(a11*a22-a12*a21)*B_5_20,1/a11*B_2_15+(a21-a22)/(a11*a22-a12*a21)*B_2_21+(a11-a12)/(a11*a22-a12*a21)*B_5_21,1/a11*B_2_16+(a21-a22)/(a11*a22-a12*a21)*B_2_22+(a11-a12)/(a11*a22-a12*a21)*B_5_22,1/a11*B_2_17+(a21-a22)/(a11*a22-a12*a21)*B_2_23+(a11-a12)/(a11*a22-a12*a21)*B_5_23,1/a11*B_2_18+(a21-a22)/(a11*a22-a12*a21)*B_2_24+(a11-a12)/(a11*a22-a12*a21)*B_5_24],[1/a11*B_3_13+(a21-a22)/(a11*a22-a12*a21)*B_3_19+(a11-a12)/(a11*a22-a12*a21)*B_6_19,1/a11*B_3_14+(a21-a22)/(a11*a22-a12*a21)*B_3_20+(a11-a12)/(a11*a22-a12*a21)*B_6_20,1/a11*B_3_15+(a21-a22)/(a11*a22-a12*a21)*B_3_21+(a11-a12)/(a11*a22-a12*a21)*B_6_21,1/a11*B_3_16+(a21-a22)/(a11*a22-a12*a21)*B_3_22+(a11-a12)/(a11*a22-a12*a21)*B_6_22,1/a11*B_3_17+(a21-a22)/(a11*a22-a12*a21)*B_3_23+(a11-a12)/(a11*a22-a12*a21)*B_6_23,1/a11*B_3_18+(a21-a22)/(a11*a22-a12*a21)*B_3_24+(a11-a12)/(a11*a22-a12*a21)*B_6_24]]),Matrix(6, 4, [[C_19_4,C_19_5,C_19_6,C_19_7],[C_20_4,C_20_5,C_20_6,C_20_7],[C_21_4,C_21_5,C_21_6,C_21_7],[C_22_4,C_22_5,C_22_6,C_22_7],[C_23_4,C_23_5,C_23_6,C_23_7],[C_24_4,C_24_5,C_24_6,C_24_7]])))+Trace(Mul(Matrix(4, 3, [[(a11-a12)*A_4_1+(-a21+a22)*A_4_4+(a31-a32)*A_4_7,(a11-a12)*A_4_2+(-a21+a22)*A_4_5+(a31-a32)*A_4_8,(a11-a12)*A_4_3+(-a21+a22)*A_4_6+(a31-a32)*A_4_9],[(a11-a12)*A_5_1+(-a21+a22)*A_5_4+(a31-a32)*A_5_7,(a11-a12)*A_5_2+(-a21+a22)*A_5_5+(a31-a32)*A_5_8,(a11-a12)*A_5_3+(-a21+a22)*A_5_6+(a31-a32)*A_5_9],[(a11-a12)*A_6_1+(-a21+a22)*A_6_4+(a31-a32)*A_6_7,(a11-a12)*A_6_2+(-a21+a22)*A_6_5+(a31-a32)*A_6_8,(a11-a12)*A_6_3+(-a21+a22)*A_6_6+(a31-a32)*A_6_9],[(a11-a12)*A_7_1+(-a21+a22)*A_7_4+(a31-a32)*A_7_7,(a11-a12)*A_7_2+(-a21+a22)*A_7_5+(a31-a32)*A_7_8,(a11-a12)*A_7_3+(-a21+a22)*A_7_6+(a31-a32)*A_7_9]]),Matrix(3, 6, [[-a32/(a21*a32-a22*a31)*B_4_25-a22/(a21*a32-a22*a31)*B_7_25,-a32/(a21*a32-a22*a31)*B_4_26-a22/(a21*a32-a22*a31)*B_7_26,-a32/(a21*a32-a22*a31)*B_4_27-a22/(a21*a32-a22*a31)*B_7_27,-a32/(a21*a32-a22*a31)*B_4_28-a22/(a21*a32-a22*a31)*B_7_28,-a32/(a21*a32-a22*a31)*B_4_29-a22/(a21*a32-a22*a31)*B_7_29,-a32/(a21*a32-a22*a31)*B_4_30-a22/(a21*a32-a22*a31)*B_7_30],[-a32/(a21*a32-a22*a31)*B_5_25-a22/(a21*a32-a22*a31)*B_8_25,-a32/(a21*a32-a22*a31)*B_5_26-a22/(a21*a32-a22*a31)*B_8_26,-a32/(a21*a32-a22*a31)*B_5_27-a22/(a21*a32-a22*a31)*B_8_27,-a32/(a21*a32-a22*a31)*B_5_28-a22/(a21*a32-a22*a31)*B_8_28,-a32/(a21*a32-a22*a31)*B_5_29-a22/(a21*a32-a22*a31)*B_8_29,-a32/(a21*a32-a22*a31)*B_5_30-a22/(a21*a32-a22*a31)*B_8_30],[-a32/(a21*a32-a22*a31)*B_6_25-a22/(a21*a32-a22*a31)*B_9_25,-a32/(a21*a32-a22*a31)*B_6_26-a22/(a21*a32-a22*a31)*B_9_26,-a32/(a21*a32-a22*a31)*B_6_27-a22/(a21*a32-a22*a31)*B_9_27,-a32/(a21*a32-a22*a31)*B_6_28-a22/(a21*a32-a22*a31)*B_9_28,-a32/(a21*a32-a22*a31)*B_6_29-a22/(a21*a32-a22*a31)*B_9_29,-a32/(a21*a32-a22*a31)*B_6_30-a22/(a21*a32-a22*a31)*B_9_30]]),Matrix(6, 4, [[C_19_4+C_25_4,C_19_1+C_25_1+C_19_5+C_25_5,C_19_2+C_25_2+C_19_6+C_25_6,C_19_3+C_25_3+C_19_7+C_25_7],[C_20_4+C_26_4,C_20_1+C_26_1+C_20_5+C_26_5,C_20_2+C_26_2+C_20_6+C_26_6,C_20_3+C_26_3+C_20_7+C_26_7],[C_21_4+C_27_4,C_21_1+C_27_1+C_21_5+C_27_5,C_21_2+C_27_2+C_21_6+C_27_6,C_21_3+C_27_3+C_21_7+C_27_7],[C_22_4+C_28_4,C_22_1+C_28_1+C_22_5+C_28_5,C_22_2+C_28_2+C_22_6+C_28_6,C_22_3+C_28_3+C_22_7+C_28_7],[C_23_4+C_29_4,C_23_1+C_29_1+C_23_5+C_29_5,C_23_2+C_29_2+C_23_6+C_29_6,C_23_3+C_29_3+C_23_7+C_29_7],[C_24_4+C_30_4,C_24_1+C_30_1+C_24_5+C_30_5,C_24_2+C_30_2+C_24_6+C_30_6,C_24_3+C_30_3+C_24_7+C_30_7]])))+Trace(Mul(Matrix(4, 3, [[(-a11+a12)*A_4_1+(a21-a22)*A_4_4+(-a31+a32)*A_4_7,(-a11+a12)*A_4_2+(a21-a22)*A_4_5+(-a31+a32)*A_4_8,(-a11+a12)*A_4_3+(a21-a22)*A_4_6+(-a31+a32)*A_4_9],[A_1_1*a11+(-a11+a12)*A_5_1-A_1_4*a21+(a21-a22)*A_5_4+A_1_7*a31+(-a31+a32)*A_5_7,A_1_2*a11+(-a11+a12)*A_5_2-A_1_5*a21+(a21-a22)*A_5_5+A_1_8*a31+(-a31+a32)*A_5_8,A_1_3*a11+(-a11+a12)*A_5_3-A_1_6*a21+(a21-a22)*A_5_6+A_1_9*a31+(-a31+a32)*A_5_9],[A_2_1*a11+(-a11+a12)*A_6_1-A_2_4*a21+(a21-a22)*A_6_4+A_2_7*a31+(-a31+a32)*A_6_7,A_2_2*a11+(-a11+a12)*A_6_2-A_2_5*a21+(a21-a22)*A_6_5+A_2_8*a31+(-a31+a32)*A_6_8,A_2_3*a11+(-a11+a12)*A_6_3-A_2_6*a21+(a21-a22)*A_6_6+A_2_9*a31+(-a31+a32)*A_6_9],[A_3_1*a11+(-a11+a12)*A_7_1-A_3_4*a21+(a21-a22)*A_7_4+A_3_7*a31+(-a31+a32)*A_7_7,A_3_2*a11+(-a11+a12)*A_7_2-A_3_5*a21+(a21-a22)*A_7_5+A_3_8*a31+(-a31+a32)*A_7_8,A_3_3*a11+(-a11+a12)*A_7_3-A_3_6*a21+(a21-a22)*A_7_6+A_3_9*a31+(-a31+a32)*A_7_9]]),Matrix(3, 6, [[-a21/(a11*a22-a12*a21)*B_1_19-1/(a11*a22-a12*a21)*a11*B_4_19-a32/(a21*a32-a22*a31)*B_4_25-a22/(a21*a32-a22*a31)*B_7_25,-a21/(a11*a22-a12*a21)*B_1_20-1/(a11*a22-a12*a21)*a11*B_4_20-a32/(a21*a32-a22*a31)*B_4_26-a22/(a21*a32-a22*a31)*B_7_26,-a21/(a11*a22-a12*a21)*B_1_21-1/(a11*a22-a12*a21)*a11*B_4_21-a32/(a21*a32-a22*a31)*B_4_27-a22/(a21*a32-a22*a31)*B_7_27,-a21/(a11*a22-a12*a21)*B_1_22-1/(a11*a22-a12*a21)*a11*B_4_22-a32/(a21*a32-a22*a31)*B_4_28-a22/(a21*a32-a22*a31)*B_7_28,-a21/(a11*a22-a12*a21)*B_1_23-1/(a11*a22-a12*a21)*a11*B_4_23-a32/(a21*a32-a22*a31)*B_4_29-a22/(a21*a32-a22*a31)*B_7_29,-a21/(a11*a22-a12*a21)*B_1_24-1/(a11*a22-a12*a21)*a11*B_4_24-a32/(a21*a32-a22*a31)*B_4_30-a22/(a21*a32-a22*a31)*B_7_30],[-a21/(a11*a22-a12*a21)*B_2_19-1/(a11*a22-a12*a21)*a11*B_5_19-a32/(a21*a32-a22*a31)*B_5_25-a22/(a21*a32-a22*a31)*B_8_25,-a21/(a11*a22-a12*a21)*B_2_20-1/(a11*a22-a12*a21)*a11*B_5_20-a32/(a21*a32-a22*a31)*B_5_26-a22/(a21*a32-a22*a31)*B_8_26,-a21/(a11*a22-a12*a21)*B_2_21-1/(a11*a22-a12*a21)*a11*B_5_21-a32/(a21*a32-a22*a31)*B_5_27-a22/(a21*a32-a22*a31)*B_8_27,-a21/(a11*a22-a12*a21)*B_2_22-1/(a11*a22-a12*a21)*a11*B_5_22-a32/(a21*a32-a22*a31)*B_5_28-a22/(a21*a32-a22*a31)*B_8_28,-a21/(a11*a22-a12*a21)*B_2_23-1/(a11*a22-a12*a21)*a11*B_5_23-a32/(a21*a32-a22*a31)*B_5_29-a22/(a21*a32-a22*a31)*B_8_29,-a21/(a11*a22-a12*a21)*B_2_24-1/(a11*a22-a12*a21)*a11*B_5_24-a32/(a21*a32-a22*a31)*B_5_30-a22/(a21*a32-a22*a31)*B_8_30],[-a21/(a11*a22-a12*a21)*B_3_19-1/(a11*a22-a12*a21)*a11*B_6_19-a32/(a21*a32-a22*a31)*B_6_25-a22/(a21*a32-a22*a31)*B_9_25,-a21/(a11*a22-a12*a21)*B_3_20-1/(a11*a22-a12*a21)*a11*B_6_20-a32/(a21*a32-a22*a31)*B_6_26-a22/(a21*a32-a22*a31)*B_9_26,-a21/(a11*a22-a12*a21)*B_3_21-1/(a11*a22-a12*a21)*a11*B_6_21-a32/(a21*a32-a22*a31)*B_6_27-a22/(a21*a32-a22*a31)*B_9_27,-a21/(a11*a22-a12*a21)*B_3_22-1/(a11*a22-a12*a21)*a11*B_6_22-a32/(a21*a32-a22*a31)*B_6_28-a22/(a21*a32-a22*a31)*B_9_28,-a21/(a11*a22-a12*a21)*B_3_23-1/(a11*a22-a12*a21)*a11*B_6_23-a32/(a21*a32-a22*a31)*B_6_29-a22/(a21*a32-a22*a31)*B_9_29,-a21/(a11*a22-a12*a21)*B_3_24-1/(a11*a22-a12*a21)*a11*B_6_24-a32/(a21*a32-a22*a31)*B_6_30-a22/(a21*a32-a22*a31)*B_9_30]]),Matrix(6, 4, [[C_19_4,C_19_1+C_25_1+C_19_5,C_19_2+C_25_2+C_19_6,C_19_3+C_25_3+C_19_7],[C_20_4,C_20_1+C_26_1+C_20_5,C_20_2+C_26_2+C_20_6,C_20_3+C_26_3+C_20_7],[C_21_4,C_21_1+C_27_1+C_21_5,C_21_2+C_27_2+C_21_6,C_21_3+C_27_3+C_21_7],[C_22_4,C_22_1+C_28_1+C_22_5,C_22_2+C_28_2+C_22_6,C_22_3+C_28_3+C_22_7],[C_23_4,C_23_1+C_29_1+C_23_5,C_23_2+C_29_2+C_23_6,C_23_3+C_29_3+C_23_7],[C_24_4,C_24_1+C_30_1+C_24_5,C_24_2+C_30_2+C_24_6,C_24_3+C_30_3+C_24_7]])))+Trace(Mul(Matrix(3, 3, [[(a11-a12)*A_1_1+(-a11+a12)*A_5_1+(-a21+a22)*A_1_4+(a21-a22)*A_5_4+(a31-a32)*A_1_7+(-a31+a32)*A_5_7,(a11-a12)*A_1_2+(-a11+a12)*A_5_2+(-a21+a22)*A_1_5+(a21-a22)*A_5_5+(a31-a32)*A_1_8+(-a31+a32)*A_5_8,(a11-a12)*A_1_3+(-a11+a12)*A_5_3+(-a21+a22)*A_1_6+(a21-a22)*A_5_6+(a31-a32)*A_1_9+(-a31+a32)*A_5_9],[(a11-a12)*A_2_1+(-a11+a12)*A_6_1+(-a21+a22)*A_2_4+(a21-a22)*A_6_4+(a31-a32)*A_2_7+(-a31+a32)*A_6_7,(a11-a12)*A_2_2+(-a11+a12)*A_6_2+(-a21+a22)*A_2_5+(a21-a22)*A_6_5+(a31-a32)*A_2_8+(-a31+a32)*A_6_8,(a11-a12)*A_2_3+(-a11+a12)*A_6_3+(-a21+a22)*A_2_6+(a21-a22)*A_6_6+(a31-a32)*A_2_9+(-a31+a32)*A_6_9],[(a11-a12)*A_3_1+(-a11+a12)*A_7_1+(-a21+a22)*A_3_4+(a21-a22)*A_7_4+(a31-a32)*A_3_7+(-a31+a32)*A_7_7,(a11-a12)*A_3_2+(-a11+a12)*A_7_2+(-a21+a22)*A_3_5+(a21-a22)*A_7_5+(a31-a32)*A_3_8+(-a31+a32)*A_7_8,(a11-a12)*A_3_3+(-a11+a12)*A_7_3+(-a21+a22)*A_3_6+(a21-a22)*A_7_6+(a31-a32)*A_3_9+(-a31+a32)*A_7_9]]),Matrix(3, 6, [[a21/(a11*a22-a12*a21)*B_1_19+1/(a11*a22-a12*a21)*a11*B_4_19,a21/(a11*a22-a12*a21)*B_1_20+1/(a11*a22-a12*a21)*a11*B_4_20,a21/(a11*a22-a12*a21)*B_1_21+1/(a11*a22-a12*a21)*a11*B_4_21,a21/(a11*a22-a12*a21)*B_1_22+1/(a11*a22-a12*a21)*a11*B_4_22,a21/(a11*a22-a12*a21)*B_1_23+1/(a11*a22-a12*a21)*a11*B_4_23,a21/(a11*a22-a12*a21)*B_1_24+1/(a11*a22-a12*a21)*a11*B_4_24],[a21/(a11*a22-a12*a21)*B_2_19+1/(a11*a22-a12*a21)*a11*B_5_19,a21/(a11*a22-a12*a21)*B_2_20+1/(a11*a22-a12*a21)*a11*B_5_20,a21/(a11*a22-a12*a21)*B_2_21+1/(a11*a22-a12*a21)*a11*B_5_21,a21/(a11*a22-a12*a21)*B_2_22+1/(a11*a22-a12*a21)*a11*B_5_22,a21/(a11*a22-a12*a21)*B_2_23+1/(a11*a22-a12*a21)*a11*B_5_23,a21/(a11*a22-a12*a21)*B_2_24+1/(a11*a22-a12*a21)*a11*B_5_24],[a21/(a11*a22-a12*a21)*B_3_19+1/(a11*a22-a12*a21)*a11*B_6_19,a21/(a11*a22-a12*a21)*B_3_20+1/(a11*a22-a12*a21)*a11*B_6_20,a21/(a11*a22-a12*a21)*B_3_21+1/(a11*a22-a12*a21)*a11*B_6_21,a21/(a11*a22-a12*a21)*B_3_22+1/(a11*a22-a12*a21)*a11*B_6_22,a21/(a11*a22-a12*a21)*B_3_23+1/(a11*a22-a12*a21)*a11*B_6_23,a21/(a11*a22-a12*a21)*B_3_24+1/(a11*a22-a12*a21)*a11*B_6_24]]),Matrix(6, 3, [[C_19_1+C_25_1,C_19_2+C_25_2,C_19_3+C_25_3],[C_20_1+C_26_1,C_20_2+C_26_2,C_20_3+C_26_3],[C_21_1+C_27_1,C_21_2+C_27_2,C_21_3+C_27_3],[C_22_1+C_28_1,C_22_2+C_28_2,C_22_3+C_28_3],[C_23_1+C_29_1,C_23_2+C_29_2,C_23_3+C_29_3],[C_24_1+C_30_1,C_24_2+C_30_2,C_24_3+C_30_3]])))+Trace(Mul(Matrix(4, 3, [[(a12-1)/a32*A_4_1-a22/a32*A_4_4+A_4_7,(a12-1)/a32*A_4_2-a22/a32*A_4_5+A_4_8,(a12-1)/a32*A_4_3-a22/a32*A_4_6+A_4_9],[(-a12+1)/a32*A_1_1+(a12-1)/a32*A_5_1+a22/a32*A_1_4-a22/a32*A_5_4-A_1_7+A_5_7,(-a12+1)/a32*A_1_2+(a12-1)/a32*A_5_2+a22/a32*A_1_5-a22/a32*A_5_5-A_1_8+A_5_8,(-a12+1)/a32*A_1_3+(a12-1)/a32*A_5_3+a22/a32*A_1_6-a22/a32*A_5_6-A_1_9+A_5_9],[(-a12+1)/a32*A_2_1+(a12-1)/a32*A_6_1+a22/a32*A_2_4-a22/a32*A_6_4-A_2_7+A_6_7,(-a12+1)/a32*A_2_2+(a12-1)/a32*A_6_2+a22/a32*A_2_5-a22/a32*A_6_5-A_2_8+A_6_8,(-a12+1)/a32*A_2_3+(a12-1)/a32*A_6_3+a22/a32*A_2_6-a22/a32*A_6_6-A_2_9+A_6_9],[(-a12+1)/a32*A_3_1+(a12-1)/a32*A_7_1+a22/a32*A_3_4-a22/a32*A_7_4-A_3_7+A_7_7,(-a12+1)/a32*A_3_2+(a12-1)/a32*A_7_2+a22/a32*A_3_5-a22/a32*A_7_5-A_3_8+A_7_8,(-a12+1)/a32*A_3_3+(a12-1)/a32*A_7_3+a22/a32*A_3_6-a22/a32*A_7_6-A_3_9+A_7_9]]),Matrix(3, 6, [[B_7_1,B_7_2,B_7_3,B_7_4,B_7_5,B_7_6],[B_8_1,B_8_2,B_8_3,B_8_4,B_8_5,B_8_6],[B_9_1,B_9_2,B_9_3,B_9_4,B_9_5,B_9_6]]),Matrix(6, 4, [[C_1_4+C_25_4,C_1_5+C_25_5,C_1_6+C_25_6,C_1_7+C_25_7],[C_2_4+C_26_4,C_2_5+C_26_5,C_2_6+C_26_6,C_2_7+C_26_7],[C_3_4+C_27_4,C_3_5+C_27_5,C_3_6+C_27_6,C_3_7+C_27_7],[C_4_4+C_28_4,C_4_5+C_28_5,C_4_6+C_28_6,C_4_7+C_28_7],[C_5_4+C_29_4,C_5_5+C_29_5,C_5_6+C_29_6,C_5_7+C_29_7],[C_6_4+C_30_4,C_6_5+C_30_5,C_6_6+C_30_6,C_6_7+C_30_7]])))

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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