Description of fast matrix multiplication algorithm: ⟨3×20×20:890⟩

Algorithm type

4XY9Z+60X3Y4Z3+22X2Y6Z2+6XY6Z2+70X2Y4Z2+32XY6Z+18X2Y4Z+6XY4Z2+98X2Y2Z2+46XY4Z+6X2Y2Z+61XY3Z+18XY2Z2+238XY2Z+205XYZ4XY9Z60X3Y4Z322X2Y6Z26XY6Z270X2Y4Z232XY6Z18X2Y4Z6XY4Z298X2Y2Z246XY4Z6X2Y2Z61XY3Z18XY2Z2238XY2Z205XYZ4*X*Y^9*Z+60*X^3*Y^4*Z^3+22*X^2*Y^6*Z^2+6*X*Y^6*Z^2+70*X^2*Y^4*Z^2+32*X*Y^6*Z+18*X^2*Y^4*Z+6*X*Y^4*Z^2+98*X^2*Y^2*Z^2+46*X*Y^4*Z+6*X^2*Y^2*Z+61*X*Y^3*Z+18*X*Y^2*Z^2+238*X*Y^2*Z+205*X*Y*Z

Algorithm definition

The algorithm ⟨3×20×20:890⟩ could be constructed using the following decomposition:

⟨3×20×20:890⟩ = ⟨2×5×5:40⟩ + ⟨1×5×5:25⟩ + ⟨1×5×5:25⟩ + ⟨2×5×5:40⟩ + ⟨2×5×5:40⟩ + ⟨1×5×5:25⟩ + ⟨1×5×5:25⟩ + ⟨1×5×5:25⟩ + ⟨2×5×5:40⟩ + ⟨2×5×5:40⟩ + ⟨1×5×5:25⟩ + ⟨2×5×5:40⟩ + ⟨2×5×5:40⟩ + ⟨2×5×5:40⟩ + ⟨1×5×5:25⟩ + ⟨1×5×5:25⟩ + ⟨2×5×5:40⟩ + ⟨2×5×5:40⟩ + ⟨2×5×5:40⟩ + ⟨2×5×5:40⟩ + ⟨1×5×5:25⟩ + ⟨2×5×5:40⟩ + ⟨2×5×5:40⟩ + ⟨1×5×5:25⟩ + ⟨2×5×5:40⟩ + ⟨2×5×5:40⟩.

This decomposition is defined by the following equality:

TraceMulA_1_1A_1_2A_1_3A_1_4A_1_5A_1_6A_1_7A_1_8A_1_9A_1_10A_1_11A_1_12A_1_13A_1_14A_1_15A_1_16A_1_17A_1_18A_1_19A_1_20A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_2_7A_2_8A_2_9A_2_10A_2_11A_2_12A_2_13A_2_14A_2_15A_2_16A_2_17A_2_18A_2_19A_2_20A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_3_7A_3_8A_3_9A_3_10A_3_11A_3_12A_3_13A_3_14A_3_15A_3_16A_3_17A_3_18A_3_19A_3_20B_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_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_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_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_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_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_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_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_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_10_1B_10_2B_10_3B_10_4B_10_5B_10_6B_10_7B_10_8B_10_9B_10_10B_10_11B_10_12B_10_13B_10_14B_10_15B_10_16B_10_17B_10_18B_10_19B_10_20B_11_1B_11_2B_11_3B_11_4B_11_5B_11_6B_11_7B_11_8B_11_9B_11_10B_11_11B_11_12B_11_13B_11_14B_11_15B_11_16B_11_17B_11_18B_11_19B_11_20B_12_1B_12_2B_12_3B_12_4B_12_5B_12_6B_12_7B_12_8B_12_9B_12_10B_12_11B_12_12B_12_13B_12_14B_12_15B_12_16B_12_17B_12_18B_12_19B_12_20B_13_1B_13_2B_13_3B_13_4B_13_5B_13_6B_13_7B_13_8B_13_9B_13_10B_13_11B_13_12B_13_13B_13_14B_13_15B_13_16B_13_17B_13_18B_13_19B_13_20B_14_1B_14_2B_14_3B_14_4B_14_5B_14_6B_14_7B_14_8B_14_9B_14_10B_14_11B_14_12B_14_13B_14_14B_14_15B_14_16B_14_17B_14_18B_14_19B_14_20B_15_1B_15_2B_15_3B_15_4B_15_5B_15_6B_15_7B_15_8B_15_9B_15_10B_15_11B_15_12B_15_13B_15_14B_15_15B_15_16B_15_17B_15_18B_15_19B_15_20B_16_1B_16_2B_16_3B_16_4B_16_5B_16_6B_16_7B_16_8B_16_9B_16_10B_16_11B_16_12B_16_13B_16_14B_16_15B_16_16B_16_17B_16_18B_16_19B_16_20B_17_1B_17_2B_17_3B_17_4B_17_5B_17_6B_17_7B_17_8B_17_9B_17_10B_17_11B_17_12B_17_13B_17_14B_17_15B_17_16B_17_17B_17_18B_17_19B_17_20B_18_1B_18_2B_18_3B_18_4B_18_5B_18_6B_18_7B_18_8B_18_9B_18_10B_18_11B_18_12B_18_13B_18_14B_18_15B_18_16B_18_17B_18_18B_18_19B_18_20B_19_1B_19_2B_19_3B_19_4B_19_5B_19_6B_19_7B_19_8B_19_9B_19_10B_19_11B_19_12B_19_13B_19_14B_19_15B_19_16B_19_17B_19_18B_19_19B_19_20B_20_1B_20_2B_20_3B_20_4B_20_5B_20_6B_20_7B_20_8B_20_9B_20_10B_20_11B_20_12B_20_13B_20_14B_20_15B_20_16B_20_17B_20_18B_20_19B_20_20C_1_1C_1_2C_1_3C_2_1C_2_2C_2_3C_3_1C_3_2C_3_3C_4_1C_4_2C_4_3C_5_1C_5_2C_5_3C_6_1C_6_2C_6_3C_7_1C_7_2C_7_3C_8_1C_8_2C_8_3C_9_1C_9_2C_9_3C_10_1C_10_2C_10_3C_11_1C_11_2C_11_3C_12_1C_12_2C_12_3C_13_1C_13_2C_13_3C_14_1C_14_2C_14_3C_15_1C_15_2C_15_3C_16_1C_16_2C_16_3C_17_1C_17_2C_17_3C_18_1C_18_2C_18_3C_19_1C_19_2C_19_3C_20_1C_20_2C_20_3=TraceMulA_2_1A_2_2A_2_3A_2_4A_2_5A_3_1A_3_2A_3_3A_3_4A_3_5B_1_1-B_6_1-B_1_11B_1_2-B_6_2-B_1_12B_1_3-B_6_3-B_1_13B_1_4-B_6_4-B_1_14B_1_5-B_6_5-B_1_15B_2_1-B_7_1-B_2_11B_2_2-B_7_2-B_2_12B_2_3-B_7_3-B_2_13B_2_4-B_7_4-B_2_14B_2_5-B_7_5-B_2_15B_3_1-B_8_1-B_3_11B_3_2-B_8_2-B_3_12B_3_3-B_8_3-B_3_13B_3_4-B_8_4-B_3_14B_3_5-B_8_5-B_3_15B_4_1-B_9_1-B_4_11B_4_2-B_9_2-B_4_12B_4_3-B_9_3-B_4_13B_4_4-B_9_4-B_4_14B_4_5-B_9_5-B_4_15B_5_1-B_10_1-B_5_11B_5_2-B_10_2-B_5_12B_5_3-B_10_3-B_5_13B_5_4-B_10_4-B_5_14B_5_5-B_10_5-B_5_15C_1_2C_1_1+C_1_3C_2_2C_2_1+C_2_3C_3_2C_3_1+C_3_3C_4_2C_4_1+C_4_3C_5_2C_5_1+C_5_3+TraceMulA_1_6A_1_7A_1_8A_1_9A_1_10B_16_1-B_1_6+B_6_6-B_16_6-B_6_11B_16_2-B_1_7+B_6_7-B_16_7-B_6_12B_16_3-B_1_8+B_6_8-B_16_8-B_6_13B_16_4-B_1_9+B_6_9-B_16_9-B_6_14B_16_5-B_1_10+B_6_10-B_16_10-B_6_15B_17_1-B_2_6+B_7_6-B_17_6-B_7_11B_17_2-B_2_7+B_7_7-B_17_7-B_7_12B_17_3-B_2_8+B_7_8-B_17_8-B_7_13B_17_4-B_2_9+B_7_9-B_17_9-B_7_14B_17_5-B_2_10+B_7_10-B_17_10-B_7_15B_18_1-B_3_6+B_8_6-B_18_6-B_8_11B_18_2-B_3_7+B_8_7-B_18_7-B_8_12B_18_3-B_3_8+B_8_8-B_18_8-B_8_13B_18_4-B_3_9+B_8_9-B_18_9-B_8_14B_18_5-B_3_10+B_8_10-B_18_10-B_8_15B_19_1-B_4_6+B_9_6-B_19_6-B_9_11B_19_2-B_4_7+B_9_7-B_19_7-B_9_12B_19_3-B_4_8+B_9_8-B_19_8-B_9_13B_19_4-B_4_9+B_9_9-B_19_9-B_9_14B_19_5-B_4_10+B_9_10-B_19_10-B_9_15B_20_1-B_5_6+B_10_6-B_20_6-B_10_11B_20_2-B_5_7+B_10_7-B_20_7-B_10_12B_20_3-B_5_8+B_10_8-B_20_8-B_10_13B_20_4-B_5_9+B_10_9-B_20_9-B_10_14B_20_5-B_5_10+B_10_10-B_20_10-B_10_15C_6_1+C_6_3C_7_1+C_7_3C_8_1+C_8_3C_9_1+C_9_3C_10_1+C_10_3+TraceMulA_1_11A_1_12A_1_13A_1_14A_1_15-B_11_6-B_1_11+B_11_11-B_16_11-B_11_7-B_1_12+B_11_12-B_16_12-B_11_8-B_1_13+B_11_13-B_16_13-B_11_9-B_1_14+B_11_14-B_16_14-B_11_10-B_1_15+B_11_15-B_16_15-B_12_6-B_2_11+B_12_11-B_17_11-B_12_7-B_2_12+B_12_12-B_17_12-B_12_8-B_2_13+B_12_13-B_17_13-B_12_9-B_2_14+B_12_14-B_17_14-B_12_10-B_2_15+B_12_15-B_17_15-B_13_6-B_3_11+B_13_11-B_18_11-B_1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5_9B_15_10C_6_1C_11_1C_7_1C_12_1C_8_1C_13_1C_9_1C_14_1C_10_1C_15_1TraceMulA_2_16A_2_17A_2_18A_2_19A_2_20A_1_1A_1_6A_1_16A_3_16A_1_2A_1_7A_1_17A_3_17A_1_3A_1_8A_1_18A_3_18A_1_4A_1_9A_1_19A_3_19A_1_5A_1_10A_1_20A_3_20B_16_1B_1_16B_16_2B_1_17B_16_3B_1_18B_16_4B_1_19B_16_5B_1_20B_17_1B_2_16B_17_2B_2_17B_17_3B_2_18B_17_4B_2_19B_17_5B_2_20B_18_1B_3_16B_18_2B_3_17B_18_3B_3_18B_18_4B_3_19B_18_5B_3_20B_19_1B_4_16B_19_2B_4_17B_19_3B_4_18B_19_4B_4_19B_19_5B_4_20B_20_1B_5_16B_20_2B_5_17B_20_3B_5_18B_20_4B_5_19B_20_5B_5_20C_1_2C_6_2C_16_2C_16_1C_1_3C_6_3C_16_3C_2_2C_7_2C_17_2C_17_1C_2_3C_7_3C_17_3C_3_2C_8_2C_18_2C_18_1C_3_3C_8_3C_18_3C_4_2C_9_2C_19_2C_19_1C_4_3C_9_3C_19_3C_5_2C_10_2C_20_2C_20_1C_5_3C_10_3C_20_3TraceMulA_2_1A_2_6A_2_16A_2_2A_2_7A_2_17A_2_3A_2_8A_2_18A_2_4A_2_9A_2_19A_2_5A_2_10A_2_20A_1_1A_3_1A_1_6A_3_6A_1_16A_3_16A_1_2A_3_2A_1_7A_3_7A_1_17A_3_17A_1_3A_3_3A_1_8A_3_8A_1_18A_3_18A_1_4A_3_4A_1_9A_3_9A_1_19A_3_19A_1_5A_3_5A_1_10A_3_10A_1_20A_3_20B_1_16B_1_17B_1_18B_1_19B_1_20B_2_16B_2_17B_2_18B_2_19B_2_20B_3_16B_3_17B_3_18B_3_19B_3_20B_4_16B_4_17B_4_18B_4_19B_4_20B_5_16B_5_17B_5_18B_5_19B_5_20C_1_2C_6_2C_16_2C_1_3C_6_3C_16_3C_2_2C_7_2C_17_2C_2_3C_7_3C_17_3C_3_2C_8_2C_18_2C_3_3C_8_3C_18_3C_4_2C_9_2C_19_2C_4_3C_9_3C_19_3C_5_2C_10_2C_20_2C_5_3C_10_3C_20_3TraceMulA_1_1A_1_6A_1_16A_1_2A_1_7A_1_17A_1_3A_1_8A_1_18A_1_4A_1_9A_1_19A_1_5A_1_10A_1_20B_16_1B_16_2B_16_3B_16_4B_16_5B_17_1B_17_2B_17_3B_17_4B_17_5B_18_1B_18_2B_18_3B_18_4B_18_5B_19_1B_19_2B_19_3B_19_4B_19_5B_20_1B_20_2B_20_3B_20_4B_20_5C_1_1C_6_1C_16_1C_1_3C_6_3C_16_3C_2_1C_7_1C_17_1C_2_3C_7_3C_17_3C_3_1C_8_1C_18_1C_3_3C_8_3C_18_3C_4_1C_9_1C_19_1C_4_3C_9_3C_19_3C_5_1C_10_1C_20_1C_5_3C_10_3C_20_3TraceMulA_2_1A_2_11A_2_2A_2_12A_2_3A_2_13A_2_4A_2_14A_2_5A_2_15A_1_1A_3_1A_1_11A_3_11A_1_2A_3_2A_1_12A_3_12A_1_3A_3_3A_1_13A_3_13A_1_4A_3_4A_1_14A_3_14A_1_5A_3_5A_1_15A_3_15B_11_1B_11_2B_11_3B_11_4B_11_5B_12_1B_12_2B_12_3B_12_4B_12_5B_13_1B_13_2B_13_3B_13_4B_13_5B_14_1B_14_2B_14_3B_14_4B_14_5B_15_1B_15_2B_15_3B_15_4B_15_5C_1_2C_11_2C_1_3C_11_3C_2_2C_12_2C_2_3C_12_3C_3_2C_13_2C_3_3C_13_3C_4_2C_14_2C_4_3C_14_3C_5_2C_15_2C_5_3C_15_3TraceMulA_2_11A_2_16A_2_12A_2_17A_2_13A_2_18A_2_14A_2_19A_2_15A_2_20A_1_11A_3_11A_1_16A_3_16A_1_12A_3_12A_1_17A_3_17A_1_13A_3_13A_1_18A_3_18A_1_14A_3_14A_1_19A_3_19A_1_15A_3_15A_1_20A_3_20B_11_16B_11_17B_11_18B_11_19B_11_20B_12_16B_12_17B_12_18B_12_19B_12_20B_13_16B_13_17B_13_18B_13_19B_13_20B_14_16B_14_17B_14_18B_14_19B_14_20B_15_16B_15_17B_15_18B_15_19B_15_20C_11_2C_16_2C_11_3C_16_3C_17_2C_12_2C_12_3C_17_3C_13_2C_18_2C_13_3C_18_3C_14_2C_19_2C_14_3C_19_3C_15_2C_20_2C_15_3C_20_3Trace(Mul(Matrix(3, 20, [[A_1_1,A_1_2,A_1_3,A_1_4,A_1_5,A_1_6,A_1_7,A_1_8,A_1_9,A_1_10,A_1_11,A_1_12,A_1_13,A_1_14,A_1_15,A_1_16,A_1_17,A_1_18,A_1_19,A_1_20],[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6,A_2_7,A_2_8,A_2_9,A_2_10,A_2_11,A_2_12,A_2_13,A_2_14,A_2_15,A_2_16,A_2_17,A_2_18,A_2_19,A_2_20],[A_3_1,A_3_2,A_3_3,A_3_4,A_3_5,A_3_6,A_3_7,A_3_8,A_3_9,A_3_10,A_3_11,A_3_12,A_3_13,A_3_14,A_3_15,A_3_16,A_3_17,A_3_18,A_3_19,A_3_20]]),Matrix(20, 20, [[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_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_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_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_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_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_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_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_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_10_1,B_10_2,B_10_3,B_10_4,B_10_5,B_10_6,B_10_7,B_10_8,B_10_9,B_10_10,B_10_11,B_10_12,B_10_13,B_10_14,B_10_15,B_10_16,B_10_17,B_10_18,B_10_19,B_10_20],[B_11_1,B_11_2,B_11_3,B_11_4,B_11_5,B_11_6,B_11_7,B_11_8,B_11_9,B_11_10,B_11_11,B_11_12,B_11_13,B_11_14,B_11_15,B_11_16,B_11_17,B_11_18,B_11_19,B_11_20],[B_12_1,B_12_2,B_12_3,B_12_4,B_12_5,B_12_6,B_12_7,B_12_8,B_12_9,B_12_10,B_12_11,B_12_12,B_12_13,B_12_14,B_12_15,B_12_16,B_12_17,B_12_18,B_12_19,B_12_20],[B_13_1,B_13_2,B_13_3,B_13_4,B_13_5,B_13_6,B_13_7,B_13_8,B_13_9,B_13_10,B_13_11,B_13_12,B_13_13,B_13_14,B_13_15,B_13_16,B_13_17,B_13_18,B_13_19,B_13_20],[B_14_1,B_14_2,B_14_3,B_14_4,B_14_5,B_14_6,B_14_7,B_14_8,B_14_9,B_14_10,B_14_11,B_14_12,B_14_13,B_14_14,B_14_15,B_14_16,B_14_17,B_14_18,B_14_19,B_14_20],[B_15_1,B_15_2,B_15_3,B_15_4,B_15_5,B_15_6,B_15_7,B_15_8,B_15_9,B_15_10,B_15_11,B_15_12,B_15_13,B_15_14,B_15_15,B_15_16,B_15_17,B_15_18,B_15_19,B_15_20],[B_16_1,B_16_2,B_16_3,B_16_4,B_16_5,B_16_6,B_16_7,B_16_8,B_16_9,B_16_10,B_16_11,B_16_12,B_16_13,B_16_14,B_16_15,B_16_16,B_16_17,B_16_18,B_16_19,B_16_20],[B_17_1,B_17_2,B_17_3,B_17_4,B_17_5,B_17_6,B_17_7,B_17_8,B_17_9,B_17_10,B_17_11,B_17_12,B_17_13,B_17_14,B_17_15,B_17_16,B_17_17,B_17_18,B_17_19,B_17_20],[B_18_1,B_18_2,B_18_3,B_18_4,B_18_5,B_18_6,B_18_7,B_18_8,B_18_9,B_18_10,B_18_11,B_18_12,B_18_13,B_18_14,B_18_15,B_18_16,B_18_17,B_18_18,B_18_19,B_18_20],[B_19_1,B_19_2,B_19_3,B_19_4,B_19_5,B_19_6,B_19_7,B_19_8,B_19_9,B_19_10,B_19_11,B_19_12,B_19_13,B_19_14,B_19_15,B_19_16,B_19_17,B_19_18,B_19_19,B_19_20],[B_20_1,B_20_2,B_20_3,B_20_4,B_20_5,B_20_6,B_20_7,B_20_8,B_20_9,B_20_10,B_20_11,B_20_12,B_20_13,B_20_14,B_20_15,B_20_16,B_20_17,B_20_18,B_20_19,B_20_20]]),Matrix(20, 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],[C_7_1,C_7_2,C_7_3],[C_8_1,C_8_2,C_8_3],[C_9_1,C_9_2,C_9_3],[C_10_1,C_10_2,C_10_3],[C_11_1,C_11_2,C_11_3],[C_12_1,C_12_2,C_12_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],[C_19_1,C_19_2,C_19_3],[C_20_1,C_20_2,C_20_3]]))) = Trace(Mul(Matrix(2, 5, [[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5],[A_3_1,A_3_2,A_3_3,A_3_4,A_3_5]]),Matrix(5, 5, [[B_1_1-B_6_1-B_1_11,B_1_2-B_6_2-B_1_12,B_1_3-B_6_3-B_1_13,B_1_4-B_6_4-B_1_14,B_1_5-B_6_5-B_1_15],[B_2_1-B_7_1-B_2_11,B_2_2-B_7_2-B_2_12,B_2_3-B_7_3-B_2_13,B_2_4-B_7_4-B_2_14,B_2_5-B_7_5-B_2_15],[B_3_1-B_8_1-B_3_11,B_3_2-B_8_2-B_3_12,B_3_3-B_8_3-B_3_13,B_3_4-B_8_4-B_3_14,B_3_5-B_8_5-B_3_15],[B_4_1-B_9_1-B_4_11,B_4_2-B_9_2-B_4_12,B_4_3-B_9_3-B_4_13,B_4_4-B_9_4-B_4_14,B_4_5-B_9_5-B_4_15],[B_5_1-B_10_1-B_5_11,B_5_2-B_10_2-B_5_12,B_5_3-B_10_3-B_5_13,B_5_4-B_10_4-B_5_14,B_5_5-B_10_5-B_5_15]]),Matrix(5, 2, [[C_1_2,C_1_1+C_1_3],[C_2_2,C_2_1+C_2_3],[C_3_2,C_3_1+C_3_3],[C_4_2,C_4_1+C_4_3],[C_5_2,C_5_1+C_5_3]])))+Trace(Mul(Matrix(1, 5, [[A_1_6,A_1_7,A_1_8,A_1_9,A_1_10]]),Matrix(5, 5, [[B_16_1-B_1_6+B_6_6-B_16_6-B_6_11,B_16_2-B_1_7+B_6_7-B_16_7-B_6_12,B_16_3-B_1_8+B_6_8-B_16_8-B_6_13,B_16_4-B_1_9+B_6_9-B_16_9-B_6_14,B_16_5-B_1_10+B_6_10-B_16_10-B_6_15],[B_17_1-B_2_6+B_7_6-B_17_6-B_7_11,B_17_2-B_2_7+B_7_7-B_17_7-B_7_12,B_17_3-B_2_8+B_7_8-B_17_8-B_7_13,B_17_4-B_2_9+B_7_9-B_17_9-B_7_14,B_17_5-B_2_10+B_7_10-B_17_10-B_7_15],[B_18_1-B_3_6+B_8_6-B_18_6-B_8_11,B_18_2-B_3_7+B_8_7-B_18_7-B_8_12,B_18_3-B_3_8+B_8_8-B_18_8-B_8_13,B_18_4-B_3_9+B_8_9-B_18_9-B_8_14,B_18_5-B_3_10+B_8_10-B_18_10-B_8_15],[B_19_1-B_4_6+B_9_6-B_19_6-B_9_11,B_19_2-B_4_7+B_9_7-B_19_7-B_9_12,B_19_3-B_4_8+B_9_8-B_19_8-B_9_13,B_19_4-B_4_9+B_9_9-B_19_9-B_9_14,B_19_5-B_4_10+B_9_10-B_19_10-B_9_15],[B_20_1-B_5_6+B_10_6-B_20_6-B_10_11,B_20_2-B_5_7+B_10_7-B_20_7-B_10_12,B_20_3-B_5_8+B_10_8-B_20_8-B_10_13,B_20_4-B_5_9+B_10_9-B_20_9-B_10_14,B_20_5-B_5_10+B_10_10-B_20_10-B_10_15]]),Matrix(5, 1, [[C_6_1+C_6_3],[C_7_1+C_7_3],[C_8_1+C_8_3],[C_9_1+C_9_3],[C_10_1+C_10_3]])))+Trace(Mul(Matrix(1, 5, [[A_1_11,A_1_12,A_1_13,A_1_14,A_1_15]]),Matrix(5, 5, [[-B_11_6-B_1_11+B_11_11-B_16_11,-B_11_7-B_1_12+B_11_12-B_16_12,-B_11_8-B_1_13+B_11_13-B_16_13,-B_11_9-B_1_14+B_11_14-B_16_14,-B_11_10-B_1_15+B_11_15-B_16_15],[-B_12_6-B_2_11+B_12_11-B_17_11,-B_12_7-B_2_12+B_12_12-B_17_12,-B_12_8-B_2_13+B_12_13-B_17_13,-B_12_9-B_2_14+B_12_14-B_17_14,-B_12_10-B_2_15+B_12_15-B_17_15],[-B_13_6-B_3_11+B_13_11-B_18_11,-B_13_7-B_3_12+B_13_12-B_18_12,-B_13_8-B_3_13+B_13_13-B_18_13,-B_13_9-B_3_14+B_13_14-B_18_14,-B_13_10-B_3_15+B_13_15-B_18_15],[-B_14_6-B_4_11+B_14_11-B_19_11,-B_14_7-B_4_12+B_14_12-B_19_12,-B_14_8-B_4_13+B_14_13-B_19_13,-B_14_9-B_4_14+B_14_14-B_19_14,-B_14_10-B_4_15+B_14_15-B_19_15],[-B_15_6-B_5_11+B_15_11-B_20_11,-B_15_7-B_5_12+B_15_12-B_20_12,-B_15_8-B_5_13+B_15_13-B_20_13,-B_15_9-B_5_14+B_15_14-B_20_14,-B_15_10-B_5_15+B_15_15-B_20_15]]),Matrix(5, 1, [[C_11_1],[C_12_1],[C_13_1],[C_14_1],[C_15_1]])))+Trace(Mul(Matrix(2, 5, [[A_2_11,A_2_12,A_2_13,A_2_14,A_2_15],[A_3_11,A_3_12,A_3_13,A_3_14,A_3_15]]),Matrix(5, 5, [[-B_11_1-B_6_11+B_11_11-B_11_16,-B_11_2-B_6_12+B_11_12-B_11_17,-B_11_3-B_6_13+B_11_13-B_11_18,-B_11_4-B_6_14+B_11_14-B_11_19,-B_11_5-B_6_15+B_11_15-B_11_20],[-B_12_1-B_7_11+B_12_11-B_12_16,-B_12_2-B_7_12+B_12_12-B_12_17,-B_12_3-B_7_13+B_12_13-B_12_18,-B_12_4-B_7_14+B_12_14-B_12_19,-B_12_5-B_7_15+B_12_15-B_12_20],[-B_13_1-B_8_11+B_13_11-B_13_16,-B_13_2-B_8_12+B_13_12-B_13_17,-B_13_3-B_8_13+B_13_13-B_13_18,-B_13_4-B_8_14+B_13_14-B_13_19,-B_13_5-B_8_15+B_13_15-B_13_20],[-B_14_1-B_9_11+B_14_11-B_14_16,-B_14_2-B_9_12+B_14_12-B_14_17,-B_14_3-B_9_13+B_14_13-B_14_18,-B_14_4-B_9_14+B_14_14-B_14_19,-B_14_5-B_9_15+B_14_15-B_14_20],[-B_15_1-B_10_11+B_15_11-B_15_16,-B_15_2-B_10_12+B_15_12-B_15_17,-B_15_3-B_10_13+B_15_13-B_15_18,-B_15_4-B_10_14+B_15_14-B_15_19,-B_15_5-B_10_15+B_15_15-B_15_20]]),Matrix(5, 2, [[C_11_2,C_11_3],[C_12_2,C_12_3],[C_13_2,C_13_3],[C_14_2,C_14_3],[C_15_2,C_15_3]])))+Trace(Mul(Matrix(2, 5, [[A_2_16,A_2_17,A_2_18,A_2_19,A_2_20],[A_3_16,A_3_17,A_3_18,A_3_19,A_3_20]]),Matrix(5, 5, [[B_16_1-B_16_11+B_1_16-B_6_16+B_16_16,B_16_2-B_16_12+B_1_17-B_6_17+B_16_17,B_16_3-B_16_13+B_1_18-B_6_18+B_16_18,B_16_4-B_16_14+B_1_19-B_6_19+B_16_19,B_16_5-B_16_15+B_1_20-B_6_20+B_16_20],[B_17_1-B_17_11+B_2_16-B_7_16+B_17_16,B_17_2-B_17_12+B_2_17-B_7_17+B_17_17,B_17_3-B_17_13+B_2_18-B_7_18+B_17_18,B_17_4-B_17_14+B_2_19-B_7_19+B_17_19,B_17_5-B_17_15+B_2_20-B_7_20+B_17_20],[B_18_1-B_18_11+B_3_16-B_8_16+B_18_16,B_18_2-B_18_12+B_3_17-B_8_17+B_18_17,B_18_3-B_18_13+B_3_18-B_8_18+B_18_18,B_18_4-B_18_14+B_3_19-B_8_19+B_18_19,B_18_5-B_18_15+B_3_20-B_8_20+B_18_20],[B_19_1-B_19_11+B_4_16-B_9_16+B_19_16,B_19_2-B_19_12+B_4_17-B_9_17+B_19_17,B_19_3-B_19_13+B_4_18-B_9_18+B_19_18,B_19_4-B_19_14+B_4_19-B_9_19+B_19_19,B_19_5-B_19_15+B_4_20-B_9_20+B_19_20],[B_20_1-B_20_11+B_5_16-B_10_16+B_20_16,B_20_2-B_20_12+B_5_17-B_10_17+B_20_17,B_20_3-B_20_13+B_5_18-B_10_18+B_20_18,B_20_4-B_20_14+B_5_19-B_10_19+B_20_19,B_20_5-B_20_15+B_5_20-B_10_20+B_20_20]]),Matrix(5, 2, [[C_16_2,C_16_1+C_16_3],[C_17_2,C_17_1+C_17_3],[C_18_2,C_18_1+C_18_3],[C_19_2,C_19_1+C_19_3],[C_20_2,C_20_1+C_20_3]])))+Trace(Mul(Matrix(1, 5, [[A_1_1+A_1_6,A_1_2+A_1_7,A_1_3+A_1_8,A_1_4+A_1_9,A_1_5+A_1_10]]),Matrix(5, 5, [[B_16_1+B_1_6,B_16_2+B_1_7,B_16_3+B_1_8,B_16_4+B_1_9,B_16_5+B_1_10],[B_17_1+B_2_6,B_17_2+B_2_7,B_17_3+B_2_8,B_17_4+B_2_9,B_17_5+B_2_10],[B_18_1+B_3_6,B_18_2+B_3_7,B_18_3+B_3_8,B_18_4+B_3_9,B_18_5+B_3_10],[B_19_1+B_4_6,B_19_2+B_4_7,B_19_3+B_4_8,B_19_4+B_4_9,B_19_5+B_4_10],[B_20_1+B_5_6,B_20_2+B_5_7,B_20_3+B_5_8,B_20_4+B_5_9,B_20_5+B_5_10]]),Matrix(5, 1, [[C_1_1+C_6_1],[C_2_1+C_7_1],[C_3_1+C_8_1],[C_4_1+C_9_1],[C_5_1+C_10_1]])))+Trace(Mul(Matrix(1, 5, [[A_1_1+A_1_11,A_1_2+A_1_12,A_1_3+A_1_13,A_1_4+A_1_14,A_1_5+A_1_15]]),Matrix(5, 5, [[B_1_11,B_1_12,B_1_13,B_1_14,B_1_15],[B_2_11,B_2_12,B_2_13,B_2_14,B_2_15],[B_3_11,B_3_12,B_3_13,B_3_14,B_3_15],[B_4_11,B_4_12,B_4_13,B_4_14,B_4_15],[B_5_11,B_5_12,B_5_13,B_5_14,B_5_15]]),Matrix(5, 1, [[C_1_1+C_11_1+C_1_3+C_11_3],[C_2_1+C_12_1+C_2_3+C_12_3],[C_3_1+C_13_1+C_3_3+C_13_3],[C_4_1+C_14_1+C_4_3+C_14_3],[C_5_1+C_15_1+C_5_3+C_15_3]])))+Trace(Mul(Matrix(1, 5, [[A_1_1-A_3_1,A_1_2-A_3_2,A_1_3-A_3_3,A_1_4-A_3_4,A_1_5-A_3_5]]),Matrix(5, 5, [[B_1_1-B_11_1-B_1_6,B_1_2-B_11_2-B_1_7,B_1_3-B_11_3-B_1_8,B_1_4-B_11_4-B_1_9,B_1_5-B_11_5-B_1_10],[B_2_1-B_12_1-B_2_6,B_2_2-B_12_2-B_2_7,B_2_3-B_12_3-B_2_8,B_2_4-B_12_4-B_2_9,B_2_5-B_12_5-B_2_10],[B_3_1-B_13_1-B_3_6,B_3_2-B_13_2-B_3_7,B_3_3-B_13_3-B_3_8,B_3_4-B_13_4-B_3_9,B_3_5-B_13_5-B_3_10],[B_4_1-B_14_1-B_4_6,B_4_2-B_14_2-B_4_7,B_4_3-B_14_3-B_4_8,B_4_4-B_14_4-B_4_9,B_4_5-B_14_5-B_4_10],[B_5_1-B_15_1-B_5_6,B_5_2-B_15_2-B_5_7,B_5_3-B_15_3-B_5_8,B_5_4-B_15_4-B_5_9,B_5_5-B_15_5-B_5_10]]),Matrix(5, 1, [[C_1_1],[C_2_1],[C_3_1],[C_4_1],[C_5_1]])))+Trace(Mul(Matrix(2, 5, [[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5],[A_3_1+A_1_6,A_3_2+A_1_7,A_3_3+A_1_8,A_3_4+A_1_9,A_3_5+A_1_10]]),Matrix(5, 5, [[B_6_1-B_1_6,B_6_2-B_1_7,B_6_3-B_1_8,B_6_4-B_1_9,B_6_5-B_1_10],[B_7_1-B_2_6,B_7_2-B_2_7,B_7_3-B_2_8,B_7_4-B_2_9,B_7_5-B_2_10],[B_8_1-B_3_6,B_8_2-B_3_7,B_8_3-B_3_8,B_8_4-B_3_9,B_8_5-B_3_10],[B_9_1-B_4_6,B_9_2-B_4_7,B_9_3-B_4_8,B_9_4-B_4_9,B_9_5-B_4_10],[B_10_1-B_5_6,B_10_2-B_5_7,B_10_3-B_5_8,B_10_4-B_5_9,B_10_5-B_5_10]]),Matrix(5, 2, [[-C_6_2,C_1_1-C_6_3],[-C_7_2,C_2_1-C_7_3],[-C_8_2,C_3_1-C_8_3],[-C_9_2,C_4_1-C_9_3],[-C_10_2,C_5_1-C_10_3]])))+Trace(Mul(Matrix(2, 5, [[A_2_1+A_2_6,A_2_2+A_2_7,A_2_3+A_2_8,A_2_4+A_2_9,A_2_5+A_2_10],[A_3_1+A_3_6,A_3_2+A_3_7,A_3_3+A_3_8,A_3_4+A_3_9,A_3_5+A_3_10]]),Matrix(5, 5, [[B_6_1+B_1_16,B_6_2+B_1_17,B_6_3+B_1_18,B_6_4+B_1_19,B_6_5+B_1_20],[B_7_1+B_2_16,B_7_2+B_2_17,B_7_3+B_2_18,B_7_4+B_2_19,B_7_5+B_2_20],[B_8_1+B_3_16,B_8_2+B_3_17,B_8_3+B_3_18,B_8_4+B_3_19,B_8_5+B_3_20],[B_9_1+B_4_16,B_9_2+B_4_17,B_9_3+B_4_18,B_9_4+B_4_19,B_9_5+B_4_20],[B_10_1+B_5_16,B_10_2+B_5_17,B_10_3+B_5_18,B_10_4+B_5_19,B_10_5+B_5_20]]),Matrix(5, 2, [[C_1_2+C_6_2,C_1_3+C_6_3],[C_2_2+C_7_2,C_2_3+C_7_3],[C_3_2+C_8_2,C_3_3+C_8_3],[C_4_2+C_9_2,C_4_3+C_9_3],[C_5_2+C_10_2,C_5_3+C_10_3]])))+Trace(Mul(Matrix(1, 5, [[A_1_6+A_1_16,A_1_7+A_1_17,A_1_8+A_1_18,A_1_9+A_1_19,A_1_10+A_1_20]]),Matrix(5, 5, [[-B_16_1+B_16_6,-B_16_2+B_16_7,-B_16_3+B_16_8,-B_16_4+B_16_9,-B_16_5+B_16_10],[-B_17_1+B_17_6,-B_17_2+B_17_7,-B_17_3+B_17_8,-B_17_4+B_17_9,-B_17_5+B_17_10],[-B_18_1+B_18_6,-B_18_2+B_18_7,-B_18_3+B_18_8,-B_18_4+B_18_9,-B_18_5+B_18_10],[-B_19_1+B_19_6,-B_19_2+B_19_7,-B_19_3+B_19_8,-B_19_4+B_19_9,-B_19_5+B_19_10],[-B_20_1+B_20_6,-B_20_2+B_20_7,-B_20_3+B_20_8,-B_20_4+B_20_9,-B_20_5+B_20_10]]),Matrix(5, 1, [[C_6_1+C_16_1],[C_7_1+C_17_1],[C_8_1+C_18_1],[C_9_1+C_19_1],[C_10_1+C_20_1]])))+Trace(Mul(Matrix(2, 5, [[-A_2_6,-A_2_7,-A_2_8,-A_2_9,-A_2_10],[A_1_6-A_3_6,A_1_7-A_3_7,A_1_8-A_3_8,A_1_9-A_3_9,A_1_10-A_3_10]]),Matrix(5, 5, [[B_6_1-B_6_6+B_11_6-B_1_16+B_6_16,B_6_2-B_6_7+B_11_7-B_1_17+B_6_17,B_6_3-B_6_8+B_11_8-B_1_18+B_6_18,B_6_4-B_6_9+B_11_9-B_1_19+B_6_19,B_6_5-B_6_10+B_11_10-B_1_20+B_6_20],[B_7_1-B_7_6+B_12_6-B_2_16+B_7_16,B_7_2-B_7_7+B_12_7-B_2_17+B_7_17,B_7_3-B_7_8+B_12_8-B_2_18+B_7_18,B_7_4-B_7_9+B_12_9-B_2_19+B_7_19,B_7_5-B_7_10+B_12_10-B_2_20+B_7_20],[B_8_1-B_8_6+B_13_6-B_3_16+B_8_16,B_8_2-B_8_7+B_13_7-B_3_17+B_8_17,B_8_3-B_8_8+B_13_8-B_3_18+B_8_18,B_8_4-B_8_9+B_13_9-B_3_19+B_8_19,B_8_5-B_8_10+B_13_10-B_3_20+B_8_20],[B_9_1-B_9_6+B_14_6-B_4_16+B_9_16,B_9_2-B_9_7+B_14_7-B_4_17+B_9_17,B_9_3-B_9_8+B_14_8-B_4_18+B_9_18,B_9_4-B_9_9+B_14_9-B_4_19+B_9_19,B_9_5-B_9_10+B_14_10-B_4_20+B_9_20],[B_10_1-B_10_6+B_15_6-B_5_16+B_10_16,B_10_2-B_10_7+B_15_7-B_5_17+B_10_17,B_10_3-B_10_8+B_15_8-B_5_18+B_10_18,B_10_4-B_10_9+B_15_9-B_5_19+B_10_19,B_10_5-B_10_10+B_15_10-B_5_20+B_10_20]]),Matrix(5, 2, [[C_6_2,C_6_3],[C_7_2,C_7_3],[C_8_2,C_8_3],[C_9_2,C_9_3],[C_10_2,C_10_3]])))+Trace(Mul(Matrix(2, 5, [[A_2_6+A_2_11,A_2_7+A_2_12,A_2_8+A_2_13,A_2_9+A_2_14,A_2_10+A_2_15],[A_3_6+A_3_11,A_3_7+A_3_12,A_3_8+A_3_13,A_3_9+A_3_14,A_3_10+A_3_15]]),Matrix(5, 5, [[B_6_11,B_6_12,B_6_13,B_6_14,B_6_15],[B_7_11,B_7_12,B_7_13,B_7_14,B_7_15],[B_8_11,B_8_12,B_8_13,B_8_14,B_8_15],[B_9_11,B_9_12,B_9_13,B_9_14,B_9_15],[B_10_11,B_10_12,B_10_13,B_10_14,B_10_15]]),Matrix(5, 2, [[C_6_2+C_11_2,C_6_1+C_11_1+C_6_3+C_11_3],[C_7_2+C_12_2,C_7_1+C_12_1+C_7_3+C_12_3],[C_8_2+C_13_2,C_8_1+C_13_1+C_8_3+C_13_3],[C_9_2+C_14_2,C_9_1+C_14_1+C_9_3+C_14_3],[C_10_2+C_15_2,C_10_1+C_15_1+C_10_3+C_15_3]])))+Trace(Mul(Matrix(2, 5, [[A_2_6+A_2_16,A_2_7+A_2_17,A_2_8+A_2_18,A_2_9+A_2_19,A_2_10+A_2_20],[A_3_6+A_3_16,A_3_7+A_3_17,A_3_8+A_3_18,A_3_9+A_3_19,A_3_10+A_3_20]]),Matrix(5, 5, [[-B_1_16+B_6_16,-B_1_17+B_6_17,-B_1_18+B_6_18,-B_1_19+B_6_19,-B_1_20+B_6_20],[-B_2_16+B_7_16,-B_2_17+B_7_17,-B_2_18+B_7_18,-B_2_19+B_7_19,-B_2_20+B_7_20],[-B_3_16+B_8_16,-B_3_17+B_8_17,-B_3_18+B_8_18,-B_3_19+B_8_19,-B_3_20+B_8_20],[-B_4_16+B_9_16,-B_4_17+B_9_17,-B_4_18+B_9_18,-B_4_19+B_9_19,-B_4_20+B_9_20],[-B_5_16+B_10_16,-B_5_17+B_10_17,-B_5_18+B_10_18,-B_5_19+B_10_19,-B_5_20+B_10_20]]),Matrix(5, 2, [[C_6_2+C_16_2,C_6_3+C_16_3],[C_7_2+C_17_2,C_7_3+C_17_3],[C_8_2+C_18_2,C_8_3+C_18_3],[C_9_2+C_19_2,C_9_3+C_19_3],[C_10_2+C_20_2,C_10_3+C_20_3]])))+Trace(Mul(Matrix(1, 5, [[A_1_11+A_1_16,A_1_12+A_1_17,A_1_13+A_1_18,A_1_14+A_1_19,A_1_15+A_1_20]]),Matrix(5, 5, [[B_16_11,B_16_12,B_16_13,B_16_14,B_16_15],[B_17_11,B_17_12,B_17_13,B_17_14,B_17_15],[B_18_11,B_18_12,B_18_13,B_18_14,B_18_15],[B_19_11,B_19_12,B_19_13,B_19_14,B_19_15],[B_20_11,B_20_12,B_20_13,B_20_14,B_20_15]]),Matrix(5, 1, [[C_11_1+C_16_1+C_11_3+C_16_3],[C_12_1+C_17_1+C_12_3+C_17_3],[C_13_1+C_18_1+C_13_3+C_18_3],[C_14_1+C_19_1+C_14_3+C_19_3],[C_15_1+C_20_1+C_15_3+C_20_3]])))+Trace(Mul(Matrix(1, 5, [[A_1_16-A_3_16,A_1_17-A_3_17,A_1_18-A_3_18,A_1_19-A_3_19,A_1_20-A_3_20]]),Matrix(5, 5, [[B_16_1-B_16_6+B_1_16-B_11_16+B_16_16,B_16_2-B_16_7+B_1_17-B_11_17+B_16_17,B_16_3-B_16_8+B_1_18-B_11_18+B_16_18,B_16_4-B_16_9+B_1_19-B_11_19+B_16_19,B_16_5-B_16_10+B_1_20-B_11_20+B_16_20],[B_17_1-B_17_6+B_2_16-B_12_16+B_17_16,B_17_2-B_17_7+B_2_17-B_12_17+B_17_17,B_17_3-B_17_8+B_2_18-B_12_18+B_17_18,B_17_4-B_17_9+B_2_19-B_12_19+B_17_19,B_17_5-B_17_10+B_2_20-B_12_20+B_17_20],[B_18_1-B_18_6+B_3_16-B_13_16+B_18_16,B_18_2-B_18_7+B_3_17-B_13_17+B_18_17,B_18_3-B_18_8+B_3_18-B_13_18+B_18_18,B_18_4-B_18_9+B_3_19-B_13_19+B_18_19,B_18_5-B_18_10+B_3_20-B_13_20+B_18_20],[B_19_1-B_19_6+B_4_16-B_14_16+B_19_16,B_19_2-B_19_7+B_4_17-B_14_17+B_19_17,B_19_3-B_19_8+B_4_18-B_14_18+B_19_18,B_19_4-B_19_9+B_4_19-B_14_19+B_19_19,B_19_5-B_19_10+B_4_20-B_14_20+B_19_20],[B_20_1-B_20_6+B_5_16-B_15_16+B_20_16,B_20_2-B_20_7+B_5_17-B_15_17+B_20_17,B_20_3-B_20_8+B_5_18-B_15_18+B_20_18,B_20_4-B_20_9+B_5_19-B_15_19+B_20_19,B_20_5-B_20_10+B_5_20-B_15_20+B_20_20]]),Matrix(5, 1, [[C_16_1],[C_17_1],[C_18_1],[C_19_1],[C_20_1]])))+Trace(Mul(Matrix(2, 5, [[A_2_16,A_2_17,A_2_18,A_2_19,A_2_20],[A_1_6+A_3_16,A_1_7+A_3_17,A_1_8+A_3_18,A_1_9+A_3_19,A_1_10+A_3_20]]),Matrix(5, 5, [[B_16_1-B_16_6-B_1_16+B_6_16,B_16_2-B_16_7-B_1_17+B_6_17,B_16_3-B_16_8-B_1_18+B_6_18,B_16_4-B_16_9-B_1_19+B_6_19,B_16_5-B_16_10-B_1_20+B_6_20],[B_17_1-B_17_6-B_2_16+B_7_16,B_17_2-B_17_7-B_2_17+B_7_17,B_17_3-B_17_8-B_2_18+B_7_18,B_17_4-B_17_9-B_2_19+B_7_19,B_17_5-B_17_10-B_2_20+B_7_20],[B_18_1-B_18_6-B_3_16+B_8_16,B_18_2-B_18_7-B_3_17+B_8_17,B_18_3-B_18_8-B_3_18+B_8_18,B_18_4-B_18_9-B_3_19+B_8_19,B_18_5-B_18_10-B_3_20+B_8_20],[B_19_1-B_19_6-B_4_16+B_9_16,B_19_2-B_19_7-B_4_17+B_9_17,B_19_3-B_19_8-B_4_18+B_9_18,B_19_4-B_19_9-B_4_19+B_9_19,B_19_5-B_19_10-B_4_20+B_9_20],[B_20_1-B_20_6-B_5_16+B_10_16,B_20_2-B_20_7-B_5_17+B_10_17,B_20_3-B_20_8-B_5_18+B_10_18,B_20_4-B_20_9-B_5_19+B_10_19,B_20_5-B_20_10-B_5_20+B_10_20]]),Matrix(5, 2, [[-C_6_2,C_16_1-C_6_3],[-C_7_2,C_17_1-C_7_3],[-C_8_2,C_18_1-C_8_3],[-C_9_2,C_19_1-C_9_3],[-C_10_2,C_20_1-C_10_3]])))+Trace(Mul(Matrix(2, 5, [[-A_2_1,-A_2_2,-A_2_3,-A_2_4,-A_2_5],[A_1_1-A_3_1+A_1_11,A_1_2-A_3_2+A_1_12,A_1_3-A_3_3+A_1_13,A_1_4-A_3_4+A_1_14,A_1_5-A_3_5+A_1_15]]),Matrix(5, 5, [[B_11_1-B_1_11,B_11_2-B_1_12,B_11_3-B_1_13,B_11_4-B_1_14,B_11_5-B_1_15],[B_12_1-B_2_11,B_12_2-B_2_12,B_12_3-B_2_13,B_12_4-B_2_14,B_12_5-B_2_15],[B_13_1-B_3_11,B_13_2-B_3_12,B_13_3-B_3_13,B_13_4-B_3_14,B_13_5-B_3_15],[B_14_1-B_4_11,B_14_2-B_4_12,B_14_3-B_4_13,B_14_4-B_4_14,B_14_5-B_4_15],[B_15_1-B_5_11,B_15_2-B_5_12,B_15_3-B_5_13,B_15_4-B_5_14,B_15_5-B_5_15]]),Matrix(5, 2, [[C_1_2+C_11_2,C_1_1+C_1_3+C_11_3],[C_2_2+C_12_2,C_2_1+C_2_3+C_12_3],[C_3_2+C_13_2,C_3_1+C_3_3+C_13_3],[C_4_2+C_14_2,C_4_1+C_4_3+C_14_3],[C_5_2+C_15_2,C_5_1+C_5_3+C_15_3]])))+Trace(Mul(Matrix(2, 5, [[-A_2_6-A_2_11,-A_2_7-A_2_12,-A_2_8-A_2_13,-A_2_9-A_2_14,-A_2_10-A_2_15],[A_1_6-A_3_6-A_3_11,A_1_7-A_3_7-A_3_12,A_1_8-A_3_8-A_3_13,A_1_9-A_3_9-A_3_14,A_1_10-A_3_10-A_3_15]]),Matrix(5, 5, [[-B_11_6+B_6_11,-B_11_7+B_6_12,-B_11_8+B_6_13,-B_11_9+B_6_14,-B_11_10+B_6_15],[-B_12_6+B_7_11,-B_12_7+B_7_12,-B_12_8+B_7_13,-B_12_9+B_7_14,-B_12_10+B_7_15],[-B_13_6+B_8_11,-B_13_7+B_8_12,-B_13_8+B_8_13,-B_13_9+B_8_14,-B_13_10+B_8_15],[-B_14_6+B_9_11,-B_14_7+B_9_12,-B_14_8+B_9_13,-B_14_9+B_9_14,-B_14_10+B_9_15],[-B_15_6+B_10_11,-B_15_7+B_10_12,-B_15_8+B_10_13,-B_15_9+B_10_14,-B_15_10+B_10_15]]),Matrix(5, 2, [[C_6_2,C_6_1+C_11_1+C_6_3],[C_7_2,C_7_1+C_12_1+C_7_3],[C_8_2,C_8_1+C_13_1+C_8_3],[C_9_2,C_9_1+C_14_1+C_9_3],[C_10_2,C_10_1+C_15_1+C_10_3]])))+Trace(Mul(Matrix(2, 5, [[-A_2_16,-A_2_17,-A_2_18,-A_2_19,-A_2_20],[A_1_11+A_1_16-A_3_16,A_1_12+A_1_17-A_3_17,A_1_13+A_1_18-A_3_18,A_1_14+A_1_19-A_3_19,A_1_15+A_1_20-A_3_20]]),Matrix(5, 5, [[-B_16_11+B_11_16,-B_16_12+B_11_17,-B_16_13+B_11_18,-B_16_14+B_11_19,-B_16_15+B_11_20],[-B_17_11+B_12_16,-B_17_12+B_12_17,-B_17_13+B_12_18,-B_17_14+B_12_19,-B_17_15+B_12_20],[-B_18_11+B_13_16,-B_18_12+B_13_17,-B_18_13+B_13_18,-B_18_14+B_13_19,-B_18_15+B_13_20],[-B_19_11+B_14_16,-B_19_12+B_14_17,-B_19_13+B_14_18,-B_19_14+B_14_19,-B_19_15+B_14_20],[-B_20_11+B_15_16,-B_20_12+B_15_17,-B_20_13+B_15_18,-B_20_14+B_15_19,-B_20_15+B_15_20]]),Matrix(5, 2, [[C_11_2+C_16_2,C_16_1+C_11_3+C_16_3],[C_17_2+C_12_2,C_17_1+C_12_3+C_17_3],[C_13_2+C_18_2,C_18_1+C_13_3+C_18_3],[C_14_2+C_19_2,C_19_1+C_14_3+C_19_3],[C_15_2+C_20_2,C_20_1+C_15_3+C_20_3]])))+Trace(Mul(Matrix(1, 5, [[A_1_6-A_3_6+A_1_11-A_3_11,A_1_7-A_3_7+A_1_12-A_3_12,A_1_8-A_3_8+A_1_13-A_3_13,A_1_9-A_3_9+A_1_14-A_3_14,A_1_10-A_3_10+A_1_15-A_3_15]]),Matrix(5, 5, [[B_11_6,B_11_7,B_11_8,B_11_9,B_11_10],[B_12_6,B_12_7,B_12_8,B_12_9,B_12_10],[B_13_6,B_13_7,B_13_8,B_13_9,B_13_10],[B_14_6,B_14_7,B_14_8,B_14_9,B_14_10],[B_15_6,B_15_7,B_15_8,B_15_9,B_15_10]]),Matrix(5, 1, [[C_6_1+C_11_1],[C_7_1+C_12_1],[C_8_1+C_13_1],[C_9_1+C_14_1],[C_10_1+C_15_1]])))+Trace(Mul(Matrix(2, 5, [[A_2_16,A_2_17,A_2_18,A_2_19,A_2_20],[A_1_1+A_1_6-A_1_16+A_3_16,A_1_2+A_1_7-A_1_17+A_3_17,A_1_3+A_1_8-A_1_18+A_3_18,A_1_4+A_1_9-A_1_19+A_3_19,A_1_5+A_1_10-A_1_20+A_3_20]]),Matrix(5, 5, [[-B_16_1+B_1_16,-B_16_2+B_1_17,-B_16_3+B_1_18,-B_16_4+B_1_19,-B_16_5+B_1_20],[-B_17_1+B_2_16,-B_17_2+B_2_17,-B_17_3+B_2_18,-B_17_4+B_2_19,-B_17_5+B_2_20],[-B_18_1+B_3_16,-B_18_2+B_3_17,-B_18_3+B_3_18,-B_18_4+B_3_19,-B_18_5+B_3_20],[-B_19_1+B_4_16,-B_19_2+B_4_17,-B_19_3+B_4_18,-B_19_4+B_4_19,-B_19_5+B_4_20],[-B_20_1+B_5_16,-B_20_2+B_5_17,-B_20_3+B_5_18,-B_20_4+B_5_19,-B_20_5+B_5_20]]),Matrix(5, 2, [[-C_1_2-C_6_2+C_16_2,C_16_1-C_1_3-C_6_3+C_16_3],[-C_2_2-C_7_2+C_17_2,C_17_1-C_2_3-C_7_3+C_17_3],[-C_3_2-C_8_2+C_18_2,C_18_1-C_3_3-C_8_3+C_18_3],[-C_4_2-C_9_2+C_19_2,C_19_1-C_4_3-C_9_3+C_19_3],[-C_5_2-C_10_2+C_20_2,C_20_1-C_5_3-C_10_3+C_20_3]])))+Trace(Mul(Matrix(2, 5, [[-A_2_1-A_2_6+A_2_16,-A_2_2-A_2_7+A_2_17,-A_2_3-A_2_8+A_2_18,-A_2_4-A_2_9+A_2_19,-A_2_5-A_2_10+A_2_20],[A_1_1-A_3_1+A_1_6-A_3_6-A_1_16+A_3_16,A_1_2-A_3_2+A_1_7-A_3_7-A_1_17+A_3_17,A_1_3-A_3_3+A_1_8-A_3_8-A_1_18+A_3_18,A_1_4-A_3_4+A_1_9-A_3_9-A_1_19+A_3_19,A_1_5-A_3_5+A_1_10-A_3_10-A_1_20+A_3_20]]),Matrix(5, 5, [[B_1_16,B_1_17,B_1_18,B_1_19,B_1_20],[B_2_16,B_2_17,B_2_18,B_2_19,B_2_20],[B_3_16,B_3_17,B_3_18,B_3_19,B_3_20],[B_4_16,B_4_17,B_4_18,B_4_19,B_4_20],[B_5_16,B_5_17,B_5_18,B_5_19,B_5_20]]),Matrix(5, 2, [[C_1_2+C_6_2-C_16_2,C_1_3+C_6_3-C_16_3],[C_2_2+C_7_2-C_17_2,C_2_3+C_7_3-C_17_3],[C_3_2+C_8_2-C_18_2,C_3_3+C_8_3-C_18_3],[C_4_2+C_9_2-C_19_2,C_4_3+C_9_3-C_19_3],[C_5_2+C_10_2-C_20_2,C_5_3+C_10_3-C_20_3]])))+Trace(Mul(Matrix(1, 5, [[-A_1_1-A_1_6+A_1_16,-A_1_2-A_1_7+A_1_17,-A_1_3-A_1_8+A_1_18,-A_1_4-A_1_9+A_1_19,-A_1_5-A_1_10+A_1_20]]),Matrix(5, 5, [[B_16_1,B_16_2,B_16_3,B_16_4,B_16_5],[B_17_1,B_17_2,B_17_3,B_17_4,B_17_5],[B_18_1,B_18_2,B_18_3,B_18_4,B_18_5],[B_19_1,B_19_2,B_19_3,B_19_4,B_19_5],[B_20_1,B_20_2,B_20_3,B_20_4,B_20_5]]),Matrix(5, 1, [[C_1_1+C_6_1-C_16_1+C_1_3+C_6_3-C_16_3],[C_2_1+C_7_1-C_17_1+C_2_3+C_7_3-C_17_3],[C_3_1+C_8_1-C_18_1+C_3_3+C_8_3-C_18_3],[C_4_1+C_9_1-C_19_1+C_4_3+C_9_3-C_19_3],[C_5_1+C_10_1-C_20_1+C_5_3+C_10_3-C_20_3]])))+Trace(Mul(Matrix(2, 5, [[A_2_1+A_2_11,A_2_2+A_2_12,A_2_3+A_2_13,A_2_4+A_2_14,A_2_5+A_2_15],[-A_1_1+A_3_1-A_1_11+A_3_11,-A_1_2+A_3_2-A_1_12+A_3_12,-A_1_3+A_3_3-A_1_13+A_3_13,-A_1_4+A_3_4-A_1_14+A_3_14,-A_1_5+A_3_5-A_1_15+A_3_15]]),Matrix(5, 5, [[B_11_1,B_11_2,B_11_3,B_11_4,B_11_5],[B_12_1,B_12_2,B_12_3,B_12_4,B_12_5],[B_13_1,B_13_2,B_13_3,B_13_4,B_13_5],[B_14_1,B_14_2,B_14_3,B_14_4,B_14_5],[B_15_1,B_15_2,B_15_3,B_15_4,B_15_5]]),Matrix(5, 2, [[C_1_2+C_11_2,C_1_3+C_11_3],[C_2_2+C_12_2,C_2_3+C_12_3],[C_3_2+C_13_2,C_3_3+C_13_3],[C_4_2+C_14_2,C_4_3+C_14_3],[C_5_2+C_15_2,C_5_3+C_15_3]])))+Trace(Mul(Matrix(2, 5, [[A_2_11+A_2_16,A_2_12+A_2_17,A_2_13+A_2_18,A_2_14+A_2_19,A_2_15+A_2_20],[-A_1_11+A_3_11-A_1_16+A_3_16,-A_1_12+A_3_12-A_1_17+A_3_17,-A_1_13+A_3_13-A_1_18+A_3_18,-A_1_14+A_3_14-A_1_19+A_3_19,-A_1_15+A_3_15-A_1_20+A_3_20]]),Matrix(5, 5, [[B_11_16,B_11_17,B_11_18,B_11_19,B_11_20],[B_12_16,B_12_17,B_12_18,B_12_19,B_12_20],[B_13_16,B_13_17,B_13_18,B_13_19,B_13_20],[B_14_16,B_14_17,B_14_18,B_14_19,B_14_20],[B_15_16,B_15_17,B_15_18,B_15_19,B_15_20]]),Matrix(5, 2, [[C_11_2+C_16_2,C_11_3+C_16_3],[C_17_2+C_12_2,C_12_3+C_17_3],[C_13_2+C_18_2,C_13_3+C_18_3],[C_14_2+C_19_2,C_14_3+C_19_3],[C_15_2+C_20_2,C_15_3+C_20_3]])))

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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