Description of fast matrix multiplication algorithm: ⟨4×14×22:844⟩

Algorithm type

8X4Y6Z4+2X3Y7Z4+4X4Y5Z4+2X3Y6Z4+2X4Y5Z3+20X4Y4Z4+2X3Y5Z4+11X2Y8Z2+2XY9Z2+2X4Y4Z3+8X2Y7Z2+4X4Y3Z3+2X2Y7Z+31X2Y6Z2+14XY8Z+2XY7Z2+2X2Y6Z+18X2Y5Z2+6XY7Z+75X2Y4Z2+42XY6Z+40X2Y3Z2+12XY5Z+99X2Y2Z2+82XY4Z+8X2YZ2+64XY3Z+154XY2Z+126XYZ8X4Y6Z42X3Y7Z44X4Y5Z42X3Y6Z42X4Y5Z320X4Y4Z42X3Y5Z411X2Y8Z22XY9Z22X4Y4Z38X2Y7Z24X4Y3Z32X2Y7Z31X2Y6Z214XY8Z2XY7Z22X2Y6Z18X2Y5Z26XY7Z75X2Y4Z242XY6Z40X2Y3Z212XY5Z99X2Y2Z282XY4Z8X2YZ264XY3Z154XY2Z126XYZ8*X^4*Y^6*Z^4+2*X^3*Y^7*Z^4+4*X^4*Y^5*Z^4+2*X^3*Y^6*Z^4+2*X^4*Y^5*Z^3+20*X^4*Y^4*Z^4+2*X^3*Y^5*Z^4+11*X^2*Y^8*Z^2+2*X*Y^9*Z^2+2*X^4*Y^4*Z^3+8*X^2*Y^7*Z^2+4*X^4*Y^3*Z^3+2*X^2*Y^7*Z+31*X^2*Y^6*Z^2+14*X*Y^8*Z+2*X*Y^7*Z^2+2*X^2*Y^6*Z+18*X^2*Y^5*Z^2+6*X*Y^7*Z+75*X^2*Y^4*Z^2+42*X*Y^6*Z+40*X^2*Y^3*Z^2+12*X*Y^5*Z+99*X^2*Y^2*Z^2+82*X*Y^4*Z+8*X^2*Y*Z^2+64*X*Y^3*Z+154*X*Y^2*Z+126*X*Y*Z

Algorithm definition

The algorithm ⟨4×14×22:844⟩ could be constructed using the following decomposition:

⟨4×14×22:844⟩ = ⟨2×5×7:56⟩ + ⟨2×5×8:64⟩ + ⟨2×4×8:52⟩ + ⟨2×5×8:64⟩ + ⟨2×5×7:56⟩ + ⟨2×5×7:56⟩ + ⟨2×5×7:56⟩ + ⟨2×5×8:64⟩ + ⟨2×4×7:46⟩ + ⟨2×5×7:56⟩ + ⟨2×5×7:56⟩ + ⟨2×5×7:56⟩ + ⟨2×5×8:64⟩ + ⟨2×4×7:46⟩ + ⟨2×4×8:52⟩.

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_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_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_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_14B_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_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_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_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_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_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_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_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_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_10_1B_10_2B_10_3B_10_4B_10_5B_10_6B_10_7B_10_8B_10_9B_10_10B_10_11B_10_12B_10_13B_10_14B_10_15B_10_16B_10_17B_10_18B_10_19B_10_20B_10_21B_10_22B_11_1B_11_2B_11_3B_11_4B_11_5B_11_6B_11_7B_11_8B_11_9B_11_10B_11_11B_11_12B_11_13B_11_14B_11_15B_11_16B_11_17B_11_18B_11_19B_11_20B_11_21B_11_22B_12_1B_12_2B_12_3B_12_4B_12_5B_12_6B_12_7B_12_8B_12_9B_12_10B_12_11B_12_12B_12_13B_12_14B_12_15B_12_16B_12_17B_12_18B_12_19B_12_20B_12_21B_12_22B_13_1B_13_2B_13_3B_13_4B_13_5B_13_6B_13_7B_13_8B_13_9B_13_10B_13_11B_13_12B_13_13B_13_14B_13_15B_13_16B_13_17B_13_18B_13_19B_13_20B_13_21B_13_22B_14_1B_14_2B_14_3B_14_4B_14_5B_14_6B_14_7B_14_8B_14_9B_14_10B_14_11B_14_12B_14_13B_14_14B_14_15B_14_16B_14_17B_14_18B_14_19B_14_20B_14_21B_14_22C_1_1C_1_2C_1_3C_1_4C_2_1C_2_2C_2_3C_2_4C_3_1C_3_2C_3_3C_3_4C_4_1C_4_2C_4_3C_4_4C_5_1C_5_2C_5_3C_5_4C_6_1C_6_2C_6_3C_6_4C_7_1C_7_2C_7_3C_7_4C_8_1C_8_2C_8_3C_8_4C_9_1C_9_2C_9_3C_9_4C_10_1C_10_2C_10_3C_10_4C_11_1C_11_2C_11_3C_11_4C_12_1C_12_2C_12_3C_12_4C_13_1C_13_2C_13_3C_13_4C_14_1C_14_2C_14_3C_14_4C_15_1C_15_2C_15_3C_15_4C_16_1C_16_2C_16_3C_16_4C_17_1C_17_2C_17_3C_17_4C_18_1C_18_2C_18_3C_18_4C_19_1C_19_2C_19_3C_19_4C_20_1C_20_2C_20_3C_20_4C_21_1C_21_2C_21_3C_21_4C_22_1C_22_2C_22_3C_22_4=TraceMulA_3_10A_3_11A_3_12A_3_13A_3_14A_4_10A_4_11A_4_12A_4_13A_4_14B_4_6+B_10_6+B_10_7B_4_14+B_10_14+B_10_8B_4_1+B_10_1+B_10_9B_4_2+B_10_2+B_10_10B_4_3+B_10_3+B_10_11B_4_4+B_10_4+B_10_12B_4_5+B_10_5+B_10_13B_1_6+B_11_6+B_11_7B_1_14+B_11_14+B_11_8B_1_1+B_11_1+B_11_9B_1_2+B_11_2+B_11_10B_1_3+B_11_3+B_11_11B_1_4+B_11_4+B_11_12B_1_5+B_11_5+B_11_13B_2_6+B_12_6+B_12_7B_2_14+B_12_14+B_12_8B_2_1+B_12_1+B_12_9B_2_2+B_12_2+B_12_10B_2_3+B_12_3+B_12_11B_2_4+B_12_4+B_12_12B_2_5+B_12_5+B_12_13B_3_6+B_13_6+B_13_7B_3_14+B_13_14+B_13_8B_3_1+B_13_1+B_13_9B_3_2+B_13_2+B_13_10B_3_3+B_13_3+B_13_11B_3_4+B_13_4+B_13_12B_3_5+B_13_5+B_13_13B_14_6+B_14_7B_14_8+B_14_14B_14_1+B_14_9B_14_2+B_14_10B_14_3+B_14_11B_14_4+B_14_12B_14_5+B_14_13C_6_1+C_6_3C_6_2+C_6_4C_14_1+C_14_3C_14_2+C_14_4C_1_1+C_1_3C_1_2+C_1_4C_2_1+C_2_3C_2_2+C_2_4C_3_1+C_3_3C_3_2+C_3_4C_4_1+C_4_3C_4_2+C_4_4C_5_1+C_5_3C_5_4+C_5_2+TraceMulA_1_4-A_3_10A_1_1-A_3_11A_1_2-A_3_12A_1_3-A_3_13-A_3_14A_2_4-A_4_10A_2_1-A_4_11A_2_2-A_4_12A_2_3-A_4_13-A_4_14B_4_6+B_10_15B_4_14+B_10_16B_4_1+B_10_17B_4_2+B_10_18B_4_3+B_10_19B_4_4+B_10_20B_4_5+B_10_21B_10_22B_1_6+B_11_15B_1_14+B_11_16B_1_1+B_11_17B_1_2+B_11_18B_1_3+B_11_19B_1_4+B_11_20B_1_5+B_11_21B_11_22B_2_6+B_12_15B_2_14+B_12_16B_2_1+B_12_17B_2_2+B_12_18B_2_3+B_12_19B_2_4+B_12_20B_2_5+B_12_21B_12_22B_3_6+B_13_15B_3_14+B_13_16B_3_1+B_13_17B_3_2+B_13_18B_3_3+B_13_19B_3_4+B_13_20B_3_5+B_13_21B_13_22B_14_15B_14_16B_14_17B_14_18B_14_19B_14_20B_14_21B_14_22C_6_1-C_15_3C_6_2-C_15_4C_14_1-C_16_3C_14_2-C_16_4C_1_1-C_17_3C_1_2-C_17_4C_2_1-C_18_3C_2_2-C_18_4C_3_1-C_19_3C_3_2-C_19_4C_4_1-C_20_3C_4_2-C_20_4C_5_1-C_21_3C_5_2-C_21_4-C_22_3-C_22_4+TraceMulA_1_4A_1_1A_1_2A_1_3A_2_4A_2_1A_2_2A_2_3B_4_7-B_4_15-B_10_15B_4_8-B_4_16-B_10_16B_4_9-B_4_17-B_10_17B_4_10-B_4_18-B_10_18B_4_11-B_4_19-B_10_19B_4_12-B_4_20-B_10_20B_4_13-B_4_21-B_10_21-B_4_22-B_10_22B_1_7-B_1_15-B_11_15B_1_8-B_1_16-B_11_16B_1_9-B_1_17-B_11_17B_1_10-B_1_18-B_11_18B_1_11-B_1_19-B_11_19B_1_12-B_1_20-B_11_20B_1_13-B_1_21-B_11_21-B_1_22-B_11_22B_2_7-B_2_15-B_12_15B_2_8-B_2_16-B_12_16B_2_9-B_2_17-B_12_17B_2_10-B_2_18-B_12_18B_2_11-B_2_19-B_12_19B_2_12-B_2_20-B_12_20B_2_13-B_2_21-B_12_21-B_2_22-B_12_22B_3_7-B_3_15-B_13_15B_3_8-B_3_16-B_13_16B_3_9-B_3_17-B_13_17B_3_10-B_3_18-B_13_18B_3_11-B_3_19-B_13_19B_3_12-B_3_20-B_13_20B_3_13-B_3_21-B_13_21-B_3_22-B_13_22-C_15_1-C_15_3-C_15_2-C_15_4-C_16_1-C_16_3-C_16_2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14_6B_14_15B_9_14B_14_14B_14_16B_9_1B_14_1B_14_17B_9_2B_14_2B_14_18B_9_3B_14_3B_14_19B_9_4B_14_4B_14_20B_9_5B_14_5B_14_21C_6_1C_6_2C_14_1C_14_2C_1_1C_1_2C_2_1C_2_2C_3_1C_3_2C_4_1C_4_2C_5_1C_5_2TraceMulA_1_5A_1_6A_1_7A_1_8A_1_9A_2_5A_2_6A_2_7A_2_8A_2_9B_5_7B_10_7B_5_15B_5_8B_10_8B_5_16B_5_9B_10_9B_5_17B_5_10B_10_10B_5_18B_5_11B_10_11B_5_19B_5_12B_10_12B_5_20B_5_13B_10_13B_5_21B_6_7B_11_7B_6_15B_6_8B_11_8B_6_16B_6_9B_11_9B_6_17B_6_10B_11_10B_6_18B_6_11B_11_11B_6_19B_6_12B_11_12B_6_20B_6_13B_11_13B_6_21B_7_7B_12_7B_7_15B_7_8B_12_8B_7_16B_7_9B_12_9B_7_17B_7_10B_12_10B_7_18B_7_11B_12_11B_7_19B_7_12B_12_12B_7_20B_7_13B_12_13B_7_21B_8_7B_13_7B_8_15B_8_8B_13_8B_8_16B_8_9B_13_9B_8_17B_8_10B_13_10B_8_18B_8_11B_13_11B_8_19B_8_12B_13_12B_8_20B_8_13B_13_13B_8_21B_9_7B_14_7B_9_15B_9_8B_14_8B_9_16B_9_9B_14_9B_9_17B_9_10B_14_10B_9_18B_9_11B_14_11B_9_19B_9_12B_14_12B_9_20B_9_13B_14_13B_9_21C_7_1C_7_2C_8_1C_8_2C_9_1C_9_2C_10_1C_10_2C_11_1C_11_2C_12_1C_12_2C_13_1C_13_2TraceMulA_1_10A_1_5A_3_10A_1_6A_1_11A_3_11A_1_7A_1_12A_3_12A_1_8A_1_13A_3_13A_1_9A_1_14A_3_14A_2_10A_2_5A_4_10A_2_6A_2_11A_4_11A_2_7A_2_12A_4_12A_2_8A_2_13A_4_13A_2_9A_2_14A_4_14B_5_6B_10_7B_10_8B_5_14B_5_1B_10_9B_5_2B_10_10B_5_3B_10_11B_5_4B_10_12B_5_5B_10_13B_6_6B_11_7B_11_8B_6_14B_6_1B_11_9B_6_2B_11_10B_6_3B_11_11B_6_4B_11_12B_6_5B_11_13B_7_6B_12_7B_12_8B_7_14B_7_1B_12_9B_7_2B_12_10B_7_3B_12_11B_7_4B_12_12B_7_5B_12_13B_8_6B_13_7B_13_8B_8_14B_8_1B_13_9B_8_2B_13_10B_8_3B_13_11B_8_4B_13_12B_8_5B_13_13B_9_6B_14_7B_14_8B_9_14B_9_1B_14_9B_9_2B_14_10B_9_3B_14_11B_9_4B_14_12B_9_5B_14_13C_6_1C_6_3C_7_3C_6_2C_6_4C_7_4C_14_1C_14_3C_8_3C_14_2C_14_4C_8_4C_1_1C_1_3C_9_3C_1_2C_1_4C_9_4C_2_1C_2_3C_10_3C_2_2C_2_4C_10_4C_3_1C_3_3C_11_3C_3_2C_3_4C_11_4C_4_1C_4_3C_12_3C_4_2C_4_4C_12_4C_5_1C_5_3C_13_3C_5_4C_5_2C_13_4TraceMulA_1_4A_3_4A_3_5A_1_1A_3_1A_3_6A_1_2A_3_2A_3_7A_1_3A_3_3A_3_8A_3_9A_2_4A_4_4A_4_5A_2_1A_4_1A_4_6A_2_2A_4_2A_4_7A_2_3A_4_3A_4_8A_4_9B_4_7B_5_15B_4_8B_5_16B_4_9B_5_17B_4_10B_5_18B_4_11B_5_19B_4_12B_5_20B_4_13B_5_21B_5_22B_1_7B_6_15B_1_8B_6_16B_1_9B_6_17B_1_10B_6_18B_1_11B_6_19B_1_12B_6_20B_1_13B_6_21B_6_22B_2_7B_7_15B_2_8B_7_16B_2_9B_7_17B_2_10B_7_18B_2_11B_7_19B_2_12B_7_20B_2_13B_7_21B_7_22B_3_7B_8_15B_3_8B_8_16B_3_9B_8_17B_3_10B_8_18B_3_11B_8_19B_3_12B_8_20B_3_13B_8_21B_8_22B_9_15B_9_16B_9_17B_9_18B_9_19B_9_20B_9_21B_9_22C_15_1C_7_1C_15_3C_15_2C_7_2C_15_4C_8_1C_16_1C_16_3C_8_2C_16_2C_16_4C_9_1C_17_1C_17_3C_9_2C_17_2C_17_4C_10_1C_18_1C_18_3C_10_2C_18_2C_18_4C_11_1C_19_1C_19_3C_11_2C_19_2C_19_4C_12_1C_20_1C_20_3C_12_2C_20_2C_20_4C_13_1C_21_1C_21_3C_13_2C_21_2C_21_4C_22_1C_22_3C_22_2C_22_4TraceMulA_3_4A_3_5A_3_1A_3_6A_3_2A_3_7A_3_8A_3_3A_4_4A_4_5A_4_1A_4_6A_4_2A_4_7A_4_3A_4_8B_4_7B_4_8B_4_9B_4_10B_4_11B_4_12B_4_13B_1_7B_1_8B_1_9B_1_10B_1_11B_1_12B_1_13B_2_7B_2_8B_2_9B_2_10B_2_11B_2_12B_2_13B_3_7B_3_8B_3_9B_3_10B_3_11B_3_12B_3_13C_15_1C_7_1C_7_3C_15_3C_15_2C_7_2C_7_4C_15_4C_8_1C_16_1C_8_3C_16_3C_8_2C_16_2C_8_4C_16_4C_9_1C_17_1C_9_3C_17_3C_9_2C_17_2C_9_4C_17_4C_10_1C_18_1C_10_3C_18_3C_10_2C_18_2C_10_4C_18_4C_11_1C_19_1C_11_3C_19_3C_11_2C_19_2C_11_4C_19_4C_12_1C_20_1C_12_3C_20_3C_12_2C_20_2C_12_4C_20_4C_13_1C_21_1C_13_3C_21_3C_13_2C_21_2C_13_4C_21_4TraceMulA_1_5A_3_5A_1_10A_3_10A_1_6A_3_6A_1_11A_3_11A_1_7A_3_7A_1_12A_3_12A_1_8A_3_8A_1_13A_3_13A_1_9A_3_9A_1_14A_3_14A_4_5A_2_5A_2_10A_4_10A_4_6A_2_6A_2_11A_4_11A_2_7A_4_7A_2_12A_4_12A_2_8A_4_8A_2_13A_4_13A_2_9A_4_9A_2_14A_4_14B_5_6B_5_14B_5_1B_5_2B_5_3B_5_4B_5_5B_6_6B_6_14B_6_1B_6_2B_6_3B_6_4B_6_5B_7_6B_7_14B_7_1B_7_2B_7_3B_7_4B_7_5B_8_6B_8_14B_8_1B_8_2B_8_3B_8_4B_8_5B_9_6B_9_14B_9_1B_9_2B_9_3B_9_4B_9_5C_7_3C_6_3C_6_4C_7_4C_8_3C_14_3C_8_4C_14_4C_1_3C_9_3C_1_4C_9_4C_2_3C_10_3C_2_4C_10_4C_3_3C_11_3C_3_4C_11_4C_4_3C_12_3C_4_4C_12_4C_5_3C_13_3C_5_4C_13_4TraceMulA_1_10A_1_5A_1_6A_1_11A_1_7A_1_12A_1_8A_1_13A_1_9A_1_14A_2_10A_2_5A_2_6A_2_11A_2_7A_2_12A_2_8A_2_13A_2_9A_2_14B_10_7B_10_8B_10_9B_10_10B_10_11B_10_12B_10_13B_11_7B_11_8B_11_9B_11_10B_11_11B_11_12B_11_13B_12_7B_12_8B_12_9B_12_10B_12_11B_12_12B_12_13B_13_7B_13_8B_13_9B_13_10B_13_11B_13_12B_13_13B_14_7B_14_8B_14_9B_14_10B_14_11B_14_12B_14_13C_6_1C_7_1C_6_3C_7_3C_6_2C_7_2C_6_4C_7_4C_8_1C_14_1C_14_3C_8_3C_8_2C_14_2C_14_4C_8_4C_1_1C_9_1C_1_3C_9_3C_1_2C_9_2C_1_4C_9_4C_2_1C_10_1C_2_3C_10_3C_2_2C_10_2C_2_4C_10_4C_3_1C_11_1C_3_3C_11_3C_3_2C_11_2C_3_4C_11_4C_4_1C_12_1C_4_3C_12_3C_4_2C_12_2C_4_4C_12_4C_5_1C_13_1C_5_3C_13_3C_5_2C_13_2C_5_4C_13_4TraceMulA_3_5A_3_6A_3_7A_3_8A_3_9A_4_5A_4_6A_4_7A_4_8A_4_9B_5_6B_4_7B_5_7B_4_8B_5_14B_5_8B_5_1B_4_9B_5_9B_5_2B_4_10B_5_10B_5_3B_4_11B_5_11B_5_4B_4_12B_5_12B_5_5B_4_13B_5_13B_6_6B_1_7B_6_7B_1_8B_6_14B_6_8B_6_1B_1_9B_6_9B_6_2B_1_10B_6_10B_6_3B_1_11B_6_11B_6_4B_1_12B_6_12B_6_5B_1_13B_6_13B_7_6B_2_7B_7_7B_2_8B_7_14B_7_8B_7_1B_2_9B_7_9B_7_2B_2_10B_7_10B_7_3B_2_11B_7_11B_7_4B_2_12B_7_12B_7_5B_2_13B_7_13B_8_6B_3_7B_8_7B_3_8B_8_14B_8_8B_8_1B_3_9B_8_9B_8_2B_3_10B_8_10B_8_3B_3_11B_8_11B_8_4B_3_12B_8_12B_8_5B_3_13B_8_13B_9_6B_9_7B_9_8B_9_14B_9_1B_9_9B_9_2B_9_10B_9_3B_9_11B_9_4B_9_12B_9_5B_9_13C_7_3C_7_4C_8_3C_8_4C_9_3C_9_4C_10_3C_10_4C_11_3C_11_4C_12_3C_12_4C_13_3C_13_4TraceMulA_1_4A_3_4A_1_5A_3_5A_1_1A_3_1A_1_6A_3_6A_1_2A_3_2A_1_7A_3_7A_1_3A_3_3A_1_8A_3_8A_1_9A_3_9A_2_4A_4_4A_2_5A_4_5A_2_1A_4_1A_2_6A_4_6A_2_2A_4_2A_2_7A_4_7A_2_3A_4_3A_2_8A_4_8A_2_9A_4_9B_5_15B_5_16B_5_17B_5_18B_5_19B_5_20B_5_21B_5_22B_6_15B_6_16B_6_17B_6_18B_6_19B_6_20B_6_21B_6_22B_7_15B_7_16B_7_17B_7_18B_7_19B_7_20B_7_21B_7_22B_8_15B_8_16B_8_17B_8_18B_8_19B_8_20B_8_21B_8_22B_9_15B_9_16B_9_17B_9_18B_9_19B_9_20B_9_21B_9_22C_7_1C_15_1C_7_2C_15_2C_8_1C_16_1C_8_2C_16_2C_9_1C_17_1C_9_2C_17_2C_10_1C_18_1C_10_2C_18_2C_11_1C_19_1C_11_2C_19_2C_12_1C_20_1C_12_2C_20_2C_13_1C_21_1C_13_2C_21_2C_22_1C_22_2TraceMulA_3_4A_3_10A_3_1A_3_11A_3_2A_3_12A_3_3A_3_13A_4_4A_4_10A_4_1A_4_11A_4_2A_4_12A_4_3A_4_13B_4_6B_4_14B_4_1B_4_2B_4_3B_4_4B_4_5B_1_6B_1_14B_1_1B_1_2B_1_3B_1_4B_1_5B_2_6B_2_14B_2_1B_2_2B_2_3B_2_4B_2_5B_3_6B_3_14B_3_1B_3_2B_3_3B_3_4B_3_5C_6_3C_15_3C_6_4C_15_4C_14_3C_16_3C_14_4C_16_4C_1_3C_17_3C_1_4C_17_4C_2_3C_18_3C_2_4C_18_4C_3_3C_19_3C_3_4C_19_4C_4_3C_20_3C_4_4C_20_4C_5_3C_21_3C_5_4C_21_4TraceMulA_1_4A_3_4A_1_1A_3_1A_1_2A_3_2A_1_3A_3_3A_2_4A_4_4A_2_1A_4_1A_2_2A_4_2A_2_3A_4_3B_4_6B_4_15B_5_15B_4_14B_4_16B_5_16B_4_1B_4_17B_5_17B_4_2B_4_18B_5_18B_4_3B_4_19B_5_19B_4_4B_4_20B_5_20B_4_5B_4_21B_5_21B_4_22B_5_22B_1_6B_1_15B_6_15B_1_14B_1_16B_6_16B_1_1B_1_17B_6_17B_1_2B_1_18B_6_18B_1_3B_1_19B_6_19B_1_4B_1_20B_6_20B_1_5B_1_21B_6_21B_1_22B_6_22B_2_6B_2_15B_7_15B_2_14B_2_16B_7_16B_2_1B_2_17B_7_17B_2_2B_2_18B_7_18B_2_3B_2_19B_7_19B_2_4B_2_20B_7_20B_2_5B_2_21B_7_21B_2_22B_7_22B_3_6B_3_15B_8_15B_3_14B_3_16B_8_16B_3_1B_3_17B_8_17B_3_2B_3_18B_8_18B_3_3B_3_19B_8_19B_3_4B_3_20B_8_20B_3_5B_3_21B_8_21B_3_22B_8_22C_15_3C_15_4C_16_3C_16_4C_17_3C_17_4C_18_3C_18_4C_19_3C_19_4C_20_3C_20_4C_21_3C_21_4C_22_3C_22_4Trace(Mul(Matrix(4, 14, [[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_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_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_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]]),Matrix(14, 22, [[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_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_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_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_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_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_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_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_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_10_1,B_10_2,B_10_3,B_10_4,B_10_5,B_10_6,B_10_7,B_10_8,B_10_9,B_10_10,B_10_11,B_10_12,B_10_13,B_10_14,B_10_15,B_10_16,B_10_17,B_10_18,B_10_19,B_10_20,B_10_21,B_10_22],[B_11_1,B_11_2,B_11_3,B_11_4,B_11_5,B_11_6,B_11_7,B_11_8,B_11_9,B_11_10,B_11_11,B_11_12,B_11_13,B_11_14,B_11_15,B_11_16,B_11_17,B_11_18,B_11_19,B_11_20,B_11_21,B_11_22],[B_12_1,B_12_2,B_12_3,B_12_4,B_12_5,B_12_6,B_12_7,B_12_8,B_12_9,B_12_10,B_12_11,B_12_12,B_12_13,B_12_14,B_12_15,B_12_16,B_12_17,B_12_18,B_12_19,B_12_20,B_12_21,B_12_22],[B_13_1,B_13_2,B_13_3,B_13_4,B_13_5,B_13_6,B_13_7,B_13_8,B_13_9,B_13_10,B_13_11,B_13_12,B_13_13,B_13_14,B_13_15,B_13_16,B_13_17,B_13_18,B_13_19,B_13_20,B_13_21,B_13_22],[B_14_1,B_14_2,B_14_3,B_14_4,B_14_5,B_14_6,B_14_7,B_14_8,B_14_9,B_14_10,B_14_11,B_14_12,B_14_13,B_14_14,B_14_15,B_14_16,B_14_17,B_14_18,B_14_19,B_14_20,B_14_21,B_14_22]]),Matrix(22, 4, [[C_1_1,C_1_2,C_1_3,C_1_4],[C_2_1,C_2_2,C_2_3,C_2_4],[C_3_1,C_3_2,C_3_3,C_3_4],[C_4_1,C_4_2,C_4_3,C_4_4],[C_5_1,C_5_2,C_5_3,C_5_4],[C_6_1,C_6_2,C_6_3,C_6_4],[C_7_1,C_7_2,C_7_3,C_7_4],[C_8_1,C_8_2,C_8_3,C_8_4],[C_9_1,C_9_2,C_9_3,C_9_4],[C_10_1,C_10_2,C_10_3,C_10_4],[C_11_1,C_11_2,C_11_3,C_11_4],[C_12_1,C_12_2,C_12_3,C_12_4],[C_13_1,C_13_2,C_13_3,C_13_4],[C_14_1,C_14_2,C_14_3,C_14_4],[C_15_1,C_15_2,C_15_3,C_15_4],[C_16_1,C_16_2,C_16_3,C_16_4],[C_17_1,C_17_2,C_17_3,C_17_4],[C_18_1,C_18_2,C_18_3,C_18_4],[C_19_1,C_19_2,C_19_3,C_19_4],[C_20_1,C_20_2,C_20_3,C_20_4],[C_21_1,C_21_2,C_21_3,C_21_4],[C_22_1,C_22_2,C_22_3,C_22_4]]))) = Trace(Mul(Matrix(2, 5, [[A_3_10,A_3_11,A_3_12,A_3_13,A_3_14],[A_4_10,A_4_11,A_4_12,A_4_13,A_4_14]]),Matrix(5, 7, [[B_4_6+B_10_6+B_10_7,B_4_14+B_10_14+B_10_8,B_4_1+B_10_1+B_10_9,B_4_2+B_10_2+B_10_10,B_4_3+B_10_3+B_10_11,B_4_4+B_10_4+B_10_12,B_4_5+B_10_5+B_10_13],[B_1_6+B_11_6+B_11_7,B_1_14+B_11_14+B_11_8,B_1_1+B_11_1+B_11_9,B_1_2+B_11_2+B_11_10,B_1_3+B_11_3+B_11_11,B_1_4+B_11_4+B_11_12,B_1_5+B_11_5+B_11_13],[B_2_6+B_12_6+B_12_7,B_2_14+B_12_14+B_12_8,B_2_1+B_12_1+B_12_9,B_2_2+B_12_2+B_12_10,B_2_3+B_12_3+B_12_11,B_2_4+B_12_4+B_12_12,B_2_5+B_12_5+B_12_13],[B_3_6+B_13_6+B_13_7,B_3_14+B_13_14+B_13_8,B_3_1+B_13_1+B_13_9,B_3_2+B_13_2+B_13_10,B_3_3+B_13_3+B_13_11,B_3_4+B_13_4+B_13_12,B_3_5+B_13_5+B_13_13],[B_14_6+B_14_7,B_14_8+B_14_14,B_14_1+B_14_9,B_14_2+B_14_10,B_14_3+B_14_11,B_14_4+B_14_12,B_14_5+B_14_13]]),Matrix(7, 2, [[C_6_1+C_6_3,C_6_2+C_6_4],[C_14_1+C_14_3,C_14_2+C_14_4],[C_1_1+C_1_3,C_1_2+C_1_4],[C_2_1+C_2_3,C_2_2+C_2_4],[C_3_1+C_3_3,C_3_2+C_3_4],[C_4_1+C_4_3,C_4_2+C_4_4],[C_5_1+C_5_3,C_5_4+C_5_2]])))+Trace(Mul(Matrix(2, 5, [[A_1_4-A_3_10,A_1_1-A_3_11,A_1_2-A_3_12,A_1_3-A_3_13,-A_3_14],[A_2_4-A_4_10,A_2_1-A_4_11,A_2_2-A_4_12,A_2_3-A_4_13,-A_4_14]]),Matrix(5, 8, [[B_4_6+B_10_15,B_4_14+B_10_16,B_4_1+B_10_17,B_4_2+B_10_18,B_4_3+B_10_19,B_4_4+B_10_20,B_4_5+B_10_21,B_10_22],[B_1_6+B_11_15,B_1_14+B_11_16,B_1_1+B_11_17,B_1_2+B_11_18,B_1_3+B_11_19,B_1_4+B_11_20,B_1_5+B_11_21,B_11_22],[B_2_6+B_12_15,B_2_14+B_12_16,B_2_1+B_12_17,B_2_2+B_12_18,B_2_3+B_12_19,B_2_4+B_12_20,B_2_5+B_12_21,B_12_22],[B_3_6+B_13_15,B_3_14+B_13_16,B_3_1+B_13_17,B_3_2+B_13_18,B_3_3+B_13_19,B_3_4+B_13_20,B_3_5+B_13_21,B_13_22],[B_14_15,B_14_16,B_14_17,B_14_18,B_14_19,B_14_20,B_14_21,B_14_22]]),Matrix(8, 2, [[C_6_1-C_15_3,C_6_2-C_15_4],[C_14_1-C_16_3,C_14_2-C_16_4],[C_1_1-C_17_3,C_1_2-C_17_4],[C_2_1-C_18_3,C_2_2-C_18_4],[C_3_1-C_19_3,C_3_2-C_19_4],[C_4_1-C_20_3,C_4_2-C_20_4],[C_5_1-C_21_3,C_5_2-C_21_4],[-C_22_3,-C_22_4]])))+Trace(Mul(Matrix(2, 4, [[A_1_4,A_1_1,A_1_2,A_1_3],[A_2_4,A_2_1,A_2_2,A_2_3]]),Matrix(4, 8, [[B_4_7-B_4_15-B_10_15,B_4_8-B_4_16-B_10_16,B_4_9-B_4_17-B_10_17,B_4_10-B_4_18-B_10_18,B_4_11-B_4_19-B_10_19,B_4_12-B_4_20-B_10_20,B_4_13-B_4_21-B_10_21,-B_4_22-B_10_22],[B_1_7-B_1_15-B_11_15,B_1_8-B_1_16-B_11_16,B_1_9-B_1_17-B_11_17,B_1_10-B_1_18-B_11_18,B_1_11-B_1_19-B_11_19,B_1_12-B_1_20-B_11_20,B_1_13-B_1_21-B_11_21,-B_1_22-B_11_22],[B_2_7-B_2_15-B_12_15,B_2_8-B_2_16-B_12_16,B_2_9-B_2_17-B_12_17,B_2_10-B_2_18-B_12_18,B_2_11-B_2_19-B_12_19,B_2_12-B_2_20-B_12_20,B_2_13-B_2_21-B_12_21,-B_2_22-B_12_22],[B_3_7-B_3_15-B_13_15,B_3_8-B_3_16-B_13_16,B_3_9-B_3_17-B_13_17,B_3_10-B_3_18-B_13_18,B_3_11-B_3_19-B_13_19,B_3_12-B_3_20-B_13_20,B_3_13-B_3_21-B_13_21,-B_3_22-B_13_22]]),Matrix(8, 2, [[-C_15_1-C_15_3,-C_15_2-C_15_4],[-C_16_1-C_16_3,-C_16_2-C_16_4],[-C_17_1-C_17_3,-C_17_2-C_17_4],[-C_18_1-C_18_3,-C_18_2-C_18_4],[-C_19_1-C_19_3,-C_19_2-C_19_4],[-C_20_1-C_20_3,-C_20_2-C_20_4],[-C_21_1-C_21_3,-C_21_2-C_21_4],[-C_22_1-C_22_3,-C_22_2-C_22_4]])))+Trace(Mul(Matrix(2, 5, [[A_1_4-A_1_10,A_1_1-A_1_11,A_1_2-A_1_12,A_1_3-A_1_13,-A_1_14],[A_2_4-A_2_10,A_2_1-A_2_11,A_2_2-A_2_12,A_2_3-A_2_13,-A_2_14]]),Matrix(5, 8, [[B_10_15,B_10_16,B_10_17,B_10_18,B_10_19,B_10_20,B_10_21,B_10_22],[B_11_15,B_11_16,B_11_17,B_11_18,B_11_19,B_11_20,B_11_21,B_11_22],[B_12_15,B_12_16,B_12_17,B_12_18,B_12_19,B_12_20,B_12_21,B_12_22],[B_13_15,B_13_16,B_13_17,B_13_18,B_13_19,B_13_20,B_13_21,B_13_22],[B_14_15,B_14_16,B_14_17,B_14_18,B_14_19,B_14_20,B_14_21,B_14_22]]),Matrix(8, 2, [[-C_6_1-C_15_1,-C_6_2-C_15_2],[-C_14_1-C_16_1,-C_14_2-C_16_2],[-C_1_1-C_17_1,-C_1_2-C_17_2],[-C_2_1-C_18_1,-C_2_2-C_18_2],[-C_3_1-C_19_1,-C_3_2-C_19_2],[-C_4_1-C_20_1,-C_4_2-C_20_2],[-C_5_1-C_21_1,-C_5_2-C_21_2],[-C_22_1,-C_22_2]])))+Trace(Mul(Matrix(2, 5, [[A_1_10-A_3_10,A_1_11-A_3_11,A_1_12-A_3_12,A_1_13-A_3_13,A_1_14-A_3_14],[A_2_10-A_4_10,A_2_11-A_4_11,A_2_12-A_4_12,A_2_13-A_4_13,A_2_14-A_4_14]]),Matrix(5, 7, [[B_5_6+B_10_6-B_10_15,B_10_14+B_5_14-B_10_16,B_5_1+B_10_1-B_10_17,B_5_2+B_10_2-B_10_18,B_5_3+B_10_3-B_10_19,B_5_4+B_10_4-B_10_20,B_5_5+B_10_5-B_10_21],[B_6_6+B_11_6-B_11_15,B_6_14+B_11_14-B_11_16,B_6_1+B_11_1-B_11_17,B_6_2+B_11_2-B_11_18,B_6_3+B_11_3-B_11_19,B_6_4+B_11_4-B_11_20,B_6_5+B_11_5-B_11_21],[B_7_6+B_12_6-B_12_15,B_7_14+B_12_14-B_12_16,B_7_1+B_12_1-B_12_17,B_7_2+B_12_2-B_12_18,B_7_3+B_12_3-B_12_19,B_7_4+B_12_4-B_12_20,B_7_5+B_12_5-B_12_21],[B_8_6+B_13_6-B_13_15,B_8_14+B_13_14-B_13_16,B_8_1+B_13_1-B_13_17,B_8_2+B_13_2-B_13_18,B_8_3+B_13_3-B_13_19,B_8_4+B_13_4-B_13_20,B_8_5+B_13_5-B_13_21],[B_9_6+B_14_6-B_14_15,B_9_14+B_14_14-B_14_16,B_9_1+B_14_1-B_14_17,B_9_2+B_14_2-B_14_18,B_9_3+B_14_3-B_14_19,B_9_4+B_14_4-B_14_20,B_9_5+B_14_5-B_14_21]]),Matrix(7, 2, [[C_6_1,C_6_2],[C_14_1,C_14_2],[C_1_1,C_1_2],[C_2_1,C_2_2],[C_3_1,C_3_2],[C_4_1,C_4_2],[C_5_1,C_5_2]])))+Trace(Mul(Matrix(2, 5, [[A_1_5,A_1_6,A_1_7,A_1_8,A_1_9],[A_2_5,A_2_6,A_2_7,A_2_8,A_2_9]]),Matrix(5, 7, [[B_5_7+B_10_7-B_5_15,B_5_8+B_10_8-B_5_16,B_5_9+B_10_9-B_5_17,B_5_10+B_10_10-B_5_18,B_5_11+B_10_11-B_5_19,B_5_12+B_10_12-B_5_20,B_5_13+B_10_13-B_5_21],[B_6_7+B_11_7-B_6_15,B_6_8+B_11_8-B_6_16,B_6_9+B_11_9-B_6_17,B_6_10+B_11_10-B_6_18,B_6_11+B_11_11-B_6_19,B_6_12+B_11_12-B_6_20,B_6_13+B_11_13-B_6_21],[B_7_7+B_12_7-B_7_15,B_7_8+B_12_8-B_7_16,B_7_9+B_12_9-B_7_17,B_7_10+B_12_10-B_7_18,B_7_11+B_12_11-B_7_19,B_7_12+B_12_12-B_7_20,B_7_13+B_12_13-B_7_21],[B_8_7+B_13_7-B_8_15,B_8_8+B_13_8-B_8_16,B_8_9+B_13_9-B_8_17,B_8_10+B_13_10-B_8_18,B_8_11+B_13_11-B_8_19,B_8_12+B_13_12-B_8_20,B_8_13+B_13_13-B_8_21],[B_9_7+B_14_7-B_9_15,B_9_8+B_14_8-B_9_16,B_9_9+B_14_9-B_9_17,B_9_10+B_14_10-B_9_18,B_9_11+B_14_11-B_9_19,B_9_12+B_14_12-B_9_20,B_9_13+B_14_13-B_9_21]]),Matrix(7, 2, [[C_7_1,C_7_2],[C_8_1,C_8_2],[C_9_1,C_9_2],[C_10_1,C_10_2],[C_11_1,C_11_2],[C_12_1,C_12_2],[C_13_1,C_13_2]])))+Trace(Mul(Matrix(2, 5, [[-A_1_10+A_1_5+A_3_10,A_1_6-A_1_11+A_3_11,A_1_7-A_1_12+A_3_12,A_1_8-A_1_13+A_3_13,A_1_9-A_1_14+A_3_14],[-A_2_10+A_2_5+A_4_10,A_2_6-A_2_11+A_4_11,A_2_7-A_2_12+A_4_12,A_2_8-A_2_13+A_4_13,A_2_9-A_2_14+A_4_14]]),Matrix(5, 7, [[B_5_6-B_10_7,-B_10_8+B_5_14,B_5_1-B_10_9,B_5_2-B_10_10,B_5_3-B_10_11,B_5_4-B_10_12,B_5_5-B_10_13],[B_6_6-B_11_7,-B_11_8+B_6_14,B_6_1-B_11_9,B_6_2-B_11_10,B_6_3-B_11_11,B_6_4-B_11_12,B_6_5-B_11_13],[B_7_6-B_12_7,-B_12_8+B_7_14,B_7_1-B_12_9,B_7_2-B_12_10,B_7_3-B_12_11,B_7_4-B_12_12,B_7_5-B_12_13],[B_8_6-B_13_7,-B_13_8+B_8_14,B_8_1-B_13_9,B_8_2-B_13_10,B_8_3-B_13_11,B_8_4-B_13_12,B_8_5-B_13_13],[B_9_6-B_14_7,-B_14_8+B_9_14,B_9_1-B_14_9,B_9_2-B_14_10,B_9_3-B_14_11,B_9_4-B_14_12,B_9_5-B_14_13]]),Matrix(7, 2, [[C_6_1+C_6_3-C_7_3,C_6_2+C_6_4-C_7_4],[C_14_1+C_14_3-C_8_3,C_14_2+C_14_4-C_8_4],[C_1_1+C_1_3-C_9_3,C_1_2+C_1_4-C_9_4],[C_2_1+C_2_3-C_10_3,C_2_2+C_2_4-C_10_4],[C_3_1+C_3_3-C_11_3,C_3_2+C_3_4-C_11_4],[C_4_1+C_4_3-C_12_3,C_4_2+C_4_4-C_12_4],[C_5_1+C_5_3-C_13_3,C_5_4+C_5_2-C_13_4]])))+Trace(Mul(Matrix(2, 5, [[A_1_4-A_3_4+A_3_5,A_1_1-A_3_1+A_3_6,A_1_2-A_3_2+A_3_7,A_1_3-A_3_3+A_3_8,A_3_9],[A_2_4-A_4_4+A_4_5,A_2_1-A_4_1+A_4_6,A_2_2-A_4_2+A_4_7,A_2_3-A_4_3+A_4_8,A_4_9]]),Matrix(5, 8, [[B_4_7+B_5_15,B_4_8+B_5_16,B_4_9+B_5_17,B_4_10+B_5_18,B_4_11+B_5_19,B_4_12+B_5_20,B_4_13+B_5_21,B_5_22],[B_1_7+B_6_15,B_1_8+B_6_16,B_1_9+B_6_17,B_1_10+B_6_18,B_1_11+B_6_19,B_1_12+B_6_20,B_1_13+B_6_21,B_6_22],[B_2_7+B_7_15,B_2_8+B_7_16,B_2_9+B_7_17,B_2_10+B_7_18,B_2_11+B_7_19,B_2_12+B_7_20,B_2_13+B_7_21,B_7_22],[B_3_7+B_8_15,B_3_8+B_8_16,B_3_9+B_8_17,B_3_10+B_8_18,B_3_11+B_8_19,B_3_12+B_8_20,B_3_13+B_8_21,B_8_22],[B_9_15,B_9_16,B_9_17,B_9_18,B_9_19,B_9_20,B_9_21,B_9_22]]),Matrix(8, 2, [[C_15_1+C_7_1+C_15_3,C_15_2+C_7_2+C_15_4],[C_8_1+C_16_1+C_16_3,C_8_2+C_16_2+C_16_4],[C_9_1+C_17_1+C_17_3,C_9_2+C_17_2+C_17_4],[C_10_1+C_18_1+C_18_3,C_10_2+C_18_2+C_18_4],[C_11_1+C_19_1+C_19_3,C_11_2+C_19_2+C_19_4],[C_12_1+C_20_1+C_20_3,C_12_2+C_20_2+C_20_4],[C_13_1+C_21_1+C_21_3,C_13_2+C_21_2+C_21_4],[C_22_1+C_22_3,C_22_2+C_22_4]])))+Trace(Mul(Matrix(2, 4, [[A_3_4-A_3_5,A_3_1-A_3_6,A_3_2-A_3_7,-A_3_8+A_3_3],[A_4_4-A_4_5,A_4_1-A_4_6,A_4_2-A_4_7,A_4_3-A_4_8]]),Matrix(4, 7, [[B_4_7,B_4_8,B_4_9,B_4_10,B_4_11,B_4_12,B_4_13],[B_1_7,B_1_8,B_1_9,B_1_10,B_1_11,B_1_12,B_1_13],[B_2_7,B_2_8,B_2_9,B_2_10,B_2_11,B_2_12,B_2_13],[B_3_7,B_3_8,B_3_9,B_3_10,B_3_11,B_3_12,B_3_13]]),Matrix(7, 2, [[C_15_1+C_7_1+C_7_3+C_15_3,C_15_2+C_7_2+C_7_4+C_15_4],[C_8_1+C_16_1+C_8_3+C_16_3,C_8_2+C_16_2+C_8_4+C_16_4],[C_9_1+C_17_1+C_9_3+C_17_3,C_9_2+C_17_2+C_9_4+C_17_4],[C_10_1+C_18_1+C_10_3+C_18_3,C_10_2+C_18_2+C_10_4+C_18_4],[C_11_1+C_19_1+C_11_3+C_19_3,C_11_2+C_19_2+C_11_4+C_19_4],[C_12_1+C_20_1+C_12_3+C_20_3,C_12_2+C_20_2+C_12_4+C_20_4],[C_13_1+C_21_1+C_13_3+C_21_3,C_13_2+C_21_2+C_13_4+C_21_4]])))+Trace(Mul(Matrix(2, 5, [[A_1_5-A_3_5-A_1_10+A_3_10,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_4_5+A_2_5-A_2_10+A_4_10,-A_4_6+A_2_6-A_2_11+A_4_11,A_2_7-A_4_7-A_2_12+A_4_12,A_2_8-A_4_8-A_2_13+A_4_13,A_2_9-A_4_9-A_2_14+A_4_14]]),Matrix(5, 7, [[B_5_6,B_5_14,B_5_1,B_5_2,B_5_3,B_5_4,B_5_5],[B_6_6,B_6_14,B_6_1,B_6_2,B_6_3,B_6_4,B_6_5],[B_7_6,B_7_14,B_7_1,B_7_2,B_7_3,B_7_4,B_7_5],[B_8_6,B_8_14,B_8_1,B_8_2,B_8_3,B_8_4,B_8_5],[B_9_6,B_9_14,B_9_1,B_9_2,B_9_3,B_9_4,B_9_5]]),Matrix(7, 2, [[C_7_3-C_6_3,-C_6_4+C_7_4],[C_8_3-C_14_3,C_8_4-C_14_4],[-C_1_3+C_9_3,-C_1_4+C_9_4],[-C_2_3+C_10_3,-C_2_4+C_10_4],[-C_3_3+C_11_3,-C_3_4+C_11_4],[-C_4_3+C_12_3,-C_4_4+C_12_4],[-C_5_3+C_13_3,-C_5_4+C_13_4]])))+Trace(Mul(Matrix(2, 5, [[-A_1_10+A_1_5,A_1_6-A_1_11,A_1_7-A_1_12,A_1_8-A_1_13,A_1_9-A_1_14],[-A_2_10+A_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]]),Matrix(5, 7, [[B_10_7,B_10_8,B_10_9,B_10_10,B_10_11,B_10_12,B_10_13],[B_11_7,B_11_8,B_11_9,B_11_10,B_11_11,B_11_12,B_11_13],[B_12_7,B_12_8,B_12_9,B_12_10,B_12_11,B_12_12,B_12_13],[B_13_7,B_13_8,B_13_9,B_13_10,B_13_11,B_13_12,B_13_13],[B_14_7,B_14_8,B_14_9,B_14_10,B_14_11,B_14_12,B_14_13]]),Matrix(7, 2, [[C_6_1-C_7_1+C_6_3-C_7_3,C_6_2-C_7_2+C_6_4-C_7_4],[-C_8_1+C_14_1+C_14_3-C_8_3,-C_8_2+C_14_2+C_14_4-C_8_4],[C_1_1-C_9_1+C_1_3-C_9_3,C_1_2-C_9_2+C_1_4-C_9_4],[C_2_1-C_10_1+C_2_3-C_10_3,C_2_2-C_10_2+C_2_4-C_10_4],[C_3_1-C_11_1+C_3_3-C_11_3,C_3_2-C_11_2+C_3_4-C_11_4],[C_4_1-C_12_1+C_4_3-C_12_3,C_4_2-C_12_2+C_4_4-C_12_4],[C_5_1-C_13_1+C_5_3-C_13_3,C_5_2-C_13_2+C_5_4-C_13_4]])))+Trace(Mul(Matrix(2, 5, [[A_3_5,A_3_6,A_3_7,A_3_8,A_3_9],[A_4_5,A_4_6,A_4_7,A_4_8,A_4_9]]),Matrix(5, 7, [[B_5_6+B_4_7+B_5_7,B_4_8+B_5_14+B_5_8,B_5_1+B_4_9+B_5_9,B_5_2+B_4_10+B_5_10,B_5_3+B_4_11+B_5_11,B_5_4+B_4_12+B_5_12,B_5_5+B_4_13+B_5_13],[B_6_6+B_1_7+B_6_7,B_1_8+B_6_14+B_6_8,B_6_1+B_1_9+B_6_9,B_6_2+B_1_10+B_6_10,B_6_3+B_1_11+B_6_11,B_6_4+B_1_12+B_6_12,B_6_5+B_1_13+B_6_13],[B_7_6+B_2_7+B_7_7,B_2_8+B_7_14+B_7_8,B_7_1+B_2_9+B_7_9,B_7_2+B_2_10+B_7_10,B_7_3+B_2_11+B_7_11,B_7_4+B_2_12+B_7_12,B_7_5+B_2_13+B_7_13],[B_8_6+B_3_7+B_8_7,B_3_8+B_8_14+B_8_8,B_8_1+B_3_9+B_8_9,B_8_2+B_3_10+B_8_10,B_8_3+B_3_11+B_8_11,B_8_4+B_3_12+B_8_12,B_8_5+B_3_13+B_8_13],[B_9_6+B_9_7,B_9_8+B_9_14,B_9_1+B_9_9,B_9_2+B_9_10,B_9_3+B_9_11,B_9_4+B_9_12,B_9_5+B_9_13]]),Matrix(7, 2, [[C_7_3,C_7_4],[C_8_3,C_8_4],[C_9_3,C_9_4],[C_10_3,C_10_4],[C_11_3,C_11_4],[C_12_3,C_12_4],[C_13_3,C_13_4]])))+Trace(Mul(Matrix(2, 5, [[A_1_4-A_3_4-A_1_5+A_3_5,A_1_1-A_3_1-A_1_6+A_3_6,A_1_2-A_3_2-A_1_7+A_3_7,A_1_3-A_3_3-A_1_8+A_3_8,-A_1_9+A_3_9],[A_2_4-A_4_4-A_2_5+A_4_5,A_2_1-A_4_1-A_2_6+A_4_6,A_2_2-A_4_2-A_2_7+A_4_7,A_2_3-A_4_3-A_2_8+A_4_8,-A_2_9+A_4_9]]),Matrix(5, 8, [[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_6_15,B_6_16,B_6_17,B_6_18,B_6_19,B_6_20,B_6_21,B_6_22],[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_8_15,B_8_16,B_8_17,B_8_18,B_8_19,B_8_20,B_8_21,B_8_22],[B_9_15,B_9_16,B_9_17,B_9_18,B_9_19,B_9_20,B_9_21,B_9_22]]),Matrix(8, 2, [[-C_7_1-C_15_1,-C_7_2-C_15_2],[-C_8_1-C_16_1,-C_8_2-C_16_2],[-C_9_1-C_17_1,-C_9_2-C_17_2],[-C_10_1-C_18_1,-C_10_2-C_18_2],[-C_11_1-C_19_1,-C_11_2-C_19_2],[-C_12_1-C_20_1,-C_12_2-C_20_2],[-C_13_1-C_21_1,-C_13_2-C_21_2],[-C_22_1,-C_22_2]])))+Trace(Mul(Matrix(2, 4, [[A_3_4-A_3_10,A_3_1-A_3_11,A_3_2-A_3_12,A_3_3-A_3_13],[A_4_4-A_4_10,A_4_1-A_4_11,A_4_2-A_4_12,A_4_3-A_4_13]]),Matrix(4, 7, [[B_4_6,B_4_14,B_4_1,B_4_2,B_4_3,B_4_4,B_4_5],[B_1_6,B_1_14,B_1_1,B_1_2,B_1_3,B_1_4,B_1_5],[B_2_6,B_2_14,B_2_1,B_2_2,B_2_3,B_2_4,B_2_5],[B_3_6,B_3_14,B_3_1,B_3_2,B_3_3,B_3_4,B_3_5]]),Matrix(7, 2, [[C_6_3+C_15_3,C_6_4+C_15_4],[C_14_3+C_16_3,C_14_4+C_16_4],[C_1_3+C_17_3,C_1_4+C_17_4],[C_2_3+C_18_3,C_2_4+C_18_4],[C_3_3+C_19_3,C_3_4+C_19_4],[C_4_3+C_20_3,C_4_4+C_20_4],[C_5_3+C_21_3,C_5_4+C_21_4]])))+Trace(Mul(Matrix(2, 4, [[A_1_4-A_3_4,A_1_1-A_3_1,A_1_2-A_3_2,A_1_3-A_3_3],[A_2_4-A_4_4,A_2_1-A_4_1,A_2_2-A_4_2,A_2_3-A_4_3]]),Matrix(4, 8, [[B_4_6-B_4_15-B_5_15,B_4_14-B_4_16-B_5_16,B_4_1-B_4_17-B_5_17,B_4_2-B_4_18-B_5_18,B_4_3-B_4_19-B_5_19,B_4_4-B_4_20-B_5_20,B_4_5-B_4_21-B_5_21,-B_4_22-B_5_22],[B_1_6-B_1_15-B_6_15,B_1_14-B_1_16-B_6_16,B_1_1-B_1_17-B_6_17,B_1_2-B_1_18-B_6_18,B_1_3-B_1_19-B_6_19,B_1_4-B_1_20-B_6_20,B_1_5-B_1_21-B_6_21,-B_1_22-B_6_22],[B_2_6-B_2_15-B_7_15,B_2_14-B_2_16-B_7_16,B_2_1-B_2_17-B_7_17,B_2_2-B_2_18-B_7_18,B_2_3-B_2_19-B_7_19,B_2_4-B_2_20-B_7_20,B_2_5-B_2_21-B_7_21,-B_2_22-B_7_22],[B_3_6-B_3_15-B_8_15,B_3_14-B_3_16-B_8_16,B_3_1-B_3_17-B_8_17,B_3_2-B_3_18-B_8_18,B_3_3-B_3_19-B_8_19,B_3_4-B_3_20-B_8_20,B_3_5-B_3_21-B_8_21,-B_3_22-B_8_22]]),Matrix(8, 2, [[C_15_3,C_15_4],[C_16_3,C_16_4],[C_17_3,C_17_4],[C_18_3,C_18_4],[C_19_3,C_19_4],[C_20_3,C_20_4],[C_21_3,C_21_4],[C_22_3,C_22_4]])))

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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