Description of fast matrix multiplication algorithm: ⟨7×20×22:2004⟩

Algorithm type

X7Y14Z7+X7Y12Z7+X4Y18Z3+4X7Y10Z7+3X7Y8Z7+3X4Y14Z4+X4Y14Z3+X3Y14Z4+X7Y6Z7+X4Y12Z4+X3Y14Z3+2X7Y6Z6+X3Y12Z4+4X4Y10Z4+X3Y12Z3+4X4Y8Z4+X3Y10Z3+3X4Y7Z4+X3Y8Z4+X4Y8Z2+9X4Y6Z4+X3Y8Z3+2X2Y10Z2+12X4Y5Z4+7X3Y6Z4+X2Y10Z+3X2Y9Z2+39X4Y4Z4+6X3Y6Z3+13X2Y8Z2+13X4Y4Z3+3X4Y3Z4+6X3Y4Z4+X2Y8Z+18X2Y7Z2+3XY8Z2+6X4Y3Z3+X4Y2Z4+8X3Y4Z3+38X2Y6Z2+XY8Z+2X3Y2Z4+X2Y6Z+15X2Y5Z2+4XY6Z2+X4Y2Z2+61X2Y4Z2+96X2Y3Z3+2XY6Z+8X2Y4Z+63X2Y3Z2+9XY5Z+5XY4Z2+144XY3Z3+6X3Y2Z+386X2Y2Z2+67XY4Z+6XY2Z3+30X3YZ+20X2Y2Z+9X2YZ2+114XY3Z+18XY2Z2+30XYZ3+9X2YZ+260XY2Z+48XYZ2+363XYZX7Y14Z7X7Y12Z7X4Y18Z34X7Y10Z73X7Y8Z73X4Y14Z4X4Y14Z3X3Y14Z4X7Y6Z7X4Y12Z4X3Y14Z32X7Y6Z6X3Y12Z44X4Y10Z4X3Y12Z34X4Y8Z4X3Y10Z33X4Y7Z4X3Y8Z4X4Y8Z29X4Y6Z4X3Y8Z32X2Y10Z212X4Y5Z47X3Y6Z4X2Y10Z3X2Y9Z239X4Y4Z46X3Y6Z313X2Y8Z213X4Y4Z33X4Y3Z46X3Y4Z4X2Y8Z18X2Y7Z23XY8Z26X4Y3Z3X4Y2Z48X3Y4Z338X2Y6Z2XY8Z2X3Y2Z4X2Y6Z15X2Y5Z24XY6Z2X4Y2Z261X2Y4Z296X2Y3Z32XY6Z8X2Y4Z63X2Y3Z29XY5Z5XY4Z2144XY3Z36X3Y2Z386X2Y2Z267XY4Z6XY2Z330X3YZ20X2Y2Z9X2YZ2114XY3Z18XY2Z230XYZ39X2YZ260XY2Z48XYZ2363XYZX^7*Y^14*Z^7+X^7*Y^12*Z^7+X^4*Y^18*Z^3+4*X^7*Y^10*Z^7+3*X^7*Y^8*Z^7+3*X^4*Y^14*Z^4+X^4*Y^14*Z^3+X^3*Y^14*Z^4+X^7*Y^6*Z^7+X^4*Y^12*Z^4+X^3*Y^14*Z^3+2*X^7*Y^6*Z^6+X^3*Y^12*Z^4+4*X^4*Y^10*Z^4+X^3*Y^12*Z^3+4*X^4*Y^8*Z^4+X^3*Y^10*Z^3+3*X^4*Y^7*Z^4+X^3*Y^8*Z^4+X^4*Y^8*Z^2+9*X^4*Y^6*Z^4+X^3*Y^8*Z^3+2*X^2*Y^10*Z^2+12*X^4*Y^5*Z^4+7*X^3*Y^6*Z^4+X^2*Y^10*Z+3*X^2*Y^9*Z^2+39*X^4*Y^4*Z^4+6*X^3*Y^6*Z^3+13*X^2*Y^8*Z^2+13*X^4*Y^4*Z^3+3*X^4*Y^3*Z^4+6*X^3*Y^4*Z^4+X^2*Y^8*Z+18*X^2*Y^7*Z^2+3*X*Y^8*Z^2+6*X^4*Y^3*Z^3+X^4*Y^2*Z^4+8*X^3*Y^4*Z^3+38*X^2*Y^6*Z^2+X*Y^8*Z+2*X^3*Y^2*Z^4+X^2*Y^6*Z+15*X^2*Y^5*Z^2+4*X*Y^6*Z^2+X^4*Y^2*Z^2+61*X^2*Y^4*Z^2+96*X^2*Y^3*Z^3+2*X*Y^6*Z+8*X^2*Y^4*Z+63*X^2*Y^3*Z^2+9*X*Y^5*Z+5*X*Y^4*Z^2+144*X*Y^3*Z^3+6*X^3*Y^2*Z+386*X^2*Y^2*Z^2+67*X*Y^4*Z+6*X*Y^2*Z^3+30*X^3*Y*Z+20*X^2*Y^2*Z+9*X^2*Y*Z^2+114*X*Y^3*Z+18*X*Y^2*Z^2+30*X*Y*Z^3+9*X^2*Y*Z+260*X*Y^2*Z+48*X*Y*Z^2+363*X*Y*Z

Algorithm definition

The algorithm ⟨7×20×22:2004⟩ could be constructed using the following decomposition:

⟨7×20×22:2004⟩ = ⟨4×10×11:312⟩ + ⟨3×10×11:252⟩ + ⟨4×10×11:312⟩ + ⟨3×10×11:252⟩ + ⟨3×10×11:252⟩ + ⟨4×10×11:312⟩ + ⟨4×10×11:312⟩.

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_20A_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_4_7A_4_8A_4_9A_4_10A_4_11A_4_12A_4_13A_4_14A_4_15A_4_16A_4_17A_4_18A_4_19A_4_20A_5_1A_5_2A_5_3A_5_4A_5_5A_5_6A_5_7A_5_8A_5_9A_5_10A_5_11A_5_12A_5_13A_5_14A_5_15A_5_16A_5_17A_5_18A_5_19A_5_20A_6_1A_6_2A_6_3A_6_4A_6_5A_6_6A_6_7A_6_8A_6_9A_6_10A_6_11A_6_12A_6_13A_6_14A_6_15A_6_16A_6_17A_6_18A_6_19A_6_20A_7_1A_7_2A_7_3A_7_4A_7_5A_7_6A_7_7A_7_8A_7_9A_7_10A_7_11A_7_12A_7_13A_7_14A_7_15A_7_16A_7_17A_7_18A_7_19A_7_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_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_22B_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_15_21B_15_22B_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_16_21B_16_22B_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_17_21B_17_22B_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_18_21B_18_22B_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_19_21B_19_22B_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_20B_20_21B_20_22C_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_7=TraceMulA_4_11A_4_12A_4_13A_4_14A_4_15A_4_16A_4_17A_4_18A_4_19A_4_20A_1_10+A_5_11A_1_1+A_5_12A_1_2+A_5_13A_1_3+A_5_14A_1_4+A_5_15A_1_5+A_5_16A_1_6+A_5_17A_1_7+A_5_18A_1_8+A_5_19A_1_9+A_5_20A_2_10+A_6_11A_2_1+A_6_12A_2_2+A_6_13A_2_3+A_6_14A_2_4+A_6_15A_2_5+A_6_16A_2_6+A_6_17A_2_7+A_6_18A_2_8+A_6_19A_2_9+A_6_20A_3_10+A_7_11A_3_1+A_7_12A_3_2+A_7_13A_3_3+A_7_14A_3_4+A_7_15A_3_5+A_7_16A_3_6+A_7_17A_3_7+A_7_18A_3_8+A_7_19A_3_9+A_7_20B_10_1+B_11_12B_10_2+B_11_13B_10_3+B_11_14B_10_4+B_11_15B_10_5+B_11_16B_10_6+B_11_17B_10_7+B_11_18B_10_8+B_11_19B_10_9+B_11_20B_10_10+B_11_21B_10_11+B_11_22B_1_1+B_12_12B_1_2+B_12_13B_1_3+B_12_14B_1_4+B_12_15B_1_5+B_12_1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_1C_15_1C_4_2C_15_2C_4_3C_15_3C_5_1C_16_1C_5_2C_16_2C_5_3C_16_3C_6_1C_17_1C_6_2C_17_2C_6_3C_17_3C_7_1C_18_1C_7_2C_18_2C_7_3C_18_3C_8_1C_19_1C_8_2C_19_2C_8_3C_19_3C_9_1C_20_1C_9_2C_20_2C_9_3C_20_3C_10_1C_21_1C_10_2C_21_2C_10_3C_21_3C_11_1C_22_1C_11_2C_22_2C_11_3C_22_3TraceMulA_1_10A_1_1A_1_2A_1_3A_1_4A_1_5A_1_6A_1_7A_1_8A_1_9A_2_10A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_2_7A_2_8A_2_9A_3_10A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_3_7A_3_8A_3_9B_10_12B_11_12B_10_13B_11_13B_10_14B_11_14B_10_15B_11_15B_10_16B_11_16B_10_17B_11_17B_10_18B_11_18B_10_19B_11_19B_10_20B_11_20B_10_21B_11_21B_10_22B_11_22B_1_12B_12_12B_1_13B_12_13B_1_14B_12_14B_1_15B_12_15B_1_16B_12_16B_1_17B_12_17B_1_18B_12_18B_1_19B_12_19B_1_20B_12_20B_1_21B_12_21B_1_22B_12_22B_2_12B_13_12B_2_13B_13_13B_2_14B_13_14B_2_15B_13_15B_2_16B_13_16B_2_17B_13_17B_2_18B_13_18B_2_19B_13_19B_2_20B_13_20B_2_21B_13_21B_2_22B_13_22B_3_12B_14_12B_3_13B_14_13B_3_14B_14_14B_3_15B_14_15B_3_16B_14_16B_3_17B_14_17B_3_18B_14_18B_3_19B_14_19B_3_20B_14_20B_3_21B_14_21B_3_22B_14_22B_4_12B_15_12B_4_13B_15_13B_4_14B_15_14B_4_15B_15_15B_4_16B_15_16B_4_17B_15_17B_4_18B_15_18B_4_19B_15_19B_4_20B_15_20B_4_21B_15_21B_4_22B_15_22B_5_12B_16_12B_5_13B_16_13B_5_14B_16_14B_5_15B_16_15B_5_16B_16_16B_5_17B_16_17B_5_18B_16_18B_5_19B_16_19B_5_20B_16_20B_5_21B_16_21B_5_22B_16_22B_6_12B_17_12B_6_13B_17_13B_6_14B_17_14B_6_15B_17_15B_6_16B_17_16B_6_17B_17_17B_6_18B_17_18B_6_19B_17_19B_6_20B_17_20B_6_21B_17_21B_6_22B_17_22B_7_12B_18_12B_7_13B_18_13B_7_14B_18_14B_7_15B_18_15B_7_16B_18_16B_7_17B_18_17B_7_18B_18_18B_7_19B_18_19B_7_20B_18_20B_7_21B_18_21B_7_22B_18_22B_8_12B_19_12B_8_13B_19_13B_8_14B_19_14B_8_15B_19_15B_8_16B_19_16B_8_17B_19_17B_8_18B_19_18B_8_19B_19_19B_8_20B_19_20B_8_21B_19_21B_8_22B_19_22B_9_12B_20_12B_9_13B_20_13B_9_14B_20_14B_9_15B_20_15B_9_16B_20_16B_9_17B_20_17B_9_18B_20_18B_9_19B_20_19B_9_20B_20_20B_9_21B_20_21B_9_22B_20_22C_12_1C_12_5C_12_2C_12_6C_12_3C_12_7C_13_1C_13_5C_13_2C_13_6C_13_3C_13_7C_14_1C_14_5C_14_2C_14_6C_14_3C_14_7C_15_1C_15_5C_15_2C_15_6C_15_3C_15_7C_16_1C_16_5C_16_2C_16_6C_16_3C_16_7C_17_1C_17_5C_17_2C_17_6C_17_3C_17_7C_18_1C_18_5C_18_2C_18_6C_18_3C_18_7C_19_1C_19_5C_19_2C_19_6C_19_3C_19_7C_20_1C_20_5C_20_2C_20_6C_20_3C_20_7C_21_1C_21_5C_21_2C_21_6C_21_3C_21_7C_22_1C_22_5C_22_2C_22_6C_22_3C_22_7TraceMulA_4_11A_4_12A_4_13A_4_14A_4_15A_4_16A_4_17A_4_18A_4_19A_4_20A_5_11A_5_12A_5_13A_5_14A_5_15A_5_16A_5_17A_5_18A_5_19A_5_20A_6_11A_6_12A_6_13A_6_14A_6_15A_6_16A_6_17A_6_18A_6_19A_6_20A_7_11A_7_12A_7_13A_7_14A_7_15A_7_16A_7_17A_7_18A_7_19A_7_20B_10_1B_11_1B_10_2B_11_2B_10_3B_11_3B_10_4B_11_4B_10_5B_11_5B_10_6B_11_6B_10_7B_11_7B_10_8B_11_8B_10_9B_11_9B_10_10B_11_10B_10_11B_11_11B_1_1B_12_1B_1_2B_12_2B_1_3B_12_3B_1_4B_12_4B_1_5B_12_5B_1_6B_12_6B_1_7B_12_7B_1_8B_12_8B_1_9B_12_9B_1_10B_12_10B_1_11B_12_11B_2_1B_13_1B_2_2B_13_2B_2_3B_13_3B_2_4B_13_4B_2_5B_13_5B_2_6B_13_6B_2_7B_13_7B_2_8B_13_8B_2_9B_13_9B_2_10B_13_10B_2_11B_13_11B_3_1B_14_1B_3_2B_14_2B_3_3B_14_3B_3_4B_14_4B_3_5B_14_5B_3_6B_14_6B_3_7B_14_7B_3_8B_14_8B_3_9B_14_9B_3_10B_14_10B_3_11B_14_11B_4_1B_15_1B_4_2B_15_2B_4_3B_15_3B_4_4B_15_4B_4_5B_15_5B_4_6B_15_6B_4_7B_15_7B_4_8B_15_8B_4_9B_15_9B_4_10B_15_10B_4_11B_15_11B_5_1B_16_1B_5_2B_16_2B_5_3B_16_3B_5_4B_16_4B_5_5B_16_5B_5_6B_16_6B_5_7B_16_7B_5_8B_16_8B_5_9B_16_9B_5_10B_16_10B_5_11B_16_11B_6_1B_17_1B_6_2B_17_2B_6_3B_17_3B_6_4B_17_4B_6_5B_17_5B_6_6B_17_6B_6_7B_17_7B_6_8B_17_8B_6_9B_17_9B_6_10B_17_10B_6_11B_17_11B_7_1B_18_1B_7_2B_18_2B_7_3B_18_3B_7_4B_18_4B_7_5B_18_5B_7_6B_18_6B_7_7B_18_7B_7_8B_18_8B_7_9B_18_9B_7_10B_18_10B_7_11B_18_11B_8_1B_19_1B_8_2B_19_2B_8_3B_19_3B_8_4B_19_4B_8_5B_19_5B_8_6B_19_6B_8_7B_19_7B_8_8B_19_8B_8_9B_19_9B_8_10B_19_10B_8_11B_19_11B_9_1B_20_1B_9_2B_20_2B_9_3B_20_3B_9_4B_20_4B_9_5B_20_5B_9_6B_20_6B_9_7B_20_7B_9_8B_20_8B_9_9B_20_9B_9_10B_20_10B_9_11B_20_11C_1_4C_1_1C_1_5C_1_2C_1_6C_1_3C_1_7C_2_4C_2_1C_2_5C_2_2C_2_6C_2_3C_2_7C_3_4C_3_1C_3_5C_3_2C_3_6C_3_3C_3_7C_4_4C_4_1C_4_5C_4_2C_4_6C_4_3C_4_7C_5_4C_5_1C_5_5C_5_2C_5_6C_5_3C_5_7C_6_4C_6_1C_6_5C_6_2C_6_6C_6_3C_6_7C_7_4C_7_1C_7_5C_7_2C_7_6C_7_3C_7_7C_8_4C_8_1C_8_5C_8_2C_8_6C_8_3C_8_7C_9_4C_9_1C_9_5C_9_2C_9_6C_9_3C_9_7C_10_4C_10_1C_10_5C_10_2C_10_6C_10_3C_10_7C_11_4C_11_1C_11_5C_11_2C_11_6C_11_3C_11_7TraceMulA_4_10A_4_11A_4_1A_4_12A_4_2A_4_13A_4_3A_4_14A_4_4A_4_15A_4_5A_4_16A_4_6A_4_17A_4_7A_4_18A_4_8A_4_19A_4_9A_4_20A_5_10A_5_11A_5_1A_5_12A_5_2A_5_13A_5_3A_5_14A_5_4A_5_15A_5_5A_5_16A_5_6A_5_17A_5_7A_5_18A_5_8A_5_19A_5_9A_5_20A_6_10A_6_11A_6_1A_6_12A_6_2A_6_13A_6_3A_6_14A_6_4A_6_15A_6_5A_6_16A_6_6A_6_17A_6_7A_6_18A_6_8A_6_19A_6_9A_6_20A_7_10A_7_11A_7_1A_7_12A_7_2A_7_13A_7_3A_7_14A_7_4A_7_15A_7_5A_7_16A_7_6A_7_17A_7_7A_7_18A_7_8A_7_19A_7_9A_7_20B_10_1B_10_2B_10_3B_10_4B_10_5B_10_6B_10_7B_10_8B_10_9B_10_10B_10_11B_1_1B_1_2B_1_3B_1_4B_1_5B_1_6B_1_7B_1_8B_1_9B_1_10B_1_11B_2_1B_2_2B_2_3B_2_4B_2_5B_2_6B_2_7B_2_8B_2_9B_2_10B_2_11B_3_1B_3_2B_3_3B_3_4B_3_5B_3_6B_3_7B_3_8B_3_9B_3_10B_3_11B_4_1B_4_2B_4_3B_4_4B_4_5B_4_6B_4_7B_4_8B_4_9B_4_10B_4_11B_5_1B_5_2B_5_3B_5_4B_5_5B_5_6B_5_7B_5_8B_5_9B_5_10B_5_11B_6_1B_6_2B_6_3B_6_4B_6_5B_6_6B_6_7B_6_8B_6_9B_6_10B_6_11B_7_1B_7_2B_7_3B_7_4B_7_5B_7_6B_7_7B_7_8B_7_9B_7_10B_7_11B_8_1B_8_2B_8_3B_8_4B_8_5B_8_6B_8_7B_8_8B_8_9B_8_10B_8_11B_9_1B_9_2B_9_3B_9_4B_9_5B_9_6B_9_7B_9_8B_9_9B_9_10B_9_11C_1_4C_12_4C_1_5C_12_5C_1_6C_12_6C_1_7C_12_7C_2_4C_13_4C_2_5C_13_5C_2_6C_13_6C_2_7C_13_7C_3_4C_14_4C_3_5C_14_5C_3_6C_14_6C_3_7C_14_7C_4_4C_15_4C_4_5C_15_5C_4_6C_15_6C_4_7C_15_7C_5_4C_16_4C_5_5C_16_5C_5_6C_16_6C_5_7C_16_7C_6_4C_17_4C_6_5C_17_5C_6_6C_17_6C_6_7C_17_7C_7_4C_18_4C_7_5C_18_5C_7_6C_18_6C_7_7C_18_7C_8_4C_19_4C_8_5C_19_5C_8_6C_19_6C_8_7C_19_7C_9_4C_20_4C_9_5C_20_5C_9_6C_20_6C_9_7C_20_7C_10_4C_21_4C_10_5C_21_5C_10_6C_21_6C_10_7C_21_7C_11_4C_22_4C_11_5C_22_5C_11_6C_22_6C_11_7C_22_7Trace(Mul(Matrix(7, 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],[A_4_1,A_4_2,A_4_3,A_4_4,A_4_5,A_4_6,A_4_7,A_4_8,A_4_9,A_4_10,A_4_11,A_4_12,A_4_13,A_4_14,A_4_15,A_4_16,A_4_17,A_4_18,A_4_19,A_4_20],[A_5_1,A_5_2,A_5_3,A_5_4,A_5_5,A_5_6,A_5_7,A_5_8,A_5_9,A_5_10,A_5_11,A_5_12,A_5_13,A_5_14,A_5_15,A_5_16,A_5_17,A_5_18,A_5_19,A_5_20],[A_6_1,A_6_2,A_6_3,A_6_4,A_6_5,A_6_6,A_6_7,A_6_8,A_6_9,A_6_10,A_6_11,A_6_12,A_6_13,A_6_14,A_6_15,A_6_16,A_6_17,A_6_18,A_6_19,A_6_20],[A_7_1,A_7_2,A_7_3,A_7_4,A_7_5,A_7_6,A_7_7,A_7_8,A_7_9,A_7_10,A_7_11,A_7_12,A_7_13,A_7_14,A_7_15,A_7_16,A_7_17,A_7_18,A_7_19,A_7_20]]),Matrix(20, 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],[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_15_21,B_15_22],[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_16_21,B_16_22],[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_17_21,B_17_22],[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_18_21,B_18_22],[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_19_21,B_19_22],[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,B_20_21,B_20_22]]),Matrix(22, 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]]))) = Trace(Mul(Matrix(4, 10, [[A_4_11,A_4_12,A_4_13,A_4_14,A_4_15,A_4_16,A_4_17,A_4_18,A_4_19,A_4_20],[A_1_10+A_5_11,A_1_1+A_5_12,A_1_2+A_5_13,A_1_3+A_5_14,A_1_4+A_5_15,A_1_5+A_5_16,A_1_6+A_5_17,A_1_7+A_5_18,A_1_8+A_5_19,A_1_9+A_5_20],[A_2_10+A_6_11,A_2_1+A_6_12,A_2_2+A_6_13,A_2_3+A_6_14,A_2_4+A_6_15,A_2_5+A_6_16,A_2_6+A_6_17,A_2_7+A_6_18,A_2_8+A_6_19,A_2_9+A_6_20],[A_3_10+A_7_11,A_3_1+A_7_12,A_3_2+A_7_13,A_3_3+A_7_14,A_3_4+A_7_15,A_3_5+A_7_16,A_3_6+A_7_17,A_3_7+A_7_18,A_3_8+A_7_19,A_3_9+A_7_20]]),Matrix(10, 11, [[B_10_1+B_11_12,B_10_2+B_11_13,B_10_3+B_11_14,B_10_4+B_11_15,B_10_5+B_11_16,B_10_6+B_11_17,B_10_7+B_11_18,B_10_8+B_11_19,B_10_9+B_11_20,B_10_10+B_11_21,B_10_11+B_11_22],[B_1_1+B_12_12,B_1_2+B_12_13,B_1_3+B_12_14,B_1_4+B_12_15,B_1_5+B_12_16,B_1_6+B_12_17,B_1_7+B_12_18,B_1_8+B_12_19,B_1_9+B_12_20,B_1_10+B_12_21,B_1_11+B_12_22],[B_2_1+B_13_12,B_2_2+B_13_13,B_2_3+B_13_14,B_2_4+B_13_15,B_2_5+B_13_16,B_2_6+B_13_17,B_2_7+B_13_18,B_2_8+B_13_19,B_2_9+B_13_20,B_2_10+B_13_21,B_2_11+B_13_22],[B_3_1+B_14_12,B_3_2+B_14_13,B_3_3+B_14_14,B_3_4+B_14_15,B_3_5+B_14_16,B_3_6+B_14_17,B_3_7+B_14_18,B_3_8+B_14_19,B_3_9+B_14_20,B_3_10+B_14_21,B_3_11+B_14_22],[B_4_1+B_15_12,B_4_2+B_15_13,B_4_3+B_15_14,B_4_4+B_15_15,B_4_5+B_15_16,B_4_6+B_15_17,B_4_7+B_15_18,B_4_8+B_15_19,B_4_9+B_15_20,B_4_10+B_15_21,B_4_11+B_15_22],[B_5_1+B_16_12,B_5_2+B_16_13,B_5_3+B_16_14,B_5_4+B_16_15,B_5_5+B_16_16,B_5_6+B_16_17,B_5_7+B_16_18,B_5_8+B_16_19,B_5_9+B_16_20,B_5_10+B_16_21,B_5_11+B_16_22],[B_6_1+B_17_12,B_6_2+B_17_13,B_6_3+B_17_14,B_6_4+B_17_15,B_6_5+B_17_16,B_6_6+B_17_17,B_6_7+B_17_18,B_6_8+B_17_19,B_6_9+B_17_20,B_6_10+B_17_21,B_6_11+B_17_22],[B_7_1+B_18_12,B_7_2+B_18_13,B_7_3+B_18_14,B_7_4+B_18_15,B_7_5+B_18_16,B_7_6+B_18_17,B_7_7+B_18_18,B_7_8+B_18_19,B_7_9+B_18_20,B_7_10+B_18_21,B_7_11+B_18_22],[B_8_1+B_19_12,B_8_2+B_19_13,B_8_3+B_19_14,B_8_4+B_19_15,B_8_5+B_19_16,B_8_6+B_19_17,B_8_7+B_19_18,B_8_8+B_19_19,B_8_9+B_19_20,B_8_10+B_19_21,B_8_11+B_19_22],[B_9_1+B_20_12,B_9_2+B_20_13,B_9_3+B_20_14,B_9_4+B_20_15,B_9_5+B_20_16,B_9_6+B_20_17,B_9_7+B_20_18,B_9_8+B_20_19,B_9_9+B_20_20,B_9_10+B_20_21,B_9_11+B_20_22]]),Matrix(11, 4, [[C_12_4,C_1_1+C_12_5,C_1_2+C_12_6,C_1_3+C_12_7],[C_13_4,C_2_1+C_13_5,C_2_2+C_13_6,C_2_3+C_13_7],[C_14_4,C_3_1+C_14_5,C_3_2+C_14_6,C_3_3+C_14_7],[C_15_4,C_4_1+C_15_5,C_4_2+C_15_6,C_4_3+C_15_7],[C_16_4,C_5_1+C_16_5,C_5_2+C_16_6,C_5_3+C_16_7],[C_17_4,C_6_1+C_17_5,C_6_2+C_17_6,C_6_3+C_17_7],[C_18_4,C_7_1+C_18_5,C_7_2+C_18_6,C_7_3+C_18_7],[C_19_4,C_8_1+C_19_5,C_8_2+C_19_6,C_8_3+C_19_7],[C_20_4,C_9_1+C_20_5,C_9_2+C_20_6,C_9_3+C_20_7],[C_21_4,C_10_1+C_21_5,C_10_2+C_21_6,C_10_3+C_21_7],[C_22_4,C_11_1+C_22_5,C_11_2+C_22_6,C_11_3+C_22_7]])))+Trace(Mul(Matrix(3, 10, [[A_1_11-A_5_11,A_1_12-A_5_12,A_1_13-A_5_13,A_1_14-A_5_14,A_1_15-A_5_15,A_1_16-A_5_16,A_1_17-A_5_17,A_1_18-A_5_18,A_1_19-A_5_19,A_1_20-A_5_20],[A_2_11-A_6_11,A_2_12-A_6_12,A_2_13-A_6_13,A_2_14-A_6_14,A_2_15-A_6_15,A_2_16-A_6_16,A_2_17-A_6_17,A_2_18-A_6_18,A_2_19-A_6_19,A_2_20-A_6_20],[A_3_11-A_7_11,A_3_12-A_7_12,A_3_13-A_7_13,A_3_14-A_7_14,A_3_15-A_7_15,A_3_16-A_7_16,A_3_17-A_7_17,A_3_18-A_7_18,A_3_19-A_7_19,A_3_20-A_7_20]]),Matrix(10, 11, [[B_11_1+B_11_12,B_11_2+B_11_13,B_11_3+B_11_14,B_11_4+B_11_15,B_11_5+B_11_16,B_11_6+B_11_17,B_11_7+B_11_18,B_11_8+B_11_19,B_11_9+B_11_20,B_11_10+B_11_21,B_11_11+B_11_22],[B_12_1+B_12_12,B_12_2+B_12_13,B_12_3+B_12_14,B_12_4+B_12_15,B_12_5+B_12_16,B_12_6+B_12_17,B_12_7+B_12_18,B_12_8+B_12_19,B_12_9+B_12_20,B_12_10+B_12_21,B_12_11+B_12_22],[B_13_1+B_13_12,B_13_2+B_13_13,B_13_3+B_13_14,B_13_4+B_13_15,B_13_5+B_13_16,B_13_6+B_13_17,B_13_7+B_13_18,B_13_8+B_13_19,B_13_9+B_13_20,B_13_10+B_13_21,B_13_11+B_13_22],[B_14_1+B_14_12,B_14_2+B_14_13,B_14_3+B_14_14,B_14_4+B_14_15,B_14_5+B_14_16,B_14_6+B_14_17,B_14_7+B_14_18,B_14_8+B_14_19,B_14_9+B_14_20,B_14_10+B_14_21,B_14_11+B_14_22],[B_15_1+B_15_12,B_15_2+B_15_13,B_15_3+B_15_14,B_15_4+B_15_15,B_15_5+B_15_16,B_15_6+B_15_17,B_15_7+B_15_18,B_15_8+B_15_19,B_15_9+B_15_20,B_15_10+B_15_21,B_15_11+B_15_22],[B_16_1+B_16_12,B_16_2+B_16_13,B_16_3+B_16_14,B_16_4+B_16_15,B_16_5+B_16_16,B_16_6+B_16_17,B_16_7+B_16_18,B_16_8+B_16_19,B_16_9+B_16_20,B_16_10+B_16_21,B_16_11+B_16_22],[B_17_1+B_17_12,B_17_2+B_17_13,B_17_3+B_17_14,B_17_4+B_17_15,B_17_5+B_17_16,B_17_6+B_17_17,B_17_7+B_17_18,B_17_8+B_17_19,B_17_9+B_17_20,B_17_10+B_17_21,B_17_11+B_17_22],[B_18_1+B_18_12,B_18_2+B_18_13,B_18_3+B_18_14,B_18_4+B_18_15,B_18_5+B_18_16,B_18_6+B_18_17,B_18_7+B_18_18,B_18_8+B_18_19,B_18_9+B_18_20,B_18_10+B_18_21,B_18_11+B_18_22],[B_19_1+B_19_12,B_19_2+B_19_13,B_19_3+B_19_14,B_19_4+B_19_15,B_19_5+B_19_16,B_19_6+B_19_17,B_19_7+B_19_18,B_19_8+B_19_19,B_19_9+B_19_20,B_19_10+B_19_21,B_19_11+B_19_22],[B_20_1+B_20_12,B_20_2+B_20_13,B_20_3+B_20_14,B_20_4+B_20_15,B_20_5+B_20_16,B_20_6+B_20_17,B_20_7+B_20_18,B_20_8+B_20_19,B_20_9+B_20_20,B_20_10+B_20_21,B_20_11+B_20_22]]),Matrix(11, 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]])))+Trace(Mul(Matrix(4, 10, [[A_4_10,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_1_10+A_5_10,-A_1_1+A_5_1,-A_1_2+A_5_2,-A_1_3+A_5_3,-A_1_4+A_5_4,-A_1_5+A_5_5,-A_1_6+A_5_6,-A_1_7+A_5_7,-A_1_8+A_5_8,-A_1_9+A_5_9],[-A_2_10+A_6_10,-A_2_1+A_6_1,-A_2_2+A_6_2,-A_2_3+A_6_3,-A_2_4+A_6_4,-A_2_5+A_6_5,-A_2_6+A_6_6,-A_2_7+A_6_7,-A_2_8+A_6_8,-A_2_9+A_6_9],[-A_3_10+A_7_10,-A_3_1+A_7_1,-A_3_2+A_7_2,-A_3_3+A_7_3,-A_3_4+A_7_4,-A_3_5+A_7_5,-A_3_6+A_7_6,-A_3_7+A_7_7,-A_3_8+A_7_8,-A_3_9+A_7_9]]),Matrix(10, 11, [[B_10_1+B_10_12,B_10_2+B_10_13,B_10_3+B_10_14,B_10_4+B_10_15,B_10_5+B_10_16,B_10_6+B_10_17,B_10_7+B_10_18,B_10_8+B_10_19,B_10_9+B_10_20,B_10_10+B_10_21,B_10_11+B_10_22],[B_1_1+B_1_12,B_1_2+B_1_13,B_1_3+B_1_14,B_1_4+B_1_15,B_1_5+B_1_16,B_1_6+B_1_17,B_1_7+B_1_18,B_1_8+B_1_19,B_1_9+B_1_20,B_1_10+B_1_21,B_1_11+B_1_22],[B_2_1+B_2_12,B_2_2+B_2_13,B_2_3+B_2_14,B_2_4+B_2_15,B_2_5+B_2_16,B_2_6+B_2_17,B_2_7+B_2_18,B_2_8+B_2_19,B_2_9+B_2_20,B_2_10+B_2_21,B_2_11+B_2_22],[B_3_1+B_3_12,B_3_2+B_3_13,B_3_3+B_3_14,B_3_4+B_3_15,B_3_5+B_3_16,B_3_6+B_3_17,B_3_7+B_3_18,B_3_8+B_3_19,B_3_9+B_3_20,B_3_10+B_3_21,B_3_11+B_3_22],[B_4_1+B_4_12,B_4_2+B_4_13,B_4_3+B_4_14,B_4_4+B_4_15,B_4_5+B_4_16,B_4_6+B_4_17,B_4_7+B_4_18,B_4_8+B_4_19,B_4_9+B_4_20,B_4_10+B_4_21,B_4_11+B_4_22],[B_5_1+B_5_12,B_5_2+B_5_13,B_5_3+B_5_14,B_5_4+B_5_15,B_5_5+B_5_16,B_5_6+B_5_17,B_5_7+B_5_18,B_5_8+B_5_19,B_5_9+B_5_20,B_5_10+B_5_21,B_5_11+B_5_22],[B_6_1+B_6_12,B_6_2+B_6_13,B_6_3+B_6_14,B_6_4+B_6_15,B_6_5+B_6_16,B_6_6+B_6_17,B_6_7+B_6_18,B_6_8+B_6_19,B_6_9+B_6_20,B_6_10+B_6_21,B_6_11+B_6_22],[B_7_1+B_7_12,B_7_2+B_7_13,B_7_3+B_7_14,B_7_4+B_7_15,B_7_5+B_7_16,B_7_6+B_7_17,B_7_7+B_7_18,B_7_8+B_7_19,B_7_9+B_7_20,B_7_10+B_7_21,B_7_11+B_7_22],[B_8_1+B_8_12,B_8_2+B_8_13,B_8_3+B_8_14,B_8_4+B_8_15,B_8_5+B_8_16,B_8_6+B_8_17,B_8_7+B_8_18,B_8_8+B_8_19,B_8_9+B_8_20,B_8_10+B_8_21,B_8_11+B_8_22],[B_9_1+B_9_12,B_9_2+B_9_13,B_9_3+B_9_14,B_9_4+B_9_15,B_9_5+B_9_16,B_9_6+B_9_17,B_9_7+B_9_18,B_9_8+B_9_19,B_9_9+B_9_20,B_9_10+B_9_21,B_9_11+B_9_22]]),Matrix(11, 4, [[C_12_4,C_12_5,C_12_6,C_12_7],[C_13_4,C_13_5,C_13_6,C_13_7],[C_14_4,C_14_5,C_14_6,C_14_7],[C_15_4,C_15_5,C_15_6,C_15_7],[C_16_4,C_16_5,C_16_6,C_16_7],[C_17_4,C_17_5,C_17_6,C_17_7],[C_18_4,C_18_5,C_18_6,C_18_7],[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]])))+Trace(Mul(Matrix(3, 10, [[A_1_10+A_1_11,A_1_1+A_1_12,A_1_2+A_1_13,A_1_3+A_1_14,A_1_4+A_1_15,A_1_5+A_1_16,A_1_6+A_1_17,A_1_7+A_1_18,A_1_8+A_1_19,A_1_9+A_1_20],[A_2_10+A_2_11,A_2_1+A_2_12,A_2_2+A_2_13,A_2_3+A_2_14,A_2_4+A_2_15,A_2_5+A_2_16,A_2_6+A_2_17,A_2_7+A_2_18,A_2_8+A_2_19,A_2_9+A_2_20],[A_3_10+A_3_11,A_3_1+A_3_12,A_3_2+A_3_13,A_3_3+A_3_14,A_3_4+A_3_15,A_3_5+A_3_16,A_3_6+A_3_17,A_3_7+A_3_18,A_3_8+A_3_19,A_3_9+A_3_20]]),Matrix(10, 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_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_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_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],[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_15_21,B_15_22],[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_16_21,B_16_22],[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_17_21,B_17_22],[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_18_21,B_18_22],[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_19_21,B_19_22],[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,B_20_21,B_20_22]]),Matrix(11, 3, [[-C_1_1+C_12_1,-C_1_2+C_12_2,-C_1_3+C_12_3],[-C_2_1+C_13_1,-C_2_2+C_13_2,-C_2_3+C_13_3],[-C_3_1+C_14_1,-C_3_2+C_14_2,-C_3_3+C_14_3],[-C_4_1+C_15_1,-C_4_2+C_15_2,-C_4_3+C_15_3],[-C_5_1+C_16_1,-C_5_2+C_16_2,-C_5_3+C_16_3],[-C_6_1+C_17_1,-C_6_2+C_17_2,-C_6_3+C_17_3],[-C_7_1+C_18_1,-C_7_2+C_18_2,-C_7_3+C_18_3],[-C_8_1+C_19_1,-C_8_2+C_19_2,-C_8_3+C_19_3],[-C_9_1+C_20_1,-C_9_2+C_20_2,-C_9_3+C_20_3],[-C_10_1+C_21_1,-C_10_2+C_21_2,-C_10_3+C_21_3],[-C_11_1+C_22_1,-C_11_2+C_22_2,-C_11_3+C_22_3]])))+Trace(Mul(Matrix(3, 10, [[A_1_10,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_10,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_10,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]]),Matrix(10, 11, [[B_10_12-B_11_12,B_10_13-B_11_13,B_10_14-B_11_14,B_10_15-B_11_15,B_10_16-B_11_16,B_10_17-B_11_17,B_10_18-B_11_18,B_10_19-B_11_19,B_10_20-B_11_20,B_10_21-B_11_21,B_10_22-B_11_22],[B_1_12-B_12_12,B_1_13-B_12_13,B_1_14-B_12_14,B_1_15-B_12_15,B_1_16-B_12_16,B_1_17-B_12_17,B_1_18-B_12_18,B_1_19-B_12_19,B_1_20-B_12_20,B_1_21-B_12_21,B_1_22-B_12_22],[B_2_12-B_13_12,B_2_13-B_13_13,B_2_14-B_13_14,B_2_15-B_13_15,B_2_16-B_13_16,B_2_17-B_13_17,B_2_18-B_13_18,B_2_19-B_13_19,B_2_20-B_13_20,B_2_21-B_13_21,B_2_22-B_13_22],[B_3_12-B_14_12,B_3_13-B_14_13,B_3_14-B_14_14,B_3_15-B_14_15,B_3_16-B_14_16,B_3_17-B_14_17,B_3_18-B_14_18,B_3_19-B_14_19,B_3_20-B_14_20,B_3_21-B_14_21,B_3_22-B_14_22],[B_4_12-B_15_12,B_4_13-B_15_13,B_4_14-B_15_14,B_4_15-B_15_15,B_4_16-B_15_16,B_4_17-B_15_17,B_4_18-B_15_18,B_4_19-B_15_19,B_4_20-B_15_20,B_4_21-B_15_21,B_4_22-B_15_22],[B_5_12-B_16_12,B_5_13-B_16_13,B_5_14-B_16_14,B_5_15-B_16_15,B_5_16-B_16_16,B_5_17-B_16_17,B_5_18-B_16_18,B_5_19-B_16_19,B_5_20-B_16_20,B_5_21-B_16_21,B_5_22-B_16_22],[B_6_12-B_17_12,B_6_13-B_17_13,B_6_14-B_17_14,B_6_15-B_17_15,B_6_16-B_17_16,B_6_17-B_17_17,B_6_18-B_17_18,B_6_19-B_17_19,B_6_20-B_17_20,B_6_21-B_17_21,B_6_22-B_17_22],[B_7_12-B_18_12,B_7_13-B_18_13,B_7_14-B_18_14,B_7_15-B_18_15,B_7_16-B_18_16,B_7_17-B_18_17,B_7_18-B_18_18,B_7_19-B_18_19,B_7_20-B_18_20,B_7_21-B_18_21,B_7_22-B_18_22],[B_8_12-B_19_12,B_8_13-B_19_13,B_8_14-B_19_14,B_8_15-B_19_15,B_8_16-B_19_16,B_8_17-B_19_17,B_8_18-B_19_18,B_8_19-B_19_19,B_8_20-B_19_20,B_8_21-B_19_21,B_8_22-B_19_22],[B_9_12-B_20_12,B_9_13-B_20_13,B_9_14-B_20_14,B_9_15-B_20_15,B_9_16-B_20_16,B_9_17-B_20_17,B_9_18-B_20_18,B_9_19-B_20_19,B_9_20-B_20_20,B_9_21-B_20_21,B_9_22-B_20_22]]),Matrix(11, 3, [[C_12_1+C_12_5,C_12_2+C_12_6,C_12_3+C_12_7],[C_13_1+C_13_5,C_13_2+C_13_6,C_13_3+C_13_7],[C_14_1+C_14_5,C_14_2+C_14_6,C_14_3+C_14_7],[C_15_1+C_15_5,C_15_2+C_15_6,C_15_3+C_15_7],[C_16_1+C_16_5,C_16_2+C_16_6,C_16_3+C_16_7],[C_17_1+C_17_5,C_17_2+C_17_6,C_17_3+C_17_7],[C_18_1+C_18_5,C_18_2+C_18_6,C_18_3+C_18_7],[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]])))+Trace(Mul(Matrix(4, 10, [[A_4_11,A_4_12,A_4_13,A_4_14,A_4_15,A_4_16,A_4_17,A_4_18,A_4_19,A_4_20],[A_5_11,A_5_12,A_5_13,A_5_14,A_5_15,A_5_16,A_5_17,A_5_18,A_5_19,A_5_20],[A_6_11,A_6_12,A_6_13,A_6_14,A_6_15,A_6_16,A_6_17,A_6_18,A_6_19,A_6_20],[A_7_11,A_7_12,A_7_13,A_7_14,A_7_15,A_7_16,A_7_17,A_7_18,A_7_19,A_7_20]]),Matrix(10, 11, [[-B_10_1+B_11_1,-B_10_2+B_11_2,-B_10_3+B_11_3,-B_10_4+B_11_4,-B_10_5+B_11_5,-B_10_6+B_11_6,-B_10_7+B_11_7,-B_10_8+B_11_8,-B_10_9+B_11_9,-B_10_10+B_11_10,-B_10_11+B_11_11],[-B_1_1+B_12_1,-B_1_2+B_12_2,-B_1_3+B_12_3,-B_1_4+B_12_4,-B_1_5+B_12_5,-B_1_6+B_12_6,-B_1_7+B_12_7,-B_1_8+B_12_8,-B_1_9+B_12_9,-B_1_10+B_12_10,-B_1_11+B_12_11],[-B_2_1+B_13_1,-B_2_2+B_13_2,-B_2_3+B_13_3,-B_2_4+B_13_4,-B_2_5+B_13_5,-B_2_6+B_13_6,-B_2_7+B_13_7,-B_2_8+B_13_8,-B_2_9+B_13_9,-B_2_10+B_13_10,-B_2_11+B_13_11],[-B_3_1+B_14_1,-B_3_2+B_14_2,-B_3_3+B_14_3,-B_3_4+B_14_4,-B_3_5+B_14_5,-B_3_6+B_14_6,-B_3_7+B_14_7,-B_3_8+B_14_8,-B_3_9+B_14_9,-B_3_10+B_14_10,-B_3_11+B_14_11],[-B_4_1+B_15_1,-B_4_2+B_15_2,-B_4_3+B_15_3,-B_4_4+B_15_4,-B_4_5+B_15_5,-B_4_6+B_15_6,-B_4_7+B_15_7,-B_4_8+B_15_8,-B_4_9+B_15_9,-B_4_10+B_15_10,-B_4_11+B_15_11],[-B_5_1+B_16_1,-B_5_2+B_16_2,-B_5_3+B_16_3,-B_5_4+B_16_4,-B_5_5+B_16_5,-B_5_6+B_16_6,-B_5_7+B_16_7,-B_5_8+B_16_8,-B_5_9+B_16_9,-B_5_10+B_16_10,-B_5_11+B_16_11],[-B_6_1+B_17_1,-B_6_2+B_17_2,-B_6_3+B_17_3,-B_6_4+B_17_4,-B_6_5+B_17_5,-B_6_6+B_17_6,-B_6_7+B_17_7,-B_6_8+B_17_8,-B_6_9+B_17_9,-B_6_10+B_17_10,-B_6_11+B_17_11],[-B_7_1+B_18_1,-B_7_2+B_18_2,-B_7_3+B_18_3,-B_7_4+B_18_4,-B_7_5+B_18_5,-B_7_6+B_18_6,-B_7_7+B_18_7,-B_7_8+B_18_8,-B_7_9+B_18_9,-B_7_10+B_18_10,-B_7_11+B_18_11],[-B_8_1+B_19_1,-B_8_2+B_19_2,-B_8_3+B_19_3,-B_8_4+B_19_4,-B_8_5+B_19_5,-B_8_6+B_19_6,-B_8_7+B_19_7,-B_8_8+B_19_8,-B_8_9+B_19_9,-B_8_10+B_19_10,-B_8_11+B_19_11],[-B_9_1+B_20_1,-B_9_2+B_20_2,-B_9_3+B_20_3,-B_9_4+B_20_4,-B_9_5+B_20_5,-B_9_6+B_20_6,-B_9_7+B_20_7,-B_9_8+B_20_8,-B_9_9+B_20_9,-B_9_10+B_20_10,-B_9_11+B_20_11]]),Matrix(11, 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],[C_7_4,C_7_1+C_7_5,C_7_2+C_7_6,C_7_3+C_7_7],[C_8_4,C_8_1+C_8_5,C_8_2+C_8_6,C_8_3+C_8_7],[C_9_4,C_9_1+C_9_5,C_9_2+C_9_6,C_9_3+C_9_7],[C_10_4,C_10_1+C_10_5,C_10_2+C_10_6,C_10_3+C_10_7],[C_11_4,C_11_1+C_11_5,C_11_2+C_11_6,C_11_3+C_11_7]])))+Trace(Mul(Matrix(4, 10, [[A_4_10+A_4_11,A_4_1+A_4_12,A_4_2+A_4_13,A_4_3+A_4_14,A_4_4+A_4_15,A_4_5+A_4_16,A_4_6+A_4_17,A_4_7+A_4_18,A_4_8+A_4_19,A_4_9+A_4_20],[A_5_10+A_5_11,A_5_1+A_5_12,A_5_2+A_5_13,A_5_3+A_5_14,A_5_4+A_5_15,A_5_5+A_5_16,A_5_6+A_5_17,A_5_7+A_5_18,A_5_8+A_5_19,A_5_9+A_5_20],[A_6_10+A_6_11,A_6_1+A_6_12,A_6_2+A_6_13,A_6_3+A_6_14,A_6_4+A_6_15,A_6_5+A_6_16,A_6_6+A_6_17,A_6_7+A_6_18,A_6_8+A_6_19,A_6_9+A_6_20],[A_7_10+A_7_11,A_7_1+A_7_12,A_7_2+A_7_13,A_7_3+A_7_14,A_7_4+A_7_15,A_7_5+A_7_16,A_7_6+A_7_17,A_7_7+A_7_18,A_7_8+A_7_19,A_7_9+A_7_20]]),Matrix(10, 11, [[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_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_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_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_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_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_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_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_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_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]]),Matrix(11, 4, [[C_1_4-C_12_4,C_1_5-C_12_5,C_1_6-C_12_6,C_1_7-C_12_7],[C_2_4-C_13_4,C_2_5-C_13_5,C_2_6-C_13_6,C_2_7-C_13_7],[C_3_4-C_14_4,C_3_5-C_14_5,C_3_6-C_14_6,C_3_7-C_14_7],[C_4_4-C_15_4,C_4_5-C_15_5,C_4_6-C_15_6,C_4_7-C_15_7],[C_5_4-C_16_4,C_5_5-C_16_5,C_5_6-C_16_6,C_5_7-C_16_7],[C_6_4-C_17_4,C_6_5-C_17_5,C_6_6-C_17_6,C_6_7-C_17_7],[C_7_4-C_18_4,C_7_5-C_18_5,C_7_6-C_18_6,C_7_7-C_18_7],[C_8_4-C_19_4,C_8_5-C_19_5,C_8_6-C_19_6,C_8_7-C_19_7],[C_9_4-C_20_4,C_9_5-C_20_5,C_9_6-C_20_6,C_9_7-C_20_7],[C_10_4-C_21_4,C_10_5-C_21_5,C_10_6-C_21_6,C_10_7-C_21_7],[C_11_4-C_22_4,C_11_5-C_22_5,C_11_6-C_22_6,C_11_7-C_22_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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