Description of fast matrix multiplication algorithm: ⟨19×19×27:5679⟩

Algorithm type

X7Y8Z11+7X8Y8Z8+X7Y7Z10+X8Y8Z7+3X14Y4Z4+3X8Y7Z7+3X7Y8Z7+3X7Y7Z8+2X4Y14Z4+X4Y4Z14+X13Y4Z4+X8Y7Z6+2X7Y7Z7+X4Y14Z3+X3Y4Z14+X14Y2Z4+X11Y2Z7+X8Y6Z6+9X7Y6Z7+3X6Y7Z7+9X6Y6Z8+X4Y9Z7+X4Y8Z8+6X4Y4Z12+X2Y14Z4+X12Y3Z4+3X7Y6Z6+7X6Y6Z7+3X4Y8Z7+X4Y4Z11+X12Y3Z3+2X11Y4Z3+X7Y5Z6+2X6Y5Z7+X4Y11Z3+2X4Y10Z4+X4Y7Z7+2X4Y6Z8+4X4Y4Z10+X4Y3Z11+2X4Y2Z12+X3Y8Z7+4X3Y4Z11+2X10Y4Z3+X8Y3Z6+X5Y5Z7+X4Y10Z3+X4Y7Z6+X4Y6Z7+X4Y2Z11+X3Y6Z8+5X2Y13Z2+X2Y11Z4+X12YZ3+X10Y3Z3+X7Y2Z7+3X6Y4Z6+2X5Y4Z7+X4Y9Z3+10X4Y8Z4+65X4Y6Z6+2X4Y4Z8+X4Y3Z9+2X4Y2Z10+X3Y10Z3+X3Y9Z4+X3Y8Z5+2X3Y3Z10+X2Y13Z+2X2Y12Z2+X2Y11Z3+X2Y10Z4+X2Y6Z8+2X5Y4Z6+35X4Y7Z4+X4Y5Z6+4X4Y4Z7+X3Y9Z3+2X3Y8Z4+X3Y5Z7+2X3Y2Z10+7X2Y11Z2+2X2Y6Z7+3X8Y4Z2+X7Y3Z4+X5Y3Z6+7X4Y7Z3+14X4Y6Z4+X4Y4Z6+4X4Y3Z7+X4YZ9+2X3Y8Z3+8X3Y7Z4+2X3Y4Z7+7X2Y10Z2+2X2Y9Z3+2X2Y8Z4+96X2Y6Z6+4X2Y4Z8+X8Y3Z2+X7Y4Z2+2X6Y3Z4+2X5Y4Z4+2X4Y7Z2+15X4Y5Z4+X4Y4Z5+4X4Y3Z6+X4Y2Z7+5X3Y7Z3+X3Y3Z7+X2Y8Z3+7X2Y7Z4+X2Y5Z6+7X8Y2Z2+X7Y3Z2+10X6Y4Z2+7X6Y2Z4+2X4Y6Z2+X4Y5Z3+250X4Y4Z4+19X3Y6Z3+X3Y5Z4+X3Y2Z7+2X2Y9Z+10X2Y8Z2+3X2Y7Z3+12X2Y6Z4+16X2Y4Z6+X2Y3Z7+19X2Y2Z8+2XY9Z2+XY5Z6+2X8YZ2+X7Y2Z2+2X6YZ4+2X5Y4Z2+13X4Y4Z3+57X4Y3Z4+4X3Y6Z2+10X3Y4Z4+X2Y8Z+3X2Y7Z2+5X2Y5Z4+7X2Y3Z6+2X2Y2Z7+2XY9Z+XY7Z3+2XY6Z4+2XY4Z6+65X6Y2Z2+X6YZ3+8X5Y4Z+2X5Y3Z2+2X5Y2Z3+9X4Y4Z2+163X4Y3Z3+33X4Y2Z4+2X3Y4Z3+19X3Y3Z4+46X2Y6Z2+53X2Y4Z4+X2Y3Z5+48X2Y2Z6+XY8Z+XY6Z3+3XY4Z5+X5Y3Z+4X5Y2Z2+7X4Y3Z2+4X4YZ4+2X3Y4Z2+5X3Y3Z3+2X3Y2Z4+16X2Y5Z2+14X2Y4Z3+22X2Y3Z4+7X2Y2Z5+7X2YZ6+12XY6Z2+2XY4Z4+6XY2Z6+2X5Y2Z+X5YZ2+43X4Y2Z2+X4YZ3+2X3Y3Z2+2X3Y2Z3+2X2Y5Z+370X2Y4Z2+407X2Y3Z3+252X2Y2Z4+72XY6Z+2XY3Z4+30XYZ6+X5YZ+2X4YZ2+38X3Y2Z2+11X2Y4Z+41X2Y3Z2+3X2Y2Z3+22X2YZ4+46XY4Z2+243XY3Z3+40XY2Z4+86X3Y2Z+42X3YZ2+2X2Y3Z+653X2Y2Z2+38XY4Z+18XY3Z2+30XY2Z3+33XYZ4+110X3YZ+82X2Y2Z+86X2YZ2+82XY3Z+316XY2Z2+53XYZ3+94X2YZ+266XY2Z+276XYZ2+256XYZX7Y8Z117X8Y8Z8X7Y7Z10X8Y8Z73X14Y4Z43X8Y7Z73X7Y8Z73X7Y7Z82X4Y14Z4X4Y4Z14X13Y4Z4X8Y7Z62X7Y7Z7X4Y14Z3X3Y4Z14X14Y2Z4X11Y2Z7X8Y6Z69X7Y6Z73X6Y7Z79X6Y6Z8X4Y9Z7X4Y8Z86X4Y4Z12X2Y14Z4X12Y3Z43X7Y6Z67X6Y6Z73X4Y8Z7X4Y4Z11X12Y3Z32X11Y4Z3X7Y5Z62X6Y5Z7X4Y11Z32X4Y10Z4X4Y7Z72X4Y6Z84X4Y4Z10X4Y3Z112X4Y2Z12X3Y8Z74X3Y4Z112X10Y4Z3X8Y3Z6X5Y5Z7X4Y10Z3X4Y7Z6X4Y6Z7X4Y2Z11X3Y6Z85X2Y13Z2X2Y11Z4X12YZ3X10Y3Z3X7Y2Z73X6Y4Z62X5Y4Z7X4Y9Z310X4Y8Z465X4Y6Z62X4Y4Z8X4Y3Z92X4Y2Z10X3Y10Z3X3Y9Z4X3Y8Z52X3Y3Z10X2Y13Z2X2Y12Z2X2Y11Z3X2Y10Z4X2Y6Z82X5Y4Z635X4Y7Z4X4Y5Z64X4Y4Z7X3Y9Z32X3Y8Z4X3Y5Z72X3Y2Z107X2Y11Z22X2Y6Z73X8Y4Z2X7Y3Z4X5Y3Z67X4Y7Z314X4Y6Z4X4Y4Z64X4Y3Z7X4YZ92X3Y8Z38X3Y7Z42X3Y4Z77X2Y10Z22X2Y9Z32X2Y8Z496X2Y6Z64X2Y4Z8X8Y3Z2X7Y4Z22X6Y3Z42X5Y4Z42X4Y7Z215X4Y5Z4X4Y4Z54X4Y3Z6X4Y2Z75X3Y7Z3X3Y3Z7X2Y8Z37X2Y7Z4X2Y5Z67X8Y2Z2X7Y3Z210X6Y4Z27X6Y2Z42X4Y6Z2X4Y5Z3250X4Y4Z419X3Y6Z3X3Y5Z4X3Y2Z72X2Y9Z10X2Y8Z23X2Y7Z312X2Y6Z416X2Y4Z6X2Y3Z719X2Y2Z82XY9Z2XY5Z62X8YZ2X7Y2Z22X6YZ42X5Y4Z213X4Y4Z357X4Y3Z44X3Y6Z210X3Y4Z4X2Y8Z3X2Y7Z25X2Y5Z47X2Y3Z62X2Y2Z72XY9ZXY7Z32XY6Z42XY4Z665X6Y2Z2X6YZ38X5Y4Z2X5Y3Z22X5Y2Z39X4Y4Z2163X4Y3Z333X4Y2Z42X3Y4Z319X3Y3Z446X2Y6Z253X2Y4Z4X2Y3Z548X2Y2Z6XY8ZXY6Z33XY4Z5X5Y3Z4X5Y2Z27X4Y3Z24X4YZ42X3Y4Z25X3Y3Z32X3Y2Z416X2Y5Z214X2Y4Z322X2Y3Z47X2Y2Z57X2YZ612XY6Z22XY4Z46XY2Z62X5Y2ZX5YZ243X4Y2Z2X4YZ32X3Y3Z22X3Y2Z32X2Y5Z370X2Y4Z2407X2Y3Z3252X2Y2Z472XY6Z2XY3Z430XYZ6X5YZ2X4YZ238X3Y2Z211X2Y4Z41X2Y3Z23X2Y2Z322X2YZ446XY4Z2243XY3Z340XY2Z486X3Y2Z42X3YZ22X2Y3Z653X2Y2Z238XY4Z18XY3Z230XY2Z333XYZ4110X3YZ82X2Y2Z86X2YZ282XY3Z316XY2Z253XYZ394X2YZ266XY2Z276XYZ2256XYZX^7*Y^8*Z^11+7*X^8*Y^8*Z^8+X^7*Y^7*Z^10+X^8*Y^8*Z^7+3*X^14*Y^4*Z^4+3*X^8*Y^7*Z^7+3*X^7*Y^8*Z^7+3*X^7*Y^7*Z^8+2*X^4*Y^14*Z^4+X^4*Y^4*Z^14+X^13*Y^4*Z^4+X^8*Y^7*Z^6+2*X^7*Y^7*Z^7+X^4*Y^14*Z^3+X^3*Y^4*Z^14+X^14*Y^2*Z^4+X^11*Y^2*Z^7+X^8*Y^6*Z^6+9*X^7*Y^6*Z^7+3*X^6*Y^7*Z^7+9*X^6*Y^6*Z^8+X^4*Y^9*Z^7+X^4*Y^8*Z^8+6*X^4*Y^4*Z^12+X^2*Y^14*Z^4+X^12*Y^3*Z^4+3*X^7*Y^6*Z^6+7*X^6*Y^6*Z^7+3*X^4*Y^8*Z^7+X^4*Y^4*Z^11+X^12*Y^3*Z^3+2*X^11*Y^4*Z^3+X^7*Y^5*Z^6+2*X^6*Y^5*Z^7+X^4*Y^11*Z^3+2*X^4*Y^10*Z^4+X^4*Y^7*Z^7+2*X^4*Y^6*Z^8+4*X^4*Y^4*Z^10+X^4*Y^3*Z^11+2*X^4*Y^2*Z^12+X^3*Y^8*Z^7+4*X^3*Y^4*Z^11+2*X^10*Y^4*Z^3+X^8*Y^3*Z^6+X^5*Y^5*Z^7+X^4*Y^10*Z^3+X^4*Y^7*Z^6+X^4*Y^6*Z^7+X^4*Y^2*Z^11+X^3*Y^6*Z^8+5*X^2*Y^13*Z^2+X^2*Y^11*Z^4+X^12*Y*Z^3+X^10*Y^3*Z^3+X^7*Y^2*Z^7+3*X^6*Y^4*Z^6+2*X^5*Y^4*Z^7+X^4*Y^9*Z^3+10*X^4*Y^8*Z^4+65*X^4*Y^6*Z^6+2*X^4*Y^4*Z^8+X^4*Y^3*Z^9+2*X^4*Y^2*Z^10+X^3*Y^10*Z^3+X^3*Y^9*Z^4+X^3*Y^8*Z^5+2*X^3*Y^3*Z^10+X^2*Y^13*Z+2*X^2*Y^12*Z^2+X^2*Y^11*Z^3+X^2*Y^10*Z^4+X^2*Y^6*Z^8+2*X^5*Y^4*Z^6+35*X^4*Y^7*Z^4+X^4*Y^5*Z^6+4*X^4*Y^4*Z^7+X^3*Y^9*Z^3+2*X^3*Y^8*Z^4+X^3*Y^5*Z^7+2*X^3*Y^2*Z^10+7*X^2*Y^11*Z^2+2*X^2*Y^6*Z^7+3*X^8*Y^4*Z^2+X^7*Y^3*Z^4+X^5*Y^3*Z^6+7*X^4*Y^7*Z^3+14*X^4*Y^6*Z^4+X^4*Y^4*Z^6+4*X^4*Y^3*Z^7+X^4*Y*Z^9+2*X^3*Y^8*Z^3+8*X^3*Y^7*Z^4+2*X^3*Y^4*Z^7+7*X^2*Y^10*Z^2+2*X^2*Y^9*Z^3+2*X^2*Y^8*Z^4+96*X^2*Y^6*Z^6+4*X^2*Y^4*Z^8+X^8*Y^3*Z^2+X^7*Y^4*Z^2+2*X^6*Y^3*Z^4+2*X^5*Y^4*Z^4+2*X^4*Y^7*Z^2+15*X^4*Y^5*Z^4+X^4*Y^4*Z^5+4*X^4*Y^3*Z^6+X^4*Y^2*Z^7+5*X^3*Y^7*Z^3+X^3*Y^3*Z^7+X^2*Y^8*Z^3+7*X^2*Y^7*Z^4+X^2*Y^5*Z^6+7*X^8*Y^2*Z^2+X^7*Y^3*Z^2+10*X^6*Y^4*Z^2+7*X^6*Y^2*Z^4+2*X^4*Y^6*Z^2+X^4*Y^5*Z^3+250*X^4*Y^4*Z^4+19*X^3*Y^6*Z^3+X^3*Y^5*Z^4+X^3*Y^2*Z^7+2*X^2*Y^9*Z+10*X^2*Y^8*Z^2+3*X^2*Y^7*Z^3+12*X^2*Y^6*Z^4+16*X^2*Y^4*Z^6+X^2*Y^3*Z^7+19*X^2*Y^2*Z^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Algorithm definition

The algorithm ⟨19×19×27:5679⟩ could be constructed using the following decomposition:

⟨19×19×27:5679⟩ = ⟨10×9×15:870⟩ + ⟨10×9×15:870⟩ + ⟨9×10×12:696⟩ + ⟨10×10×12:795⟩ + ⟨9×10×15:870⟩ + ⟨9×9×12:600⟩ + ⟨10×10×15:978⟩.

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_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_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_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_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_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_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_8_1A_8_2A_8_3A_8_4A_8_5A_8_6A_8_7A_8_8A_8_9A_8_10A_8_11A_8_12A_8_13A_8_14A_8_15A_8_16A_8_17A_8_18A_8_19A_9_1A_9_2A_9_3A_9_4A_9_5A_9_6A_9_7A_9_8A_9_9A_9_10A_9_11A_9_12A_9_13A_9_14A_9_15A_9_16A_9_17A_9_18A_9_19A_10_1A_10_2A_10_3A_10_4A_10_5A_10_6A_10_7A_10_8A_10_9A_10_10A_10_11A_10_12A_10_13A_10_14A_10_15A_10_16A_10_17A_10_18A_10_19A_11_1A_11_2A_11_3A_11_4A_11_5A_11_6A_11_7A_11_8A_11_9A_11_10A_11_11A_11_12A_11_13A_11_14A_11_15A_11_16A_11_17A_11_18A_11_19A_12_1A_12_2A_12_3A_12_4A_12_5A_12_6A_12_7A_12_8A_12_9A_12_10A_12_11A_12_12A_12_13A_12_14A_12_15A_12_16A_12_17A_12_18A_12_19A_13_1A_13_2A_13_3A_13_4A_13_5A_13_6A_13_7A_13_8A_13_9A_13_10A_13_11A_13_12A_13_13A_13_14A_13_15A_13_16A_13_17A_13_18A_13_19A_14_1A_14_2A_14_3A_14_4A_14_5A_14_6A_14_7A_14_8A_14_9A_14_10A_14_11A_14_12A_14_13A_14_14A_14_15A_14_16A_14_17A_14_18A_14_19A_15_1A_15_2A_15_3A_15_4A_15_5A_15_6A_15_7A_15_8A_15_9A_15_10A_15_11A_15_12A_15_13A_15_14A_15_15A_15_16A_15_17A_15_18A_15_19A_16_1A_16_2A_16_3A_16_4A_16_5A_16_6A_16_7A_16_8A_16_9A_16_10A_16_11A_16_12A_16_13A_16_14A_16_15A_16_16A_16_17A_16_18A_16_19A_17_1A_17_2A_17_3A_17_4A_17_5A_17_6A_17_7A_17_8A_17_9A_17_10A_17_11A_17_12A_17_13A_17_14A_17_15A_17_16A_17_17A_17_18A_17_19A_18_1A_18_2A_18_3A_18_4A_18_5A_18_6A_18_7A_18_8A_18_9A_18_10A_18_11A_18_12A_18_13A_18_14A_18_15A_18_16A_18_17A_18_18A_18_19A_19_1A_19_2A_19_3A_19_4A_19_5A_19_6A_19_7A_19_8A_19_9A_19_10A_19_11A_19_12A_19_13A_19_14A_19_15A_19_16A_19_17A_19_18A_19_19B_1_1B_1_2B_1_3B_1_4B_1_5B_1_6B_1_7B_1_8B_1_9B_1_10B_1_11B_1_12B_1_13B_1_14B_1_15B_1_16B_1_17B_1_18B_1_19B_1_20B_1_21B_1_22B_1_23B_1_24B_1_25B_1_26B_1_27B_2_1B_2_2B_2_3B_2_4B_2_5B_2_6B_2_7B_2_8B_2_9B_2_10B_2_11B_2_12B_2_13B_2_14B_2_15B_2_16B_2_17B_2_18B_2_19B_2_20B_2_21B_2_22B_2_23B_2_24B_2_25B_2_26B_2_27B_3_1B_3_2B_3_3B_3_4B_3_5B_3_6B_3_7B_3_8B_3_9B_3_10B_3_11B_3_12B_3_13B_3_14B_3_15B_3_16B_3_17B_3_18B_3_19B_3_20B_3_21B_3_22B_3_23B_3_24B_3_25B_3_26B_3_27B_4_1B_4_2B_4_3B_4_4B_4_5B_4_6B_4_7B_4_8B_4_9B_4_10B_4_11B_4_12B_4_13B_4_14B_4_15B_4_16B_4_17B_4_18B_4_19B_4_20B_4_21B_4_22B_4_23B_4_24B_4_25B_4_26B_4_27B_5_1B_5_2B_5_3B_5_4B_5_5B_5_6B_5_7B_5_8B_5_9B_5_10B_5_11B_5_12B_5_13B_5_14B_5_15B_5_16B_5_17B_5_18B_5_19B_5_20B_5_21B_5_22B_5_23B_5_24B_5_25B_5_26B_5_27B_6_1B_6_2B_6_3B_6_4B_6_5B_6_6B_6_7B_6_8B_6_9B_6_10B_6_11B_6_12B_6_13B_6_14B_6_15B_6_16B_6_17B_6_18B_6_19B_6_20B_6_21B_6_22B_6_23B_6_24B_6_25B_6_26B_6_27B_7_1B_7_2B_7_3B_7_4B_7_5B_7_6B_7_7B_7_8B_7_9B_7_10B_7_11B_7_12B_7_13B_7_14B_7_15B_7_16B_7_17B_7_18B_7_19B_7_20B_7_21B_7_22B_7_23B_7_24B_7_25B_7_26B_7_27B_8_1B_8_2B_8_3B_8_4B_8_5B_8_6B_8_7B_8_8B_8_9B_8_10B_8_11B_8_12B_8_13B_8_14B_8_15B_8_16B_8_17B_8_18B_8_19B_8_20B_8_21B_8_22B_8_23B_8_24B_8_25B_8_26B_8_27B_9_1B_9_2B_9_3B_9_4B_9_5B_9_6B_9_7B_9_8B_9_9B_9_10B_9_11B_9_12B_9_13B_9_14B_9_15B_9_16B_9_17B_9_18B_9_19B_9_20B_9_21B_9_22B_9_23B_9_24B_9_25B_9_26B_9_27B_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_10_23B_10_24B_10_25B_10_26B_10_27B_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_11_23B_11_24B_11_25B_11_26B_11_27B_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_12_23B_12_24B_12_25B_12_26B_12_27B_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_13_23B_13_24B_13_25B_13_26B_13_27B_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_14_23B_14_24B_14_25B_14_26B_14_27B_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_15_23B_15_24B_15_25B_15_26B_15_27B_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_16_23B_16_24B_16_25B_16_26B_16_27B_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_17_23B_17_24B_17_25B_17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19, [[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_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_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_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_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_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_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_8_1,A_8_2,A_8_3,A_8_4,A_8_5,A_8_6,A_8_7,A_8_8,A_8_9,A_8_10,A_8_11,A_8_12,A_8_13,A_8_14,A_8_15,A_8_16,A_8_17,A_8_18,A_8_19],[A_9_1,A_9_2,A_9_3,A_9_4,A_9_5,A_9_6,A_9_7,A_9_8,A_9_9,A_9_10,A_9_11,A_9_12,A_9_13,A_9_14,A_9_15,A_9_16,A_9_17,A_9_18,A_9_19],[A_10_1,A_10_2,A_10_3,A_10_4,A_10_5,A_10_6,A_10_7,A_10_8,A_10_9,A_10_10,A_10_11,A_10_12,A_10_13,A_10_14,A_10_15,A_10_16,A_10_17,A_10_18,A_10_19],[A_11_1,A_11_2,A_11_3,A_11_4,A_11_5,A_11_6,A_11_7,A_11_8,A_11_9,A_11_10,A_11_11,A_11_12,A_11_13,A_11_14,A_11_15,A_11_16,A_11_17,A_11_18,A_11_19],[A_12_1,A_12_2,A_12_3,A_12_4,A_12_5,A_12_6,A_12_7,A_12_8,A_12_9,A_12_10,A_12_11,A_12_12,A_12_13,A_12_14,A_12_15,A_12_16,A_12_17,A_12_18,A_12_19],[A_13_1,A_13_2,A_13_3,A_13_4,A_13_5,A_13_6,A_13_7,A_13_8,A_13_9,A_13_10,A_13_11,A_13_12,A_13_13,A_13_14,A_13_15,A_13_16,A_13_17,A_13_18,A_13_19],[A_14_1,A_14_2,A_14_3,A_14_4,A_14_5,A_14_6,A_14_7,A_14_8,A_14_9,A_14_10,A_14_11,A_14_12,A_14_13,A_14_14,A_14_15,A_14_16,A_14_17,A_14_18,A_14_19],[A_15_1,A_15_2,A_15_3,A_15_4,A_15_5,A_15_6,A_15_7,A_15_8,A_15_9,A_15_10,A_15_11,A_15_12,A_15_13,A_15_14,A_15_15,A_15_16,A_15_17,A_15_18,A_15_19],[A_16_1,A_16_2,A_16_3,A_16_4,A_16_5,A_16_6,A_16_7,A_16_8,A_16_9,A_16_10,A_16_11,A_16_12,A_16_13,A_16_14,A_16_15,A_16_16,A_16_17,A_16_18,A_16_19],[A_17_1,A_17_2,A_17_3,A_17_4,A_17_5,A_17_6,A_17_7,A_17_8,A_17_9,A_17_10,A_17_11,A_17_12,A_17_13,A_17_14,A_17_15,A_17_16,A_17_17,A_17_18,A_17_19],[A_18_1,A_18_2,A_18_3,A_18_4,A_18_5,A_18_6,A_18_7,A_18_8,A_18_9,A_18_10,A_18_11,A_18_12,A_18_13,A_18_14,A_18_15,A_18_16,A_18_17,A_18_18,A_18_19],[A_19_1,A_19_2,A_19_3,A_19_4,A_19_5,A_19_6,A_19_7,A_19_8,A_19_9,A_19_10,A_19_11,A_19_12,A_19_13,A_19_14,A_19_15,A_19_16,A_19_17,A_19_18,A_19_19]]),Matrix(19, 27, [[B_1_1,B_1_2,B_1_3,B_1_4,B_1_5,B_1_6,B_1_7,B_1_8,B_1_9,B_1_10,B_1_11,B_1_12,B_1_13,B_1_14,B_1_15,B_1_16,B_1_17,B_1_18,B_1_19,B_1_20,B_1_21,B_1_22,B_1_23,B_1_24,B_1_25,B_1_26,B_1_27],[B_2_1,B_2_2,B_2_3,B_2_4,B_2_5,B_2_6,B_2_7,B_2_8,B_2_9,B_2_10,B_2_11,B_2_12,B_2_13,B_2_14,B_2_15,B_2_16,B_2_17,B_2_18,B_2_19,B_2_20,B_2_21,B_2_22,B_2_23,B_2_24,B_2_25,B_2_26,B_2_27],[B_3_1,B_3_2,B_3_3,B_3_4,B_3_5,B_3_6,B_3_7,B_3_8,B_3_9,B_3_10,B_3_11,B_3_12,B_3_13,B_3_14,B_3_15,B_3_16,B_3_17,B_3_18,B_3_19,B_3_20,B_3_21,B_3_22,B_3_23,B_3_24,B_3_25,B_3_26,B_3_27],[B_4_1,B_4_2,B_4_3,B_4_4,B_4_5,B_4_6,B_4_7,B_4_8,B_4_9,B_4_10,B_4_11,B_4_12,B_4_13,B_4_14,B_4_15,B_4_16,B_4_17,B_4_18,B_4_19,B_4_20,B_4_21,B_4_22,B_4_23,B_4_24,B_4_25,B_4_26,B_4_27],[B_5_1,B_5_2,B_5_3,B_5_4,B_5_5,B_5_6,B_5_7,B_5_8,B_5_9,B_5_10,B_5_11,B_5_12,B_5_13,B_5_14,B_5_15,B_5_16,B_5_17,B_5_18,B_5_19,B_5_20,B_5_21,B_5_22,B_5_23,B_5_24,B_5_25,B_5_26,B_5_27],[B_6_1,B_6_2,B_6_3,B_6_4,B_6_5,B_6_6,B_6_7,B_6_8,B_6_9,B_6_10,B_6_11,B_6_12,B_6_13,B_6_14,B_6_15,B_6_16,B_6_17,B_6_18,B_6_19,B_6_20,B_6_21,B_6_22,B_6_23,B_6_24,B_6_25,B_6_26,B_6_27],[B_7_1,B_7_2,B_7_3,B_7_4,B_7_5,B_7_6,B_7_7,B_7_8,B_7_9,B_7_10,B_7_11,B_7_12,B_7_13,B_7_14,B_7_15,B_7_16,B_7_17,B_7_18,B_7_19,B_7_20,B_7_21,B_7_22,B_7_23,B_7_24,B_7_25,B_7_26,B_7_27],[B_8_1,B_8_2,B_8_3,B_8_4,B_8_5,B_8_6,B_8_7,B_8_8,B_8_9,B_8_10,B_8_11,B_8_12,B_8_13,B_8_14,B_8_15,B_8_16,B_8_17,B_8_18,B_8_19,B_8_20,B_8_21,B_8_22,B_8_23,B_8_24,B_8_25,B_8_26,B_8_27],[B_9_1,B_9_2,B_9_3,B_9_4,B_9_5,B_9_6,B_9_7,B_9_8,B_9_9,B_9_10,B_9_11,B_9_12,B_9_13,B_9_14,B_9_15,B_9_16,B_9_17,B_9_18,B_9_19,B_9_20,B_9_21,B_9_22,B_9_23,B_9_24,B_9_25,B_9_26,B_9_27],[B_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_10_23,B_10_24,B_10_25,B_10_26,B_10_27],[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_11_23,B_11_24,B_11_25,B_11_26,B_11_27],[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_12_23,B_12_24,B_12_25,B_12_26,B_12_27],[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_13_23,B_13_24,B_13_25,B_13_26,B_13_27],[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_14_23,B_14_24,B_14_25,B_14_26,B_14_27],[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_15_23,B_15_24,B_15_25,B_15_26,B_15_27],[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_16_23,B_16_24,B_16_25,B_16_26,B_16_27],[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_17_23,B_17_24,B_17_25,B_17_26,B_17_27],[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_18_23,B_18_24,B_18_25,B_18_26,B_18_27],[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_19_23,B_19_24,B_19_25,B_19_26,B_19_27]]),Matrix(27, 19, [[C_1_1,C_1_2,C_1_3,C_1_4,C_1_5,C_1_6,C_1_7,C_1_8,C_1_9,C_1_10,C_1_11,C_1_12,C_1_13,C_1_14,C_1_15,C_1_16,C_1_17,C_1_18,C_1_19],[C_2_1,C_2_2,C_2_3,C_2_4,C_2_5,C_2_6,C_2_7,C_2_8,C_2_9,C_2_10,C_2_11,C_2_12,C_2_13,C_2_14,C_2_15,C_2_16,C_2_17,C_2_18,C_2_19],[C_3_1,C_3_2,C_3_3,C_3_4,C_3_5,C_3_6,C_3_7,C_3_8,C_3_9,C_3_10,C_3_11,C_3_12,C_3_13,C_3_14,C_3_15,C_3_16,C_3_17,C_3_18,C_3_19],[C_4_1,C_4_2,C_4_3,C_4_4,C_4_5,C_4_6,C_4_7,C_4_8,C_4_9,C_4_10,C_4_11,C_4_12,C_4_13,C_4_14,C_4_15,C_4_16,C_4_17,C_4_18,C_4_19],[C_5_1,C_5_2,C_5_3,C_5_4,C_5_5,C_5_6,C_5_7,C_5_8,C_5_9,C_5_10,C_5_11,C_5_12,C_5_13,C_5_14,C_5_15,C_5_16,C_5_17,C_5_18,C_5_19],[C_6_1,C_6_2,C_6_3,C_6_4,C_6_5,C_6_6,C_6_7,C_6_8,C_6_9,C_6_10,C_6_11,C_6_12,C_6_13,C_6_14,C_6_15,C_6_16,C_6_17,C_6_18,C_6_19],[C_7_1,C_7_2,C_7_3,C_7_4,C_7_5,C_7_6,C_7_7,C_7_8,C_7_9,C_7_10,C_7_11,C_7_12,C_7_13,C_7_14,C_7_15,C_7_16,C_7_17,C_7_18,C_7_19],[C_8_1,C_8_2,C_8_3,C_8_4,C_8_5,C_8_6,C_8_7,C_8_8,C_8_9,C_8_10,C_8_11,C_8_12,C_8_13,C_8_14,C_8_15,C_8_16,C_8_17,C_8_18,C_8_19],[C_9_1,C_9_2,C_9_3,C_9_4,C_9_5,C_9_6,C_9_7,C_9_8,C_9_9,C_9_10,C_9_11,C_9_12,C_9_13,C_9_14,C_9_15,C_9_16,C_9_17,C_9_18,C_9_19],[C_10_1,C_10_2,C_10_3,C_10_4,C_10_5,C_10_6,C_10_7,C_10_8,C_10_9,C_10_10,C_10_11,C_10_12,C_10_13,C_10_14,C_10_15,C_10_16,C_10_17,C_10_18,C_10_19],[C_11_1,C_11_2,C_11_3,C_11_4,C_11_5,C_11_6,C_11_7,C_11_8,C_11_9,C_11_10,C_11_11,C_11_12,C_11_13,C_11_14,C_11_15,C_11_16,C_11_17,C_11_18,C_11_19],[C_12_1,C_12_2,C_12_3,C_12_4,C_12_5,C_12_6,C_12_7,C_12_8,C_12_9,C_12_10,C_12_11,C_12_12,C_12_13,C_12_14,C_12_15,C_12_16,C_12_17,C_12_18,C_12_19],[C_13_1,C_13_2,C_13_3,C_13_4,C_13_5,C_13_6,C_13_7,C_13_8,C_13_9,C_13_10,C_13_11,C_13_12,C_13_13,C_13_14,C_13_15,C_13_16,C_13_17,C_13_18,C_13_19],[C_14_1,C_14_2,C_14_3,C_14_4,C_14_5,C_14_6,C_14_7,C_14_8,C_14_9,C_14_10,C_14_11,C_14_12,C_14_13,C_14_14,C_14_15,C_14_16,C_14_17,C_14_18,C_14_19],[C_15_1,C_15_2,C_15_3,C_15_4,C_15_5,C_15_6,C_15_7,C_15_8,C_15_9,C_15_10,C_15_11,C_15_12,C_15_13,C_15_14,C_15_15,C_15_16,C_15_17,C_15_18,C_15_19],[C_16_1,C_16_2,C_16_3,C_16_4,C_16_5,C_16_6,C_16_7,C_16_8,C_16_9,C_16_10,C_16_11,C_16_12,C_16_13,C_16_14,C_16_15,C_16_16,C_16_17,C_16_18,C_16_19],[C_17_1,C_17_2,C_17_3,C_17_4,C_17_5,C_17_6,C_17_7,C_17_8,C_17_9,C_17_10,C_17_11,C_17_12,C_17_13,C_17_14,C_17_15,C_17_16,C_17_17,C_17_18,C_17_19],[C_18_1,C_18_2,C_18_3,C_18_4,C_18_5,C_18_6,C_18_7,C_18_8,C_18_9,C_18_10,C_18_11,C_18_12,C_18_13,C_18_14,C_18_15,C_18_16,C_18_17,C_18_18,C_18_19],[C_19_1,C_19_2,C_19_3,C_19_4,C_19_5,C_19_6,C_19_7,C_19_8,C_19_9,C_19_10,C_19_11,C_19_12,C_19_13,C_19_14,C_19_15,C_19_16,C_19_17,C_19_18,C_19_19],[C_20_1,C_20_2,C_20_3,C_20_4,C_20_5,C_20_6,C_20_7,C_20_8,C_20_9,C_20_10,C_20_11,C_20_12,C_20_13,C_20_14,C_20_15,C_20_16,C_20_17,C_20_18,C_20_19],[C_21_1,C_21_2,C_21_3,C_21_4,C_21_5,C_21_6,C_21_7,C_21_8,C_21_9,C_21_10,C_21_11,C_21_12,C_21_13,C_21_14,C_21_15,C_21_16,C_21_17,C_21_18,C_21_19],[C_22_1,C_22_2,C_22_3,C_22_4,C_22_5,C_22_6,C_22_7,C_22_8,C_22_9,C_22_10,C_22_11,C_22_12,C_22_13,C_22_14,C_22_15,C_22_16,C_22_17,C_22_18,C_22_19],[C_23_1,C_23_2,C_23_3,C_23_4,C_23_5,C_23_6,C_23_7,C_23_8,C_23_9,C_23_10,C_23_11,C_23_12,C_23_13,C_23_14,C_23_15,C_23_16,C_23_17,C_23_18,C_23_19],[C_24_1,C_24_2,C_24_3,C_24_4,C_24_5,C_24_6,C_24_7,C_24_8,C_24_9,C_24_10,C_24_11,C_24_12,C_24_13,C_24_14,C_24_15,C_24_16,C_24_17,C_24_18,C_24_19],[C_25_1,C_25_2,C_25_3,C_25_4,C_25_5,C_25_6,C_25_7,C_25_8,C_25_9,C_25_10,C_25_11,C_25_12,C_25_13,C_25_14,C_25_15,C_25_16,C_25_17,C_25_18,C_25_19],[C_26_1,C_26_2,C_26_3,C_26_4,C_26_5,C_26_6,C_26_7,C_26_8,C_26_9,C_26_10,C_26_11,C_26_12,C_26_13,C_26_14,C_26_15,C_26_16,C_26_17,C_26_18,C_26_19],[C_27_1,C_27_2,C_27_3,C_27_4,C_27_5,C_27_6,C_27_7,C_27_8,C_27_9,C_27_10,C_27_11,C_27_12,C_27_13,C_27_14,C_27_15,C_27_16,C_27_17,C_27_18,C_27_19]]))) = Trace(Mul(Matrix(10, 9, [[A_5_6-A_5_11,A_5_7-A_5_12,A_5_8-A_5_13,A_5_9-A_5_14,A_5_10-A_5_15,A_5_1-A_5_16,A_5_2-A_5_17,A_5_3-A_5_18,A_5_4-A_5_19],[A_11_6-A_11_11,A_11_7-A_11_12,A_11_8-A_11_13,A_11_9-A_11_14,A_11_10-A_11_15,A_11_1-A_11_16,A_11_2-A_11_17,A_11_3-A_11_18,A_11_4-A_11_19],[A_12_6-A_12_11,A_12_7-A_12_12,A_12_8-A_12_13,A_12_9-A_12_14,A_12_10-A_12_15,A_12_1-A_12_16,A_12_2-A_12_17,A_12_3-A_12_18,A_12_4-A_12_19],[A_13_6-A_13_11,A_13_7-A_13_12,A_13_8-A_13_13,A_13_9-A_13_14,A_13_10-A_13_15,A_13_1-A_13_16,A_13_2-A_13_17,A_13_3-A_13_18,A_13_4-A_13_19],[A_14_6-A_14_11,A_14_7-A_14_12,A_14_8-A_14_13,A_14_9-A_14_14,A_14_10-A_14_15,A_14_1-A_14_16,A_14_2-A_14_17,A_14_3-A_14_18,A_14_4-A_14_19],[A_15_6-A_15_11,A_15_7-A_15_12,A_15_8-A_15_13,A_15_9-A_15_14,A_15_10-A_15_15,A_15_1-A_15_16,A_15_2-A_15_17,A_15_3-A_15_18,A_15_4-A_15_19],[A_16_6-A_16_11,A_16_7-A_16_12,A_16_8-A_16_13,A_16_9-A_16_14,A_16_10-A_16_15,A_16_1-A_16_16,A_16_2-A_16_17,A_16_3-A_16_18,A_16_4-A_16_19],[A_17_6-A_17_11,A_17_7-A_17_12,A_17_8-A_17_13,A_17_9-A_17_14,A_17_10-A_17_15,A_17_1-A_17_16,A_17_2-A_17_17,A_17_3-A_17_18,A_17_4-A_17_19],[A_18_6-A_18_11,A_18_7-A_18_12,A_18_8-A_18_13,A_18_9-A_18_14,A_18_10-A_18_15,A_18_1-A_18_16,A_18_2-A_18_17,A_18_3-A_18_18,A_18_4-A_18_19],[A_19_6-A_19_11,A_19_7-A_19_12,A_19_8-A_19_13,A_19_9-A_19_14,A_19_10-A_19_15,A_19_1-A_19_16,A_19_2-A_19_17,A_19_3-A_19_18,A_19_4-A_19_19]]),Matrix(9, 15, [[B_6_13,B_6_14,B_6_15,-B_6_1+B_6_16,-B_6_2+B_6_17,-B_6_3+B_6_18,-B_6_4+B_6_19,-B_6_5+B_6_20,-B_6_6+B_6_21,-B_6_7+B_6_22,-B_6_8+B_6_23,-B_6_9+B_6_24,-B_6_10+B_6_25,-B_6_11+B_6_26,-B_6_12+B_6_27],[B_7_13,B_7_14,B_7_15,-B_7_1+B_7_16,-B_7_2+B_7_17,-B_7_3+B_7_18,-B_7_4+B_7_19,-B_7_5+B_7_20,-B_7_6+B_7_21,-B_7_7+B_7_22,-B_7_8+B_7_23,-B_7_9+B_7_24,-B_7_10+B_7_25,-B_7_11+B_7_26,-B_7_12+B_7_27],[B_8_13,B_8_14,B_8_15,-B_8_1+B_8_16,-B_8_2+B_8_17,-B_8_3+B_8_18,-B_8_4+B_8_19,-B_8_5+B_8_20,-B_8_6+B_8_21,-B_8_7+B_8_22,-B_8_8+B_8_23,-B_8_9+B_8_24,-B_8_10+B_8_25,-B_8_11+B_8_26,-B_8_12+B_8_27],[B_9_13,B_9_14,B_9_15,-B_9_1+B_9_16,-B_9_2+B_9_17,-B_9_3+B_9_18,-B_9_4+B_9_19,-B_9_5+B_9_20,-B_9_6+B_9_21,-B_9_7+B_9_22,-B_9_8+B_9_23,-B_9_9+B_9_24,-B_9_10+B_9_25,-B_9_11+B_9_26,-B_9_12+B_9_27],[B_10_13,B_10_14,B_10_15,-B_10_1+B_10_16,-B_10_2+B_10_17,-B_10_3+B_10_18,-B_10_4+B_10_19,-B_10_5+B_10_20,-B_10_6+B_10_21,-B_10_7+B_10_22,-B_10_8+B_10_23,-B_10_9+B_10_24,-B_10_10+B_10_25,-B_10_11+B_10_26,-B_10_12+B_10_27],[B_1_13,B_1_14,B_1_15,-B_1_1+B_1_16,-B_1_2+B_1_17,-B_1_3+B_1_18,-B_1_4+B_1_19,-B_1_5+B_1_20,-B_1_6+B_1_21,-B_1_7+B_1_22,-B_1_8+B_1_23,-B_1_9+B_1_24,-B_1_10+B_1_25,-B_1_11+B_1_26,-B_1_12+B_1_27],[B_2_13,B_2_14,B_2_15,-B_2_1+B_2_16,-B_2_2+B_2_17,-B_2_3+B_2_18,-B_2_4+B_2_19,-B_2_5+B_2_20,-B_2_6+B_2_21,-B_2_7+B_2_22,-B_2_8+B_2_23,-B_2_9+B_2_24,-B_2_10+B_2_25,-B_2_11+B_2_26,-B_2_12+B_2_27],[B_3_13,B_3_14,B_3_15,-B_3_1+B_3_16,-B_3_2+B_3_17,-B_3_3+B_3_18,-B_3_4+B_3_19,-B_3_5+B_3_20,-B_3_6+B_3_21,-B_3_7+B_3_22,-B_3_8+B_3_23,-B_3_9+B_3_24,-B_3_10+B_3_25,-B_3_11+B_3_26,-B_3_12+B_3_27],[B_4_13,B_4_14,B_4_15,-B_4_1+B_4_16,-B_4_2+B_4_17,-B_4_3+B_4_18,-B_4_4+B_4_19,-B_4_5+B_4_20,-B_4_6+B_4_21,-B_4_7+B_4_22,-B_4_8+B_4_23,-B_4_9+B_4_24,-B_4_10+B_4_25,-B_4_11+B_4_26,-B_4_12+B_4_27]]),Matrix(15, 10, [[C_13_5,-C_13_6+C_13_11,-C_13_7+C_13_12,-C_13_8+C_13_13,-C_13_9+C_13_14,-C_13_10+C_13_15,-C_13_1+C_13_16,-C_13_2+C_13_17,-C_13_3+C_13_18,-C_13_4+C_13_19],[C_14_5,-C_14_6+C_14_11,-C_14_7+C_14_12,-C_14_8+C_14_13,-C_14_9+C_14_14,-C_14_10+C_14_15,-C_14_1+C_14_16,-C_14_2+C_14_17,-C_14_3+C_14_18,-C_14_4+C_14_19],[C_15_5,-C_15_6+C_15_11,-C_15_7+C_15_12,-C_15_8+C_15_13,-C_15_9+C_15_14,-C_15_10+C_15_15,-C_15_1+C_15_16,-C_15_2+C_15_17,-C_15_3+C_15_18,-C_15_4+C_15_19],[C_16_5,-C_16_6+C_16_11,-C_16_7+C_16_12,-C_16_8+C_16_13,-C_16_9+C_16_14,-C_16_10+C_16_15,-C_16_1+C_16_16,-C_16_2+C_16_17,-C_16_3+C_16_18,-C_16_4+C_16_19],[C_17_5,-C_17_6+C_17_11,-C_17_7+C_17_12,-C_17_8+C_17_13,-C_17_9+C_17_14,-C_17_10+C_17_15,-C_17_1+C_17_16,-C_17_2+C_17_17,-C_17_3+C_17_18,-C_17_4+C_17_19],[C_18_5,-C_18_6+C_18_11,-C_18_7+C_18_12,-C_18_8+C_18_13,-C_18_9+C_18_14,-C_18_10+C_18_15,-C_18_1+C_18_16,-C_18_2+C_18_17,-C_18_3+C_18_18,-C_18_4+C_18_19],[C_19_5,-C_19_6+C_19_11,-C_19_7+C_19_12,-C_19_8+C_19_13,-C_19_9+C_19_14,-C_19_10+C_19_15,-C_19_1+C_19_16,-C_19_2+C_19_17,-C_19_3+C_19_18,-C_19_4+C_19_19],[C_20_5,-C_20_6+C_20_11,-C_20_7+C_20_12,-C_20_8+C_20_13,-C_20_9+C_20_14,-C_20_10+C_20_15,-C_20_1+C_20_16,-C_20_2+C_20_17,-C_20_3+C_20_18,-C_20_4+C_20_19],[C_21_5,-C_21_6+C_21_11,-C_21_7+C_21_12,-C_21_8+C_21_13,-C_21_9+C_21_14,-C_21_10+C_21_15,-C_21_1+C_21_16,-C_21_2+C_21_17,-C_21_3+C_21_18,-C_21_4+C_21_19],[C_22_5,-C_22_6+C_22_11,-C_22_7+C_22_12,-C_22_8+C_22_13,-C_22_9+C_22_14,-C_22_10+C_22_15,-C_22_1+C_22_16,-C_22_2+C_22_17,-C_22_3+C_22_18,-C_22_4+C_22_19],[C_23_5,-C_23_6+C_23_11,-C_23_7+C_23_12,-C_23_8+C_23_13,-C_23_9+C_23_14,-C_23_10+C_23_15,-C_23_1+C_23_16,-C_23_2+C_23_17,-C_23_3+C_23_18,-C_23_4+C_23_19],[C_24_5,-C_24_6+C_24_11,-C_24_7+C_24_12,-C_24_8+C_24_13,-C_24_9+C_24_14,-C_24_10+C_24_15,-C_24_1+C_24_16,-C_24_2+C_24_17,-C_24_3+C_24_18,-C_24_4+C_24_19],[C_25_5,-C_25_6+C_25_11,-C_25_7+C_25_12,-C_25_8+C_25_13,-C_25_9+C_25_14,-C_25_10+C_25_15,-C_25_1+C_25_16,-C_25_2+C_25_17,-C_25_3+C_25_18,-C_25_4+C_25_19],[C_26_5,-C_26_6+C_26_11,-C_26_7+C_26_12,-C_26_8+C_26_13,-C_26_9+C_26_14,-C_26_10+C_26_15,-C_26_1+C_26_16,-C_26_2+C_26_17,-C_26_3+C_26_18,-C_26_4+C_26_19],[C_27_5,-C_27_6+C_27_11,-C_27_7+C_27_12,-C_27_8+C_27_13,-C_27_9+C_27_14,-C_27_10+C_27_15,-C_27_1+C_27_16,-C_27_2+C_27_17,-C_27_3+C_27_18,-C_27_4+C_27_19]])))+Trace(Mul(Matrix(10, 9, [[A_5_6,A_5_7,A_5_8,A_5_9,A_5_10,A_5_1,A_5_2,A_5_3,A_5_4],[A_6_6+A_11_6,A_6_7+A_11_7,A_6_8+A_11_8,A_6_9+A_11_9,A_6_10+A_11_10,A_6_1+A_11_1,A_6_2+A_11_2,A_6_3+A_11_3,A_6_4+A_11_4],[A_7_6+A_12_6,A_7_7+A_12_7,A_7_8+A_12_8,A_7_9+A_12_9,A_7_10+A_12_10,A_7_1+A_12_1,A_7_2+A_12_2,A_7_3+A_12_3,A_7_4+A_12_4],[A_8_6+A_13_6,A_8_7+A_13_7,A_8_8+A_13_8,A_8_9+A_13_9,A_8_10+A_13_10,A_8_1+A_13_1,A_8_2+A_13_2,A_8_3+A_13_3,A_8_4+A_13_4],[A_9_6+A_14_6,A_9_7+A_14_7,A_9_8+A_14_8,A_9_9+A_14_9,A_9_10+A_14_10,A_9_1+A_14_1,A_9_2+A_14_2,A_9_3+A_14_3,A_9_4+A_14_4],[A_10_6+A_15_6,A_10_7+A_15_7,A_10_8+A_15_8,A_10_9+A_15_9,A_10_10+A_15_10,A_10_1+A_15_1,A_10_2+A_15_2,A_10_3+A_15_3,A_10_4+A_15_4],[A_1_6+A_16_6,A_1_7+A_16_7,A_1_8+A_16_8,A_1_9+A_16_9,A_1_10+A_16_10,A_1_1+A_16_1,A_1_2+A_16_2,A_1_3+A_16_3,A_1_4+A_16_4],[A_2_6+A_17_6,A_2_7+A_17_7,A_2_8+A_17_8,A_2_9+A_17_9,A_2_10+A_17_10,A_2_1+A_17_1,A_2_2+A_17_2,A_2_3+A_17_3,A_2_4+A_17_4],[A_3_6+A_18_6,A_3_7+A_18_7,A_3_8+A_18_8,A_3_9+A_18_9,A_3_10+A_18_10,A_3_1+A_18_1,A_3_2+A_18_2,A_3_3+A_18_3,A_3_4+A_18_4],[A_4_6+A_19_6,A_4_7+A_19_7,A_4_8+A_19_8,A_4_9+A_19_9,A_4_10+A_19_10,A_4_1+A_19_1,A_4_2+A_19_2,A_4_3+A_19_3,A_4_4+A_19_4]]),Matrix(9, 15, [[B_6_13+B_11_13,B_6_14+B_11_14,B_6_15+B_11_15,B_6_16+B_11_16,B_6_17+B_11_17,B_6_18+B_11_18,B_6_19+B_11_19,B_6_20+B_11_20,B_6_21+B_11_21,B_6_22+B_11_22,B_6_23+B_11_23,B_6_24+B_11_24,B_6_25+B_11_25,B_6_26+B_11_26,B_6_27+B_11_27],[B_7_13+B_12_13,B_7_14+B_12_14,B_7_15+B_12_15,B_7_16+B_12_16,B_7_17+B_12_17,B_7_18+B_12_18,B_7_19+B_12_19,B_7_20+B_12_20,B_7_21+B_12_21,B_7_22+B_12_22,B_7_23+B_12_23,B_7_24+B_12_24,B_7_25+B_12_25,B_7_26+B_12_26,B_7_27+B_12_27],[B_8_13+B_13_13,B_8_14+B_13_14,B_8_15+B_13_15,B_8_16+B_13_16,B_8_17+B_13_17,B_8_18+B_13_18,B_8_19+B_13_19,B_8_20+B_13_20,B_8_21+B_13_21,B_8_22+B_13_22,B_8_23+B_13_23,B_8_24+B_13_24,B_8_25+B_13_25,B_8_26+B_13_26,B_8_27+B_13_27],[B_9_13+B_14_13,B_9_14+B_14_14,B_9_15+B_14_15,B_9_16+B_14_16,B_9_17+B_14_17,B_9_18+B_14_18,B_9_19+B_14_19,B_9_20+B_14_20,B_9_21+B_14_21,B_9_22+B_14_22,B_9_23+B_14_23,B_9_24+B_14_24,B_9_25+B_14_25,B_9_26+B_14_26,B_9_27+B_14_27],[B_10_13+B_15_13,B_10_14+B_15_14,B_10_15+B_15_15,B_10_16+B_15_16,B_10_17+B_15_17,B_10_18+B_15_18,B_10_19+B_15_19,B_10_20+B_15_20,B_10_21+B_15_21,B_10_22+B_15_22,B_10_23+B_15_23,B_10_24+B_15_24,B_10_25+B_15_25,B_10_26+B_15_26,B_10_27+B_15_27],[B_1_13+B_16_13,B_1_14+B_16_14,B_1_15+B_16_15,B_1_16+B_16_16,B_1_17+B_16_17,B_1_18+B_16_18,B_1_19+B_16_19,B_1_20+B_16_20,B_1_21+B_16_21,B_1_22+B_16_22,B_1_23+B_16_23,B_1_24+B_16_24,B_1_25+B_16_25,B_1_26+B_16_26,B_1_27+B_16_27],[B_2_13+B_17_13,B_2_14+B_17_14,B_2_15+B_17_15,B_2_16+B_17_16,B_2_17+B_17_17,B_2_18+B_17_18,B_2_19+B_17_19,B_2_20+B_17_20,B_2_21+B_17_21,B_2_22+B_17_22,B_2_23+B_17_23,B_2_24+B_17_24,B_2_25+B_17_25,B_2_26+B_17_26,B_2_27+B_17_27],[B_3_13+B_18_13,B_3_14+B_18_14,B_3_15+B_18_15,B_3_16+B_18_16,B_3_17+B_18_17,B_3_18+B_18_18,B_3_19+B_18_19,B_3_20+B_18_20,B_3_21+B_18_21,B_3_22+B_18_22,B_3_23+B_18_23,B_3_24+B_18_24,B_3_25+B_18_25,B_3_26+B_18_26,B_3_27+B_18_27],[B_4_13+B_19_13,B_4_14+B_19_14,B_4_15+B_19_15,B_4_16+B_19_16,B_4_17+B_19_17,B_4_18+B_19_18,B_4_19+B_19_19,B_4_20+B_19_20,B_4_21+B_19_21,B_4_22+B_19_22,B_4_23+B_19_23,B_4_24+B_19_24,B_4_25+B_19_25,B_4_26+B_19_26,B_4_27+B_19_27]]),Matrix(15, 10, [[C_13_5,C_13_11,C_13_12,C_13_13,C_13_14,C_13_15,C_13_16,C_13_17,C_13_18,C_13_19],[C_14_5,C_14_11,C_14_12,C_14_13,C_14_14,C_14_15,C_14_16,C_14_17,C_14_18,C_14_19],[C_15_5,C_15_11,C_15_12,C_15_13,C_15_14,C_15_15,C_15_16,C_15_17,C_15_18,C_15_19],[C_1_5+C_16_5,C_1_11+C_16_11,C_1_12+C_16_12,C_1_13+C_16_13,C_1_14+C_16_14,C_1_15+C_16_15,C_1_16+C_16_16,C_1_17+C_16_17,C_1_18+C_16_18,C_1_19+C_16_19],[C_2_5+C_17_5,C_2_11+C_17_11,C_2_12+C_17_12,C_2_13+C_17_13,C_2_14+C_17_14,C_2_15+C_17_15,C_2_16+C_17_16,C_2_17+C_17_17,C_2_18+C_17_18,C_2_19+C_17_19],[C_3_5+C_18_5,C_3_11+C_18_11,C_3_12+C_18_12,C_3_13+C_18_13,C_3_14+C_18_14,C_3_15+C_18_15,C_3_16+C_18_16,C_3_17+C_18_17,C_3_18+C_18_18,C_3_19+C_18_19],[C_4_5+C_19_5,C_4_11+C_19_11,C_4_12+C_19_12,C_4_13+C_19_13,C_4_14+C_19_14,C_4_15+C_19_15,C_4_16+C_19_16,C_4_17+C_19_17,C_4_18+C_19_18,C_4_19+C_19_19],[C_5_5+C_20_5,C_5_11+C_20_11,C_5_12+C_20_12,C_5_13+C_20_13,C_5_14+C_20_14,C_5_15+C_20_15,C_5_16+C_20_16,C_5_17+C_20_17,C_5_18+C_20_18,C_5_19+C_20_19],[C_6_5+C_21_5,C_6_11+C_21_11,C_6_12+C_21_12,C_6_13+C_21_13,C_6_14+C_21_14,C_6_15+C_21_15,C_6_16+C_21_16,C_6_17+C_21_17,C_6_18+C_21_18,C_6_19+C_21_19],[C_7_5+C_22_5,C_7_11+C_22_11,C_7_12+C_22_12,C_7_13+C_22_13,C_7_14+C_22_14,C_7_15+C_22_15,C_7_16+C_22_16,C_7_17+C_22_17,C_7_18+C_22_18,C_7_19+C_22_19],[C_8_5+C_23_5,C_8_11+C_23_11,C_8_12+C_23_12,C_8_13+C_23_13,C_8_14+C_23_14,C_8_15+C_23_15,C_8_16+C_23_16,C_8_17+C_23_17,C_8_18+C_23_18,C_8_19+C_23_19],[C_9_5+C_24_5,C_9_11+C_24_11,C_9_12+C_24_12,C_9_13+C_24_13,C_9_14+C_24_14,C_9_15+C_24_15,C_9_16+C_24_16,C_9_17+C_24_17,C_9_18+C_24_18,C_9_19+C_24_19],[C_10_5+C_25_5,C_10_11+C_25_11,C_10_12+C_25_12,C_10_13+C_25_13,C_10_14+C_25_14,C_10_15+C_25_15,C_10_16+C_25_16,C_10_17+C_25_17,C_10_18+C_25_18,C_10_19+C_25_19],[C_11_5+C_26_5,C_11_11+C_26_11,C_11_12+C_26_12,C_11_13+C_26_13,C_11_14+C_26_14,C_11_15+C_26_15,C_11_16+C_26_16,C_11_17+C_26_17,C_11_18+C_26_18,C_11_19+C_26_19],[C_12_5+C_27_5,C_12_11+C_27_11,C_12_12+C_27_12,C_12_13+C_27_13,C_12_14+C_27_14,C_12_15+C_27_15,C_12_16+C_27_16,C_12_17+C_27_17,C_12_18+C_27_18,C_12_19+C_27_19]])))+Trace(Mul(Matrix(9, 10, [[A_6_5,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_7_5,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_8_5,A_8_11,A_8_12,A_8_13,A_8_14,A_8_15,A_8_16,A_8_17,A_8_18,A_8_19],[A_9_5,A_9_11,A_9_12,A_9_13,A_9_14,A_9_15,A_9_16,A_9_17,A_9_18,A_9_19],[A_10_5,A_10_11,A_10_12,A_10_13,A_10_14,A_10_15,A_10_16,A_10_17,A_10_18,A_10_19],[A_1_5,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_2_5,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_3_5,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_4_5,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]]),Matrix(10, 12, [[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_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_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_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_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_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_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_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_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_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]]),Matrix(12, 9, [[C_1_6,C_1_7,C_1_8,C_1_9,C_1_10,C_1_1,C_1_2,C_1_3,C_1_4],[C_2_6,C_2_7,C_2_8,C_2_9,C_2_10,C_2_1,C_2_2,C_2_3,C_2_4],[C_3_6,C_3_7,C_3_8,C_3_9,C_3_10,C_3_1,C_3_2,C_3_3,C_3_4],[C_4_6,C_4_7,C_4_8,C_4_9,C_4_10,C_4_1,C_4_2,C_4_3,C_4_4],[C_5_6,C_5_7,C_5_8,C_5_9,C_5_10,C_5_1,C_5_2,C_5_3,C_5_4],[C_6_6,C_6_7,C_6_8,C_6_9,C_6_10,C_6_1,C_6_2,C_6_3,C_6_4],[C_7_6,C_7_7,C_7_8,C_7_9,C_7_10,C_7_1,C_7_2,C_7_3,C_7_4],[C_8_6,C_8_7,C_8_8,C_8_9,C_8_10,C_8_1,C_8_2,C_8_3,C_8_4],[C_9_6,C_9_7,C_9_8,C_9_9,C_9_10,C_9_1,C_9_2,C_9_3,C_9_4],[C_10_6,C_10_7,C_10_8,C_10_9,C_10_10,C_10_1,C_10_2,C_10_3,C_10_4],[C_11_6,C_11_7,C_11_8,C_11_9,C_11_10,C_11_1,C_11_2,C_11_3,C_11_4],[C_12_6,C_12_7,C_12_8,C_12_9,C_12_10,C_12_1,C_12_2,C_12_3,C_12_4]])))+Trace(Mul(Matrix(10, 10, [[A_5_5,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_11_5,A_11_11,A_11_12,A_11_13,A_11_14,A_11_15,A_11_16,A_11_17,A_11_18,A_11_19],[A_12_5,A_12_11,A_12_12,A_12_13,A_12_14,A_12_15,A_12_16,A_12_17,A_12_18,A_12_19],[A_13_5,A_13_11,A_13_12,A_13_13,A_13_14,A_13_15,A_13_16,A_13_17,A_13_18,A_13_19],[A_14_5,A_14_11,A_14_12,A_14_13,A_14_14,A_14_15,A_14_16,A_14_17,A_14_18,A_14_19],[A_15_5,A_15_11,A_15_12,A_15_13,A_15_14,A_15_15,A_15_16,A_15_17,A_15_18,A_15_19],[A_16_5,A_16_11,A_16_12,A_16_13,A_16_14,A_16_15,A_16_16,A_16_17,A_16_18,A_16_19],[A_17_5,A_17_11,A_17_12,A_17_13,A_17_14,A_17_15,A_17_16,A_17_17,A_17_18,A_17_19],[A_18_5,A_18_11,A_18_12,A_18_13,A_18_14,A_18_15,A_18_16,A_18_17,A_18_18,A_18_19],[A_19_5,A_19_11,A_19_12,A_19_13,A_19_14,A_19_15,A_19_16,A_19_17,A_19_18,A_19_19]]),Matrix(10, 12, [[B_5_1-B_5_16,B_5_2-B_5_17,B_5_3-B_5_18,B_5_4-B_5_19,B_5_5-B_5_20,B_5_6-B_5_21,B_5_7-B_5_22,B_5_8-B_5_23,B_5_9-B_5_24,B_5_10-B_5_25,B_5_11-B_5_26,B_5_12-B_5_27],[B_6_1+B_11_1-B_6_16-B_11_16,B_6_2+B_11_2-B_6_17-B_11_17,B_6_3+B_11_3-B_6_18-B_11_18,B_6_4+B_11_4-B_6_19-B_11_19,B_6_5+B_11_5-B_6_20-B_11_20,B_6_6+B_11_6-B_6_21-B_11_21,B_6_7+B_11_7-B_6_22-B_11_22,B_6_8+B_11_8-B_6_23-B_11_23,B_6_9+B_11_9-B_6_24-B_11_24,B_6_10+B_11_10-B_6_25-B_11_25,B_6_11+B_11_11-B_6_26-B_11_26,B_6_12+B_11_12-B_6_27-B_11_27],[B_7_1+B_12_1-B_7_16-B_12_16,B_7_2+B_12_2-B_7_17-B_12_17,B_7_3+B_12_3-B_7_18-B_12_18,B_7_4+B_12_4-B_7_19-B_12_19,B_7_5+B_12_5-B_7_20-B_12_20,B_7_6+B_12_6-B_12_21-B_7_21,B_7_7+B_12_7-B_12_22-B_7_22,B_7_8+B_12_8-B_7_23-B_12_23,B_7_9+B_12_9-B_7_24-B_12_24,B_7_10+B_12_10-B_7_25-B_12_25,B_7_11+B_12_11-B_7_26-B_12_26,B_7_12+B_12_12-B_7_27-B_12_27],[B_8_1+B_13_1-B_8_16-B_13_16,B_8_2+B_13_2-B_8_17-B_13_17,B_8_3+B_13_3-B_8_18-B_13_18,B_8_4+B_13_4-B_8_19-B_13_19,B_8_5+B_13_5-B_8_20-B_13_20,B_8_6+B_13_6-B_8_21-B_13_21,B_8_7+B_13_7-B_8_22-B_13_22,B_8_8+B_13_8-B_8_23-B_13_23,B_8_9+B_13_9-B_8_24-B_13_24,B_8_10+B_13_10-B_8_25-B_13_25,B_8_11+B_13_11-B_8_26-B_13_26,B_8_12+B_13_12-B_8_27-B_13_27],[B_9_1+B_14_1-B_9_16-B_14_16,B_9_2+B_14_2-B_9_17-B_14_17,B_9_3+B_14_3-B_9_18-B_14_18,B_9_4+B_14_4-B_9_19-B_14_19,B_9_5+B_14_5-B_9_20-B_14_20,B_9_6+B_14_6-B_9_21-B_14_21,B_9_7+B_14_7-B_9_22-B_14_22,B_9_8+B_14_8-B_9_23-B_14_23,B_9_9+B_14_9-B_9_24-B_14_24,B_9_10+B_14_10-B_9_25-B_14_25,B_9_11+B_14_11-B_9_26-B_14_26,B_9_12+B_14_12-B_9_27-B_14_27],[B_10_1+B_15_1-B_10_16-B_15_16,B_10_2+B_15_2-B_10_17-B_15_17,B_10_3+B_15_3-B_10_18-B_15_18,B_10_4+B_15_4-B_10_19-B_15_19,B_10_5+B_15_5-B_10_20-B_15_20,B_10_6+B_15_6-B_10_21-B_15_21,B_10_7+B_15_7-B_10_22-B_15_22,B_10_8+B_15_8-B_10_23-B_15_23,B_10_9+B_15_9-B_10_24-B_15_24,B_10_10+B_15_10-B_10_25-B_15_25,B_10_11+B_15_11-B_10_26-B_15_26,B_10_12+B_15_12-B_10_27-B_15_27],[B_1_1+B_16_1-B_1_16-B_16_16,B_1_2+B_16_2-B_1_17-B_16_17,B_1_3+B_16_3-B_1_18-B_16_18,B_1_4+B_16_4-B_1_19-B_16_19,B_1_5+B_16_5-B_1_20-B_16_20,B_1_6+B_16_6-B_1_21-B_16_21,B_1_7+B_16_7-B_1_22-B_16_22,B_1_8+B_16_8-B_1_23-B_16_23,B_1_9+B_16_9-B_1_24-B_16_24,B_1_10+B_16_10-B_1_25-B_16_25,B_1_11+B_16_11-B_1_26-B_16_26,B_1_12+B_16_12-B_1_27-B_16_27],[B_2_1+B_17_1-B_2_16-B_17_16,B_2_2+B_17_2-B_2_17-B_17_17,B_2_3+B_17_3-B_2_18-B_17_18,B_2_4+B_17_4-B_2_19-B_17_19,B_2_5+B_17_5-B_2_20-B_17_20,B_2_6+B_17_6-B_2_21-B_17_21,B_2_7+B_17_7-B_2_22-B_17_22,B_2_8+B_17_8-B_2_23-B_17_23,B_2_9+B_17_9-B_2_24-B_17_24,B_2_10+B_17_10-B_2_25-B_17_25,B_2_11+B_17_11-B_2_26-B_17_26,B_2_12+B_17_12-B_2_27-B_17_27],[B_3_1+B_18_1-B_3_16-B_18_16,B_3_2+B_18_2-B_3_17-B_18_17,B_3_3+B_18_3-B_3_18-B_18_18,B_3_4+B_18_4-B_3_19-B_18_19,B_3_5+B_18_5-B_3_20-B_18_20,B_3_6+B_18_6-B_3_21-B_18_21,B_3_7+B_18_7-B_3_22-B_18_22,B_3_8+B_18_8-B_3_23-B_18_23,B_3_9+B_18_9-B_3_24-B_18_24,B_3_10+B_18_10-B_3_25-B_18_25,B_3_11+B_18_11-B_3_26-B_18_26,B_3_12+B_18_12-B_3_27-B_18_27],[B_4_1+B_19_1-B_4_16-B_19_16,B_4_2+B_19_2-B_4_17-B_19_17,B_4_3+B_19_3-B_4_18-B_19_18,B_4_4+B_19_4-B_4_19-B_19_19,B_4_5+B_19_5-B_4_20-B_19_20,B_4_6+B_19_6-B_4_21-B_19_21,B_4_7+B_19_7-B_4_22-B_19_22,B_4_8+B_19_8-B_4_23-B_19_23,B_4_9+B_19_9-B_4_24-B_19_24,B_4_10+B_19_10-B_4_25-B_19_25,B_4_11+B_19_11-B_4_26-B_19_26,B_4_12+B_19_12-B_4_27-B_19_27]]),Matrix(12, 10, [[C_1_5,C_1_11,C_1_12,C_1_13,C_1_14,C_1_15,C_1_16,C_1_17,C_1_18,C_1_19],[C_2_5,C_2_11,C_2_12,C_2_13,C_2_14,C_2_15,C_2_16,C_2_17,C_2_18,C_2_19],[C_3_5,C_3_11,C_3_12,C_3_13,C_3_14,C_3_15,C_3_16,C_3_17,C_3_18,C_3_19],[C_4_5,C_4_11,C_4_12,C_4_13,C_4_14,C_4_15,C_4_16,C_4_17,C_4_18,C_4_19],[C_5_5,C_5_11,C_5_12,C_5_13,C_5_14,C_5_15,C_5_16,C_5_17,C_5_18,C_5_19],[C_6_5,C_6_11,C_6_12,C_6_13,C_6_14,C_6_15,C_6_16,C_6_17,C_6_18,C_6_19],[C_7_5,C_7_11,C_7_12,C_7_13,C_7_14,C_7_15,C_7_16,C_7_17,C_7_18,C_7_19],[C_8_5,C_8_11,C_8_12,C_8_13,C_8_14,C_8_15,C_8_16,C_8_17,C_8_18,C_8_19],[C_9_5,C_9_11,C_9_12,C_9_13,C_9_14,C_9_15,C_9_16,C_9_17,C_9_18,C_9_19],[C_10_5,C_10_11,C_10_12,C_10_13,C_10_14,C_10_15,C_10_16,C_10_17,C_10_18,C_10_19],[C_11_5,C_11_11,C_11_12,C_11_13,C_11_14,C_11_15,C_11_16,C_11_17,C_11_18,C_11_19],[C_12_5,C_12_11,C_12_12,C_12_13,C_12_14,C_12_15,C_12_16,C_12_17,C_12_18,C_12_19]])))+Trace(Mul(Matrix(9, 10, [[A_6_5+A_11_5,-A_6_6-A_11_6+A_6_11+A_11_11,-A_6_7-A_11_7+A_6_12+A_11_12,-A_6_8-A_11_8+A_6_13+A_11_13,-A_6_9-A_11_9+A_6_14+A_11_14,-A_6_10-A_11_10+A_6_15+A_11_15,-A_6_1-A_11_1+A_6_16+A_11_16,-A_6_2-A_11_2+A_6_17+A_11_17,-A_6_3-A_11_3+A_6_18+A_11_18,-A_6_4-A_11_4+A_6_19+A_11_19],[A_7_5+A_12_5,-A_7_6-A_12_6+A_7_11+A_12_11,-A_7_7-A_12_7+A_7_12+A_12_12,-A_7_8-A_12_8+A_7_13+A_12_13,-A_7_9-A_12_9+A_7_14+A_12_14,-A_7_10-A_12_10+A_7_15+A_12_15,-A_7_1-A_12_1+A_7_16+A_12_16,-A_7_2-A_12_2+A_7_17+A_12_17,-A_7_3-A_12_3+A_7_18+A_12_18,-A_7_4-A_12_4+A_7_19+A_12_19],[A_8_5+A_13_5,-A_8_6-A_13_6+A_8_11+A_13_11,-A_8_7-A_13_7+A_8_12+A_13_12,-A_8_8-A_13_8+A_8_13+A_13_13,-A_8_9-A_13_9+A_8_14+A_13_14,-A_8_10-A_13_10+A_8_15+A_13_15,-A_8_1-A_13_1+A_8_16+A_13_16,-A_8_2-A_13_2+A_8_17+A_13_17,-A_8_3-A_13_3+A_8_18+A_13_18,-A_8_4-A_13_4+A_8_19+A_13_19],[A_9_5+A_14_5,-A_9_6-A_14_6+A_9_11+A_14_11,-A_9_7-A_14_7+A_9_12+A_14_12,-A_9_8-A_14_8+A_9_13+A_14_13,-A_9_9-A_14_9+A_9_14+A_14_14,-A_9_10-A_14_10+A_9_15+A_14_15,-A_9_1-A_14_1+A_9_16+A_14_16,-A_9_2-A_14_2+A_9_17+A_14_17,-A_9_3-A_14_3+A_9_18+A_14_18,-A_9_4-A_14_4+A_9_19+A_14_19],[A_10_5+A_15_5,-A_10_6-A_15_6+A_10_11+A_15_11,-A_10_7-A_15_7+A_10_12+A_15_12,-A_10_8-A_15_8+A_10_13+A_15_13,-A_10_9-A_15_9+A_10_14+A_15_14,-A_10_10-A_15_10+A_10_15+A_15_15,-A_10_1-A_15_1+A_10_16+A_15_16,-A_10_2-A_15_2+A_10_17+A_15_17,-A_10_3-A_15_3+A_10_18+A_15_18,-A_10_4-A_15_4+A_10_19+A_15_19],[A_1_5+A_16_5,-A_1_6-A_16_6+A_1_11+A_16_11,-A_1_7-A_16_7+A_1_12+A_16_12,-A_1_8-A_16_8+A_1_13+A_16_13,-A_1_9-A_16_9+A_1_14+A_16_14,-A_1_10-A_16_10+A_1_15+A_16_15,-A_1_1-A_16_1+A_1_16+A_16_16,-A_1_2-A_16_2+A_1_17+A_16_17,-A_1_3-A_16_3+A_1_18+A_16_18,-A_1_4-A_16_4+A_1_19+A_16_19],[A_2_5+A_17_5,-A_2_6-A_17_6+A_2_11+A_17_11,-A_2_7-A_17_7+A_2_12+A_17_12,-A_2_8-A_17_8+A_2_13+A_17_13,-A_2_9-A_17_9+A_2_14+A_17_14,-A_2_10-A_17_10+A_2_15+A_17_15,-A_2_1-A_17_1+A_2_16+A_17_16,-A_2_2-A_17_2+A_2_17+A_17_17,-A_2_3-A_17_3+A_2_18+A_17_18,-A_2_4-A_17_4+A_2_19+A_17_19],[A_3_5+A_18_5,-A_3_6-A_18_6+A_3_11+A_18_11,-A_3_7-A_18_7+A_3_12+A_18_12,-A_3_8-A_18_8+A_3_13+A_18_13,-A_3_9-A_18_9+A_3_14+A_18_14,-A_3_10-A_18_10+A_3_15+A_18_15,-A_3_1-A_18_1+A_3_16+A_18_16,-A_3_2-A_18_2+A_3_17+A_18_17,-A_3_3-A_18_3+A_3_18+A_18_18,-A_3_4-A_18_4+A_3_19+A_18_19],[A_4_5+A_19_5,-A_4_6-A_19_6+A_4_11+A_19_11,-A_4_7-A_19_7+A_4_12+A_19_12,-A_4_8-A_19_8+A_4_13+A_19_13,-A_4_9-A_19_9+A_4_14+A_19_14,-A_4_10-A_19_10+A_4_15+A_19_15,-A_4_1-A_19_1+A_4_16+A_19_16,-A_4_2-A_19_2+A_4_17+A_19_17,-A_4_3-A_19_3+A_4_18+A_19_18,-A_4_4-A_19_4+A_4_19+A_19_19]]),Matrix(10, 15, [[B_5_13,B_5_14,B_5_15,B_5_16,B_5_17,B_5_18,B_5_19,B_5_20,B_5_21,B_5_22,B_5_23,B_5_24,B_5_25,B_5_26,B_5_27],[B_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_11_23,B_11_24,B_11_25,B_11_26,B_11_27],[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_12_23,B_12_24,B_12_25,B_12_26,B_12_27],[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_13_23,B_13_24,B_13_25,B_13_26,B_13_27],[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_14_23,B_14_24,B_14_25,B_14_26,B_14_27],[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_15_23,B_15_24,B_15_25,B_15_26,B_15_27],[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_16_23,B_16_24,B_16_25,B_16_26,B_16_27],[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_17_23,B_17_24,B_17_25,B_17_26,B_17_27],[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_18_23,B_18_24,B_18_25,B_18_26,B_18_27],[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_19_23,B_19_24,B_19_25,B_19_26,B_19_27]]),Matrix(15, 9, [[C_13_6,C_13_7,C_13_8,C_13_9,C_13_10,C_13_1,C_13_2,C_13_3,C_13_4],[C_14_6,C_14_7,C_14_8,C_14_9,C_14_10,C_14_1,C_14_2,C_14_3,C_14_4],[C_15_6,C_15_7,C_15_8,C_15_9,C_15_10,C_15_1,C_15_2,C_15_3,C_15_4],[C_16_6,C_16_7,C_16_8,C_16_9,C_16_10,C_16_1,C_16_2,C_16_3,C_16_4],[C_17_6,C_17_7,C_17_8,C_17_9,C_17_10,C_17_1,C_17_2,C_17_3,C_17_4],[C_18_6,C_18_7,C_18_8,C_18_9,C_18_10,C_18_1,C_18_2,C_18_3,C_18_4],[C_19_6,C_19_7,C_19_8,C_19_9,C_19_10,C_19_1,C_19_2,C_19_3,C_19_4],[C_20_6,C_20_7,C_20_8,C_20_9,C_20_10,C_20_1,C_20_2,C_20_3,C_20_4],[C_21_6,C_21_7,C_21_8,C_21_9,C_21_10,C_21_1,C_21_2,C_21_3,C_21_4],[C_22_6,C_22_7,C_22_8,C_22_9,C_22_10,C_22_1,C_22_2,C_22_3,C_22_4],[C_23_6,C_23_7,C_23_8,C_23_9,C_23_10,C_23_1,C_23_2,C_23_3,C_23_4],[C_24_6,C_24_7,C_24_8,C_24_9,C_24_10,C_24_1,C_24_2,C_24_3,C_24_4],[C_25_6,C_25_7,C_25_8,C_25_9,C_25_10,C_25_1,C_25_2,C_25_3,C_25_4],[C_26_6,C_26_7,C_26_8,C_26_9,C_26_10,C_26_1,C_26_2,C_26_3,C_26_4],[C_27_6,C_27_7,C_27_8,C_27_9,C_27_10,C_27_1,C_27_2,C_27_3,C_27_4]])))+Trace(Mul(Matrix(9, 9, [[A_6_6,A_6_7,A_6_8,A_6_9,A_6_10,A_6_1,A_6_2,A_6_3,A_6_4],[A_7_6,A_7_7,A_7_8,A_7_9,A_7_10,A_7_1,A_7_2,A_7_3,A_7_4],[A_8_6,A_8_7,A_8_8,A_8_9,A_8_10,A_8_1,A_8_2,A_8_3,A_8_4],[A_9_6,A_9_7,A_9_8,A_9_9,A_9_10,A_9_1,A_9_2,A_9_3,A_9_4],[A_10_6,A_10_7,A_10_8,A_10_9,A_10_10,A_10_1,A_10_2,A_10_3,A_10_4],[A_1_6,A_1_7,A_1_8,A_1_9,A_1_10,A_1_1,A_1_2,A_1_3,A_1_4],[A_2_6,A_2_7,A_2_8,A_2_9,A_2_10,A_2_1,A_2_2,A_2_3,A_2_4],[A_3_6,A_3_7,A_3_8,A_3_9,A_3_10,A_3_1,A_3_2,A_3_3,A_3_4],[A_4_6,A_4_7,A_4_8,A_4_9,A_4_10,A_4_1,A_4_2,A_4_3,A_4_4]]),Matrix(9, 12, [[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_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_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_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_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_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_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_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_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]]),Matrix(12, 9, [[C_1_6+C_16_6-C_1_11-C_16_11,C_1_7+C_16_7-C_1_12-C_16_12,C_1_8+C_16_8-C_1_13-C_16_13,C_1_9+C_16_9-C_1_14-C_16_14,C_1_10+C_16_10-C_1_15-C_16_15,C_1_1+C_16_1-C_1_16-C_16_16,C_1_2+C_16_2-C_1_17-C_16_17,C_1_3+C_16_3-C_1_18-C_16_18,C_1_4+C_16_4-C_1_19-C_16_19],[C_2_6+C_17_6-C_2_11-C_17_11,C_2_7+C_17_7-C_2_12-C_17_12,C_2_8+C_17_8-C_2_13-C_17_13,C_2_9+C_17_9-C_2_14-C_17_14,C_2_10+C_17_10-C_2_15-C_17_15,C_2_1+C_17_1-C_2_16-C_17_16,C_2_2+C_17_2-C_2_17-C_17_17,C_2_3+C_17_3-C_2_18-C_17_18,C_2_4+C_17_4-C_2_19-C_17_19],[C_3_6+C_18_6-C_3_11-C_18_11,C_3_7+C_18_7-C_3_12-C_18_12,C_3_8+C_18_8-C_3_13-C_18_13,C_3_9+C_18_9-C_3_14-C_18_14,C_3_10+C_18_10-C_3_15-C_18_15,C_3_1+C_18_1-C_3_16-C_18_16,C_3_2+C_18_2-C_3_17-C_18_17,C_3_3+C_18_3-C_3_18-C_18_18,C_3_4+C_18_4-C_3_19-C_18_19],[C_4_6+C_19_6-C_4_11-C_19_11,C_4_7+C_19_7-C_4_12-C_19_12,C_4_8+C_19_8-C_4_13-C_19_13,C_4_9+C_19_9-C_4_14-C_19_14,C_4_10+C_19_10-C_4_15-C_19_15,C_4_1+C_19_1-C_4_16-C_19_16,C_4_2+C_19_2-C_4_17-C_19_17,C_4_3+C_19_3-C_4_18-C_19_18,C_4_4+C_19_4-C_4_19-C_19_19],[C_5_6+C_20_6-C_5_11-C_20_11,C_5_7+C_20_7-C_5_12-C_20_12,C_5_8+C_20_8-C_5_13-C_20_13,C_5_9+C_20_9-C_5_14-C_20_14,C_5_10+C_20_10-C_5_15-C_20_15,C_5_1+C_20_1-C_5_16-C_20_16,C_5_2+C_20_2-C_5_17-C_20_17,C_5_3+C_20_3-C_5_18-C_20_18,C_5_4+C_20_4-C_5_19-C_20_19],[C_6_6+C_21_6-C_6_11-C_21_11,C_6_7+C_21_7-C_6_12-C_21_12,C_6_8+C_21_8-C_6_13-C_21_13,C_6_9+C_21_9-C_6_14-C_21_14,C_6_10+C_21_10-C_6_15-C_21_15,C_6_1+C_21_1-C_6_16-C_21_16,C_6_2+C_21_2-C_6_17-C_21_17,C_6_3+C_21_3-C_6_18-C_21_18,C_6_4+C_21_4-C_6_19-C_21_19],[C_7_6+C_22_6-C_7_11-C_22_11,C_7_7+C_22_7-C_7_12-C_22_12,C_7_8+C_22_8-C_7_13-C_22_13,C_7_9+C_22_9-C_7_14-C_22_14,C_7_10+C_22_10-C_7_15-C_22_15,C_7_1+C_22_1-C_7_16-C_22_16,C_7_2+C_22_2-C_7_17-C_22_17,C_7_3+C_22_3-C_7_18-C_22_18,C_7_4+C_22_4-C_7_19-C_22_19],[C_8_6+C_23_6-C_8_11-C_23_11,C_8_7+C_23_7-C_8_12-C_23_12,C_8_8+C_23_8-C_8_13-C_23_13,C_8_9+C_23_9-C_8_14-C_23_14,C_8_10+C_23_10-C_8_15-C_23_15,C_8_1+C_23_1-C_8_16-C_23_16,C_8_2+C_23_2-C_8_17-C_23_17,C_8_3+C_23_3-C_8_18-C_23_18,C_8_4+C_23_4-C_8_19-C_23_19],[C_9_6+C_24_6-C_9_11-C_24_11,C_9_7+C_24_7-C_9_12-C_24_12,C_9_8+C_24_8-C_9_13-C_24_13,C_9_9+C_24_9-C_9_14-C_24_14,C_9_10+C_24_10-C_9_15-C_24_15,C_9_1+C_24_1-C_9_16-C_24_16,C_9_2+C_24_2-C_9_17-C_24_17,C_9_3+C_24_3-C_9_18-C_24_18,C_9_4+C_24_4-C_9_19-C_24_19],[C_10_6+C_25_6-C_10_11-C_25_11,C_10_7+C_25_7-C_10_12-C_25_12,C_10_8+C_25_8-C_10_13-C_25_13,C_10_9+C_25_9-C_10_14-C_25_14,C_10_10+C_25_10-C_10_15-C_25_15,C_10_1+C_25_1-C_10_16-C_25_16,C_10_2+C_25_2-C_10_17-C_25_17,C_10_3+C_25_3-C_10_18-C_25_18,C_10_4+C_25_4-C_10_19-C_25_19],[C_11_6+C_26_6-C_11_11-C_26_11,C_11_7+C_26_7-C_11_12-C_26_12,C_11_8+C_26_8-C_11_13-C_26_13,C_11_9+C_26_9-C_11_14-C_26_14,C_11_10+C_26_10-C_11_15-C_26_15,C_11_1+C_26_1-C_11_16-C_26_16,C_11_2+C_26_2-C_11_17-C_26_17,C_11_3+C_26_3-C_11_18-C_26_18,C_11_4+C_26_4-C_11_19-C_26_19],[C_12_6+C_27_6-C_12_11-C_27_11,C_12_7+C_27_7-C_12_12-C_27_12,C_12_8+C_27_8-C_12_13-C_27_13,C_12_9+C_27_9-C_12_14-C_27_14,C_12_10+C_27_10-C_12_15-C_27_15,C_12_1+C_27_1-C_12_16-C_27_16,C_12_2+C_27_2-C_12_17-C_27_17,C_12_3+C_27_3-C_12_18-C_27_18,C_12_4+C_27_4-C_12_19-C_27_19]])))+Trace(Mul(Matrix(10, 10, [[A_5_5,-A_5_6+A_5_11,-A_5_7+A_5_12,-A_5_8+A_5_13,-A_5_9+A_5_14,-A_5_10+A_5_15,-A_5_1+A_5_16,-A_5_2+A_5_17,-A_5_3+A_5_18,-A_5_4+A_5_19],[A_11_5,-A_6_6-A_11_6+A_11_11,-A_6_7-A_11_7+A_11_12,-A_6_8-A_11_8+A_11_13,-A_6_9-A_11_9+A_11_14,-A_6_10-A_11_10+A_11_15,-A_6_1-A_11_1+A_11_16,-A_6_2-A_11_2+A_11_17,-A_6_3-A_11_3+A_11_18,-A_6_4-A_11_4+A_11_19],[A_12_5,-A_7_6-A_12_6+A_12_11,-A_7_7-A_12_7+A_12_12,-A_7_8-A_12_8+A_12_13,-A_7_9-A_12_9+A_12_14,-A_7_10-A_12_10+A_12_15,-A_7_1-A_12_1+A_12_16,-A_7_2-A_12_2+A_12_17,-A_7_3-A_12_3+A_12_18,-A_7_4-A_12_4+A_12_19],[A_13_5,-A_8_6-A_13_6+A_13_11,-A_8_7-A_13_7+A_13_12,-A_8_8-A_13_8+A_13_13,-A_8_9-A_13_9+A_13_14,-A_8_10-A_13_10+A_13_15,-A_8_1-A_13_1+A_13_16,-A_8_2-A_13_2+A_13_17,-A_8_3-A_13_3+A_13_18,-A_8_4-A_13_4+A_13_19],[A_14_5,-A_9_6-A_14_6+A_14_11,-A_9_7-A_14_7+A_14_12,-A_9_8-A_14_8+A_14_13,-A_9_9-A_14_9+A_14_14,-A_9_10-A_14_10+A_14_15,-A_9_1-A_14_1+A_14_16,-A_9_2-A_14_2+A_14_17,-A_9_3-A_14_3+A_14_18,-A_9_4-A_14_4+A_14_19],[A_15_5,-A_10_6-A_15_6+A_15_11,-A_10_7-A_15_7+A_15_12,-A_10_8-A_15_8+A_15_13,-A_10_9-A_15_9+A_15_14,-A_10_10-A_15_10+A_15_15,-A_10_1-A_15_1+A_15_16,-A_10_2-A_15_2+A_15_17,-A_10_3-A_15_3+A_15_18,-A_10_4-A_15_4+A_15_19],[A_16_5,-A_1_6-A_16_6+A_16_11,-A_1_7-A_16_7+A_16_12,-A_1_8-A_16_8+A_16_13,-A_1_9-A_16_9+A_16_14,-A_1_10-A_16_10+A_16_15,-A_1_1-A_16_1+A_16_16,-A_1_2-A_16_2+A_16_17,-A_1_3-A_16_3+A_16_18,-A_1_4-A_16_4+A_16_19],[A_17_5,-A_2_6-A_17_6+A_17_11,-A_2_7-A_17_7+A_17_12,-A_2_8-A_17_8+A_17_13,-A_2_9-A_17_9+A_17_14,-A_2_10-A_17_10+A_17_15,-A_2_1-A_17_1+A_17_16,-A_2_2-A_17_2+A_17_17,-A_2_3-A_17_3+A_17_18,-A_2_4-A_17_4+A_17_19],[A_18_5,-A_3_6-A_18_6+A_18_11,-A_3_7-A_18_7+A_18_12,-A_3_8-A_18_8+A_18_13,-A_3_9-A_18_9+A_18_14,-A_3_10-A_18_10+A_18_15,-A_3_1-A_18_1+A_18_16,-A_3_2-A_18_2+A_18_17,-A_3_3-A_18_3+A_18_18,-A_3_4-A_18_4+A_18_19],[A_19_5,-A_4_6-A_19_6+A_19_11,-A_4_7-A_19_7+A_19_12,-A_4_8-A_19_8+A_19_13,-A_4_9-A_19_9+A_19_14,-A_4_10-A_19_10+A_19_15,-A_4_1-A_19_1+A_19_16,-A_4_2-A_19_2+A_19_17,-A_4_3-A_19_3+A_19_18,-A_4_4-A_19_4+A_19_19]]),Matrix(10, 15, 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10, [[C_13_5,-C_13_6+C_13_11,-C_13_7+C_13_12,-C_13_8+C_13_13,-C_13_9+C_13_14,-C_13_10+C_13_15,-C_13_1+C_13_16,-C_13_2+C_13_17,-C_13_3+C_13_18,-C_13_4+C_13_19],[C_14_5,-C_14_6+C_14_11,-C_14_7+C_14_12,-C_14_8+C_14_13,-C_14_9+C_14_14,-C_14_10+C_14_15,-C_14_1+C_14_16,-C_14_2+C_14_17,-C_14_3+C_14_18,-C_14_4+C_14_19],[C_15_5,-C_15_6+C_15_11,-C_15_7+C_15_12,-C_15_8+C_15_13,-C_15_9+C_15_14,-C_15_10+C_15_15,-C_15_1+C_15_16,-C_15_2+C_15_17,-C_15_3+C_15_18,-C_15_4+C_15_19],[C_1_5+C_16_5,-C_16_6+C_1_11+C_16_11,-C_16_7+C_1_12+C_16_12,-C_16_8+C_1_13+C_16_13,-C_16_9+C_1_14+C_16_14,-C_16_10+C_1_15+C_16_15,-C_16_1+C_1_16+C_16_16,-C_16_2+C_1_17+C_16_17,-C_16_3+C_1_18+C_16_18,-C_16_4+C_1_19+C_16_19],[C_2_5+C_17_5,-C_17_6+C_2_11+C_17_11,-C_17_7+C_2_12+C_17_12,-C_17_8+C_2_13+C_17_13,-C_17_9+C_2_14+C_17_14,-C_17_10+C_2_15+C_17_15,-C_17_1+C_2_16+C_17_16,-C_17_2+C_2_17+C_17_17,-C_17_3+C_2_18+C_17_18,-C_17_4+C_2_19+C_17_19],[C_3_5+C_18_5,-C_18_6+C_3_11+C_18_11,-C_18_7+C_3_12+C_18_12,-C_18_8+C_3_13+C_18_13,-C_18_9+C_3_14+C_18_14,-C_18_10+C_3_15+C_18_15,-C_18_1+C_3_16+C_18_16,-C_18_2+C_3_17+C_18_17,-C_18_3+C_3_18+C_18_18,-C_18_4+C_3_19+C_18_19],[C_4_5+C_19_5,-C_19_6+C_4_11+C_19_11,-C_19_7+C_4_12+C_19_12,-C_19_8+C_4_13+C_19_13,-C_19_9+C_4_14+C_19_14,-C_19_10+C_4_15+C_19_15,-C_19_1+C_4_16+C_19_16,-C_19_2+C_4_17+C_19_17,-C_19_3+C_4_18+C_19_18,-C_19_4+C_4_19+C_19_19],[C_5_5+C_20_5,-C_20_6+C_5_11+C_20_11,-C_20_7+C_5_12+C_20_12,-C_20_8+C_5_13+C_20_13,-C_20_9+C_5_14+C_20_14,-C_20_10+C_5_15+C_20_15,-C_20_1+C_5_16+C_20_16,-C_20_2+C_5_17+C_20_17,-C_20_3+C_5_18+C_20_18,-C_20_4+C_5_19+C_20_19],[C_6_5+C_21_5,-C_21_6+C_6_11+C_21_11,-C_21_7+C_6_12+C_21_12,-C_21_8+C_6_13+C_21_13,-C_21_9+C_6_14+C_21_14,-C_21_10+C_6_15+C_21_15,-C_21_1+C_6_16+C_21_16,-C_21_2+C_6_17+C_21_17,-C_21_3+C_6_18+C_21_18,-C_21_4+C_6_19+C_21_19],[C_7_5+C_22_5,-C_22_6+C_7_11+C_22_11,-C_22_7+C_7_12+C_22_12,-C_22_8+C_7_13+C_22_13,-C_22_9+C_7_14+C_22_14,-C_22_10+C_7_15+C_22_15,-C_22_1+C_7_16+C_22_16,-C_22_2+C_7_17+C_22_17,-C_22_3+C_7_18+C_22_18,-C_22_4+C_7_19+C_22_19],[C_8_5+C_23_5,-C_23_6+C_8_11+C_23_11,-C_23_7+C_8_12+C_23_12,-C_23_8+C_8_13+C_23_13,-C_23_9+C_8_14+C_23_14,-C_23_10+C_8_15+C_23_15,-C_23_1+C_8_16+C_23_16,-C_23_2+C_8_17+C_23_17,-C_23_3+C_8_18+C_23_18,-C_23_4+C_8_19+C_23_19],[C_9_5+C_24_5,-C_24_6+C_9_11+C_24_11,-C_24_7+C_9_12+C_24_12,-C_24_8+C_9_13+C_24_13,-C_24_9+C_9_14+C_24_14,-C_24_10+C_9_15+C_24_15,-C_24_1+C_9_16+C_24_16,-C_24_2+C_9_17+C_24_17,-C_24_3+C_9_18+C_24_18,-C_24_4+C_9_19+C_24_19],[C_10_5+C_25_5,-C_25_6+C_10_11+C_25_11,-C_25_7+C_10_12+C_25_12,-C_25_8+C_10_13+C_25_13,-C_25_9+C_10_14+C_25_14,-C_25_10+C_10_15+C_25_15,-C_25_1+C_10_16+C_25_16,-C_25_2+C_10_17+C_25_17,-C_25_3+C_10_18+C_25_18,-C_25_4+C_10_19+C_25_19],[C_11_5+C_26_5,-C_26_6+C_11_11+C_26_11,-C_26_7+C_11_12+C_26_12,-C_26_8+C_11_13+C_26_13,-C_26_9+C_11_14+C_26_14,-C_26_10+C_11_15+C_26_15,-C_26_1+C_11_16+C_26_16,-C_26_2+C_11_17+C_26_17,-C_26_3+C_11_18+C_26_18,-C_26_4+C_11_19+C_26_19],[C_12_5+C_27_5,-C_27_6+C_12_11+C_27_11,-C_27_7+C_12_12+C_27_12,-C_27_8+C_12_13+C_27_13,-C_27_9+C_12_14+C_27_14,-C_27_10+C_12_15+C_27_15,-C_27_1+C_12_16+C_27_16,-C_27_2+C_12_17+C_27_17,-C_27_3+C_12_18+C_27_18,-C_27_4+C_12_19+C_27_19]])))

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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