Description of fast matrix multiplication algorithm: ⟨19×22×24:5742⟩

Algorithm type

16X8Y12Z12+16X7Y10Z11+24X4Y12Z12+X8Y8Z11+X8Y8Z10+X7Y7Z12+16X4Y10Z11+3X8Y8Z8+X7Y7Z10+8X3Y10Z11+3X8Y8Z7+2X12Y4Z6+16X11Y6Z5+X8Y8Z6+7X7Y7Z8+X6Y8Z8+18X11Y4Z6+X6Y8Z7+5X12Y4Z4+X7Y7Z6+4X6Y8Z6+3X6Y6Z8+2X5Y7Z8+6X11Y4Z4+X6Y8Z5+X6Y7Z6+3X10Y4Z4+X5Y7Z6+16X6Y6Z5+3X5Y6Z6+8X8Y4Z4+128X6Y6Z4+16X6Y4Z6+8X5Y6Z5+8X4Y8Z4+128X4Y6Z6+2X4Y4Z8+6X7Y4Z4+8X5Y4Z6+6X4Y7Z4+16X4Y6Z5+6X4Y4Z7+X4Y3Z8+16X3Y6Z6+192X6Y6Z2+4X4Y8Z2+2X4Y6Z4+8X4Y4Z6+2X3Y7Z4+3X3Y3Z8+X2Y8Z4+208X2Y6Z6+4X5Y4Z4+X4Y7Z2+2X4Y5Z4+2X4Y4Z5+4X3Y6Z4+18X3Y4Z6+24X2Y6Z5+8XY6Z6+15X6Y4Z2+32X6Y3Z3+9X6Y2Z4+141X4Y4Z4+3X3Y7Z2+128X3Y3Z6+X2Y8Z2+X2Y6Z4+16X2Y4Z6+4X6Y2Z3+9X5Y4Z2+3X5Y2Z4+9X4Y4Z3+20X4Y3Z4+21X3Y4Z4+X2Y7Z2+8XY4Z6+50X6Y2Z2+6X4Y4Z2+64X4Y3Z3+4X4Y2Z4+10X3Y4Z3+25X3Y3Z4+6X2Y6Z2+17X2Y4Z4+8X2Y2Z6+16X5Y2Z2+4X4Y3Z2+4X3Y4Z2+240X3Y3Z3+X2Y3Z4+64X4Y2Z2+384X3Y3Z2+225X2Y4Z2+288X2Y3Z3+73X2Y2Z4+24XY6Z+576X3Y3Z+26X3Y2Z2+12X2Y4Z+37X2Y3Z2+8X2Y2Z3+8X2YZ4+28XY4Z2+288XY3Z3+5XY2Z4+64X3Y2Z+12X3YZ2+497X2Y2Z2+30XY4Z+20XY2Z3+2XYZ4+76X3YZ+98X2Y2Z+62X2YZ2+32XY3Z+101XY2Z2+20XYZ3+116X2YZ+234XY2Z+134XYZ2+300XYZ16X8Y12Z1216X7Y10Z1124X4Y12Z12X8Y8Z11X8Y8Z10X7Y7Z1216X4Y10Z113X8Y8Z8X7Y7Z108X3Y10Z113X8Y8Z72X12Y4Z616X11Y6Z5X8Y8Z67X7Y7Z8X6Y8Z818X11Y4Z6X6Y8Z75X12Y4Z4X7Y7Z64X6Y8Z63X6Y6Z82X5Y7Z86X11Y4Z4X6Y8Z5X6Y7Z63X10Y4Z4X5Y7Z616X6Y6Z53X5Y6Z68X8Y4Z4128X6Y6Z416X6Y4Z68X5Y6Z58X4Y8Z4128X4Y6Z62X4Y4Z86X7Y4Z48X5Y4Z66X4Y7Z416X4Y6Z56X4Y4Z7X4Y3Z816X3Y6Z6192X6Y6Z24X4Y8Z22X4Y6Z48X4Y4Z62X3Y7Z43X3Y3Z8X2Y8Z4208X2Y6Z64X5Y4Z4X4Y7Z22X4Y5Z42X4Y4Z54X3Y6Z418X3Y4Z624X2Y6Z58XY6Z615X6Y4Z232X6Y3Z39X6Y2Z4141X4Y4Z43X3Y7Z2128X3Y3Z6X2Y8Z2X2Y6Z416X2Y4Z64X6Y2Z39X5Y4Z23X5Y2Z49X4Y4Z320X4Y3Z421X3Y4Z4X2Y7Z28XY4Z650X6Y2Z26X4Y4Z264X4Y3Z34X4Y2Z410X3Y4Z325X3Y3Z46X2Y6Z217X2Y4Z48X2Y2Z616X5Y2Z24X4Y3Z24X3Y4Z2240X3Y3Z3X2Y3Z464X4Y2Z2384X3Y3Z2225X2Y4Z2288X2Y3Z373X2Y2Z424XY6Z576X3Y3Z26X3Y2Z212X2Y4Z37X2Y3Z28X2Y2Z38X2YZ428XY4Z2288XY3Z35XY2Z464X3Y2Z12X3YZ2497X2Y2Z230XY4Z20XY2Z32XYZ476X3YZ98X2Y2Z62X2YZ232XY3Z101XY2Z220XYZ3116X2YZ234XY2Z134XYZ2300XYZ16*X^8*Y^12*Z^12+16*X^7*Y^10*Z^11+24*X^4*Y^12*Z^12+X^8*Y^8*Z^11+X^8*Y^8*Z^10+X^7*Y^7*Z^12+16*X^4*Y^10*Z^11+3*X^8*Y^8*Z^8+X^7*Y^7*Z^10+8*X^3*Y^10*Z^11+3*X^8*Y^8*Z^7+2*X^12*Y^4*Z^6+16*X^11*Y^6*Z^5+X^8*Y^8*Z^6+7*X^7*Y^7*Z^8+X^6*Y^8*Z^8+18*X^11*Y^4*Z^6+X^6*Y^8*Z^7+5*X^12*Y^4*Z^4+X^7*Y^7*Z^6+4*X^6*Y^8*Z^6+3*X^6*Y^6*Z^8+2*X^5*Y^7*Z^8+6*X^11*Y^4*Z^4+X^6*Y^8*Z^5+X^6*Y^7*Z^6+3*X^10*Y^4*Z^4+X^5*Y^7*Z^6+16*X^6*Y^6*Z^5+3*X^5*Y^6*Z^6+8*X^8*Y^4*Z^4+128*X^6*Y^6*Z^4+16*X^6*Y^4*Z^6+8*X^5*Y^6*Z^5+8*X^4*Y^8*Z^4+128*X^4*Y^6*Z^6+2*X^4*Y^4*Z^8+6*X^7*Y^4*Z^4+8*X^5*Y^4*Z^6+6*X^4*Y^7*Z^4+16*X^4*Y^6*Z^5+6*X^4*Y^4*Z^7+X^4*Y^3*Z^8+16*X^3*Y^6*Z^6+192*X^6*Y^6*Z^2+4*X^4*Y^8*Z^2+2*X^4*Y^6*Z^4+8*X^4*Y^4*Z^6+2*X^3*Y^7*Z^4+3*X^3*Y^3*Z^8+X^2*Y^8*Z^4+208*X^2*Y^6*Z^6+4*X^5*Y^4*Z^4+X^4*Y^7*Z^2+2*X^4*Y^5*Z^4+2*X^4*Y^4*Z^5+4*X^3*Y^6*Z^4+18*X^3*Y^4*Z^6+24*X^2*Y^6*Z^5+8*X*Y^6*Z^6+15*X^6*Y^4*Z^2+32*X^6*Y^3*Z^3+9*X^6*Y^2*Z^4+141*X^4*Y^4*Z^4+3*X^3*Y^7*Z^2+128*X^3*Y^3*Z^6+X^2*Y^8*Z^2+X^2*Y^6*Z^4+16*X^2*Y^4*Z^6+4*X^6*Y^2*Z^3+9*X^5*Y^4*Z^2+3*X^5*Y^2*Z^4+9*X^4*Y^4*Z^3+20*X^4*Y^3*Z^4+21*X^3*Y^4*Z^4+X^2*Y^7*Z^2+8*X*Y^4*Z^6+50*X^6*Y^2*Z^2+6*X^4*Y^4*Z^2+64*X^4*Y^3*Z^3+4*X^4*Y^2*Z^4+10*X^3*Y^4*Z^3+25*X^3*Y^3*Z^4+6*X^2*Y^6*Z^2+17*X^2*Y^4*Z^4+8*X^2*Y^2*Z^6+16*X^5*Y^2*Z^2+4*X^4*Y^3*Z^2+4*X^3*Y^4*Z^2+240*X^3*Y^3*Z^3+X^2*Y^3*Z^4+64*X^4*Y^2*Z^2+384*X^3*Y^3*Z^2+225*X^2*Y^4*Z^2+288*X^2*Y^3*Z^3+73*X^2*Y^2*Z^4+24*X*Y^6*Z+576*X^3*Y^3*Z+26*X^3*Y^2*Z^2+12*X^2*Y^4*Z+37*X^2*Y^3*Z^2+8*X^2*Y^2*Z^3+8*X^2*Y*Z^4+28*X*Y^4*Z^2+288*X*Y^3*Z^3+5*X*Y^2*Z^4+64*X^3*Y^2*Z+12*X^3*Y*Z^2+497*X^2*Y^2*Z^2+30*X*Y^4*Z+20*X*Y^2*Z^3+2*X*Y*Z^4+76*X^3*Y*Z+98*X^2*Y^2*Z+62*X^2*Y*Z^2+32*X*Y^3*Z+101*X*Y^2*Z^2+20*X*Y*Z^3+116*X^2*Y*Z+234*X*Y^2*Z+134*X*Y*Z^2+300*X*Y*Z

Algorithm definition

The algorithm ⟨19×22×24:5742⟩ could be constructed using the following decomposition:

⟨19×22×24:5742⟩ = ⟨10×12×12:928⟩ + ⟨9×12×12:800⟩ + ⟨10×10×12:795⟩ + ⟨9×12×12:800⟩ + ⟨9×10×12:696⟩ + ⟨10×12×12:928⟩ + ⟨10×10×12:795⟩.

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_1_21A_1_22A_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_2_21A_2_22A_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_3_21A_3_22A_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_4_21A_4_22A_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_5_21A_5_22A_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_6_21A_6_22A_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_20A_7_21A_7_22A_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_8_20A_8_21A_8_22A_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_9_20A_9_21A_9_22A_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_10_20A_10_21A_10_22A_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_11_20A_11_21A_11_22A_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_12_20A_12_21A_12_22A_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_13_20A_13_21A_13_22A_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_14_20A_14_21A_14_22A_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_15_20A_15_21A_15_22A_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_16_20A_16_21A_16_22A_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_17_20A_17_21A_17_22A_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_18_20A_18_21A_18_22A_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_19A_19_20A_19_21A_19_22B_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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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_12C_9_13C_21_13C_9_14C_21_14C_9_15C_21_15C_9_16C_21_16C_9_17C_21_17C_9_18C_21_18C_9_19C_21_19C_10_10C_22_10C_10_11C_22_11C_10_12C_22_12C_10_13C_22_13C_10_14C_22_14C_10_15C_22_15C_10_16C_22_16C_10_17C_22_17C_10_18C_22_18C_10_19C_22_19C_11_10C_23_10C_11_11C_23_11C_11_12C_23_12C_11_13C_23_13C_11_14C_23_14C_11_15C_23_15C_11_16C_23_16C_11_17C_23_17C_11_18C_23_18C_11_19C_23_19C_12_10C_24_10C_12_11C_24_11C_12_12C_24_12C_12_13C_24_13C_12_14C_24_14C_12_15C_24_15C_12_16C_24_16C_12_17C_24_17C_12_18C_24_18C_12_19C_24_19Trace(Mul(Matrix(19, 22, [[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_1_21,A_1_22],[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_2_21,A_2_22],[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_3_21,A_3_22],[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_4_21,A_4_22],[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_5_21,A_5_22],[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_6_21,A_6_22],[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,A_7_21,A_7_22],[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_8_20,A_8_21,A_8_22],[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_9_20,A_9_21,A_9_22],[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_10_20,A_10_21,A_10_22],[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_11_20,A_11_21,A_11_22],[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_12_20,A_12_21,A_12_22],[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_13_20,A_13_21,A_13_22],[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_14_20,A_14_21,A_14_22],[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_15_20,A_15_21,A_15_22],[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_16_20,A_16_21,A_16_22],[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_17_20,A_17_21,A_17_22],[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_18_20,A_18_21,A_18_22],[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,A_19_20,A_19_21,A_19_22]]),Matrix(22, 24, [[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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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,B_20_23,B_20_24],[B_21_1,B_21_2,B_21_3,B_21_4,B_21_5,B_21_6,B_21_7,B_21_8,B_21_9,B_21_10,B_21_11,B_21_12,B_21_13,B_21_14,B_21_15,B_21_16,B_21_17,B_21_18,B_21_19,B_21_20,B_21_21,B_21_22,B_21_23,B_21_24],[B_22_1,B_22_2,B_22_3,B_22_4,B_22_5,B_22_6,B_22_7,B_22_8,B_22_9,B_22_10,B_22_11,B_22_12,B_22_13,B_22_14,B_22_15,B_22_16,B_22_17,B_22_18,B_22_19,B_22_20,B_22_21,B_22_22,B_22_23,B_22_24]]),Matrix(24, 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]]))) = Trace(Mul(Matrix(10, 12, [[A_10_2,A_10_3,A_10_13,A_10_14,A_10_15,A_10_16,A_10_17,A_10_18,A_10_19,A_10_20,A_10_21,A_10_22],[A_11_2,A_11_3,A_8_1+A_11_13,A_8_11+A_11_14,A_8_12+A_11_15,A_8_4+A_11_16,A_8_5+A_11_17,A_8_6+A_11_18,A_8_7+A_11_19,A_8_8+A_11_20,A_8_9+A_11_21,A_8_10+A_11_22],[A_12_2,A_12_3,A_9_1+A_12_13,A_9_11+A_12_14,A_9_12+A_12_15,A_9_4+A_12_16,A_9_5+A_12_17,A_9_6+A_12_18,A_9_7+A_12_19,A_9_8+A_12_20,A_9_9+A_12_21,A_9_10+A_12_22],[A_13_2,A_13_3,A_1_1+A_13_13,A_1_11+A_13_14,A_1_12+A_13_15,A_1_4+A_13_16,A_1_5+A_13_17,A_1_6+A_13_18,A_1_7+A_13_19,A_1_8+A_13_20,A_1_9+A_13_21,A_1_10+A_13_22],[A_14_2,A_14_3,A_2_1+A_14_13,A_2_11+A_14_14,A_2_12+A_14_15,A_2_4+A_14_16,A_2_5+A_14_17,A_2_6+A_14_18,A_2_7+A_14_19,A_2_8+A_14_20,A_2_9+A_14_21,A_2_10+A_14_22],[A_15_2,A_15_3,A_3_1+A_15_13,A_3_11+A_15_14,A_3_12+A_15_15,A_3_4+A_15_16,A_3_5+A_15_17,A_3_6+A_15_18,A_3_7+A_15_19,A_3_8+A_15_20,A_3_9+A_15_21,A_3_10+A_15_22],[A_16_2,A_16_3,A_4_1+A_16_13,A_4_11+A_16_14,A_4_12+A_16_15,A_4_4+A_16_16,A_4_5+A_16_17,A_4_6+A_16_18,A_4_7+A_16_19,A_4_8+A_16_20,A_4_9+A_16_21,A_4_10+A_16_22],[A_17_2,A_17_3,A_5_1+A_17_13,A_5_11+A_17_14,A_5_12+A_17_15,A_5_4+A_17_16,A_5_5+A_17_17,A_5_6+A_17_18,A_5_7+A_17_19,A_5_8+A_17_20,A_5_9+A_17_21,A_5_10+A_17_22],[A_18_2,A_18_3,A_6_1+A_18_13,A_6_11+A_18_14,A_6_12+A_18_15,A_6_4+A_18_16,A_6_5+A_18_17,A_6_6+A_18_18,A_6_7+A_18_19,A_6_8+A_18_20,A_6_9+A_18_21,A_6_10+A_18_22],[A_19_2,A_19_3,A_7_1+A_19_13,A_7_11+A_19_14,A_7_12+A_19_15,A_7_4+A_19_16,A_7_5+A_19_17,A_7_6+A_19_18,A_7_7+A_19_19,A_7_8+A_19_20,A_7_9+A_19_21,A_7_10+A_19_22]]),Matrix(12, 12, [[B_2_4,B_2_5,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_3_4,B_3_5,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_1_1+B_13_4,B_1_2+B_13_5,B_1_3+B_13_15,B_1_13+B_13_16,B_1_14+B_13_17,B_1_6+B_13_18,B_1_7+B_13_19,B_1_8+B_13_20,B_1_9+B_13_21,B_1_10+B_13_22,B_1_11+B_13_23,B_1_12+B_13_24],[B_11_1+B_14_4,B_11_2+B_14_5,B_11_3+B_14_15,B_11_13+B_14_16,B_11_14+B_14_17,B_11_6+B_14_18,B_11_7+B_14_19,B_11_8+B_14_20,B_11_9+B_14_21,B_11_10+B_14_22,B_11_11+B_14_23,B_11_12+B_14_24],[B_12_1+B_15_4,B_12_2+B_15_5,B_12_3+B_15_15,B_12_13+B_15_16,B_12_14+B_15_17,B_12_6+B_15_18,B_12_7+B_15_19,B_12_8+B_15_20,B_12_9+B_15_21,B_12_10+B_15_22,B_12_11+B_15_23,B_12_12+B_15_24],[B_4_1+B_16_4,B_4_2+B_16_5,B_4_3+B_16_15,B_4_13+B_16_16,B_4_14+B_16_17,B_4_6+B_16_18,B_4_7+B_16_19,B_4_8+B_16_20,B_4_9+B_16_21,B_4_10+B_16_22,B_4_11+B_16_23,B_4_12+B_16_24],[B_5_1+B_17_4,B_5_2+B_17_5,B_5_3+B_17_15,B_5_13+B_17_16,B_5_14+B_17_17,B_5_6+B_17_18,B_5_7+B_17_19,B_5_8+B_17_20,B_5_9+B_17_21,B_5_10+B_17_22,B_5_11+B_17_23,B_5_12+B_17_24],[B_6_1+B_18_4,B_6_2+B_18_5,B_6_3+B_18_15,B_6_13+B_18_16,B_6_14+B_18_17,B_6_6+B_18_18,B_6_7+B_18_19,B_6_8+B_18_20,B_6_9+B_18_21,B_6_10+B_18_22,B_6_11+B_18_23,B_6_12+B_18_24],[B_7_1+B_19_4,B_7_2+B_19_5,B_7_3+B_19_15,B_7_13+B_19_16,B_7_14+B_19_17,B_7_6+B_19_18,B_7_7+B_19_19,B_7_8+B_19_20,B_7_9+B_19_21,B_7_10+B_19_22,B_7_11+B_19_23,B_7_12+B_19_24],[B_8_1+B_20_4,B_8_2+B_20_5,B_8_3+B_20_15,B_8_13+B_20_16,B_8_14+B_20_17,B_8_6+B_20_18,B_8_7+B_20_19,B_8_8+B_20_20,B_8_9+B_20_21,B_8_10+B_20_22,B_8_11+B_20_23,B_8_12+B_20_24],[B_9_1+B_21_4,B_9_2+B_21_5,B_9_3+B_21_15,B_9_13+B_21_16,B_9_14+B_21_17,B_9_6+B_21_18,B_9_7+B_21_19,B_9_8+B_21_20,B_9_9+B_21_21,B_9_10+B_21_22,B_9_11+B_21_23,B_9_12+B_21_24],[B_10_1+B_22_4,B_10_2+B_22_5,B_10_3+B_22_15,B_10_13+B_22_16,B_10_14+B_22_17,B_10_6+B_22_18,B_10_7+B_22_19,B_10_8+B_22_20,B_10_9+B_22_21,B_10_10+B_22_22,B_10_11+B_22_23,B_10_12+B_22_24]]),Matrix(12, 10, [[C_4_10,C_1_8+C_4_11,C_1_9+C_4_12,C_1_1+C_4_13,C_1_2+C_4_14,C_1_3+C_4_15,C_1_4+C_4_16,C_1_5+C_4_17,C_1_6+C_4_18,C_1_7+C_4_19],[C_5_10,C_2_8+C_5_11,C_2_9+C_5_12,C_2_1+C_5_13,C_2_2+C_5_14,C_2_3+C_5_15,C_2_4+C_5_16,C_2_5+C_5_17,C_2_6+C_5_18,C_2_7+C_5_19],[C_15_10,C_3_8+C_15_11,C_3_9+C_15_12,C_3_1+C_15_13,C_3_2+C_15_14,C_3_3+C_15_15,C_3_4+C_15_16,C_3_5+C_15_17,C_3_6+C_15_18,C_3_7+C_15_19],[C_16_10,C_13_8+C_16_11,C_13_9+C_16_12,C_13_1+C_16_13,C_13_2+C_16_14,C_13_3+C_16_15,C_13_4+C_16_16,C_13_5+C_16_17,C_13_6+C_16_18,C_13_7+C_16_19],[C_17_10,C_14_8+C_17_11,C_14_9+C_17_12,C_14_1+C_17_13,C_14_2+C_17_14,C_14_3+C_17_15,C_14_4+C_17_16,C_14_5+C_17_17,C_14_6+C_17_18,C_14_7+C_17_19],[C_18_10,C_6_8+C_18_11,C_6_9+C_18_12,C_6_1+C_18_13,C_6_2+C_18_14,C_6_3+C_18_15,C_6_4+C_18_16,C_6_5+C_18_17,C_6_6+C_18_18,C_6_7+C_18_19],[C_19_10,C_7_8+C_19_11,C_7_9+C_19_12,C_7_1+C_19_13,C_7_2+C_19_14,C_7_3+C_19_15,C_7_4+C_19_16,C_7_5+C_19_17,C_7_6+C_19_18,C_7_7+C_19_19],[C_20_10,C_8_8+C_20_11,C_8_9+C_20_12,C_8_1+C_20_13,C_8_2+C_20_14,C_8_3+C_20_15,C_8_4+C_20_16,C_8_5+C_20_17,C_8_6+C_20_18,C_8_7+C_20_19],[C_21_10,C_9_8+C_21_11,C_9_9+C_21_12,C_9_1+C_21_13,C_9_2+C_21_14,C_9_3+C_21_15,C_9_4+C_21_16,C_9_5+C_21_17,C_9_6+C_21_18,C_9_7+C_21_19],[C_22_10,C_10_8+C_22_11,C_10_9+C_22_12,C_10_1+C_22_13,C_10_2+C_22_14,C_10_3+C_22_15,C_10_4+C_22_16,C_10_5+C_22_17,C_10_6+C_22_18,C_10_7+C_22_19],[C_23_10,C_11_8+C_23_11,C_11_9+C_23_12,C_11_1+C_23_13,C_11_2+C_23_14,C_11_3+C_23_15,C_11_4+C_23_16,C_11_5+C_23_17,C_11_6+C_23_18,C_11_7+C_23_19],[C_24_10,C_12_8+C_24_11,C_12_9+C_24_12,C_12_1+C_24_13,C_12_2+C_24_14,C_12_3+C_24_15,C_12_4+C_24_16,C_12_5+C_24_17,C_12_6+C_24_18,C_12_7+C_24_19]])))+Trace(Mul(Matrix(9, 12, [[A_8_2-A_11_2,A_8_3-A_11_3,A_8_13-A_11_13,A_8_14-A_11_14,A_8_15-A_11_15,A_8_16-A_11_16,A_8_17-A_11_17,A_8_18-A_11_18,A_8_19-A_11_19,A_8_20-A_11_20,A_8_21-A_11_21,A_8_22-A_11_22],[A_9_2-A_12_2,A_9_3-A_12_3,A_9_13-A_12_13,A_9_14-A_12_14,A_9_15-A_12_15,A_9_16-A_12_16,A_9_17-A_12_17,A_9_18-A_12_18,A_9_19-A_12_19,A_9_20-A_12_20,A_9_21-A_12_21,A_9_22-A_12_22],[A_1_2-A_13_2,A_1_3-A_13_3,A_1_13-A_13_13,A_1_14-A_13_14,A_1_15-A_13_15,A_1_16-A_13_16,A_1_17-A_13_17,A_1_18-A_13_18,A_1_19-A_13_19,A_1_20-A_13_20,A_1_21-A_13_21,A_1_22-A_13_22],[A_2_2-A_14_2,A_2_3-A_14_3,A_2_13-A_14_13,A_2_14-A_14_14,A_2_15-A_14_15,A_2_16-A_14_16,A_2_17-A_14_17,A_2_18-A_14_18,A_2_19-A_14_19,A_2_20-A_14_20,A_2_21-A_14_21,A_2_22-A_14_22],[A_3_2-A_15_2,A_3_3-A_15_3,A_3_13-A_15_13,A_3_14-A_15_14,A_3_15-A_15_15,A_3_16-A_15_16,A_3_17-A_15_17,A_3_18-A_15_18,A_3_19-A_15_19,A_3_20-A_15_20,A_3_21-A_15_21,A_3_22-A_15_22],[A_4_2-A_16_2,A_4_3-A_16_3,A_4_13-A_16_13,A_4_14-A_16_14,A_4_15-A_16_15,A_4_16-A_16_16,A_4_17-A_16_17,A_4_18-A_16_18,A_4_19-A_16_19,A_4_20-A_16_20,A_4_21-A_16_21,A_4_22-A_16_22],[A_5_2-A_17_2,A_5_3-A_17_3,A_5_13-A_17_13,A_5_14-A_17_14,A_5_15-A_17_15,A_5_16-A_17_16,A_5_17-A_17_17,A_5_18-A_17_18,A_5_19-A_17_19,A_5_20-A_17_20,A_5_21-A_17_21,A_5_22-A_17_22],[A_6_2-A_18_2,A_6_3-A_18_3,A_6_13-A_18_13,A_6_14-A_18_14,A_6_15-A_18_15,A_6_16-A_18_16,A_6_17-A_18_17,A_6_18-A_18_18,A_6_19-A_18_19,A_6_20-A_18_20,A_6_21-A_18_21,A_6_22-A_18_22],[A_7_2-A_19_2,A_7_3-A_19_3,A_7_13-A_19_13,A_7_14-A_19_14,A_7_15-A_19_15,A_7_16-A_19_16,A_7_17-A_19_17,A_7_18-A_19_18,A_7_19-A_19_19,A_7_20-A_19_20,A_7_21-A_19_21,A_7_22-A_19_22]]),Matrix(12, 12, [[B_2_1+B_2_4,B_2_2+B_2_5,B_2_3+B_2_15,B_2_13+B_2_16,B_2_14+B_2_17,B_2_6+B_2_18,B_2_7+B_2_19,B_2_8+B_2_20,B_2_9+B_2_21,B_2_10+B_2_22,B_2_11+B_2_23,B_2_12+B_2_24],[B_3_1+B_3_4,B_3_2+B_3_5,B_3_3+B_3_15,B_3_13+B_3_16,B_3_14+B_3_17,B_3_6+B_3_18,B_3_7+B_3_19,B_3_8+B_3_20,B_3_9+B_3_21,B_3_10+B_3_22,B_3_11+B_3_23,B_3_12+B_3_24],[B_13_1+B_13_4,B_13_2+B_13_5,B_13_3+B_13_15,B_13_13+B_13_16,B_13_14+B_13_17,B_13_6+B_13_18,B_13_7+B_13_19,B_13_8+B_13_20,B_13_9+B_13_21,B_13_10+B_13_22,B_13_11+B_13_23,B_13_12+B_13_24],[B_14_1+B_14_4,B_14_2+B_14_5,B_14_3+B_14_15,B_14_13+B_14_16,B_14_14+B_14_17,B_14_6+B_14_18,B_14_7+B_14_19,B_14_8+B_14_20,B_14_9+B_14_21,B_14_10+B_14_22,B_14_11+B_14_23,B_14_12+B_14_24],[B_15_1+B_15_4,B_15_2+B_15_5,B_15_3+B_15_15,B_15_13+B_15_16,B_15_14+B_15_17,B_15_6+B_15_18,B_15_7+B_15_19,B_15_8+B_15_20,B_15_9+B_15_21,B_15_10+B_15_22,B_15_11+B_15_23,B_15_12+B_15_24],[B_16_1+B_16_4,B_16_2+B_16_5,B_16_3+B_16_15,B_16_13+B_16_16,B_16_14+B_16_17,B_16_6+B_16_18,B_16_7+B_16_19,B_16_8+B_16_20,B_16_9+B_16_21,B_16_10+B_16_22,B_16_11+B_16_23,B_16_12+B_16_24],[B_17_1+B_17_4,B_17_2+B_17_5,B_17_3+B_17_15,B_17_13+B_17_16,B_17_14+B_17_17,B_17_6+B_17_18,B_17_7+B_17_19,B_17_8+B_17_20,B_17_9+B_17_21,B_17_10+B_17_22,B_17_11+B_17_23,B_17_12+B_17_24],[B_18_1+B_18_4,B_18_2+B_18_5,B_18_3+B_18_15,B_18_13+B_18_16,B_18_14+B_18_17,B_18_6+B_18_18,B_18_7+B_18_19,B_18_8+B_18_20,B_18_9+B_18_21,B_18_10+B_18_22,B_18_11+B_18_23,B_18_12+B_18_24],[B_19_1+B_19_4,B_19_2+B_19_5,B_19_3+B_19_15,B_19_13+B_19_16,B_19_14+B_19_17,B_19_6+B_19_18,B_19_7+B_19_19,B_19_8+B_19_20,B_19_9+B_19_21,B_19_10+B_19_22,B_19_11+B_19_23,B_19_12+B_19_24],[B_20_1+B_20_4,B_20_2+B_20_5,B_20_3+B_20_15,B_20_13+B_20_16,B_20_14+B_20_17,B_20_6+B_20_18,B_20_7+B_20_19,B_20_8+B_20_20,B_20_9+B_20_21,B_20_10+B_20_22,B_20_11+B_20_23,B_20_12+B_20_24],[B_21_1+B_21_4,B_21_2+B_21_5,B_21_3+B_21_15,B_21_13+B_21_16,B_21_14+B_21_17,B_21_6+B_21_18,B_21_7+B_21_19,B_21_8+B_21_20,B_21_9+B_21_21,B_21_10+B_21_22,B_21_11+B_21_23,B_21_12+B_21_24],[B_22_1+B_22_4,B_22_2+B_22_5,B_22_3+B_22_15,B_22_13+B_22_16,B_22_14+B_22_17,B_22_6+B_22_18,B_22_7+B_22_19,B_22_8+B_22_20,B_22_9+B_22_21,B_22_10+B_22_22,B_22_11+B_22_23,B_22_12+B_22_24]]),Matrix(12, 9, [[C_1_8,C_1_9,C_1_1,C_1_2,C_1_3,C_1_4,C_1_5,C_1_6,C_1_7],[C_2_8,C_2_9,C_2_1,C_2_2,C_2_3,C_2_4,C_2_5,C_2_6,C_2_7],[C_3_8,C_3_9,C_3_1,C_3_2,C_3_3,C_3_4,C_3_5,C_3_6,C_3_7],[C_13_8,C_13_9,C_13_1,C_13_2,C_13_3,C_13_4,C_13_5,C_13_6,C_13_7],[C_14_8,C_14_9,C_14_1,C_14_2,C_14_3,C_14_4,C_14_5,C_14_6,C_14_7],[C_6_8,C_6_9,C_6_1,C_6_2,C_6_3,C_6_4,C_6_5,C_6_6,C_6_7],[C_7_8,C_7_9,C_7_1,C_7_2,C_7_3,C_7_4,C_7_5,C_7_6,C_7_7],[C_8_8,C_8_9,C_8_1,C_8_2,C_8_3,C_8_4,C_8_5,C_8_6,C_8_7],[C_9_8,C_9_9,C_9_1,C_9_2,C_9_3,C_9_4,C_9_5,C_9_6,C_9_7],[C_10_8,C_10_9,C_10_1,C_10_2,C_10_3,C_10_4,C_10_5,C_10_6,C_10_7],[C_11_8,C_11_9,C_11_1,C_11_2,C_11_3,C_11_4,C_11_5,C_11_6,C_11_7],[C_12_8,C_12_9,C_12_1,C_12_2,C_12_3,C_12_4,C_12_5,C_12_6,C_12_7]])))+Trace(Mul(Matrix(10, 10, [[A_10_1,A_10_11,A_10_12,A_10_4,A_10_5,A_10_6,A_10_7,A_10_8,A_10_9,A_10_10],[-A_8_1+A_11_1,-A_8_11+A_11_11,-A_8_12+A_11_12,-A_8_4+A_11_4,-A_8_5+A_11_5,-A_8_6+A_11_6,-A_8_7+A_11_7,-A_8_8+A_11_8,-A_8_9+A_11_9,-A_8_10+A_11_10],[-A_9_1+A_12_1,-A_9_11+A_12_11,-A_9_12+A_12_12,-A_9_4+A_12_4,-A_9_5+A_12_5,-A_9_6+A_12_6,-A_9_7+A_12_7,-A_9_8+A_12_8,-A_9_9+A_12_9,-A_9_10+A_12_10],[-A_1_1+A_13_1,-A_1_11+A_13_11,-A_1_12+A_13_12,-A_1_4+A_13_4,-A_1_5+A_13_5,-A_1_6+A_13_6,-A_1_7+A_13_7,-A_1_8+A_13_8,-A_1_9+A_13_9,-A_1_10+A_13_10],[-A_2_1+A_14_1,-A_2_11+A_14_11,-A_2_12+A_14_12,-A_2_4+A_14_4,-A_2_5+A_14_5,-A_2_6+A_14_6,-A_2_7+A_14_7,-A_2_8+A_14_8,-A_2_9+A_14_9,-A_2_10+A_14_10],[-A_3_1+A_15_1,-A_3_11+A_15_11,-A_3_12+A_15_12,-A_3_4+A_15_4,-A_3_5+A_15_5,-A_3_6+A_15_6,-A_3_7+A_15_7,-A_3_8+A_15_8,-A_3_9+A_15_9,-A_3_10+A_15_10],[-A_4_1+A_16_1,-A_4_11+A_16_11,-A_4_12+A_16_12,-A_4_4+A_16_4,-A_4_5+A_16_5,-A_4_6+A_16_6,-A_4_7+A_16_7,-A_4_8+A_16_8,-A_4_9+A_16_9,-A_4_10+A_16_10],[-A_5_1+A_17_1,-A_5_11+A_17_11,-A_5_12+A_17_12,-A_5_4+A_17_4,-A_5_5+A_17_5,-A_5_6+A_17_6,-A_5_7+A_17_7,-A_5_8+A_17_8,-A_5_9+A_17_9,-A_5_10+A_17_10],[-A_6_1+A_18_1,-A_6_11+A_18_11,-A_6_12+A_18_12,-A_6_4+A_18_4,-A_6_5+A_18_5,-A_6_6+A_18_6,-A_6_7+A_18_7,-A_6_8+A_18_8,-A_6_9+A_18_9,-A_6_10+A_18_10],[-A_7_1+A_19_1,-A_7_11+A_19_11,-A_7_12+A_19_12,-A_7_4+A_19_4,-A_7_5+A_19_5,-A_7_6+A_19_6,-A_7_7+A_19_7,-A_7_8+A_19_8,-A_7_9+A_19_9,-A_7_10+A_19_10]]),Matrix(10, 12, [[B_1_1+B_1_4,B_1_2+B_1_5,B_1_3+B_1_15,B_1_13+B_1_16,B_1_14+B_1_17,B_1_6+B_1_18,B_1_7+B_1_19,B_1_8+B_1_20,B_1_9+B_1_21,B_1_10+B_1_22,B_1_11+B_1_23,B_1_12+B_1_24],[B_11_1+B_11_4,B_11_2+B_11_5,B_11_3+B_11_15,B_11_13+B_11_16,B_11_14+B_11_17,B_11_6+B_11_18,B_11_7+B_11_19,B_11_8+B_11_20,B_11_9+B_11_21,B_11_10+B_11_22,B_11_11+B_11_23,B_11_12+B_11_24],[B_12_1+B_12_4,B_12_2+B_12_5,B_12_3+B_12_15,B_12_13+B_12_16,B_12_14+B_12_17,B_12_6+B_12_18,B_12_7+B_12_19,B_12_8+B_12_20,B_12_9+B_12_21,B_12_10+B_12_22,B_12_11+B_12_23,B_12_12+B_12_24],[B_4_1+B_4_4,B_4_2+B_4_5,B_4_3+B_4_15,B_4_13+B_4_16,B_4_14+B_4_17,B_4_6+B_4_18,B_4_7+B_4_19,B_4_8+B_4_20,B_4_9+B_4_21,B_4_10+B_4_22,B_4_11+B_4_23,B_4_12+B_4_24],[B_5_1+B_5_4,B_5_2+B_5_5,B_5_3+B_5_15,B_5_13+B_5_16,B_5_14+B_5_17,B_5_6+B_5_18,B_5_7+B_5_19,B_5_8+B_5_20,B_5_9+B_5_21,B_5_10+B_5_22,B_5_11+B_5_23,B_5_12+B_5_24],[B_6_1+B_6_4,B_6_2+B_6_5,B_6_3+B_6_15,B_6_13+B_6_16,B_6_14+B_6_17,B_6_6+B_6_18,B_6_7+B_6_19,B_6_8+B_6_20,B_6_9+B_6_21,B_6_10+B_6_22,B_6_11+B_6_23,B_6_12+B_6_24],[B_7_1+B_7_4,B_7_2+B_7_5,B_7_3+B_7_15,B_7_13+B_7_16,B_7_14+B_7_17,B_7_6+B_7_18,B_7_7+B_7_19,B_7_8+B_7_20,B_7_9+B_7_21,B_7_10+B_7_22,B_7_11+B_7_23,B_7_12+B_7_24],[B_8_1+B_8_4,B_8_2+B_8_5,B_8_3+B_8_15,B_8_13+B_8_16,B_8_14+B_8_17,B_8_6+B_8_18,B_8_7+B_8_19,B_8_8+B_8_20,B_8_9+B_8_21,B_8_10+B_8_22,B_8_11+B_8_23,B_8_12+B_8_24],[B_9_1+B_9_4,B_9_2+B_9_5,B_9_3+B_9_15,B_9_13+B_9_16,B_9_14+B_9_17,B_9_6+B_9_18,B_9_7+B_9_19,B_9_8+B_9_20,B_9_9+B_9_21,B_9_10+B_9_22,B_9_11+B_9_23,B_9_12+B_9_24],[B_10_1+B_10_4,B_10_2+B_10_5,B_10_3+B_10_15,B_10_13+B_10_16,B_10_14+B_10_17,B_10_6+B_10_18,B_10_7+B_10_19,B_10_8+B_10_20,B_10_9+B_10_21,B_10_10+B_10_22,B_10_11+B_10_23,B_10_12+B_10_24]]),Matrix(12, 10, [[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_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_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_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_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_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_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_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_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_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_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_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]])))+Trace(Mul(Matrix(9, 12, [[A_8_2,A_8_3,A_8_1+A_8_13,A_8_11+A_8_14,A_8_12+A_8_15,A_8_4+A_8_16,A_8_5+A_8_17,A_8_6+A_8_18,A_8_7+A_8_19,A_8_8+A_8_20,A_8_9+A_8_21,A_8_10+A_8_22],[A_9_2,A_9_3,A_9_1+A_9_13,A_9_11+A_9_14,A_9_12+A_9_15,A_9_4+A_9_16,A_9_5+A_9_17,A_9_6+A_9_18,A_9_7+A_9_19,A_9_8+A_9_20,A_9_9+A_9_21,A_9_10+A_9_22],[A_1_2,A_1_3,A_1_1+A_1_13,A_1_11+A_1_14,A_1_12+A_1_15,A_1_4+A_1_16,A_1_5+A_1_17,A_1_6+A_1_18,A_1_7+A_1_19,A_1_8+A_1_20,A_1_9+A_1_21,A_1_10+A_1_22],[A_2_2,A_2_3,A_2_1+A_2_13,A_2_11+A_2_14,A_2_12+A_2_15,A_2_4+A_2_16,A_2_5+A_2_17,A_2_6+A_2_18,A_2_7+A_2_19,A_2_8+A_2_20,A_2_9+A_2_21,A_2_10+A_2_22],[A_3_2,A_3_3,A_3_1+A_3_13,A_3_11+A_3_14,A_3_12+A_3_15,A_3_4+A_3_16,A_3_5+A_3_17,A_3_6+A_3_18,A_3_7+A_3_19,A_3_8+A_3_20,A_3_9+A_3_21,A_3_10+A_3_22],[A_4_2,A_4_3,A_4_1+A_4_13,A_4_11+A_4_14,A_4_12+A_4_15,A_4_4+A_4_16,A_4_5+A_4_17,A_4_6+A_4_18,A_4_7+A_4_19,A_4_8+A_4_20,A_4_9+A_4_21,A_4_10+A_4_22],[A_5_2,A_5_3,A_5_1+A_5_13,A_5_11+A_5_14,A_5_12+A_5_15,A_5_4+A_5_16,A_5_5+A_5_17,A_5_6+A_5_18,A_5_7+A_5_19,A_5_8+A_5_20,A_5_9+A_5_21,A_5_10+A_5_22],[A_6_2,A_6_3,A_6_1+A_6_13,A_6_11+A_6_14,A_6_12+A_6_15,A_6_4+A_6_16,A_6_5+A_6_17,A_6_6+A_6_18,A_6_7+A_6_19,A_6_8+A_6_20,A_6_9+A_6_21,A_6_10+A_6_22],[A_7_2,A_7_3,A_7_1+A_7_13,A_7_11+A_7_14,A_7_12+A_7_15,A_7_4+A_7_16,A_7_5+A_7_17,A_7_6+A_7_18,A_7_7+A_7_19,A_7_8+A_7_20,A_7_9+A_7_21,A_7_10+A_7_22]]),Matrix(12, 12, [[B_2_4,B_2_5,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_3_4,B_3_5,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_13_4,B_13_5,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_14_4,B_14_5,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_15_4,B_15_5,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_16_4,B_16_5,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_17_4,B_17_5,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_18_4,B_18_5,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_19_4,B_19_5,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_20_4,B_20_5,B_20_15,B_20_16,B_20_17,B_20_18,B_20_19,B_20_20,B_20_21,B_20_22,B_20_23,B_20_24],[B_21_4,B_21_5,B_21_15,B_21_16,B_21_17,B_21_18,B_21_19,B_21_20,B_21_21,B_21_22,B_21_23,B_21_24],[B_22_4,B_22_5,B_22_15,B_22_16,B_22_17,B_22_18,B_22_19,B_22_20,B_22_21,B_22_22,B_22_23,B_22_24]]),Matrix(12, 9, [[-C_1_8+C_4_8,-C_1_9+C_4_9,-C_1_1+C_4_1,C_4_2-C_1_2,-C_1_3+C_4_3,-C_1_4+C_4_4,-C_1_5+C_4_5,-C_1_6+C_4_6,-C_1_7+C_4_7],[-C_2_8+C_5_8,-C_2_9+C_5_9,-C_2_1+C_5_1,-C_2_2+C_5_2,-C_2_3+C_5_3,-C_2_4+C_5_4,-C_2_5+C_5_5,-C_2_6+C_5_6,-C_2_7+C_5_7],[-C_3_8+C_15_8,-C_3_9+C_15_9,-C_3_1+C_15_1,-C_3_2+C_15_2,-C_3_3+C_15_3,-C_3_4+C_15_4,-C_3_5+C_15_5,-C_3_6+C_15_6,-C_3_7+C_15_7],[-C_13_8+C_16_8,-C_13_9+C_16_9,-C_13_1+C_16_1,-C_13_2+C_16_2,-C_13_3+C_16_3,-C_13_4+C_16_4,-C_13_5+C_16_5,-C_13_6+C_16_6,-C_13_7+C_16_7],[-C_14_8+C_17_8,-C_14_9+C_17_9,-C_14_1+C_17_1,-C_14_2+C_17_2,-C_14_3+C_17_3,-C_14_4+C_17_4,-C_14_5+C_17_5,-C_14_6+C_17_6,-C_14_7+C_17_7],[-C_6_8+C_18_8,-C_6_9+C_18_9,-C_6_1+C_18_1,-C_6_2+C_18_2,-C_6_3+C_18_3,-C_6_4+C_18_4,-C_6_5+C_18_5,-C_6_6+C_18_6,-C_6_7+C_18_7],[-C_7_8+C_19_8,-C_7_9+C_19_9,-C_7_1+C_19_1,-C_7_2+C_19_2,-C_7_3+C_19_3,-C_7_4+C_19_4,-C_7_5+C_19_5,-C_7_6+C_19_6,-C_7_7+C_19_7],[-C_8_8+C_20_8,-C_8_9+C_20_9,-C_8_1+C_20_1,-C_8_2+C_20_2,-C_8_3+C_20_3,-C_8_4+C_20_4,-C_8_5+C_20_5,-C_8_6+C_20_6,-C_8_7+C_20_7],[-C_9_8+C_21_8,-C_9_9+C_21_9,-C_9_1+C_21_1,-C_9_2+C_21_2,-C_9_3+C_21_3,-C_9_4+C_21_4,-C_9_5+C_21_5,-C_9_6+C_21_6,-C_9_7+C_21_7],[-C_10_8+C_22_8,-C_10_9+C_22_9,-C_10_1+C_22_1,-C_10_2+C_22_2,-C_10_3+C_22_3,-C_10_4+C_22_4,-C_10_5+C_22_5,-C_10_6+C_22_6,-C_10_7+C_22_7],[-C_11_8+C_23_8,-C_11_9+C_23_9,-C_11_1+C_23_1,-C_11_2+C_23_2,-C_11_3+C_23_3,-C_11_4+C_23_4,-C_11_5+C_23_5,-C_11_6+C_23_6,-C_11_7+C_23_7],[-C_12_8+C_24_8,-C_12_9+C_24_9,-C_12_1+C_24_1,-C_12_2+C_24_2,-C_12_3+C_24_3,-C_12_4+C_24_4,-C_12_5+C_24_5,-C_12_6+C_24_6,-C_12_7+C_24_7]])))+Trace(Mul(Matrix(9, 10, [[A_8_1,A_8_11,A_8_12,A_8_4,A_8_5,A_8_6,A_8_7,A_8_8,A_8_9,A_8_10],[A_9_1,A_9_11,A_9_12,A_9_4,A_9_5,A_9_6,A_9_7,A_9_8,A_9_9,A_9_10],[A_1_1,A_1_11,A_1_12,A_1_4,A_1_5,A_1_6,A_1_7,A_1_8,A_1_9,A_1_10],[A_2_1,A_2_11,A_2_12,A_2_4,A_2_5,A_2_6,A_2_7,A_2_8,A_2_9,A_2_10],[A_3_1,A_3_11,A_3_12,A_3_4,A_3_5,A_3_6,A_3_7,A_3_8,A_3_9,A_3_10],[A_4_1,A_4_11,A_4_12,A_4_4,A_4_5,A_4_6,A_4_7,A_4_8,A_4_9,A_4_10],[A_5_1,A_5_11,A_5_12,A_5_4,A_5_5,A_5_6,A_5_7,A_5_8,A_5_9,A_5_10],[A_6_1,A_6_11,A_6_12,A_6_4,A_6_5,A_6_6,A_6_7,A_6_8,A_6_9,A_6_10],[A_7_1,A_7_11,A_7_12,A_7_4,A_7_5,A_7_6,A_7_7,A_7_8,A_7_9,A_7_10]]),Matrix(10, 12, [[B_1_4-B_13_4,B_1_5-B_13_5,B_1_15-B_13_15,B_1_16-B_13_16,B_1_17-B_13_17,B_1_18-B_13_18,B_1_19-B_13_19,B_1_20-B_13_20,B_1_21-B_13_21,B_1_22-B_13_22,B_1_23-B_13_23,B_1_24-B_13_24],[B_11_4-B_14_4,B_11_5-B_14_5,B_11_15-B_14_15,B_11_16-B_14_16,B_11_17-B_14_17,B_11_18-B_14_18,B_11_19-B_14_19,B_11_20-B_14_20,B_11_21-B_14_21,B_11_22-B_14_22,B_11_23-B_14_23,B_11_24-B_14_24],[B_12_4-B_15_4,B_12_5-B_15_5,B_12_15-B_15_15,B_12_16-B_15_16,B_12_17-B_15_17,B_12_18-B_15_18,B_12_19-B_15_19,B_12_20-B_15_20,B_12_21-B_15_21,B_12_22-B_15_22,B_12_23-B_15_23,B_12_24-B_15_24],[B_4_4-B_16_4,B_4_5-B_16_5,B_4_15-B_16_15,B_4_16-B_16_16,B_4_17-B_16_17,B_4_18-B_16_18,B_4_19-B_16_19,B_4_20-B_16_20,B_4_21-B_16_21,B_4_22-B_16_22,B_4_23-B_16_23,B_4_24-B_16_24],[B_5_4-B_17_4,B_5_5-B_17_5,B_5_15-B_17_15,B_5_16-B_17_16,B_5_17-B_17_17,B_5_18-B_17_18,B_5_19-B_17_19,B_5_20-B_17_20,B_5_21-B_17_21,B_5_22-B_17_22,B_5_23-B_17_23,B_5_24-B_17_24],[B_6_4-B_18_4,B_6_5-B_18_5,B_6_15-B_18_15,B_6_16-B_18_16,B_6_17-B_18_17,B_6_18-B_18_18,B_6_19-B_18_19,B_6_20-B_18_20,B_6_21-B_18_21,B_6_22-B_18_22,B_6_23-B_18_23,B_6_24-B_18_24],[B_7_4-B_19_4,B_7_5-B_19_5,B_7_15-B_19_15,B_7_16-B_19_16,B_7_17-B_19_17,B_7_18-B_19_18,B_7_19-B_19_19,B_7_20-B_19_20,B_7_21-B_19_21,B_7_22-B_19_22,B_7_23-B_19_23,B_7_24-B_19_24],[B_8_4-B_20_4,B_8_5-B_20_5,B_8_15-B_20_15,B_8_16-B_20_16,B_8_17-B_20_17,B_8_18-B_20_18,B_8_19-B_20_19,B_8_20-B_20_20,B_8_21-B_20_21,B_8_22-B_20_22,B_8_23-B_20_23,B_8_24-B_20_24],[B_9_4-B_21_4,B_9_5-B_21_5,B_9_15-B_21_15,B_9_16-B_21_16,B_9_17-B_21_17,B_9_18-B_21_18,B_9_19-B_21_19,B_9_20-B_21_20,B_9_21-B_21_21,B_9_22-B_21_22,B_9_23-B_21_23,B_9_24-B_21_24],[B_10_4-B_22_4,B_10_5-B_22_5,B_10_15-B_22_15,B_10_16-B_22_16,B_10_17-B_22_17,B_10_18-B_22_18,B_10_19-B_22_19,B_10_20-B_22_20,B_10_21-B_22_21,B_10_22-B_22_22,B_10_23-B_22_23,B_10_24-B_22_24]]),Matrix(12, 9, [[C_4_8+C_4_11,C_4_9+C_4_12,C_4_1+C_4_13,C_4_2+C_4_14,C_4_3+C_4_15,C_4_4+C_4_16,C_4_5+C_4_17,C_4_6+C_4_18,C_4_7+C_4_19],[C_5_8+C_5_11,C_5_9+C_5_12,C_5_1+C_5_13,C_5_2+C_5_14,C_5_3+C_5_15,C_5_4+C_5_16,C_5_5+C_5_17,C_5_6+C_5_18,C_5_7+C_5_19],[C_15_8+C_15_11,C_15_9+C_15_12,C_15_1+C_15_13,C_15_2+C_15_14,C_15_3+C_15_15,C_15_4+C_15_16,C_15_5+C_15_17,C_15_6+C_15_18,C_15_7+C_15_19],[C_16_8+C_16_11,C_16_9+C_16_12,C_16_1+C_16_13,C_16_2+C_16_14,C_16_3+C_16_15,C_16_4+C_16_16,C_16_5+C_16_17,C_16_6+C_16_18,C_16_7+C_16_19],[C_17_8+C_17_11,C_17_9+C_17_12,C_17_1+C_17_13,C_17_2+C_17_14,C_17_3+C_17_15,C_17_4+C_17_16,C_17_5+C_17_17,C_17_6+C_17_18,C_17_7+C_17_19],[C_18_8+C_18_11,C_18_9+C_18_12,C_18_1+C_18_13,C_18_2+C_18_14,C_18_3+C_18_15,C_18_4+C_18_16,C_18_5+C_18_17,C_18_6+C_18_18,C_18_7+C_18_19],[C_19_8+C_19_11,C_19_9+C_19_12,C_19_1+C_19_13,C_19_2+C_19_14,C_19_3+C_19_15,C_19_4+C_19_16,C_19_5+C_19_17,C_19_6+C_19_18,C_19_7+C_19_19],[C_20_8+C_20_11,C_20_9+C_20_12,C_20_1+C_20_13,C_20_2+C_20_14,C_20_3+C_20_15,C_20_4+C_20_16,C_20_5+C_20_17,C_20_6+C_20_18,C_20_7+C_20_19],[C_21_8+C_21_11,C_21_9+C_21_12,C_21_1+C_21_13,C_21_2+C_21_14,C_21_3+C_21_15,C_21_4+C_21_16,C_21_5+C_21_17,C_21_6+C_21_18,C_21_7+C_21_19],[C_22_8+C_22_11,C_22_9+C_22_12,C_22_1+C_22_13,C_22_2+C_22_14,C_22_3+C_22_15,C_22_4+C_22_16,C_22_5+C_22_17,C_22_6+C_22_18,C_22_7+C_22_19],[C_23_8+C_23_11,C_23_9+C_23_12,C_23_1+C_23_13,C_23_2+C_23_14,C_23_3+C_23_15,C_23_4+C_23_16,C_23_5+C_23_17,C_23_6+C_23_18,C_23_7+C_23_19],[C_24_8+C_24_11,C_24_9+C_24_12,C_24_1+C_24_13,C_24_2+C_24_14,C_24_3+C_24_15,C_24_4+C_24_16,C_24_5+C_24_17,C_24_6+C_24_18,C_24_7+C_24_19]])))+Trace(Mul(Matrix(10, 12, [[A_10_2,A_10_3,A_10_13,A_10_14,A_10_15,A_10_16,A_10_17,A_10_18,A_10_19,A_10_20,A_10_21,A_10_22],[A_11_2,A_11_3,A_11_13,A_11_14,A_11_15,A_11_16,A_11_17,A_11_18,A_11_19,A_11_20,A_11_21,A_11_22],[A_12_2,A_12_3,A_12_13,A_12_14,A_12_15,A_12_16,A_12_17,A_12_18,A_12_19,A_12_20,A_12_21,A_12_22],[A_13_2,A_13_3,A_13_13,A_13_14,A_13_15,A_13_16,A_13_17,A_13_18,A_13_19,A_13_20,A_13_21,A_13_22],[A_14_2,A_14_3,A_14_13,A_14_14,A_14_15,A_14_16,A_14_17,A_14_18,A_14_19,A_14_20,A_14_21,A_14_22],[A_15_2,A_15_3,A_15_13,A_15_14,A_15_15,A_15_16,A_15_17,A_15_18,A_15_19,A_15_20,A_15_21,A_15_22],[A_16_2,A_16_3,A_16_13,A_16_14,A_16_15,A_16_16,A_16_17,A_16_18,A_16_19,A_16_20,A_16_21,A_16_22],[A_17_2,A_17_3,A_17_13,A_17_14,A_17_15,A_17_16,A_17_17,A_17_18,A_17_19,A_17_20,A_17_21,A_17_22],[A_18_2,A_18_3,A_18_13,A_18_14,A_18_15,A_18_16,A_18_17,A_18_18,A_18_19,A_18_20,A_18_21,A_18_22],[A_19_2,A_19_3,A_19_13,A_19_14,A_19_15,A_19_16,A_19_17,A_19_18,A_19_19,A_19_20,A_19_21,A_19_22]]),Matrix(12, 12, [[B_2_1,B_2_2,B_2_3,B_2_13,B_2_14,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_13,B_3_14,B_3_6,B_3_7,B_3_8,B_3_9,B_3_10,B_3_11,B_3_12],[-B_1_1+B_13_1,-B_1_2+B_13_2,-B_1_3+B_13_3,-B_1_13+B_13_13,-B_1_14+B_13_14,-B_1_6+B_13_6,-B_1_7+B_13_7,-B_1_8+B_13_8,-B_1_9+B_13_9,-B_1_10+B_13_10,-B_1_11+B_13_11,-B_1_12+B_13_12],[-B_11_1+B_14_1,-B_11_2+B_14_2,-B_11_3+B_14_3,-B_11_13+B_14_13,-B_11_14+B_14_14,-B_11_6+B_14_6,-B_11_7+B_14_7,-B_11_8+B_14_8,-B_11_9+B_14_9,-B_11_10+B_14_10,-B_11_11+B_14_11,-B_11_12+B_14_12],[-B_12_1+B_15_1,-B_12_2+B_15_2,-B_12_3+B_15_3,-B_12_13+B_15_13,-B_12_14+B_15_14,-B_12_6+B_15_6,-B_12_7+B_15_7,-B_12_8+B_15_8,-B_12_9+B_15_9,-B_12_10+B_15_10,-B_12_11+B_15_11,-B_12_12+B_15_12],[-B_4_1+B_16_1,-B_4_2+B_16_2,-B_4_3+B_16_3,-B_4_13+B_16_13,-B_4_14+B_16_14,-B_4_6+B_16_6,-B_4_7+B_16_7,-B_4_8+B_16_8,-B_4_9+B_16_9,-B_4_10+B_16_10,-B_4_11+B_16_11,-B_4_12+B_16_12],[-B_5_1+B_17_1,-B_5_2+B_17_2,-B_5_3+B_17_3,-B_5_13+B_17_13,-B_5_14+B_17_14,-B_5_6+B_17_6,-B_5_7+B_17_7,-B_5_8+B_17_8,-B_5_9+B_17_9,-B_5_10+B_17_10,-B_5_11+B_17_11,-B_5_12+B_17_12],[-B_6_1+B_18_1,-B_6_2+B_18_2,-B_6_3+B_18_3,-B_6_13+B_18_13,-B_6_14+B_18_14,-B_6_6+B_18_6,-B_6_7+B_18_7,-B_6_8+B_18_8,-B_6_9+B_18_9,-B_6_10+B_18_10,-B_6_11+B_18_11,-B_6_12+B_18_12],[-B_7_1+B_19_1,-B_7_2+B_19_2,-B_7_3+B_19_3,-B_7_13+B_19_13,-B_7_14+B_19_14,-B_7_6+B_19_6,-B_7_7+B_19_7,-B_7_8+B_19_8,-B_7_9+B_19_9,-B_7_10+B_19_10,-B_7_11+B_19_11,-B_7_12+B_19_12],[-B_8_1+B_20_1,-B_8_2+B_20_2,-B_8_3+B_20_3,-B_8_13+B_20_13,-B_8_14+B_20_14,-B_8_6+B_20_6,-B_8_7+B_20_7,-B_8_8+B_20_8,-B_8_9+B_20_9,-B_8_10+B_20_10,-B_8_11+B_20_11,-B_8_12+B_20_12],[-B_9_1+B_21_1,-B_9_2+B_21_2,-B_9_3+B_21_3,-B_9_13+B_21_13,-B_9_14+B_21_14,-B_9_6+B_21_6,-B_9_7+B_21_7,-B_9_8+B_21_8,-B_9_9+B_21_9,-B_9_10+B_21_10,-B_9_11+B_21_11,-B_9_12+B_21_12],[-B_10_1+B_22_1,-B_10_2+B_22_2,-B_10_3+B_22_3,-B_10_13+B_22_13,-B_10_14+B_22_14,-B_10_6+B_22_6,-B_10_7+B_22_7,-B_10_8+B_22_8,-B_10_9+B_22_9,-B_10_10+B_22_10,-B_10_11+B_22_11,-B_10_12+B_22_12]]),Matrix(12, 10, [[C_1_10,C_1_8+C_1_11,C_1_9+C_1_12,C_1_1+C_1_13,C_1_2+C_1_14,C_1_3+C_1_15,C_1_4+C_1_16,C_1_5+C_1_17,C_1_6+C_1_18,C_1_7+C_1_19],[C_2_10,C_2_8+C_2_11,C_2_9+C_2_12,C_2_1+C_2_13,C_2_2+C_2_14,C_2_3+C_2_15,C_2_4+C_2_16,C_2_5+C_2_17,C_2_6+C_2_18,C_2_7+C_2_19],[C_3_10,C_3_8+C_3_11,C_3_9+C_3_12,C_3_1+C_3_13,C_3_2+C_3_14,C_3_3+C_3_15,C_3_4+C_3_16,C_3_5+C_3_17,C_3_6+C_3_18,C_3_7+C_3_19],[C_13_10,C_13_8+C_13_11,C_13_9+C_13_12,C_13_1+C_13_13,C_13_2+C_13_14,C_13_3+C_13_15,C_13_4+C_13_16,C_13_5+C_13_17,C_13_6+C_13_18,C_13_7+C_13_19],[C_14_10,C_14_8+C_14_11,C_14_9+C_14_12,C_14_1+C_14_13,C_14_2+C_14_14,C_14_3+C_14_15,C_14_4+C_14_16,C_14_5+C_14_17,C_14_6+C_14_18,C_14_7+C_14_19],[C_6_10,C_6_8+C_6_11,C_6_9+C_6_12,C_6_1+C_6_13,C_6_2+C_6_14,C_6_3+C_6_15,C_6_4+C_6_16,C_6_5+C_6_17,C_6_6+C_6_18,C_6_7+C_6_19],[C_7_10,C_7_8+C_7_11,C_7_9+C_7_12,C_7_1+C_7_13,C_7_2+C_7_14,C_7_3+C_7_15,C_7_4+C_7_16,C_7_5+C_7_17,C_7_6+C_7_18,C_7_7+C_7_19],[C_8_10,C_8_8+C_8_11,C_8_9+C_8_12,C_8_1+C_8_13,C_8_2+C_8_14,C_8_3+C_8_15,C_8_4+C_8_16,C_8_5+C_8_17,C_8_6+C_8_18,C_8_7+C_8_19],[C_9_10,C_9_8+C_9_11,C_9_9+C_9_12,C_9_1+C_9_13,C_9_2+C_9_14,C_9_3+C_9_15,C_9_4+C_9_16,C_9_5+C_9_17,C_9_6+C_9_18,C_9_7+C_9_19],[C_10_10,C_10_8+C_10_11,C_10_9+C_10_12,C_10_1+C_10_13,C_10_2+C_10_14,C_10_3+C_10_15,C_10_4+C_10_16,C_10_5+C_10_17,C_10_6+C_10_18,C_10_7+C_10_19],[C_11_10,C_11_8+C_11_11,C_11_9+C_11_12,C_11_1+C_11_13,C_11_2+C_11_14,C_11_3+C_11_15,C_11_4+C_11_16,C_11_5+C_11_17,C_11_6+C_11_18,C_11_7+C_11_19],[C_12_10,C_12_8+C_12_11,C_12_9+C_12_12,C_12_1+C_12_13,C_12_2+C_12_14,C_12_3+C_12_15,C_12_4+C_12_16,C_12_5+C_12_17,C_12_6+C_12_18,C_12_7+C_12_19]])))+Trace(Mul(Matrix(10, 10, [[A_10_1+A_10_13,A_10_11+A_10_14,A_10_12+A_10_15,A_10_4+A_10_16,A_10_5+A_10_17,A_10_6+A_10_18,A_10_7+A_10_19,A_10_8+A_10_20,A_10_9+A_10_21,A_10_10+A_10_22],[A_11_1+A_11_13,A_11_11+A_11_14,A_11_12+A_11_15,A_11_4+A_11_16,A_11_5+A_11_17,A_11_6+A_11_18,A_11_7+A_11_19,A_11_8+A_11_20,A_11_9+A_11_21,A_11_10+A_11_22],[A_12_1+A_12_13,A_12_11+A_12_14,A_12_12+A_12_15,A_12_4+A_12_16,A_12_5+A_12_17,A_12_6+A_12_18,A_12_7+A_12_19,A_12_8+A_12_20,A_12_9+A_12_21,A_12_10+A_12_22],[A_13_1+A_13_13,A_13_11+A_13_14,A_13_12+A_13_15,A_13_4+A_13_16,A_13_5+A_13_17,A_13_6+A_13_18,A_13_7+A_13_19,A_13_8+A_13_20,A_13_9+A_13_21,A_13_10+A_13_22],[A_14_1+A_14_13,A_14_11+A_14_14,A_14_12+A_14_15,A_14_4+A_14_16,A_14_5+A_14_17,A_14_6+A_14_18,A_14_7+A_14_19,A_14_8+A_14_20,A_14_9+A_14_21,A_14_10+A_14_22],[A_15_1+A_15_13,A_15_11+A_15_14,A_15_12+A_15_15,A_15_4+A_15_16,A_15_5+A_15_17,A_15_6+A_15_18,A_15_7+A_15_19,A_15_8+A_15_20,A_15_9+A_15_21,A_15_10+A_15_22],[A_16_1+A_16_13,A_16_11+A_16_14,A_16_12+A_16_15,A_16_4+A_16_16,A_16_5+A_16_17,A_16_6+A_16_18,A_16_7+A_16_19,A_16_8+A_16_20,A_16_9+A_16_21,A_16_10+A_16_22],[A_17_1+A_17_13,A_17_11+A_17_14,A_17_12+A_17_15,A_17_4+A_17_16,A_17_5+A_17_17,A_17_6+A_17_18,A_17_7+A_17_19,A_17_8+A_17_20,A_17_9+A_17_21,A_17_10+A_17_22],[A_18_1+A_18_13,A_18_11+A_18_14,A_18_12+A_18_15,A_18_4+A_18_16,A_18_5+A_18_17,A_18_6+A_18_18,A_18_7+A_18_19,A_18_8+A_18_20,A_18_9+A_18_21,A_18_10+A_18_22],[A_19_1+A_19_13,A_19_11+A_19_14,A_19_12+A_19_15,A_19_4+A_19_16,A_19_5+A_19_17,A_19_6+A_19_18,A_19_7+A_19_19,A_19_8+A_19_20,A_19_9+A_19_21,A_19_10+A_19_22]]),Matrix(10, 12, [[B_1_1,B_1_2,B_1_3,B_1_13,B_1_14,B_1_6,B_1_7,B_1_8,B_1_9,B_1_10,B_1_11,B_1_12],[B_11_1,B_11_2,B_11_3,B_11_13,B_11_14,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_13,B_12_14,B_12_6,B_12_7,B_12_8,B_12_9,B_12_10,B_12_11,B_12_12],[B_4_1,B_4_2,B_4_3,B_4_13,B_4_14,B_4_6,B_4_7,B_4_8,B_4_9,B_4_10,B_4_11,B_4_12],[B_5_1,B_5_2,B_5_3,B_5_13,B_5_14,B_5_6,B_5_7,B_5_8,B_5_9,B_5_10,B_5_11,B_5_12],[B_6_1,B_6_2,B_6_3,B_6_13,B_6_14,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_13,B_7_14,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_13,B_8_14,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_13,B_9_14,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_13,B_10_14,B_10_6,B_10_7,B_10_8,B_10_9,B_10_10,B_10_11,B_10_12]]),Matrix(12, 10, [[C_1_10-C_4_10,C_1_11-C_4_11,C_1_12-C_4_12,C_1_13-C_4_13,C_1_14-C_4_14,C_1_15-C_4_15,C_1_16-C_4_16,C_1_17-C_4_17,C_1_18-C_4_18,C_1_19-C_4_19],[C_2_10-C_5_10,C_2_11-C_5_11,C_2_12-C_5_12,C_2_13-C_5_13,C_2_14-C_5_14,C_2_15-C_5_15,C_2_16-C_5_16,C_2_17-C_5_17,C_2_18-C_5_18,C_2_19-C_5_19],[C_3_10-C_15_10,C_3_11-C_15_11,C_3_12-C_15_12,C_3_13-C_15_13,C_3_14-C_15_14,C_3_15-C_15_15,C_3_16-C_15_16,C_3_17-C_15_17,C_3_18-C_15_18,C_3_19-C_15_19],[C_13_10-C_16_10,C_13_11-C_16_11,C_13_12-C_16_12,C_13_13-C_16_13,C_13_14-C_16_14,C_13_15-C_16_15,C_13_16-C_16_16,C_13_17-C_16_17,C_13_18-C_16_18,C_13_19-C_16_19],[C_14_10-C_17_10,C_14_11-C_17_11,C_14_12-C_17_12,C_14_13-C_17_13,C_14_14-C_17_14,C_14_15-C_17_15,C_14_16-C_17_16,C_14_17-C_17_17,C_14_18-C_17_18,C_14_19-C_17_19],[C_6_10-C_18_10,C_6_11-C_18_11,C_6_12-C_18_12,C_6_13-C_18_13,C_6_14-C_18_14,C_6_15-C_18_15,C_6_16-C_18_16,C_6_17-C_18_17,C_6_18-C_18_18,C_6_19-C_18_19],[C_7_10-C_19_10,C_7_11-C_19_11,C_7_12-C_19_12,C_7_13-C_19_13,C_7_14-C_19_14,C_7_15-C_19_15,C_7_16-C_19_16,C_7_17-C_19_17,C_7_18-C_19_18,C_7_19-C_19_19],[C_8_10-C_20_10,C_8_11-C_20_11,C_8_12-C_20_12,C_8_13-C_20_13,C_8_14-C_20_14,C_8_15-C_20_15,C_8_16-C_20_16,C_8_17-C_20_17,C_8_18-C_20_18,C_8_19-C_20_19],[C_9_10-C_21_10,C_9_11-C_21_11,C_9_12-C_21_12,C_9_13-C_21_13,C_9_14-C_21_14,C_9_15-C_21_15,C_9_16-C_21_16,C_9_17-C_21_17,C_9_18-C_21_18,C_9_19-C_21_19],[C_10_10-C_22_10,C_10_11-C_22_11,C_10_12-C_22_12,C_10_13-C_22_13,C_10_14-C_22_14,C_10_15-C_22_15,C_10_16-C_22_16,C_10_17-C_22_17,C_10_18-C_22_18,C_10_19-C_22_19],[C_11_10-C_23_10,C_11_11-C_23_11,C_11_12-C_23_12,C_11_13-C_23_13,C_11_14-C_23_14,C_11_15-C_23_15,C_11_16-C_23_16,C_11_17-C_23_17,C_11_18-C_23_18,C_11_19-C_23_19],[C_12_10-C_24_10,C_12_11-C_24_11,C_12_12-C_24_12,C_12_13-C_24_13,C_12_14-C_24_14,C_12_15-C_24_15,C_12_16-C_24_16,C_12_17-C_24_17,C_12_18-C_24_18,C_12_19-C_24_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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