Description of fast matrix multiplication algorithm: ⟨14×19×27:4316⟩

Algorithm type

X12⁢Y14⁢Z14+X11⁢Y11⁢Z13+X8⁢Y13⁢Z8+X7⁢Y10⁢Z8+X6⁢Y13⁢Z6+2⁢X8⁢Y8⁢Z7+X7⁢Y8⁢Z8+2⁢X8⁢Y8⁢Z6+X8⁢Y7⁢Z7+X8⁢Y6⁢Z8+7⁢X7⁢Y8⁢Z7+2⁢X7⁢Y7⁢Z8+X6⁢Y8⁢Z8+X8⁢Y6⁢Z7+X7⁢Y8⁢Z6+X7⁢Y7⁢Z7+X7⁢Y6⁢Z8+3⁢X6⁢Y8⁢Z7+X5⁢Y8⁢Z8+2⁢X8⁢Y8⁢Z4+2⁢X7⁢Y7⁢Z6+X6⁢Y7⁢Z7+X6⁢Y6⁢Z8+X5⁢Y8⁢Z7+X4⁢Y12⁢Z4+X4⁢Y8⁢Z8+X8⁢Y4⁢Z7+X7⁢Y4⁢Z8+X6⁢Y7⁢Z6+6⁢X6⁢Y6⁢Z7+X5⁢Y6⁢Z8+X4⁢Y4⁢Z11+X8⁢Y4⁢Z6+X7⁢Y4⁢Z7+3⁢X6⁢Y6⁢Z6+2⁢X4⁢Y10⁢Z4+X3⁢Y10⁢Z4+X3⁢Y4⁢Z10+2⁢X9⁢Y4⁢Z3+X8⁢Y4⁢Z4+X7⁢Y3⁢Z6+3⁢X5⁢Y5⁢Z6+2⁢X4⁢Y9⁢Z3+18⁢X4⁢Y8⁢Z4+64⁢X4⁢Y6⁢Z6+X4⁢Y5⁢Z7+2⁢X4⁢Y4⁢Z8+2⁢X3⁢Y9⁢Z4+X9⁢Y3⁢Z3+2⁢X8⁢Y4⁢Z3+2⁢X4⁢Y8⁢Z3+16⁢X4⁢Y7⁢Z4+32⁢X4⁢Y6⁢Z5+32⁢X4⁢Y5⁢Z6+5⁢X4⁢Y4⁢Z7+2⁢X3⁢Y9⁢Z3+5⁢X3⁢Y8⁢Z4+X3⁢Y3⁢Z9+6⁢X2⁢Y11⁢Z2+3⁢X6⁢Y4⁢Z4+2⁢X4⁢Y8⁢Z2+8⁢X4⁢Y7⁢Z3+10⁢X4⁢Y6⁢Z4+X4⁢Y4⁢Z6+3⁢X3⁢Y8⁢Z3+6⁢X3⁢Y7⁢Z4+X3⁢Y5⁢Z6+X3⁢Y3⁢Z8+X3⁢Y2⁢Z9+6⁢X2⁢Y10⁢Z2+X2⁢Y8⁢Z4+48⁢X2⁢Y6⁢Z6+2⁢X7⁢Y3⁢Z3+X5⁢Y4⁢Z4+2⁢X4⁢Y7⁢Z2+5⁢X4⁢Y6⁢Z3+X4⁢Y5⁢Z4+2⁢X3⁢Y7⁢Z3+5⁢X3⁢Y6⁢Z4+X3⁢Y3⁢Z7+2⁢X2⁢Y9⁢Z2+2⁢X2⁢Y7⁢Z4+56⁢X2⁢Y6⁢Z5+57⁢X2⁢Y5⁢Z6+2⁢X6⁢Y4⁢Z2+X4⁢Y6⁢Z2+148⁢X4⁢Y4⁢Z4+10⁢X3⁢Y6⁢Z3+X3⁢Y5⁢Z4+X3⁢Y3⁢Z6+2⁢X2⁢Y9⁢Z+7⁢X2⁢Y8⁢Z2+2⁢X2⁢Y6⁢Z4+32⁢X2⁢Y5⁢Z5+X2⁢Y4⁢Z6+2⁢X⁢Y9⁢Z2+2⁢X⁢Y7⁢Z4+X6⁢Y3⁢Z2+20⁢X4⁢Y4⁢Z3+19⁢X4⁢Y3⁢Z4+2⁢X3⁢Y6⁢Z2+2⁢X3⁢Y5⁢Z3+17⁢X3⁢Y4⁢Z4+X3⁢Y2⁢Z6+10⁢X2⁢Y7⁢Z2+64⁢X2⁢Y6⁢Z3+X2⁢Y4⁢Z5+2⁢X2⁢Y3⁢Z6+2⁢X⁢Y9⁢Z+3⁢X⁢Y8⁢Z2+X⁢Y4⁢Z6+17⁢X6⁢Y2⁢Z2+4⁢X5⁢Y4⁢Z+X5⁢Y3⁢Z2+14⁢X4⁢Y4⁢Z2+65⁢X4⁢Y3⁢Z3+12⁢X4⁢Y2⁢Z4+3⁢X3⁢Y5⁢Z2+3⁢X3⁢Y4⁢Z3+15⁢X3⁢Y3⁢Z4+44⁢X2⁢Y6⁢Z2+2⁢X2⁢Y5⁢Z3+36⁢X2⁢Y4⁢Z4+11⁢X2⁢Y2⁢Z6+2⁢X⁢Y7⁢Z2+56⁢X⁢Y6⁢Z3+X⁢Y3⁢Z6+X6⁢Y⁢Z2+X5⁢Y3⁢Z+X4⁢Y4⁢Z+2⁢X4⁢Y3⁢Z2+X4⁢Y2⁢Z3+X4⁢Y⁢Z4+2⁢X3⁢Y4⁢Z2+5⁢X3⁢Y3⁢Z3+X3⁢Y2⁢Z4+3⁢X2⁢Y6⁢Z+8⁢X2⁢Y5⁢Z2+7⁢X2⁢Y4⁢Z3+7⁢X2⁢Y3⁢Z4+X2⁢Y2⁢Z5+2⁢X2⁢Y⁢Z6+41⁢X⁢Y5⁢Z3+X⁢Y4⁢Z4+X⁢Y2⁢Z6+4⁢X4⁢Y3⁢Z+39⁢X4⁢Y2⁢Z2+X3⁢Y3⁢Z2+X3⁢Y2⁢Z3+5⁢X2⁢Y5⁢Z+271⁢X2⁢Y4⁢Z2+322⁢X2⁢Y3⁢Z3+123⁢X2⁢Y2⁢Z4+40⁢X⁢Y6⁢Z+X⁢Y5⁢Z2+X⁢Y4⁢Z3+5⁢X⁢Y3⁢Z4+X⁢Y⁢Z6+2⁢X4⁢Y2⁢Z+X4⁢Y⁢Z2+2⁢X3⁢Y2⁢Z2+5⁢X2⁢Y4⁢Z+28⁢X2⁢Y3⁢Z2+4⁢X2⁢Y2⁢Z3+5⁢X2⁢Y⁢Z4+2⁢X⁢Y5⁢Z+30⁢X⁢Y4⁢Z2+338⁢X⁢Y3⁢Z3+2⁢X⁢Y2⁢Z4+34⁢X3⁢Y2⁢Z+2⁢X3⁢Y⁢Z2+X2⁢Y3⁢Z+478⁢X2⁢Y2⁢Z2+X2⁢Y⁢Z3+42⁢X⁢Y4⁢Z+29⁢X⁢Y3⁢Z2+25⁢X⁢Y2⁢Z3+2⁢X⁢Y⁢Z4+34⁢X3⁢Y⁢Z+49⁢X2⁢Y2⁢Z+21⁢X2⁢Y⁢Z2+66⁢X⁢Y3⁢Z+179⁢X⁢Y2⁢Z2+25⁢X⁢Y⁢Z3+46⁢X2⁢Y⁢Z+275⁢X⁢Y2⁢Z+232⁢X⁢Y⁢Z2+328⁢X⁢Y⁢ZX12Y14Z14X11Y11Z13X8Y13Z8X7Y10Z8X6Y13Z62X8Y8Z7X7Y8Z82X8Y8Z6X8Y7Z7X8Y6Z87X7Y8Z72X7Y7Z8X6Y8Z8X8Y6Z7X7Y8Z6X7Y7Z7X7Y6Z83X6Y8Z7X5Y8Z82X8Y8Z42X7Y7Z6X6Y7Z7X6Y6Z8X5Y8Z7X4Y12Z4X4Y8Z8X8Y4Z7X7Y4Z8X6Y7Z66X6Y6Z7X5Y6Z8X4Y4Z11X8Y4Z6X7Y4Z73X6Y6Z62X4Y10Z4X3Y10Z4X3Y4Z102X9Y4Z3X8Y4Z4X7Y3Z63X5Y5Z62X4Y9Z318X4Y8Z464X4Y6Z6X4Y5Z72X4Y4Z82X3Y9Z4X9Y3Z32X8Y4Z32X4Y8Z316X4Y7Z432X4Y6Z532X4Y5Z65X4Y4Z72X3Y9Z35X3Y8Z4X3Y3Z96X2Y11Z23X6Y4Z42X4Y8Z28X4Y7Z310X4Y6Z4X4Y4Z63X3Y8Z36X3Y7Z4X3Y5Z6X3Y3Z8X3Y2Z96X2Y10Z2X2Y8Z448X2Y6Z62X7Y3Z3X5Y4Z42X4Y7Z25X4Y6Z3X4Y5Z42X3Y7Z35X3Y6Z4X3Y3Z72X2Y9Z22X2Y7Z456X2Y6Z557X2Y5Z62X6Y4Z2X4Y6Z2148X4Y4Z410X3Y6Z3X3Y5Z4X3Y3Z62X2Y9Z7X2Y8Z22X2Y6Z432X2Y5Z5X2Y4Z62XY9Z22XY7Z4X6Y3Z220X4Y4Z319X4Y3Z42X3Y6Z22X3Y5Z317X3Y4Z4X3Y2Z610X2Y7Z264X2Y6Z3X2Y4Z52X2Y3Z62XY9Z3XY8Z2XY4Z617X6Y2Z24X5Y4ZX5Y3Z214X4Y4Z265X4Y3Z312X4Y2Z43X3Y5Z23X3Y4Z315X3Y3Z444X2Y6Z22X2Y5Z336X2Y4Z411X2Y2Z62XY7Z256XY6Z3XY3Z6X6YZ2X5Y3ZX4Y4Z2X4Y3Z2X4Y2Z3X4YZ42X3Y4Z25X3Y3Z3X3Y2Z43X2Y6Z8X2Y5Z27X2Y4Z37X2Y3Z4X2Y2Z52X2YZ641XY5Z3XY4Z4XY2Z64X4Y3Z39X4Y2Z2X3Y3Z2X3Y2Z35X2Y5Z271X2Y4Z2322X2Y3Z3123X2Y2Z440XY6ZXY5Z2XY4Z35XY3Z4XYZ62X4Y2ZX4YZ22X3Y2Z25X2Y4Z28X2Y3Z24X2Y2Z35X2YZ42XY5Z30XY4Z2338XY3Z32XY2Z434X3Y2Z2X3YZ2X2Y3Z478X2Y2Z2X2YZ342XY4Z29XY3Z225XY2Z32XYZ434X3YZ49X2Y2Z21X2YZ266XY3Z179XY2Z225XYZ346X2YZ275XY2Z232XYZ2328XYZX^12*Y^14*Z^14+X^11*Y^11*Z^13+X^8*Y^13*Z^8+X^7*Y^10*Z^8+X^6*Y^13*Z^6+2*X^8*Y^8*Z^7+X^7*Y^8*Z^8+2*X^8*Y^8*Z^6+X^8*Y^7*Z^7+X^8*Y^6*Z^8+7*X^7*Y^8*Z^7+2*X^7*Y^7*Z^8+X^6*Y^8*Z^8+X^8*Y^6*Z^7+X^7*Y^8*Z^6+X^7*Y^7*Z^7+X^7*Y^6*Z^8+3*X^6*Y^8*Z^7+X^5*Y^8*Z^8+2*X^8*Y^8*Z^4+2*X^7*Y^7*Z^6+X^6*Y^7*Z^7+X^6*Y^6*Z^8+X^5*Y^8*Z^7+X^4*Y^12*Z^4+X^4*Y^8*Z^8+X^8*Y^4*Z^7+X^7*Y^4*Z^8+X^6*Y^7*Z^6+6*X^6*Y^6*Z^7+X^5*Y^6*Z^8+X^4*Y^4*Z^11+X^8*Y^4*Z^6+X^7*Y^4*Z^7+3*X^6*Y^6*Z^6+2*X^4*Y^10*Z^4+X^3*Y^10*Z^4+X^3*Y^4*Z^10+2*X^9*Y^4*Z^3+X^8*Y^4*Z^4+X^7*Y^3*Z^6+3*X^5*Y^5*Z^6+2*X^4*Y^9*Z^3+18*X^4*Y^8*Z^4+64*X^4*Y^6*Z^6+X^4*Y^5*Z^7+2*X^4*Y^4*Z^8+2*X^3*Y^9*Z^4+X^9*Y^3*Z^3+2*X^8*Y^4*Z^3+2*X^4*Y^8*Z^3+16*X^4*Y^7*Z^4+32*X^4*Y^6*Z^5+32*X^4*Y^5*Z^6+5*X^4*Y^4*Z^7+2*X^3*Y^9*Z^3+5*X^3*Y^8*Z^4+X^3*Y^3*Z^9+6*X^2*Y^11*Z^2+3*X^6*Y^4*Z^4+2*X^4*Y^8*Z^2+8*X^4*Y^7*Z^3+10*X^4*Y^6*Z^4+X^4*Y^4*Z^6+3*X^3*Y^8*Z^3+6*X^3*Y^7*Z^4+X^3*Y^5*Z^6+X^3*Y^3*Z^8+X^3*Y^2*Z^9+6*X^2*Y^10*Z^2+X^2*Y^8*Z^4+48*X^2*Y^6*Z^6+2*X^7*Y^3*Z^3+X^5*Y^4*Z^4+2*X^4*Y^7*Z^2+5*X^4*Y^6*Z^3+X^4*Y^5*Z^4+2*X^3*Y^7*Z^3+5*X^3*Y^6*Z^4+X^3*Y^3*Z^7+2*X^2*Y^9*Z^2+2*X^2*Y^7*Z^4+56*X^2*Y^6*Z^5+57*X^2*Y^5*Z^6+2*X^6*Y^4*Z^2+X^4*Y^6*Z^2+148*X^4*Y^4*Z^4+10*X^3*Y^6*Z^3+X^3*Y^5*Z^4+X^3*Y^3*Z^6+2*X^2*Y^9*Z+7*X^2*Y^8*Z^2+2*X^2*Y^6*Z^4+32*X^2*Y^5*Z^5+X^2*Y^4*Z^6+2*X*Y^9*Z^2+2*X*Y^7*Z^4+X^6*Y^3*Z^2+20*X^4*Y^4*Z^3+19*X^4*Y^3*Z^4+2*X^3*Y^6*Z^2+2*X^3*Y^5*Z^3+17*X^3*Y^4*Z^4+X^3*Y^2*Z^6+10*X^2*Y^7*Z^2+64*X^2*Y^6*Z^3+X^2*Y^4*Z^5+2*X^2*Y^3*Z^6+2*X*Y^9*Z+3*X*Y^8*Z^2+X*Y^4*Z^6+17*X^6*Y^2*Z^2+4*X^5*Y^4*Z+X^5*Y^3*Z^2+14*X^4*Y^4*Z^2+65*X^4*Y^3*Z^3+12*X^4*Y^2*Z^4+3*X^3*Y^5*Z^2+3*X^3*Y^4*Z^3+15*X^3*Y^3*Z^4+44*X^2*Y^6*Z^2+2*X^2*Y^5*Z^3+36*X^2*Y^4*Z^4+11*X^2*Y^2*Z^6+2*X*Y^7*Z^2+56*X*Y^6*Z^3+X*Y^3*Z^6+X^6*Y*Z^2+X^5*Y^3*Z+X^4*Y^4*Z+2*X^4*Y^3*Z^2+X^4*Y^2*Z^3+X^4*Y*Z^4+2*X^3*Y^4*Z^2+5*X^3*Y^3*Z^3+X^3*Y^2*Z^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Algorithm definition

The algorithm ⟨14×19×27:4316⟩ could be constructed using the following decomposition:

⟨14×19×27:4316⟩ = ⟨8×10×15:795⟩ + ⟨6×10×12:488⟩ + ⟨8×9×15:705⟩ + ⟨6×10×15:600⟩ + ⟨6×9×15:532⟩ + ⟨8×10×12:636⟩ + ⟨8×9×12:560⟩.

This decomposition is defined by the following equality:

Trace⁡Mul⁡A_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_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_26B_17_27B_18_1B_18_2B_18_3B_18_4B_18_5B_18_6B_18_7B_18_8B_18_9B_18_10B_18_11B_18_12B_18_13B_18_14B_18_15B_18_16B_18_17B_18_18B_18_19B_18_20B_18_21B_18_22B_18_23B_18_24B_18_25B_18_26B_18_27B_19_1B_19_2B_19_3B_19_4B_19_5B_19_6B_19_7B_19_8B_19_9B_19_10B_19_11B_19_12B_19_13B_19_14B_19_15B_19_16B_19_17B_19_18B_19_19B_19_20B_19_21B_19_22B_19_23B_19_24B_19_25B_19_26B_19_27C_1_1C_1_2C_1_3C_1_4C_1_5C_1_6C_1_7C_1_8C_1_9C_1_10C_1_11C_1_12C_1_13C_1_14C_2_1C_2_2C_2_3C_2_4C_2_5C_2_6C_2_7C_2_8C_2_9C_2_10C_2_11C_2_12C_2_13C_2_14C_3_1C_3_2C_3_3C_3_4C_3_5C_3_6C_3_7C_3_8C_3_9C_3_10C_3_11C_3_12C_3_13C_3_14C_4_1C_4_2C_4_3C_4_4C_4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4_3C_14_11C_14_4C_14_12C_14_5C_14_13C_14_6C_14_14C_15_1C_15_9C_15_2C_15_10C_15_3C_15_11C_15_4C_15_12C_15_5C_15_13C_15_6C_15_14C_16_1C_16_9C_16_2C_16_10C_16_3C_16_11C_16_4C_16_12C_16_5C_16_13C_16_6C_16_14C_17_1C_17_9C_17_2C_17_10C_17_3C_17_11C_17_4C_17_12C_17_5C_17_13C_17_6C_17_14C_18_1C_18_9C_18_2C_18_10C_18_3C_18_11C_18_4C_18_12C_18_5C_18_13C_18_6C_18_14C_19_1C_19_9C_19_2C_19_10C_19_3C_19_11C_19_4C_19_12C_19_5C_19_13C_19_6C_19_14C_20_1C_20_9C_20_2C_20_10C_20_3C_20_11C_20_4C_20_12C_20_5C_20_13C_20_6C_20_14C_21_1C_21_9C_21_2C_21_10C_21_3C_21_11C_21_4C_21_12C_21_5C_21_13C_21_6C_21_14C_22_1C_22_9C_22_2C_22_10C_22_3C_22_11C_22_4C_22_12C_22_5C_22_13C_22_6C_22_14C_23_1C_23_9C_23_2C_23_10C_23_3C_23_11C_23_4C_23_12C_23_5C_23_13C_23_6C_23_14C_24_1C_24_9C_24_2C_24_10C_24_3C_24_11C_24_4C_24_12C_24_5C_24_13C_24_6C_24_14C_25_1C_25_9C_25_2C_25_10C_25_3C_25_11C_25_4C_25_12C_25_5C_25_13C_25_6C_25_14C_26_1C_26_9C_26_2C_26_10C_26_3C_26_11C_26_4C_26_12C_26_5C_26_13C_26_6C_26_14C_27_1C_27_9C_27_2C_27_10C_27_3C_27_11C_27_4C_27_12C_27_5C_27_13C_27_6C_27_14TraceMulA_7_5A_7_11A_7_12A_7_13A_7_14A_7_15A_7_16A_7_17A_7_18A_7_19A_8_5A_8_11A_8_12A_8_13A_8_14A_8_15A_8_16A_8_17A_8_18A_8_19A_9_5A_9_11A_9_12A_9_13A_9_14A_9_15A_9_16A_9_17A_9_18A_9_19A_10_5A_10_11A_10_12A_10_13A_10_14A_10_15A_10_16A_10_17A_10_18A_10_19A_11_5A_11_11A_11_12A_11_13A_11_14A_11_15A_11_16A_11_17A_11_18A_11_19A_12_5A_12_11A_12_12A_12_13A_12_14A_12_15A_12_16A_12_17A_12_18A_12_19A_13_5A_13_11A_13_12A_13_13A_13_14A_13_15A_13_16A_13_17A_13_18A_13_19A_14_5A_14_11A_14_12A_14_13A_14_14A_14_15A_14_16A_14_17A_14_18A_14_19B_5_1B_5_2B_5_3B_5_4B_5_5B_5_6B_5_7B_5_8B_5_9B_5_10B_5_11B_5_12B_6_1B_11_1B_6_2B_11_2B_6_3B_11_3B_6_4B_11_4B_6_5B_11_5B_6_6B_11_6B_6_7B_11_7B_6_8B_11_8B_6_9B_11_9B_6_10B_11_10B_6_11B_11_11B_6_12B_11_12B_7_1B_12_1B_7_2B_12_2B_7_3B_12_3B_7_4B_12_4B_7_5B_12_5B_7_6B_12_6B_7_7B_12_7B_7_8B_12_8B_7_9B_12_9B_7_10B_12_10B_7_11B_12_11B_7_12B_12_12B_8_1B_13_1B_8_2B_13_2B_8_3B_13_3B_8_4B_13_4B_8_5B_13_5B_8_6B_13_6B_8_7B_13_7B_8_8B_13_8B_8_9B_13_9B_8_10B_13_10B_8_11B_13_11B_8_12B_13_12B_9_1B_14_1B_9_2B_14_2B_9_3B_14_3B_9_4B_14_4B_9_5B_14_5B_9_6B_14_6B_9_7B_14_7B_9_8B_14_8B_9_9B_14_9B_9_10B_14_10B_9_11B_14_11B_9_12B_14_12B_10_1B_15_1B_10_2B_15_2B_10_3B_15_3B_10_4B_15_4B_10_5B_15_5B_10_6B_15_6B_10_7B_15_7B_10_8B_15_8B_10_9B_15_9B_10_10B_15_10B_10_11B_15_11B_10_12B_15_12B_1_1B_16_1B_1_2B_16_2B_1_3B_16_3B_1_4B_16_4B_1_5B_16_5B_1_6B_16_6B_1_7B_16_7B_1_8B_16_8B_1_9B_16_9B_1_10B_16_10B_1_11B_16_11B_1_12B_16_12B_2_1B_17_1B_2_2B_17_2B_2_3B_17_3B_2_4B_17_4B_2_5B_17_5B_2_6B_17_6B_2_7B_17_7B_2_8B_17_8B_2_9B_17_9B_2_10B_17_10B_2_11B_17_11B_2_12B_17_12B_3_1B_18_1B_3_2B_18_2B_3_3B_18_3B_3_4B_18_4B_3_5B_18_5B_3_6B_18_6B_3_7B_18_7B_3_8B_18_8B_3_9B_18_9B_3_10B_18_10B_3_11B_18_11B_3_12B_18_12B_4_1B_19_1B_4_2B_19_2B_4_3B_19_3B_4_4B_19_4B_4_5B_19_5B_4_6B_19_6B_4_7B_19_7B_4_8B_19_8B_4_9B_19_9B_4_10B_19_10B_4_11B_19_11B_4_12B_19_12C_1_7C_1_8C_1_1C_1_9C_1_2C_1_10C_1_3C_1_11C_1_4C_1_12C_1_5C_1_13C_1_6C_1_14C_2_7C_2_8C_2_1C_2_9C_2_2C_2_10C_2_3C_2_11C_2_4C_2_12C_2_5C_2_13C_2_6C_2_14C_3_7C_3_8C_3_1C_3_9C_3_2C_3_10C_3_3C_3_11C_3_4C_3_12C_3_5C_3_13C_3_6C_3_14C_4_7C_4_8C_4_1C_4_9C_4_2C_4_10C_4_3C_4_11C_4_4C_4_12C_4_5C_4_13C_4_6C_4_14C_5_7C_5_8C_5_1C_5_9C_5_2C_5_10C_5_3C_5_11C_5_4C_5_12C_5_5C_5_13C_5_6C_5_14C_6_7C_6_8C_6_1C_6_9C_6_2C_6_10C_6_3C_6_11C_6_4C_6_12C_6_5C_6_13C_6_6C_6_14C_7_7C_7_8C_7_1C_7_9C_7_2C_7_10C_7_3C_7_11C_7_4C_7_12C_7_5C_7_13C_7_6C_7_14C_8_7C_8_8C_8_1C_8_9C_8_2C_8_10C_8_3C_8_11C_8_4C_8_12C_8_5C_8_13C_8_6C_8_14C_9_7C_9_8C_9_1C_9_9C_9_2C_9_10C_9_3C_9_11C_9_4C_9_12C_9_5C_9_13C_9_6C_9_14C_10_7C_10_8C_10_1C_10_9C_10_2C_10_10C_10_3C_10_11C_10_4C_10_12C_10_5C_10_13C_10_6C_10_14C_11_7C_11_8C_11_1C_11_9C_11_2C_11_10C_11_3C_11_11C_11_4C_11_12C_11_5C_11_13C_11_6C_11_14C_12_7C_12_8C_12_1C_12_9C_12_2C_12_10C_12_3C_12_11C_12_4C_12_12C_12_5C_12_13C_12_6C_12_14TraceMulA_7_6A_7_11A_7_7A_7_12A_7_8A_7_13A_7_9A_7_14A_7_10A_7_15A_7_1A_7_16A_7_2A_7_17A_7_3A_7_18A_7_4A_7_19A_8_6A_8_11A_8_7A_8_12A_8_8A_8_13A_8_9A_8_14A_8_10A_8_15A_8_1A_8_16A_8_2A_8_17A_8_3A_8_18A_8_4A_8_19A_9_6A_9_11A_9_7A_9_12A_9_8A_9_13A_9_9A_9_14A_9_10A_9_15A_9_1A_9_16A_9_2A_9_17A_9_3A_9_18A_9_4A_9_19A_10_6A_10_11A_10_7A_10_12A_10_8A_10_13A_10_9A_10_14A_10_10A_10_15A_10_1A_10_16A_10_2A_10_17A_10_3A_10_18A_10_4A_10_19A_11_6A_11_11A_11_7A_11_12A_11_8A_11_13A_11_9A_11_14A_11_10A_11_15A_11_1A_11_16A_11_2A_11_17A_11_3A_11_18A_11_4A_11_19A_12_6A_12_11A_12_7A_12_12A_12_8A_12_13A_12_9A_12_14A_12_10A_12_15A_12_1A_12_16A_12_2A_12_17A_12_3A_12_18A_12_4A_12_19A_13_6A_13_11A_13_7A_13_12A_13_8A_13_13A_13_9A_13_14A_13_10A_13_15A_13_1A_13_16A_13_2A_13_17A_13_3A_13_18A_13_4A_13_19A_14_6A_14_11A_14_7A_14_12A_14_8A_14_13A_14_9A_14_14A_14_10A_14_15A_14_1A_14_16A_14_2A_14_17A_14_3A_14_18A_14_4A_14_19B_6_1B_6_2B_6_3B_6_4B_6_5B_6_6B_6_7B_6_8B_6_9B_6_10B_6_11B_6_12B_7_1B_7_2B_7_3B_7_4B_7_5B_7_6B_7_7B_7_8B_7_9B_7_10B_7_11B_7_12B_8_1B_8_2B_8_3B_8_4B_8_5B_8_6B_8_7B_8_8B_8_9B_8_10B_8_11B_8_12B_9_1B_9_2B_9_3B_9_4B_9_5B_9_6B_9_7B_9_8B_9_9B_9_10B_9_11B_9_12B_10_1B_10_2B_10_3B_10_4B_10_5B_10_6B_10_7B_10_8B_10_9B_10_10B_10_11B_10_12B_1_1B_1_2B_1_3B_1_4B_1_5B_1_6B_1_7B_1_8B_1_9B_1_10B_1_11B_1_12B_2_1B_2_2B_2_3B_2_4B_2_5B_2_6B_2_7B_2_8B_2_9B_2_10B_2_11B_2_12B_3_1B_3_2B_3_3B_3_4B_3_5B_3_6B_3_7B_3_8B_3_9B_3_10B_3_11B_3_12B_4_1B_4_2B_4_3B_4_4B_4_5B_4_6B_4_7B_4_8B_4_9B_4_10B_4_11B_4_12C_1_7C_16_7C_1_8C_16_8C_1_9C_16_9C_1_10C_16_10C_1_11C_16_11C_1_12C_16_12C_1_13C_16_13C_1_14C_16_14C_2_7C_17_7C_2_8C_17_8C_2_9C_17_9C_2_10C_17_10C_2_11C_17_11C_2_12C_17_12C_2_13C_17_13C_2_14C_17_14C_3_7C_18_7C_3_8C_18_8C_3_9C_18_9C_3_10C_18_10C_3_11C_18_11C_3_12C_18_12C_3_13C_18_13C_3_14C_18_14C_4_7C_19_7C_4_8C_19_8C_4_9C_19_9C_4_10C_19_10C_4_11C_19_11C_4_12C_19_12C_4_13C_19_13C_4_14C_19_14C_5_7C_20_7C_5_8C_20_8C_5_9C_20_9C_5_10C_20_10C_5_11C_20_11C_5_12C_20_12C_5_13C_20_13C_5_14C_20_14C_6_7C_21_7C_6_8C_21_8C_6_9C_21_9C_6_10C_21_10C_6_11C_21_11C_6_12C_21_12C_6_13C_21_13C_6_14C_21_14C_7_7C_22_7C_7_8C_22_8C_7_9C_22_9C_7_10C_22_10C_7_11C_22_11C_7_12C_22_12C_7_13C_22_13C_7_14C_22_14C_8_7C_23_7C_8_8C_23_8C_8_9C_23_9C_8_10C_23_10C_8_11C_23_11C_8_12C_23_12C_8_13C_23_13C_8_14C_23_14C_9_7C_24_7C_9_8C_24_8C_9_9C_24_9C_9_10C_24_10C_9_11C_24_11C_9_12C_24_12C_9_13C_24_13C_9_14C_24_14C_10_7C_25_7C_10_8C_25_8C_10_9C_25_9C_10_10C_25_10C_10_11C_25_11C_10_12C_25_12C_10_13C_25_13C_10_14C_25_14C_11_7C_26_7C_11_8C_26_8C_11_9C_26_9C_11_10C_26_10C_11_11C_26_11C_11_12C_26_12C_11_13C_26_13C_11_14C_26_14C_12_7C_27_7C_12_8C_27_8C_12_9C_27_9C_12_10C_27_10C_12_11C_27_11C_12_12C_27_12C_12_13C_27_13C_12_14C_27_14Trace(Mul(Matrix(14, 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]]),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, 14, [[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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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]]))) = Trace(Mul(Matrix(8, 10, [[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_1_6+A_9_11,A_1_7+A_9_12,A_1_8+A_9_13,A_1_9+A_9_14,A_1_10+A_9_15,A_1_1+A_9_16,A_1_2+A_9_17,A_1_3+A_9_18,A_1_4+A_9_19],[A_10_5,A_2_6+A_10_11,A_2_7+A_10_12,A_2_8+A_10_13,A_2_9+A_10_14,A_2_10+A_10_15,A_2_1+A_10_16,A_2_2+A_10_17,A_2_3+A_10_18,A_2_4+A_10_19],[A_11_5,A_3_6+A_11_11,A_3_7+A_11_12,A_3_8+A_11_13,A_3_9+A_11_14,A_3_10+A_11_15,A_3_1+A_11_16,A_3_2+A_11_17,A_3_3+A_11_18,A_3_4+A_11_19],[A_12_5,A_4_6+A_12_11,A_4_7+A_12_12,A_4_8+A_12_13,A_4_9+A_12_14,A_4_10+A_12_15,A_4_1+A_12_16,A_4_2+A_12_17,A_4_3+A_12_18,A_4_4+A_12_19],[A_13_5,A_5_6+A_13_11,A_5_7+A_13_12,A_5_8+A_13_13,A_5_9+A_13_14,A_5_10+A_13_15,A_5_1+A_13_16,A_5_2+A_13_17,A_5_3+A_13_18,A_5_4+A_13_19],[A_14_5,A_6_6+A_14_11,A_6_7+A_14_12,A_6_8+A_14_13,A_6_9+A_14_14,A_6_10+A_14_15,A_6_1+A_14_16,A_6_2+A_14_17,A_6_3+A_14_18,A_6_4+A_14_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_6_1+B_11_16,B_6_2+B_11_17,B_6_3+B_11_18,B_6_4+B_11_19,B_6_5+B_11_20,B_6_6+B_11_21,B_6_7+B_11_22,B_6_8+B_11_23,B_6_9+B_11_24,B_6_10+B_11_25,B_6_11+B_11_26,B_6_12+B_11_27],[B_12_13,B_12_14,B_12_15,B_7_1+B_12_16,B_7_2+B_12_17,B_7_3+B_12_18,B_7_4+B_12_19,B_7_5+B_12_20,B_7_6+B_12_21,B_7_7+B_12_22,B_7_8+B_12_23,B_7_9+B_12_24,B_7_10+B_12_25,B_7_11+B_12_26,B_7_12+B_12_27],[B_13_13,B_13_14,B_13_15,B_8_1+B_13_16,B_8_2+B_13_17,B_8_3+B_13_18,B_8_4+B_13_19,B_8_5+B_13_20,B_8_6+B_13_21,B_8_7+B_13_22,B_8_8+B_13_23,B_8_9+B_13_24,B_8_10+B_13_25,B_8_11+B_13_26,B_8_12+B_13_27],[B_14_13,B_14_14,B_14_15,B_9_1+B_14_16,B_9_2+B_14_17,B_9_3+B_14_18,B_9_4+B_14_19,B_9_5+B_14_20,B_9_6+B_14_21,B_9_7+B_14_22,B_9_8+B_14_23,B_9_9+B_14_24,B_9_10+B_14_25,B_9_11+B_14_26,B_9_12+B_14_27],[B_15_13,B_15_14,B_15_15,B_10_1+B_15_16,B_10_2+B_15_17,B_10_3+B_15_18,B_10_4+B_15_19,B_10_5+B_15_20,B_10_6+B_15_21,B_10_7+B_15_22,B_10_8+B_15_23,B_10_9+B_15_24,B_10_10+B_15_25,B_10_11+B_15_26,B_10_12+B_15_27],[B_16_13,B_16_14,B_16_15,B_1_1+B_16_16,B_1_2+B_16_17,B_1_3+B_16_18,B_1_4+B_16_19,B_1_5+B_16_20,B_1_6+B_16_21,B_1_7+B_16_22,B_1_8+B_16_23,B_1_9+B_16_24,B_1_10+B_16_25,B_1_11+B_16_26,B_1_12+B_16_27],[B_17_13,B_17_14,B_17_15,B_2_1+B_17_16,B_2_2+B_17_17,B_2_3+B_17_18,B_2_4+B_17_19,B_2_5+B_17_20,B_2_6+B_17_21,B_2_7+B_17_22,B_2_8+B_17_23,B_2_9+B_17_24,B_2_10+B_17_25,B_2_11+B_17_26,B_2_12+B_17_27],[B_18_13,B_18_14,B_18_15,B_3_1+B_18_16,B_3_2+B_18_17,B_3_3+B_18_18,B_3_4+B_18_19,B_3_5+B_18_20,B_3_6+B_18_21,B_3_7+B_18_22,B_3_8+B_18_23,B_3_9+B_18_24,B_3_10+B_18_25,B_3_11+B_18_26,B_3_12+B_18_27],[B_19_13,B_19_14,B_19_15,B_4_1+B_19_16,B_4_2+B_19_17,B_4_3+B_19_18,B_4_4+B_19_19,B_4_5+B_19_20,B_4_6+B_19_21,B_4_7+B_19_22,B_4_8+B_19_23,B_4_9+B_19_24,B_4_10+B_19_25,B_4_11+B_19_26,B_4_12+B_19_27]]),Matrix(15, 8, [[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_14_7,C_14_8,C_14_9,C_14_10,C_14_11,C_14_12,C_14_13,C_14_14],[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_16_7,C_16_8,C_1_1+C_16_9,C_1_2+C_16_10,C_1_3+C_16_11,C_1_4+C_16_12,C_1_5+C_16_13,C_1_6+C_16_14],[C_17_7,C_17_8,C_2_1+C_17_9,C_2_2+C_17_10,C_2_3+C_17_11,C_2_4+C_17_12,C_2_5+C_17_13,C_2_6+C_17_14],[C_18_7,C_18_8,C_3_1+C_18_9,C_3_2+C_18_10,C_3_3+C_18_11,C_3_4+C_18_12,C_3_5+C_18_13,C_3_6+C_18_14],[C_19_7,C_19_8,C_4_1+C_19_9,C_4_2+C_19_10,C_4_3+C_19_11,C_4_4+C_19_12,C_4_5+C_19_13,C_4_6+C_19_14],[C_20_7,C_20_8,C_5_1+C_20_9,C_5_2+C_20_10,C_5_3+C_20_11,C_5_4+C_20_12,C_5_5+C_20_13,C_5_6+C_20_14],[C_21_7,C_21_8,C_6_1+C_21_9,C_6_2+C_21_10,C_6_3+C_21_11,C_6_4+C_21_12,C_6_5+C_21_13,C_6_6+C_21_14],[C_22_7,C_22_8,C_7_1+C_22_9,C_7_2+C_22_10,C_7_3+C_22_11,C_7_4+C_22_12,C_7_5+C_22_13,C_7_6+C_22_14],[C_23_7,C_23_8,C_8_1+C_23_9,C_8_2+C_23_10,C_8_3+C_23_11,C_8_4+C_23_12,C_8_5+C_23_13,C_8_6+C_23_14],[C_24_7,C_24_8,C_9_1+C_24_9,C_9_2+C_24_10,C_9_3+C_24_11,C_9_4+C_24_12,C_9_5+C_24_13,C_9_6+C_24_14],[C_25_7,C_25_8,C_10_1+C_25_9,C_10_2+C_25_10,C_10_3+C_25_11,C_10_4+C_25_12,C_10_5+C_25_13,C_10_6+C_25_14],[C_26_7,C_26_8,C_11_1+C_26_9,C_11_2+C_26_10,C_11_3+C_26_11,C_11_4+C_26_12,C_11_5+C_26_13,C_11_6+C_26_14],[C_27_7,C_27_8,C_12_1+C_27_9,C_12_2+C_27_10,C_12_3+C_27_11,C_12_4+C_27_12,C_12_5+C_27_13,C_12_6+C_27_14]])))+Trace(Mul(Matrix(6, 10, [[A_1_5-A_9_5,A_1_11-A_9_11,A_1_12-A_9_12,A_1_13-A_9_13,A_1_14-A_9_14,A_1_15-A_9_15,A_1_16-A_9_16,A_1_17-A_9_17,A_1_18-A_9_18,A_1_19-A_9_19],[A_2_5-A_10_5,A_2_11-A_10_11,A_2_12-A_10_12,A_2_13-A_10_13,A_2_14-A_10_14,A_2_15-A_10_15,A_2_16-A_10_16,A_2_17-A_10_17,A_2_18-A_10_18,A_2_19-A_10_19],[A_3_5-A_11_5,A_3_11-A_11_11,A_3_12-A_11_12,A_3_13-A_11_13,A_3_14-A_11_14,A_3_15-A_11_15,A_3_16-A_11_16,A_3_17-A_11_17,A_3_18-A_11_18,A_3_19-A_11_19],[A_4_5-A_12_5,A_4_11-A_12_11,A_4_12-A_12_12,A_4_13-A_12_13,A_4_14-A_12_14,A_4_15-A_12_15,A_4_16-A_12_16,A_4_17-A_12_17,A_4_18-A_12_18,A_4_19-A_12_19],[A_5_5-A_13_5,A_5_11-A_13_11,A_5_12-A_13_12,A_5_13-A_13_13,A_5_14-A_13_14,A_5_15-A_13_15,A_5_16-A_13_16,A_5_17-A_13_17,A_5_18-A_13_18,A_5_19-A_13_19],[A_6_5-A_14_5,A_6_11-A_14_11,A_6_12-A_14_12,A_6_13-A_14_13,A_6_14-A_14_14,A_6_15-A_14_15,A_6_16-A_14_16,A_6_17-A_14_17,A_6_18-A_14_18,A_6_19-A_14_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_11_1+B_11_16,B_11_2+B_11_17,B_11_3+B_11_18,B_11_4+B_11_19,B_11_5+B_11_20,B_11_6+B_11_21,B_11_7+B_11_22,B_11_8+B_11_23,B_11_9+B_11_24,B_11_10+B_11_25,B_11_11+B_11_26,B_11_12+B_11_27],[B_12_1+B_12_16,B_12_2+B_12_17,B_12_3+B_12_18,B_12_4+B_12_19,B_12_5+B_12_20,B_12_6+B_12_21,B_12_7+B_12_22,B_12_8+B_12_23,B_12_9+B_12_24,B_12_10+B_12_25,B_12_11+B_12_26,B_12_12+B_12_27],[B_13_1+B_13_16,B_13_2+B_13_17,B_13_3+B_13_18,B_13_4+B_13_19,B_13_5+B_13_20,B_13_6+B_13_21,B_13_7+B_13_22,B_13_8+B_13_23,B_13_9+B_13_24,B_13_10+B_13_25,B_13_11+B_13_26,B_13_12+B_13_27],[B_14_1+B_14_16,B_14_2+B_14_17,B_14_3+B_14_18,B_14_4+B_14_19,B_14_5+B_14_20,B_14_6+B_14_21,B_14_7+B_14_22,B_14_8+B_14_23,B_14_9+B_14_24,B_14_10+B_14_25,B_14_11+B_14_26,B_14_12+B_14_27],[B_15_1+B_15_16,B_15_2+B_15_17,B_15_3+B_15_18,B_15_4+B_15_19,B_15_5+B_15_20,B_15_6+B_15_21,B_15_7+B_15_22,B_15_8+B_15_23,B_15_9+B_15_24,B_15_10+B_15_25,B_15_11+B_15_26,B_15_12+B_15_27],[B_16_1+B_16_16,B_16_2+B_16_17,B_16_3+B_16_18,B_16_4+B_16_19,B_16_5+B_16_20,B_16_6+B_16_21,B_16_7+B_16_22,B_16_8+B_16_23,B_16_9+B_16_24,B_16_10+B_16_25,B_16_11+B_16_26,B_16_12+B_16_27],[B_17_1+B_17_16,B_17_2+B_17_17,B_17_3+B_17_18,B_17_4+B_17_19,B_17_5+B_17_20,B_17_6+B_17_21,B_17_7+B_17_22,B_17_8+B_17_23,B_17_9+B_17_24,B_17_10+B_17_25,B_17_11+B_17_26,B_17_12+B_17_27],[B_18_1+B_18_16,B_18_2+B_18_17,B_18_3+B_18_18,B_18_4+B_18_19,B_18_5+B_18_20,B_18_6+B_18_21,B_18_7+B_18_22,B_18_8+B_18_23,B_18_9+B_18_24,B_18_10+B_18_25,B_18_11+B_18_26,B_18_12+B_18_27],[B_19_1+B_19_16,B_19_2+B_19_17,B_19_3+B_19_18,B_19_4+B_19_19,B_19_5+B_19_20,B_19_6+B_19_21,B_19_7+B_19_22,B_19_8+B_19_23,B_19_9+B_19_24,B_19_10+B_19_25,B_19_11+B_19_26,B_19_12+B_19_27]]),Matrix(12, 6, [[C_1_1,C_1_2,C_1_3,C_1_4,C_1_5,C_1_6],[C_2_1,C_2_2,C_2_3,C_2_4,C_2_5,C_2_6],[C_3_1,C_3_2,C_3_3,C_3_4,C_3_5,C_3_6],[C_4_1,C_4_2,C_4_3,C_4_4,C_4_5,C_4_6],[C_5_1,C_5_2,C_5_3,C_5_4,C_5_5,C_5_6],[C_6_1,C_6_2,C_6_3,C_6_4,C_6_5,C_6_6],[C_7_1,C_7_2,C_7_3,C_7_4,C_7_5,C_7_6],[C_8_1,C_8_2,C_8_3,C_8_4,C_8_5,C_8_6],[C_9_1,C_9_2,C_9_3,C_9_4,C_9_5,C_9_6],[C_10_1,C_10_2,C_10_3,C_10_4,C_10_5,C_10_6],[C_11_1,C_11_2,C_11_3,C_11_4,C_11_5,C_11_6],[C_12_1,C_12_2,C_12_3,C_12_4,C_12_5,C_12_6]])))+Trace(Mul(Matrix(8, 9, [[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_1_6+A_9_6,-A_1_7+A_9_7,-A_1_8+A_9_8,-A_1_9+A_9_9,-A_1_10+A_9_10,-A_1_1+A_9_1,-A_1_2+A_9_2,-A_1_3+A_9_3,-A_1_4+A_9_4],[-A_2_6+A_10_6,-A_2_7+A_10_7,-A_2_8+A_10_8,-A_2_9+A_10_9,-A_2_10+A_10_10,-A_2_1+A_10_1,-A_2_2+A_10_2,-A_2_3+A_10_3,-A_2_4+A_10_4],[-A_3_6+A_11_6,-A_3_7+A_11_7,-A_3_8+A_11_8,-A_3_9+A_11_9,-A_3_10+A_11_10,-A_3_1+A_11_1,-A_3_2+A_11_2,-A_3_3+A_11_3,-A_3_4+A_11_4],[-A_4_6+A_12_6,-A_4_7+A_12_7,-A_4_8+A_12_8,-A_4_9+A_12_9,-A_4_10+A_12_10,-A_4_1+A_12_1,-A_4_2+A_12_2,-A_4_3+A_12_3,-A_4_4+A_12_4],[-A_5_6+A_13_6,-A_5_7+A_13_7,-A_5_8+A_13_8,-A_5_9+A_13_9,-A_5_10+A_13_10,-A_5_1+A_13_1,-A_5_2+A_13_2,-A_5_3+A_13_3,-A_5_4+A_13_4],[-A_6_6+A_14_6,-A_6_7+A_14_7,-A_6_8+A_14_8,-A_6_9+A_14_9,-A_6_10+A_14_10,-A_6_1+A_14_1,-A_6_2+A_14_2,-A_6_3+A_14_3,-A_6_4+A_14_4]]),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, 8, [[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_14_7,C_14_8,C_14_9,C_14_10,C_14_11,C_14_12,C_14_13,C_14_14],[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_16_7,C_16_8,C_16_9,C_16_10,C_16_11,C_16_12,C_16_13,C_16_14],[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_18_7,C_18_8,C_18_9,C_18_10,C_18_11,C_18_12,C_18_13,C_18_14],[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_20_7,C_20_8,C_20_9,C_20_10,C_20_11,C_20_12,C_20_13,C_20_14],[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_22_7,C_22_8,C_22_9,C_22_10,C_22_11,C_22_12,C_22_13,C_22_14],[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_24_7,C_24_8,C_24_9,C_24_10,C_24_11,C_24_12,C_24_13,C_24_14],[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_26_7,C_26_8,C_26_9,C_26_10,C_26_11,C_26_12,C_26_13,C_26_14],[C_27_7,C_27_8,C_27_9,C_27_10,C_27_11,C_27_12,C_27_13,C_27_14]])))+Trace(Mul(Matrix(6, 10, [[A_1_5,A_1_6+A_1_11,A_1_7+A_1_12,A_1_8+A_1_13,A_1_9+A_1_14,A_1_10+A_1_15,A_1_1+A_1_16,A_1_2+A_1_17,A_1_3+A_1_18,A_1_4+A_1_19],[A_2_5,A_2_6+A_2_11,A_2_7+A_2_12,A_2_8+A_2_13,A_2_9+A_2_14,A_2_10+A_2_15,A_2_1+A_2_16,A_2_2+A_2_17,A_2_3+A_2_18,A_2_4+A_2_19],[A_3_5,A_3_6+A_3_11,A_3_7+A_3_12,A_3_8+A_3_13,A_3_9+A_3_14,A_3_10+A_3_15,A_3_1+A_3_16,A_3_2+A_3_17,A_3_3+A_3_18,A_3_4+A_3_19],[A_4_5,A_4_6+A_4_11,A_4_7+A_4_12,A_4_8+A_4_13,A_4_9+A_4_14,A_4_10+A_4_15,A_4_1+A_4_16,A_4_2+A_4_17,A_4_3+A_4_18,A_4_4+A_4_19],[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_6_5,A_6_6+A_6_11,A_6_7+A_6_12,A_6_8+A_6_13,A_6_9+A_6_14,A_6_10+A_6_15,A_6_1+A_6_16,A_6_2+A_6_17,A_6_3+A_6_18,A_6_4+A_6_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, 6, [[C_13_1,C_13_2,C_13_3,C_13_4,C_13_5,C_13_6],[C_14_1,C_14_2,C_14_3,C_14_4,C_14_5,C_14_6],[C_15_1,C_15_2,C_15_3,C_15_4,C_15_5,C_15_6],[-C_1_1+C_16_1,-C_1_2+C_16_2,-C_1_3+C_16_3,-C_1_4+C_16_4,-C_1_5+C_16_5,-C_1_6+C_16_6],[-C_2_1+C_17_1,-C_2_2+C_17_2,-C_2_3+C_17_3,-C_2_4+C_17_4,-C_2_5+C_17_5,-C_2_6+C_17_6],[-C_3_1+C_18_1,-C_3_2+C_18_2,-C_3_3+C_18_3,-C_3_4+C_18_4,-C_3_5+C_18_5,-C_3_6+C_18_6],[-C_4_1+C_19_1,-C_4_2+C_19_2,-C_4_3+C_19_3,-C_4_4+C_19_4,-C_4_5+C_19_5,-C_4_6+C_19_6],[-C_5_1+C_20_1,-C_5_2+C_20_2,-C_5_3+C_20_3,-C_5_4+C_20_4,-C_5_5+C_20_5,-C_5_6+C_20_6],[-C_6_1+C_21_1,-C_6_2+C_21_2,-C_6_3+C_21_3,-C_6_4+C_21_4,-C_6_5+C_21_5,-C_6_6+C_21_6],[-C_7_1+C_22_1,-C_7_2+C_22_2,-C_7_3+C_22_3,-C_7_4+C_22_4,-C_7_5+C_22_5,-C_7_6+C_22_6],[-C_8_1+C_23_1,-C_8_2+C_23_2,-C_8_3+C_23_3,-C_8_4+C_23_4,-C_8_5+C_23_5,-C_8_6+C_23_6],[-C_9_1+C_24_1,-C_9_2+C_24_2,-C_9_3+C_24_3,-C_9_4+C_24_4,-C_9_5+C_24_5,-C_9_6+C_24_6],[-C_10_1+C_25_1,-C_10_2+C_25_2,-C_10_3+C_25_3,-C_10_4+C_25_4,-C_10_5+C_25_5,-C_10_6+C_25_6],[-C_11_1+C_26_1,-C_11_2+C_26_2,-C_11_3+C_26_3,-C_11_4+C_26_4,-C_11_5+C_26_5,-C_11_6+C_26_6],[-C_12_1+C_27_1,-C_12_2+C_27_2,-C_12_3+C_27_3,-C_12_4+C_27_4,-C_12_5+C_27_5,-C_12_6+C_27_6]])))+Trace(Mul(Matrix(6, 9, [[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],[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_6_7,A_6_8,A_6_9,A_6_10,A_6_1,A_6_2,A_6_3,A_6_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, 6, [[C_13_1+C_13_9,C_13_2+C_13_10,C_13_3+C_13_11,C_13_4+C_13_12,C_13_5+C_13_13,C_13_6+C_13_14],[C_14_1+C_14_9,C_14_2+C_14_10,C_14_3+C_14_11,C_14_4+C_14_12,C_14_5+C_14_13,C_14_6+C_14_14],[C_15_1+C_15_9,C_15_2+C_15_10,C_15_3+C_15_11,C_15_4+C_15_12,C_15_5+C_15_13,C_15_6+C_15_14],[C_16_1+C_16_9,C_16_2+C_16_10,C_16_3+C_16_11,C_16_4+C_16_12,C_16_5+C_16_13,C_16_6+C_16_14],[C_17_1+C_17_9,C_17_2+C_17_10,C_17_3+C_17_11,C_17_4+C_17_12,C_17_5+C_17_13,C_17_6+C_17_14],[C_18_1+C_18_9,C_18_2+C_18_10,C_18_3+C_18_11,C_18_4+C_18_12,C_18_5+C_18_13,C_18_6+C_18_14],[C_19_1+C_19_9,C_19_2+C_19_10,C_19_3+C_19_11,C_19_4+C_19_12,C_19_5+C_19_13,C_19_6+C_19_14],[C_20_1+C_20_9,C_20_2+C_20_10,C_20_3+C_20_11,C_20_4+C_20_12,C_20_5+C_20_13,C_20_6+C_20_14],[C_21_1+C_21_9,C_21_2+C_21_10,C_21_3+C_21_11,C_21_4+C_21_12,C_21_5+C_21_13,C_21_6+C_21_14],[C_22_1+C_22_9,C_22_2+C_22_10,C_22_3+C_22_11,C_22_4+C_22_12,C_22_5+C_22_13,C_22_6+C_22_14],[C_23_1+C_23_9,C_23_2+C_23_10,C_23_3+C_23_11,C_23_4+C_23_12,C_23_5+C_23_13,C_23_6+C_23_14],[C_24_1+C_24_9,C_24_2+C_24_10,C_24_3+C_24_11,C_24_4+C_24_12,C_24_5+C_24_13,C_24_6+C_24_14],[C_25_1+C_25_9,C_25_2+C_25_10,C_25_3+C_25_11,C_25_4+C_25_12,C_25_5+C_25_13,C_25_6+C_25_14],[C_26_1+C_26_9,C_26_2+C_26_10,C_26_3+C_26_11,C_26_4+C_26_12,C_26_5+C_26_13,C_26_6+C_26_14],[C_27_1+C_27_9,C_27_2+C_27_10,C_27_3+C_27_11,C_27_4+C_27_12,C_27_5+C_27_13,C_27_6+C_27_14]])))+Trace(Mul(Matrix(8, 10, [[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_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]]),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_6_1+B_11_1,-B_6_2+B_11_2,-B_6_3+B_11_3,-B_6_4+B_11_4,-B_6_5+B_11_5,-B_6_6+B_11_6,-B_6_7+B_11_7,-B_6_8+B_11_8,-B_6_9+B_11_9,-B_6_10+B_11_10,-B_6_11+B_11_11,-B_6_12+B_11_12],[-B_7_1+B_12_1,-B_7_2+B_12_2,-B_7_3+B_12_3,-B_7_4+B_12_4,-B_7_5+B_12_5,-B_7_6+B_12_6,-B_7_7+B_12_7,-B_7_8+B_12_8,-B_7_9+B_12_9,-B_7_10+B_12_10,-B_7_11+B_12_11,-B_7_12+B_12_12],[-B_8_1+B_13_1,-B_8_2+B_13_2,-B_8_3+B_13_3,-B_8_4+B_13_4,-B_8_5+B_13_5,-B_8_6+B_13_6,-B_8_7+B_13_7,-B_8_8+B_13_8,-B_8_9+B_13_9,-B_8_10+B_13_10,-B_8_11+B_13_11,-B_8_12+B_13_12],[-B_9_1+B_14_1,-B_9_2+B_14_2,-B_9_3+B_14_3,-B_9_4+B_14_4,-B_9_5+B_14_5,-B_9_6+B_14_6,-B_9_7+B_14_7,-B_9_8+B_14_8,-B_9_9+B_14_9,-B_9_10+B_14_10,-B_9_11+B_14_11,-B_9_12+B_14_12],[-B_10_1+B_15_1,-B_10_2+B_15_2,-B_10_3+B_15_3,-B_10_4+B_15_4,-B_10_5+B_15_5,-B_10_6+B_15_6,-B_10_7+B_15_7,-B_10_8+B_15_8,-B_10_9+B_15_9,-B_10_10+B_15_10,-B_10_11+B_15_11,-B_10_12+B_15_12],[-B_1_1+B_16_1,-B_1_2+B_16_2,-B_1_3+B_16_3,-B_1_4+B_16_4,-B_1_5+B_16_5,-B_1_6+B_16_6,-B_1_7+B_16_7,-B_1_8+B_16_8,-B_1_9+B_16_9,-B_1_10+B_16_10,-B_1_11+B_16_11,-B_1_12+B_16_12],[-B_2_1+B_17_1,-B_2_2+B_17_2,-B_2_3+B_17_3,-B_2_4+B_17_4,-B_2_5+B_17_5,-B_2_6+B_17_6,-B_2_7+B_17_7,-B_2_8+B_17_8,-B_2_9+B_17_9,-B_2_10+B_17_10,-B_2_11+B_17_11,-B_2_12+B_17_12],[-B_3_1+B_18_1,-B_3_2+B_18_2,-B_3_3+B_18_3,-B_3_4+B_18_4,-B_3_5+B_18_5,-B_3_6+B_18_6,-B_3_7+B_18_7,-B_3_8+B_18_8,-B_3_9+B_18_9,-B_3_10+B_18_10,-B_3_11+B_18_11,-B_3_12+B_18_12],[-B_4_1+B_19_1,-B_4_2+B_19_2,-B_4_3+B_19_3,-B_4_4+B_19_4,-B_4_5+B_19_5,-B_4_6+B_19_6,-B_4_7+B_19_7,-B_4_8+B_19_8,-B_4_9+B_19_9,-B_4_10+B_19_10,-B_4_11+B_19_11,-B_4_12+B_19_12]]),Matrix(12, 8, [[C_1_7,C_1_8,C_1_1+C_1_9,C_1_2+C_1_10,C_1_3+C_1_11,C_1_4+C_1_12,C_1_5+C_1_13,C_1_6+C_1_14],[C_2_7,C_2_8,C_2_1+C_2_9,C_2_2+C_2_10,C_2_3+C_2_11,C_2_4+C_2_12,C_2_5+C_2_13,C_2_6+C_2_14],[C_3_7,C_3_8,C_3_1+C_3_9,C_3_2+C_3_10,C_3_3+C_3_11,C_3_4+C_3_12,C_3_5+C_3_13,C_3_6+C_3_14],[C_4_7,C_4_8,C_4_1+C_4_9,C_4_2+C_4_10,C_4_3+C_4_11,C_4_4+C_4_12,C_4_5+C_4_13,C_4_6+C_4_14],[C_5_7,C_5_8,C_5_1+C_5_9,C_5_2+C_5_10,C_5_3+C_5_11,C_5_4+C_5_12,C_5_5+C_5_13,C_5_6+C_5_14],[C_6_7,C_6_8,C_6_1+C_6_9,C_6_2+C_6_10,C_6_3+C_6_11,C_6_4+C_6_12,C_6_5+C_6_13,C_6_6+C_6_14],[C_7_7,C_7_8,C_7_1+C_7_9,C_7_2+C_7_10,C_7_3+C_7_11,C_7_4+C_7_12,C_7_5+C_7_13,C_7_6+C_7_14],[C_8_7,C_8_8,C_8_1+C_8_9,C_8_2+C_8_10,C_8_3+C_8_11,C_8_4+C_8_12,C_8_5+C_8_13,C_8_6+C_8_14],[C_9_7,C_9_8,C_9_1+C_9_9,C_9_2+C_9_10,C_9_3+C_9_11,C_9_4+C_9_12,C_9_5+C_9_13,C_9_6+C_9_14],[C_10_7,C_10_8,C_10_1+C_10_9,C_10_2+C_10_10,C_10_3+C_10_11,C_10_4+C_10_12,C_10_5+C_10_13,C_10_6+C_10_14],[C_11_7,C_11_8,C_11_1+C_11_9,C_11_2+C_11_10,C_11_3+C_11_11,C_11_4+C_11_12,C_11_5+C_11_13,C_11_6+C_11_14],[C_12_7,C_12_8,C_12_1+C_12_9,C_12_2+C_12_10,C_12_3+C_12_11,C_12_4+C_12_12,C_12_5+C_12_13,C_12_6+C_12_14]])))+Trace(Mul(Matrix(8, 9, [[A_7_6+A_7_11,A_7_7+A_7_12,A_7_8+A_7_13,A_7_9+A_7_14,A_7_10+A_7_15,A_7_1+A_7_16,A_7_2+A_7_17,A_7_3+A_7_18,A_7_4+A_7_19],[A_8_6+A_8_11,A_8_7+A_8_12,A_8_8+A_8_13,A_8_9+A_8_14,A_8_10+A_8_15,A_8_1+A_8_16,A_8_2+A_8_17,A_8_3+A_8_18,A_8_4+A_8_19],[A_9_6+A_9_11,A_9_7+A_9_12,A_9_8+A_9_13,A_9_9+A_9_14,A_9_10+A_9_15,A_9_1+A_9_16,A_9_2+A_9_17,A_9_3+A_9_18,A_9_4+A_9_19],[A_10_6+A_10_11,A_10_7+A_10_12,A_10_8+A_10_13,A_10_9+A_10_14,A_10_10+A_10_15,A_10_1+A_10_16,A_10_2+A_10_17,A_10_3+A_10_18,A_10_4+A_10_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]]),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, 8, [[C_1_7-C_16_7,C_1_8-C_16_8,C_1_9-C_16_9,C_1_10-C_16_10,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_2_7-C_17_7,C_2_8-C_17_8,C_2_9-C_17_9,C_2_10-C_17_10,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_3_7-C_18_7,C_3_8-C_18_8,C_3_9-C_18_9,C_3_10-C_18_10,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_4_7-C_19_7,C_4_8-C_19_8,C_4_9-C_19_9,C_4_10-C_19_10,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_5_7-C_20_7,C_5_8-C_20_8,C_5_9-C_20_9,C_5_10-C_20_10,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_6_7-C_21_7,C_6_8-C_21_8,C_6_9-C_21_9,C_6_10-C_21_10,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_7_7-C_22_7,C_7_8-C_22_8,C_7_9-C_22_9,C_7_10-C_22_10,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_8_7-C_23_7,C_8_8-C_23_8,C_8_9-C_23_9,C_8_10-C_23_10,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_9_7-C_24_7,C_9_8-C_24_8,C_9_9-C_24_9,C_9_10-C_24_10,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_10_7-C_25_7,C_10_8-C_25_8,C_10_9-C_25_9,C_10_10-C_25_10,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_11_7-C_26_7,C_11_8-C_26_8,C_11_9-C_26_9,C_11_10-C_26_10,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_12_7-C_27_7,C_12_8-C_27_8,C_12_9-C_27_9,C_12_10-C_27_10,C_12_11-C_27_11,C_12_12-C_27_12,C_12_13-C_27_13,C_12_14-C_27_14]])))

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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