Description of fast matrix multiplication algorithm: ⟨13×21×30:4874⟩

Algorithm type

X13Y14Z12+X13Y11Z11+X12Y12Z11+X12Y12Z9+X13Y10Z8+X8Y17Z4+X8Y12Z8+X7Y12Z8+X6Y17Z4+X5Y12Z8+X8Y12Z4+X8Y8Z8+X7Y12Z5+X7Y8Z8+2X8Y7Z7+X8Y6Z8+3X7Y8Z7+3X7Y8Z6+4X7Y7Z7+3X6Y8Z7+X8Y7Z5+7X8Y6Z6+X8Y4Z8+X6Y7Z7+X8Y5Z6+4X7Y6Z6+2X6Y6Z7+X5Y11Z3+2X8Y5Z5+2X7Y6Z5+2X7Y5Z6+2X6Y6Z6+X5Y8Z5+X5Y7Z6+X4Y11Z3+X4Y10Z4+2X3Y11Z4+X7Y4Z6+2X6Y6Z5+X5Y8Z4+X5Y6Z6+X5Y4Z8+X4Y11Z2+X4Y10Z3+2X3Y10Z4+X6Y5Z5+X4Y10Z2+X4Y9Z3+4X4Y8Z4+144X4Y6Z6+X3Y11Z2+X3Y9Z4+X7Y4Z4+X6Y6Z3+48X6Y5Z4+X4Y10Z+X4Y9Z2+4X4Y8Z3+3X4Y7Z4+32X4Y6Z5+2X3Y9Z3+X3Y8Z4+96X5Y5Z4+X5Y4Z5+5X4Y8Z2+X4Y7Z3+11X4Y6Z4+3X4Y4Z6+X3Y8Z3+64X2Y9Z3+216X2Y6Z6+72X6Y5Z2+2X5Y4Z4+2X4Y5Z4+3X4Y4Z5+4X3Y6Z4+48X2Y6Z5+96XY9Z3+96X5Y5Z2+7X4Y6Z2+91X4Y4Z4+X2Y8Z2+X2Y6Z4+50X4Y5Z2+10X4Y4Z3+15X4Y3Z4+21X3Y4Z4+144X2Y6Z3+X4Y4Z2+64X4Y3Z3+16X4Y2Z4+X3Y6Z+X3Y5Z2+24X3Y4Z3+7X3Y3Z4+8X2Y6Z2+2X2Y4Z4+216XY6Z3+2X4Y3Z2+8X4Y2Z3+3X3Y4Z2+6X3Y3Z3+4X3Y2Z4+15X2Y5Z2+9X2Y4Z3+X2Y3Z4+31X4Y2Z2+X3Y3Z2+3X3Y2Z3+6X2Y5Z+147X2Y4Z2+704X2Y3Z3+20X2Y2Z4+4XY5Z2+5X3Y2Z2+25X2Y4Z+25X2Y3Z2+6X2Y2Z3+10XY4Z2+984XY3Z3+16X2Y3Z+353X2Y2Z2+46XY4Z+61X2Y2Z+57X2YZ2+31XY2Z2+66X2YZ+263XY2Z+23XYZ2+219XYZX13Y14Z12X13Y11Z11X12Y12Z11X12Y12Z9X13Y10Z8X8Y17Z4X8Y12Z8X7Y12Z8X6Y17Z4X5Y12Z8X8Y12Z4X8Y8Z8X7Y12Z5X7Y8Z82X8Y7Z7X8Y6Z83X7Y8Z73X7Y8Z64X7Y7Z73X6Y8Z7X8Y7Z57X8Y6Z6X8Y4Z8X6Y7Z7X8Y5Z64X7Y6Z62X6Y6Z7X5Y11Z32X8Y5Z52X7Y6Z52X7Y5Z62X6Y6Z6X5Y8Z5X5Y7Z6X4Y11Z3X4Y10Z42X3Y11Z4X7Y4Z62X6Y6Z5X5Y8Z4X5Y6Z6X5Y4Z8X4Y11Z2X4Y10Z32X3Y10Z4X6Y5Z5X4Y10Z2X4Y9Z34X4Y8Z4144X4Y6Z6X3Y11Z2X3Y9Z4X7Y4Z4X6Y6Z348X6Y5Z4X4Y10ZX4Y9Z24X4Y8Z33X4Y7Z432X4Y6Z52X3Y9Z3X3Y8Z496X5Y5Z4X5Y4Z55X4Y8Z2X4Y7Z311X4Y6Z43X4Y4Z6X3Y8Z364X2Y9Z3216X2Y6Z672X6Y5Z22X5Y4Z42X4Y5Z43X4Y4Z54X3Y6Z448X2Y6Z596XY9Z396X5Y5Z27X4Y6Z291X4Y4Z4X2Y8Z2X2Y6Z450X4Y5Z210X4Y4Z315X4Y3Z421X3Y4Z4144X2Y6Z3X4Y4Z264X4Y3Z316X4Y2Z4X3Y6ZX3Y5Z224X3Y4Z37X3Y3Z48X2Y6Z22X2Y4Z4216XY6Z32X4Y3Z28X4Y2Z33X3Y4Z26X3Y3Z34X3Y2Z415X2Y5Z29X2Y4Z3X2Y3Z431X4Y2Z2X3Y3Z23X3Y2Z36X2Y5Z147X2Y4Z2704X2Y3Z320X2Y2Z44XY5Z25X3Y2Z225X2Y4Z25X2Y3Z26X2Y2Z310XY4Z2984XY3Z316X2Y3Z353X2Y2Z246XY4Z61X2Y2Z57X2YZ231XY2Z266X2YZ263XY2Z23XYZ2219XYZX^13*Y^14*Z^12+X^13*Y^11*Z^11+X^12*Y^12*Z^11+X^12*Y^12*Z^9+X^13*Y^10*Z^8+X^8*Y^17*Z^4+X^8*Y^12*Z^8+X^7*Y^12*Z^8+X^6*Y^17*Z^4+X^5*Y^12*Z^8+X^8*Y^12*Z^4+X^8*Y^8*Z^8+X^7*Y^12*Z^5+X^7*Y^8*Z^8+2*X^8*Y^7*Z^7+X^8*Y^6*Z^8+3*X^7*Y^8*Z^7+3*X^7*Y^8*Z^6+4*X^7*Y^7*Z^7+3*X^6*Y^8*Z^7+X^8*Y^7*Z^5+7*X^8*Y^6*Z^6+X^8*Y^4*Z^8+X^6*Y^7*Z^7+X^8*Y^5*Z^6+4*X^7*Y^6*Z^6+2*X^6*Y^6*Z^7+X^5*Y^11*Z^3+2*X^8*Y^5*Z^5+2*X^7*Y^6*Z^5+2*X^7*Y^5*Z^6+2*X^6*Y^6*Z^6+X^5*Y^8*Z^5+X^5*Y^7*Z^6+X^4*Y^11*Z^3+X^4*Y^10*Z^4+2*X^3*Y^11*Z^4+X^7*Y^4*Z^6+2*X^6*Y^6*Z^5+X^5*Y^8*Z^4+X^5*Y^6*Z^6+X^5*Y^4*Z^8+X^4*Y^11*Z^2+X^4*Y^10*Z^3+2*X^3*Y^10*Z^4+X^6*Y^5*Z^5+X^4*Y^10*Z^2+X^4*Y^9*Z^3+4*X^4*Y^8*Z^4+144*X^4*Y^6*Z^6+X^3*Y^11*Z^2+X^3*Y^9*Z^4+X^7*Y^4*Z^4+X^6*Y^6*Z^3+48*X^6*Y^5*Z^4+X^4*Y^10*Z+X^4*Y^9*Z^2+4*X^4*Y^8*Z^3+3*X^4*Y^7*Z^4+32*X^4*Y^6*Z^5+2*X^3*Y^9*Z^3+X^3*Y^8*Z^4+96*X^5*Y^5*Z^4+X^5*Y^4*Z^5+5*X^4*Y^8*Z^2+X^4*Y^7*Z^3+11*X^4*Y^6*Z^4+3*X^4*Y^4*Z^6+X^3*Y^8*Z^3+64*X^2*Y^9*Z^3+216*X^2*Y^6*Z^6+72*X^6*Y^5*Z^2+2*X^5*Y^4*Z^4+2*X^4*Y^5*Z^4+3*X^4*Y^4*Z^5+4*X^3*Y^6*Z^4+48*X^2*Y^6*Z^5+96*X*Y^9*Z^3+96*X^5*Y^5*Z^2+7*X^4*Y^6*Z^2+91*X^4*Y^4*Z^4+X^2*Y^8*Z^2+X^2*Y^6*Z^4+50*X^4*Y^5*Z^2+10*X^4*Y^4*Z^3+15*X^4*Y^3*Z^4+21*X^3*Y^4*Z^4+144*X^2*Y^6*Z^3+X^4*Y^4*Z^2+64*X^4*Y^3*Z^3+16*X^4*Y^2*Z^4+X^3*Y^6*Z+X^3*Y^5*Z^2+24*X^3*Y^4*Z^3+7*X^3*Y^3*Z^4+8*X^2*Y^6*Z^2+2*X^2*Y^4*Z^4+216*X*Y^6*Z^3+2*X^4*Y^3*Z^2+8*X^4*Y^2*Z^3+3*X^3*Y^4*Z^2+6*X^3*Y^3*Z^3+4*X^3*Y^2*Z^4+15*X^2*Y^5*Z^2+9*X^2*Y^4*Z^3+X^2*Y^3*Z^4+31*X^4*Y^2*Z^2+X^3*Y^3*Z^2+3*X^3*Y^2*Z^3+6*X^2*Y^5*Z+147*X^2*Y^4*Z^2+704*X^2*Y^3*Z^3+20*X^2*Y^2*Z^4+4*X*Y^5*Z^2+5*X^3*Y^2*Z^2+25*X^2*Y^4*Z+25*X^2*Y^3*Z^2+6*X^2*Y^2*Z^3+10*X*Y^4*Z^2+984*X*Y^3*Z^3+16*X^2*Y^3*Z+353*X^2*Y^2*Z^2+46*X*Y^4*Z+61*X^2*Y^2*Z+57*X^2*Y*Z^2+31*X*Y^2*Z^2+66*X^2*Y*Z+263*X*Y^2*Z+23*X*Y*Z^2+219*X*Y*Z

Algorithm definition

The algorithm ⟨13×21×30:4874⟩ could be constructed using the following decomposition:

⟨13×21×30:4874⟩ = ⟨7×12×18:1000⟩ + ⟨6×12×12:560⟩ + ⟨7×9×18:744⟩ + ⟨6×12×18:800⟩ + ⟨6×9×18:600⟩ + ⟨7×12×12:660⟩ + ⟨7×9×12:510⟩.

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_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_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_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_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_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_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_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_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_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_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_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_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_21B_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_1_28B_1_29B_1_30B_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_2_28B_2_29B_2_30B_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_3_28B_3_29B_3_30B_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_4_28B_4_29B_4_30B_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_5_28B_5_29B_5_30B_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_6_28B_6_29B_6_30B_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_7_28B_7_29B_7_30B_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_8_28B_8_29B_8_30B_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_9_28B_9_29B_9_30B_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_10_28B_10_29B_10_30B_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_11_28B_11_29B_11_30B_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_12_28B_12_29B_12_30B_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_13_28B_13_29B_13_30B_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_14_28B_14_29B_14_30B_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_15_28B_15_29B_15_30B_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_16_28B_16_29B_16_30B_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_17_28B_17_29B_17_30B_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_18_28B_18_29B_18_30B_19_1B_19_2B_19_3B_19_4B_19_5B_19_6B_1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21, [[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_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_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_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_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_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_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_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_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_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_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_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_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]]),Matrix(21, 30, [[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_1_28,B_1_29,B_1_30],[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_2_28,B_2_29,B_2_30],[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_3_28,B_3_29,B_3_30],[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_4_28,B_4_29,B_4_30],[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_5_28,B_5_29,B_5_30],[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_6_28,B_6_29,B_6_30],[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_7_28,B_7_29,B_7_30],[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_8_28,B_8_29,B_8_30],[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_9_28,B_9_29,B_9_30],[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_10_28,B_10_29,B_10_30],[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_11_28,B_11_29,B_11_30],[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_12_28,B_12_29,B_12_30],[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_13_28,B_13_29,B_13_30],[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_14_28,B_14_29,B_14_30],[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_15_28,B_15_29,B_15_30],[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_16_28,B_16_29,B_16_30],[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_17_28,B_17_29,B_17_30],[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_18_28,B_18_29,B_18_30],[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,B_19_28,B_19_29,B_19_30],[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_20_25,B_20_26,B_20_27,B_20_28,B_20_29,B_20_30],[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_21_25,B_21_26,B_21_27,B_21_28,B_21_29,B_21_30]]),Matrix(30, 13, [[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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_28_1,C_28_2,C_28_3,C_28_4,C_28_5,C_28_6,C_28_7,C_28_8,C_28_9,C_28_10,C_28_11,C_28_12,C_28_13],[C_29_1,C_29_2,C_29_3,C_29_4,C_29_5,C_29_6,C_29_7,C_29_8,C_29_9,C_29_10,C_29_11,C_29_12,C_29_13],[C_30_1,C_30_2,C_30_3,C_30_4,C_30_5,C_30_6,C_30_7,C_30_8,C_30_9,C_30_10,C_30_11,C_30_12,C_30_13]]))) = Trace(Mul(Matrix(7, 12, [[A_7_5,A_7_6,A_7_1,A_7_2,A_7_3,A_7_15,A_7_16,A_7_17,A_7_18,A_7_19,A_7_20,A_7_21],[A_8_5,A_8_6,A_8_1,A_1_7+A_8_2,A_1_8+A_8_3,A_1_9+A_8_15,A_1_10+A_8_16,A_1_11+A_8_17,A_1_12+A_8_18,A_1_13+A_8_19,A_1_14+A_8_20,A_1_4+A_8_21],[A_9_5,A_9_6,A_9_1,A_2_7+A_9_2,A_2_8+A_9_3,A_2_9+A_9_15,A_2_10+A_9_16,A_2_11+A_9_17,A_2_12+A_9_18,A_2_13+A_9_19,A_2_14+A_9_20,A_2_4+A_9_21],[A_10_5,A_10_6,A_10_1,A_3_7+A_10_2,A_3_8+A_10_3,A_3_9+A_10_15,A_3_10+A_10_16,A_3_11+A_10_17,A_3_12+A_10_18,A_3_13+A_10_19,A_3_14+A_10_20,A_3_4+A_10_21],[A_11_5,A_11_6,A_11_1,A_4_7+A_11_2,A_4_8+A_11_3,A_4_9+A_11_15,A_4_10+A_11_16,A_4_11+A_11_17,A_4_12+A_11_18,A_4_13+A_11_19,A_4_14+A_11_20,A_4_4+A_11_21],[A_12_5,A_12_6,A_12_1,A_5_7+A_12_2,A_5_8+A_12_3,A_5_9+A_12_15,A_5_10+A_12_16,A_5_11+A_12_17,A_5_12+A_12_18,A_5_13+A_12_19,A_5_14+A_12_20,A_5_4+A_12_21],[A_13_5,A_13_6,A_13_1,A_6_7+A_13_2,A_6_8+A_13_3,A_6_9+A_13_15,A_6_10+A_13_16,A_6_11+A_13_17,A_6_12+A_13_18,A_6_13+A_13_19,A_6_14+A_13_20,A_6_4+A_13_21]]),Matrix(12, 18, [[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_9,B_5_10,B_5_11,B_5_12,B_5_28,B_5_29,B_5_30],[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_9,B_6_10,B_6_11,B_6_12,B_6_28,B_6_29,B_6_30],[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_9,B_1_10,B_1_11,B_1_12,B_1_28,B_1_29,B_1_30],[B_2_14,B_2_15,B_2_16,B_2_17,B_2_18,B_2_19,B_7_1+B_2_20,B_7_2+B_2_21,B_7_3+B_2_22,B_7_4+B_2_23,B_7_5+B_2_24,B_7_6+B_2_9,B_7_7+B_2_10,B_7_8+B_2_11,B_2_12+B_7_25,B_7_26+B_2_28,B_7_27+B_2_29,B_7_13+B_2_30],[B_3_14,B_3_15,B_3_16,B_3_17,B_3_18,B_3_19,B_8_1+B_3_20,B_8_2+B_3_21,B_8_3+B_3_22,B_8_4+B_3_23,B_8_5+B_3_24,B_8_6+B_3_9,B_8_7+B_3_10,B_8_8+B_3_11,B_3_12+B_8_25,B_8_26+B_3_28,B_8_27+B_3_29,B_8_13+B_3_30],[B_15_14,B_15_15,B_15_16,B_15_17,B_15_18,B_15_19,B_9_1+B_15_20,B_9_2+B_15_21,B_9_3+B_15_22,B_9_4+B_15_23,B_9_5+B_15_24,B_9_6+B_15_9,B_9_7+B_15_10,B_9_8+B_15_11,B_9_25+B_15_12,B_9_26+B_15_28,B_9_27+B_15_29,B_9_13+B_15_30],[B_16_14,B_16_15,B_16_16,B_16_17,B_16_18,B_16_19,B_10_1+B_16_20,B_10_2+B_16_21,B_10_3+B_16_22,B_10_4+B_16_23,B_10_5+B_16_24,B_10_6+B_16_9,B_10_7+B_16_10,B_10_8+B_16_11,B_10_25+B_16_12,B_10_26+B_16_28,B_10_27+B_16_29,B_10_13+B_16_30],[B_17_14,B_17_15,B_17_16,B_17_17,B_17_18,B_17_19,B_11_1+B_17_20,B_11_2+B_17_21,B_11_3+B_17_22,B_11_4+B_17_23,B_11_5+B_17_24,B_11_6+B_17_9,B_11_7+B_17_10,B_11_8+B_17_11,B_11_25+B_17_12,B_11_26+B_17_28,B_11_27+B_17_29,B_11_13+B_17_30],[B_18_14,B_18_15,B_18_16,B_18_17,B_18_18,B_18_19,B_12_1+B_18_20,B_12_2+B_18_21,B_12_3+B_18_22,B_12_4+B_18_23,B_12_5+B_18_24,B_12_6+B_18_9,B_12_7+B_18_10,B_12_8+B_18_11,B_12_25+B_18_12,B_12_26+B_18_28,B_12_27+B_18_29,B_12_13+B_18_30],[B_19_14,B_19_15,B_19_16,B_19_17,B_19_18,B_19_19,B_13_1+B_19_20,B_13_2+B_19_21,B_13_3+B_19_22,B_13_4+B_19_23,B_13_5+B_19_24,B_13_6+B_19_9,B_13_7+B_19_10,B_13_8+B_19_11,B_13_25+B_19_12,B_13_26+B_19_28,B_13_27+B_19_29,B_13_13+B_19_30],[B_20_14,B_20_15,B_20_16,B_20_17,B_20_18,B_20_19,B_14_1+B_20_20,B_14_2+B_20_21,B_14_3+B_20_22,B_14_4+B_20_23,B_14_5+B_20_24,B_14_6+B_20_9,B_14_7+B_20_10,B_14_8+B_20_11,B_14_25+B_20_12,B_14_26+B_20_28,B_14_27+B_20_29,B_14_13+B_20_30],[B_21_14,B_21_15,B_21_16,B_21_17,B_21_18,B_21_19,B_4_1+B_21_20,B_4_2+B_21_21,B_4_3+B_21_22,B_4_4+B_21_23,B_4_5+B_21_24,B_4_6+B_21_9,B_4_7+B_21_10,B_4_8+B_21_11,B_4_25+B_21_12,B_4_26+B_21_28,B_4_27+B_21_29,B_4_13+B_21_30]]),Matrix(18, 7, [[C_14_7,C_14_8,C_14_9,C_14_10,C_14_11,C_14_12,C_14_13],[C_15_7,C_15_8,C_15_9,C_15_10,C_15_11,C_15_12,C_15_13],[C_16_7,C_16_8,C_16_9,C_16_10,C_16_11,C_16_12,C_16_13],[C_17_7,C_17_8,C_17_9,C_17_10,C_17_11,C_17_12,C_17_13],[C_18_7,C_18_8,C_18_9,C_18_10,C_18_11,C_18_12,C_18_13],[C_19_7,C_19_8,C_19_9,C_19_10,C_19_11,C_19_12,C_19_13],[C_20_7,C_1_1+C_20_8,C_1_2+C_20_9,C_1_3+C_20_10,C_1_4+C_20_11,C_1_5+C_20_12,C_1_6+C_20_13],[C_21_7,C_2_1+C_21_8,C_2_2+C_21_9,C_2_3+C_21_10,C_2_4+C_21_11,C_2_5+C_21_12,C_2_6+C_21_13],[C_22_7,C_3_1+C_22_8,C_3_2+C_22_9,C_3_3+C_22_10,C_3_4+C_22_11,C_3_5+C_22_12,C_3_6+C_22_13],[C_23_7,C_4_1+C_23_8,C_4_2+C_23_9,C_4_3+C_23_10,C_4_4+C_23_11,C_4_5+C_23_12,C_4_6+C_23_13],[C_24_7,C_5_1+C_24_8,C_5_2+C_24_9,C_5_3+C_24_10,C_5_4+C_24_11,C_5_5+C_24_12,C_5_6+C_24_13],[C_9_7,C_6_1+C_9_8,C_6_2+C_9_9,C_6_3+C_9_10,C_6_4+C_9_11,C_6_5+C_9_12,C_6_6+C_9_13],[C_10_7,C_7_1+C_10_8,C_7_2+C_10_9,C_7_3+C_10_10,C_7_4+C_10_11,C_7_5+C_10_12,C_7_6+C_10_13],[C_11_7,C_8_1+C_11_8,C_8_2+C_11_9,C_8_3+C_11_10,C_8_4+C_11_11,C_8_5+C_11_12,C_8_6+C_11_13],[C_12_7,C_25_1+C_12_8,C_25_2+C_12_9,C_25_3+C_12_10,C_25_4+C_12_11,C_25_5+C_12_12,C_25_6+C_12_13],[C_28_7,C_26_1+C_28_8,C_26_2+C_28_9,C_26_3+C_28_10,C_26_4+C_28_11,C_26_5+C_28_12,C_26_6+C_28_13],[C_29_7,C_27_1+C_29_8,C_27_2+C_29_9,C_27_3+C_29_10,C_27_4+C_29_11,C_27_5+C_29_12,C_27_6+C_29_13],[C_30_7,C_13_1+C_30_8,C_13_2+C_30_9,C_13_3+C_30_10,C_13_4+C_30_11,C_13_5+C_30_12,C_13_6+C_30_13]])))+Trace(Mul(Matrix(6, 12, [[A_1_5-A_8_5,A_1_6-A_8_6,A_1_1-A_8_1,A_1_2-A_8_2,A_1_3-A_8_3,A_1_15-A_8_15,A_1_16-A_8_16,A_1_17-A_8_17,A_1_18-A_8_18,A_1_19-A_8_19,A_1_20-A_8_20,A_1_21-A_8_21],[A_2_5-A_9_5,A_2_6-A_9_6,A_2_1-A_9_1,A_2_2-A_9_2,A_2_3-A_9_3,A_2_15-A_9_15,A_2_16-A_9_16,A_2_17-A_9_17,A_2_18-A_9_18,A_2_19-A_9_19,A_2_20-A_9_20,A_2_21-A_9_21],[A_3_5-A_10_5,A_3_6-A_10_6,A_3_1-A_10_1,A_3_2-A_10_2,A_3_3-A_10_3,A_3_15-A_10_15,A_3_16-A_10_16,A_3_17-A_10_17,A_3_18-A_10_18,A_3_19-A_10_19,A_3_20-A_10_20,A_3_21-A_10_21],[A_4_5-A_11_5,A_4_6-A_11_6,A_4_1-A_11_1,A_4_2-A_11_2,A_4_3-A_11_3,A_4_15-A_11_15,A_4_16-A_11_16,A_4_17-A_11_17,A_4_18-A_11_18,A_4_19-A_11_19,A_4_20-A_11_20,A_4_21-A_11_21],[A_5_5-A_12_5,A_5_6-A_12_6,A_5_1-A_12_1,A_5_2-A_12_2,A_5_3-A_12_3,A_5_15-A_12_15,A_5_16-A_12_16,A_5_17-A_12_17,A_5_18-A_12_18,A_5_19-A_12_19,A_5_20-A_12_20,A_5_21-A_12_21],[A_6_5-A_13_5,A_6_6-A_13_6,A_6_1-A_13_1,A_6_2-A_13_2,A_6_3-A_13_3,A_6_15-A_13_15,A_6_16-A_13_16,A_6_17-A_13_17,A_6_18-A_13_18,A_6_19-A_13_19,A_6_20-A_13_20,A_6_21-A_13_21]]),Matrix(12, 12, [[B_5_1+B_5_20,B_5_2+B_5_21,B_5_3+B_5_22,B_5_4+B_5_23,B_5_5+B_5_24,B_5_6+B_5_9,B_5_7+B_5_10,B_5_8+B_5_11,B_5_12+B_5_25,B_5_26+B_5_28,B_5_27+B_5_29,B_5_13+B_5_30],[B_6_1+B_6_20,B_6_2+B_6_21,B_6_3+B_6_22,B_6_4+B_6_23,B_6_5+B_6_24,B_6_6+B_6_9,B_6_7+B_6_10,B_6_8+B_6_11,B_6_12+B_6_25,B_6_26+B_6_28,B_6_27+B_6_29,B_6_13+B_6_30],[B_1_1+B_1_20,B_1_2+B_1_21,B_1_3+B_1_22,B_1_4+B_1_23,B_1_5+B_1_24,B_1_6+B_1_9,B_1_7+B_1_10,B_1_8+B_1_11,B_1_12+B_1_25,B_1_26+B_1_28,B_1_27+B_1_29,B_1_13+B_1_30],[B_2_1+B_2_20,B_2_2+B_2_21,B_2_3+B_2_22,B_2_4+B_2_23,B_2_5+B_2_24,B_2_6+B_2_9,B_2_7+B_2_10,B_2_8+B_2_11,B_2_12+B_2_25,B_2_26+B_2_28,B_2_27+B_2_29,B_2_13+B_2_30],[B_3_1+B_3_20,B_3_2+B_3_21,B_3_3+B_3_22,B_3_4+B_3_23,B_3_5+B_3_24,B_3_6+B_3_9,B_3_7+B_3_10,B_3_8+B_3_11,B_3_12+B_3_25,B_3_26+B_3_28,B_3_27+B_3_29,B_3_13+B_3_30],[B_15_1+B_15_20,B_15_2+B_15_21,B_15_3+B_15_22,B_15_4+B_15_23,B_15_5+B_15_24,B_15_6+B_15_9,B_15_7+B_15_10,B_15_8+B_15_11,B_15_12+B_15_25,B_15_26+B_15_28,B_15_27+B_15_29,B_15_13+B_15_30],[B_16_1+B_16_20,B_16_2+B_16_21,B_16_3+B_16_22,B_16_4+B_16_23,B_16_5+B_16_24,B_16_6+B_16_9,B_16_7+B_16_10,B_16_8+B_16_11,B_16_12+B_16_25,B_16_26+B_16_28,B_16_27+B_16_29,B_16_13+B_16_30],[B_17_1+B_17_20,B_17_2+B_17_21,B_17_3+B_17_22,B_17_4+B_17_23,B_17_5+B_17_24,B_17_6+B_17_9,B_17_7+B_17_10,B_17_8+B_17_11,B_17_12+B_17_25,B_17_26+B_17_28,B_17_27+B_17_29,B_17_13+B_17_30],[B_18_1+B_18_20,B_18_2+B_18_21,B_18_3+B_18_22,B_18_4+B_18_23,B_18_5+B_18_24,B_18_6+B_18_9,B_18_7+B_18_10,B_18_8+B_18_11,B_18_12+B_18_25,B_18_26+B_18_28,B_18_27+B_18_29,B_18_13+B_18_30],[B_19_1+B_19_20,B_19_2+B_19_21,B_19_3+B_19_22,B_19_4+B_19_23,B_19_5+B_19_24,B_19_6+B_19_9,B_19_7+B_19_10,B_19_8+B_19_11,B_19_12+B_19_25,B_19_26+B_19_28,B_19_27+B_19_29,B_19_13+B_19_30],[B_20_1+B_20_20,B_20_2+B_20_21,B_20_3+B_20_22,B_20_4+B_20_23,B_20_5+B_20_24,B_20_6+B_20_9,B_20_7+B_20_10,B_20_8+B_20_11,B_20_12+B_20_25,B_20_26+B_20_28,B_20_27+B_20_29,B_20_13+B_20_30],[B_21_1+B_21_20,B_21_2+B_21_21,B_21_3+B_21_22,B_21_4+B_21_23,B_21_5+B_21_24,B_21_6+B_21_9,B_21_7+B_21_10,B_21_8+B_21_11,B_21_12+B_21_25,B_21_26+B_21_28,B_21_27+B_21_29,B_21_13+B_21_30]]),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_25_1,C_25_2,C_25_3,C_25_4,C_25_5,C_25_6],[C_26_1,C_26_2,C_26_3,C_26_4,C_26_5,C_26_6],[C_27_1,C_27_2,C_27_3,C_27_4,C_27_5,C_27_6],[C_13_1,C_13_2,C_13_3,C_13_4,C_13_5,C_13_6]])))+Trace(Mul(Matrix(7, 9, [[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_4],[-A_1_7+A_8_7,-A_1_8+A_8_8,-A_1_9+A_8_9,-A_1_10+A_8_10,-A_1_11+A_8_11,-A_1_12+A_8_12,-A_1_13+A_8_13,-A_1_14+A_8_14,-A_1_4+A_8_4],[-A_2_7+A_9_7,-A_2_8+A_9_8,-A_2_9+A_9_9,-A_2_10+A_9_10,-A_2_11+A_9_11,-A_2_12+A_9_12,-A_2_13+A_9_13,-A_2_14+A_9_14,-A_2_4+A_9_4],[-A_3_7+A_10_7,-A_3_8+A_10_8,-A_3_9+A_10_9,-A_3_10+A_10_10,-A_3_11+A_10_11,-A_3_12+A_10_12,-A_3_13+A_10_13,-A_3_14+A_10_14,-A_3_4+A_10_4],[-A_4_7+A_11_7,-A_4_8+A_11_8,-A_4_9+A_11_9,-A_4_10+A_11_10,-A_4_11+A_11_11,-A_4_12+A_11_12,-A_4_13+A_11_13,-A_4_14+A_11_14,-A_4_4+A_11_4],[-A_5_7+A_12_7,-A_5_8+A_12_8,-A_5_9+A_12_9,-A_5_10+A_12_10,-A_5_11+A_12_11,-A_5_12+A_12_12,-A_5_13+A_12_13,-A_5_14+A_12_14,-A_5_4+A_12_4],[-A_6_7+A_13_7,-A_6_8+A_13_8,-A_6_9+A_13_9,-A_6_10+A_13_10,-A_6_11+A_13_11,-A_6_12+A_13_12,-A_6_13+A_13_13,-A_6_14+A_13_14,-A_6_4+A_13_4]]),Matrix(9, 18, [[B_7_14,B_7_15,B_7_16,B_7_17,B_7_18,B_7_19,B_7_1+B_7_20,B_7_2+B_7_21,B_7_3+B_7_22,B_7_4+B_7_23,B_7_5+B_7_24,B_7_6+B_7_9,B_7_7+B_7_10,B_7_8+B_7_11,B_7_12+B_7_25,B_7_26+B_7_28,B_7_27+B_7_29,B_7_13+B_7_30],[B_8_14,B_8_15,B_8_16,B_8_17,B_8_18,B_8_19,B_8_1+B_8_20,B_8_2+B_8_21,B_8_3+B_8_22,B_8_4+B_8_23,B_8_5+B_8_24,B_8_6+B_8_9,B_8_7+B_8_10,B_8_8+B_8_11,B_8_12+B_8_25,B_8_26+B_8_28,B_8_27+B_8_29,B_8_13+B_8_30],[B_9_14,B_9_15,B_9_16,B_9_17,B_9_18,B_9_19,B_9_1+B_9_20,B_9_2+B_9_21,B_9_3+B_9_22,B_9_4+B_9_23,B_9_5+B_9_24,B_9_6+B_9_9,B_9_7+B_9_10,B_9_8+B_9_11,B_9_12+B_9_25,B_9_26+B_9_28,B_9_27+B_9_29,B_9_13+B_9_30],[B_10_14,B_10_15,B_10_16,B_10_17,B_10_18,B_10_19,B_10_1+B_10_20,B_10_2+B_10_21,B_10_3+B_10_22,B_10_4+B_10_23,B_10_5+B_10_24,B_10_6+B_10_9,B_10_7+B_10_10,B_10_8+B_10_11,B_10_12+B_10_25,B_10_26+B_10_28,B_10_27+B_10_29,B_10_13+B_10_30],[B_11_14,B_11_15,B_11_16,B_11_17,B_11_18,B_11_19,B_11_1+B_11_20,B_11_2+B_11_21,B_11_3+B_11_22,B_11_4+B_11_23,B_11_5+B_11_24,B_11_6+B_11_9,B_11_7+B_11_10,B_11_8+B_11_11,B_11_12+B_11_25,B_11_26+B_11_28,B_11_27+B_11_29,B_11_13+B_11_30],[B_12_14,B_12_15,B_12_16,B_12_17,B_12_18,B_12_19,B_12_1+B_12_20,B_12_2+B_12_21,B_12_3+B_12_22,B_12_4+B_12_23,B_12_5+B_12_24,B_12_6+B_12_9,B_12_7+B_12_10,B_12_8+B_12_11,B_12_12+B_12_25,B_12_26+B_12_28,B_12_27+B_12_29,B_12_13+B_12_30],[B_13_14,B_13_15,B_13_16,B_13_17,B_13_18,B_13_19,B_13_1+B_13_20,B_13_2+B_13_21,B_13_3+B_13_22,B_13_4+B_13_23,B_13_5+B_13_24,B_13_6+B_13_9,B_13_7+B_13_10,B_13_8+B_13_11,B_13_12+B_13_25,B_13_26+B_13_28,B_13_27+B_13_29,B_13_13+B_13_30],[B_14_14,B_14_15,B_14_16,B_14_17,B_14_18,B_14_19,B_14_1+B_14_20,B_14_2+B_14_21,B_14_3+B_14_22,B_14_4+B_14_23,B_14_5+B_14_24,B_14_6+B_14_9,B_14_7+B_14_10,B_14_8+B_14_11,B_14_12+B_14_25,B_14_26+B_14_28,B_14_27+B_14_29,B_14_13+B_14_30],[B_4_14,B_4_15,B_4_16,B_4_17,B_4_18,B_4_19,B_4_1+B_4_20,B_4_2+B_4_21,B_4_3+B_4_22,B_4_4+B_4_23,B_4_5+B_4_24,B_4_6+B_4_9,B_4_7+B_4_10,B_4_8+B_4_11,B_4_12+B_4_25,B_4_26+B_4_28,B_4_27+B_4_29,B_4_13+B_4_30]]),Matrix(18, 7, [[C_14_7,C_14_8,C_14_9,C_14_10,C_14_11,C_14_12,C_14_13],[C_15_7,C_15_8,C_15_9,C_15_10,C_15_11,C_15_12,C_15_13],[C_16_7,C_16_8,C_16_9,C_16_10,C_16_11,C_16_12,C_16_13],[C_17_7,C_17_8,C_17_9,C_17_10,C_17_11,C_17_12,C_17_13],[C_18_7,C_18_8,C_18_9,C_18_10,C_18_11,C_18_12,C_18_13],[C_19_7,C_19_8,C_19_9,C_19_10,C_19_11,C_19_12,C_19_13],[C_20_7,C_20_8,C_20_9,C_20_10,C_20_11,C_20_12,C_20_13],[C_21_7,C_21_8,C_21_9,C_21_10,C_21_11,C_21_12,C_21_13],[C_22_7,C_22_8,C_22_9,C_22_10,C_22_11,C_22_12,C_22_13],[C_23_7,C_23_8,C_23_9,C_23_10,C_23_11,C_23_12,C_23_13],[C_24_7,C_24_8,C_24_9,C_24_10,C_24_11,C_24_12,C_24_13],[C_9_7,C_9_8,C_9_9,C_9_10,C_9_11,C_9_12,C_9_13],[C_10_7,C_10_8,C_10_9,C_10_10,C_10_11,C_10_12,C_10_13],[C_11_7,C_11_8,C_11_9,C_11_10,C_11_11,C_11_12,C_11_13],[C_12_7,C_12_8,C_12_9,C_12_10,C_12_11,C_12_12,C_12_13],[C_28_7,C_28_8,C_28_9,C_28_10,C_28_11,C_28_12,C_28_13],[C_29_7,C_29_8,C_29_9,C_29_10,C_29_11,C_29_12,C_29_13],[C_30_7,C_30_8,C_30_9,C_30_10,C_30_11,C_30_12,C_30_13]])))+Trace(Mul(Matrix(6, 12, [[A_1_5,A_1_6,A_1_1,A_1_2+A_1_7,A_1_3+A_1_8,A_1_9+A_1_15,A_1_10+A_1_16,A_1_11+A_1_17,A_1_12+A_1_18,A_1_13+A_1_19,A_1_14+A_1_20,A_1_4+A_1_21],[A_2_5,A_2_6,A_2_1,A_2_2+A_2_7,A_2_3+A_2_8,A_2_9+A_2_15,A_2_10+A_2_16,A_2_11+A_2_17,A_2_12+A_2_18,A_2_13+A_2_19,A_2_14+A_2_20,A_2_4+A_2_21],[A_3_5,A_3_6,A_3_1,A_3_2+A_3_7,A_3_3+A_3_8,A_3_9+A_3_15,A_3_10+A_3_16,A_3_11+A_3_17,A_3_12+A_3_18,A_3_13+A_3_19,A_3_14+A_3_20,A_3_4+A_3_21],[A_4_5,A_4_6,A_4_1,A_4_2+A_4_7,A_4_3+A_4_8,A_4_9+A_4_15,A_4_10+A_4_16,A_4_11+A_4_17,A_4_12+A_4_18,A_4_13+A_4_19,A_4_14+A_4_20,A_4_4+A_4_21],[A_5_5,A_5_6,A_5_1,A_5_2+A_5_7,A_5_3+A_5_8,A_5_9+A_5_15,A_5_10+A_5_16,A_5_11+A_5_17,A_5_12+A_5_18,A_5_13+A_5_19,A_5_14+A_5_20,A_5_4+A_5_21],[A_6_5,A_6_6,A_6_1,A_6_2+A_6_7,A_6_3+A_6_8,A_6_9+A_6_15,A_6_10+A_6_16,A_6_11+A_6_17,A_6_12+A_6_18,A_6_13+A_6_19,A_6_14+A_6_20,A_6_4+A_6_21]]),Matrix(12, 18, [[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_9,B_5_10,B_5_11,B_5_12,B_5_28,B_5_29,B_5_30],[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_9,B_6_10,B_6_11,B_6_12,B_6_28,B_6_29,B_6_30],[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_9,B_1_10,B_1_11,B_1_12,B_1_28,B_1_29,B_1_30],[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_9,B_2_10,B_2_11,B_2_12,B_2_28,B_2_29,B_2_30],[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_9,B_3_10,B_3_11,B_3_12,B_3_28,B_3_29,B_3_30],[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_9,B_15_10,B_15_11,B_15_12,B_15_28,B_15_29,B_15_30],[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_9,B_16_10,B_16_11,B_16_12,B_16_28,B_16_29,B_16_30],[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_9,B_17_10,B_17_11,B_17_12,B_17_28,B_17_29,B_17_30],[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_9,B_18_10,B_18_11,B_18_12,B_18_28,B_18_29,B_18_30],[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_9,B_19_10,B_19_11,B_19_12,B_19_28,B_19_29,B_19_30],[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_20_9,B_20_10,B_20_11,B_20_12,B_20_28,B_20_29,B_20_30],[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_21_9,B_21_10,B_21_11,B_21_12,B_21_28,B_21_29,B_21_30]]),Matrix(18, 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_16_1,C_16_2,C_16_3,C_16_4,C_16_5,C_16_6],[C_17_1,C_17_2,C_17_3,C_17_4,C_17_5,C_17_6],[C_18_1,C_18_2,C_18_3,C_18_4,C_18_5,C_18_6],[C_19_1,C_19_2,C_19_3,C_19_4,C_19_5,C_19_6],[-C_1_1+C_20_1,-C_1_2+C_20_2,-C_1_3+C_20_3,-C_1_4+C_20_4,-C_1_5+C_20_5,-C_1_6+C_20_6],[-C_2_1+C_21_1,-C_2_2+C_21_2,-C_2_3+C_21_3,-C_2_4+C_21_4,-C_2_5+C_21_5,-C_2_6+C_21_6],[-C_3_1+C_22_1,-C_3_2+C_22_2,-C_3_3+C_22_3,-C_3_4+C_22_4,-C_3_5+C_22_5,-C_3_6+C_22_6],[-C_4_1+C_23_1,-C_4_2+C_23_2,-C_4_3+C_23_3,-C_4_4+C_23_4,-C_4_5+C_23_5,-C_4_6+C_23_6],[-C_5_1+C_24_1,-C_5_2+C_24_2,-C_5_3+C_24_3,-C_5_4+C_24_4,-C_5_5+C_24_5,-C_5_6+C_24_6],[-C_6_1+C_9_1,-C_6_2+C_9_2,-C_6_3+C_9_3,-C_6_4+C_9_4,-C_6_5+C_9_5,-C_6_6+C_9_6],[-C_7_1+C_10_1,-C_7_2+C_10_2,-C_7_3+C_10_3,-C_7_4+C_10_4,-C_7_5+C_10_5,-C_7_6+C_10_6],[-C_8_1+C_11_1,-C_8_2+C_11_2,-C_8_3+C_11_3,-C_8_4+C_11_4,-C_8_5+C_11_5,-C_8_6+C_11_6],[C_12_1-C_25_1,C_12_2-C_25_2,C_12_3-C_25_3,C_12_4-C_25_4,C_12_5-C_25_5,C_12_6-C_25_6],[-C_26_1+C_28_1,-C_26_2+C_28_2,-C_26_3+C_28_3,-C_26_4+C_28_4,-C_26_5+C_28_5,-C_26_6+C_28_6],[-C_27_1+C_29_1,-C_27_2+C_29_2,-C_27_3+C_29_3,-C_27_4+C_29_4,-C_27_5+C_29_5,-C_27_6+C_29_6],[-C_13_1+C_30_1,-C_13_2+C_30_2,-C_13_3+C_30_3,-C_13_4+C_30_4,-C_13_5+C_30_5,-C_13_6+C_30_6]])))+Trace(Mul(Matrix(6, 9, [[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_4],[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_4],[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_4],[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_4],[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_4],[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_4]]),Matrix(9, 18, [[-B_2_14+B_7_14,-B_2_15+B_7_15,-B_2_16+B_7_16,-B_2_17+B_7_17,-B_2_18+B_7_18,-B_2_19+B_7_19,-B_2_20+B_7_20,B_7_21-B_2_21,B_7_22-B_2_22,-B_2_23+B_7_23,-B_2_24+B_7_24,-B_2_9+B_7_9,-B_2_10+B_7_10,-B_2_11+B_7_11,-B_2_12+B_7_12,B_7_28-B_2_28,B_7_29-B_2_29,B_7_30-B_2_30],[-B_3_14+B_8_14,-B_3_15+B_8_15,-B_3_16+B_8_16,-B_3_17+B_8_17,-B_3_18+B_8_18,-B_3_19+B_8_19,-B_3_20+B_8_20,B_8_21-B_3_21,B_8_22-B_3_22,-B_3_23+B_8_23,-B_3_24+B_8_24,-B_3_9+B_8_9,-B_3_10+B_8_10,-B_3_11+B_8_11,-B_3_12+B_8_12,B_8_28-B_3_28,B_8_29-B_3_29,B_8_30-B_3_30],[B_9_14-B_15_14,B_9_15-B_15_15,B_9_16-B_15_16,B_9_17-B_15_17,B_9_18-B_15_18,B_9_19-B_15_19,B_9_20-B_15_20,B_9_21-B_15_21,B_9_22-B_15_22,B_9_23-B_15_23,B_9_24-B_15_24,B_9_9-B_15_9,B_9_10-B_15_10,B_9_11-B_15_11,B_9_12-B_15_12,B_9_28-B_15_28,B_9_29-B_15_29,B_9_30-B_15_30],[B_10_14-B_16_14,B_10_15-B_16_15,B_10_16-B_16_16,B_10_17-B_16_17,B_10_18-B_16_18,B_10_19-B_16_19,B_10_20-B_16_20,B_10_21-B_16_21,B_10_22-B_16_22,B_10_23-B_16_23,B_10_24-B_16_24,B_10_9-B_16_9,B_10_10-B_16_10,B_10_11-B_16_11,B_10_12-B_16_12,B_10_28-B_16_28,B_10_29-B_16_29,B_10_30-B_16_30],[B_11_14-B_17_14,B_11_15-B_17_15,B_11_16-B_17_16,B_11_17-B_17_17,B_11_18-B_17_18,B_11_19-B_17_19,B_11_20-B_17_20,B_11_21-B_17_21,B_11_22-B_17_22,B_11_23-B_17_23,B_11_24-B_17_24,B_11_9-B_17_9,B_11_10-B_17_10,B_11_11-B_17_11,B_11_12-B_17_12,B_11_28-B_17_28,B_11_29-B_17_29,B_11_30-B_17_30],[B_12_14-B_18_14,B_12_15-B_18_15,B_12_16-B_18_16,B_12_17-B_18_17,B_12_18-B_18_18,B_12_19-B_18_19,B_12_20-B_18_20,B_12_21-B_18_21,B_12_22-B_18_22,B_12_23-B_18_23,B_12_24-B_18_24,B_12_9-B_18_9,B_12_10-B_18_10,B_12_11-B_18_11,B_12_12-B_18_12,B_12_28-B_18_28,B_12_29-B_18_29,B_12_30-B_18_30],[B_13_14-B_19_14,B_13_15-B_19_15,B_13_16-B_19_16,B_13_17-B_19_17,B_13_18-B_19_18,B_13_19-B_19_19,B_13_20-B_19_20,B_13_21-B_19_21,B_13_22-B_19_22,B_13_23-B_19_23,B_13_24-B_19_24,B_13_9-B_19_9,B_13_10-B_19_10,B_13_11-B_19_11,B_13_12-B_19_12,B_13_28-B_19_28,B_13_29-B_19_29,B_13_30-B_19_30],[B_14_14-B_20_14,B_14_15-B_20_15,B_14_16-B_20_16,B_14_17-B_20_17,B_14_18-B_20_18,B_14_19-B_20_19,B_14_20-B_20_20,B_14_21-B_20_21,B_14_22-B_20_22,B_14_23-B_20_23,B_14_24-B_20_24,B_14_9-B_20_9,B_14_10-B_20_10,B_14_11-B_20_11,B_14_12-B_20_12,B_14_28-B_20_28,B_14_29-B_20_29,B_14_30-B_20_30],[B_4_14-B_21_14,B_4_15-B_21_15,B_4_16-B_21_16,B_4_17-B_21_17,B_4_18-B_21_18,B_4_19-B_21_19,B_4_20-B_21_20,B_4_21-B_21_21,B_4_22-B_21_22,B_4_23-B_21_23,B_4_24-B_21_24,B_4_9-B_21_9,B_4_10-B_21_10,B_4_11-B_21_11,B_4_12-B_21_12,B_4_28-B_21_28,B_4_29-B_21_29,B_4_30-B_21_30]]),Matrix(18, 6, [[C_14_1+C_14_8,C_14_2+C_14_9,C_14_3+C_14_10,C_14_4+C_14_11,C_14_5+C_14_12,C_14_6+C_14_13],[C_15_1+C_15_8,C_15_2+C_15_9,C_15_3+C_15_10,C_15_4+C_15_11,C_15_5+C_15_12,C_15_6+C_15_13],[C_16_1+C_16_8,C_16_2+C_16_9,C_16_3+C_16_10,C_16_4+C_16_11,C_16_5+C_16_12,C_16_6+C_16_13],[C_17_1+C_17_8,C_17_2+C_17_9,C_17_3+C_17_10,C_17_4+C_17_11,C_17_5+C_17_12,C_17_6+C_17_13],[C_18_1+C_18_8,C_18_2+C_18_9,C_18_3+C_18_10,C_18_4+C_18_11,C_18_5+C_18_12,C_18_6+C_18_13],[C_19_1+C_19_8,C_19_2+C_19_9,C_19_3+C_19_10,C_19_4+C_19_11,C_19_5+C_19_12,C_19_6+C_19_13],[C_20_1+C_20_8,C_20_2+C_20_9,C_20_3+C_20_10,C_20_4+C_20_11,C_20_5+C_20_12,C_20_6+C_20_13],[C_21_1+C_21_8,C_21_2+C_21_9,C_21_3+C_21_10,C_21_4+C_21_11,C_21_5+C_21_12,C_21_6+C_21_13],[C_22_1+C_22_8,C_22_2+C_22_9,C_22_3+C_22_10,C_22_4+C_22_11,C_22_5+C_22_12,C_22_6+C_22_13],[C_23_1+C_23_8,C_23_2+C_23_9,C_23_3+C_23_10,C_23_4+C_23_11,C_23_5+C_23_12,C_23_6+C_23_13],[C_24_1+C_24_8,C_24_2+C_24_9,C_24_3+C_24_10,C_24_4+C_24_11,C_24_5+C_24_12,C_24_6+C_24_13],[C_9_1+C_9_8,C_9_2+C_9_9,C_9_3+C_9_10,C_9_4+C_9_11,C_9_5+C_9_12,C_9_6+C_9_13],[C_10_1+C_10_8,C_10_2+C_10_9,C_10_3+C_10_10,C_10_4+C_10_11,C_10_5+C_10_12,C_10_6+C_10_13],[C_11_1+C_11_8,C_11_2+C_11_9,C_11_3+C_11_10,C_11_4+C_11_11,C_11_5+C_11_12,C_11_6+C_11_13],[C_12_1+C_12_8,C_12_2+C_12_9,C_12_3+C_12_10,C_12_4+C_12_11,C_12_5+C_12_12,C_12_6+C_12_13],[C_28_1+C_28_8,C_28_2+C_28_9,C_28_3+C_28_10,C_28_4+C_28_11,C_28_5+C_28_12,C_28_6+C_28_13],[C_29_1+C_29_8,C_29_2+C_29_9,C_29_3+C_29_10,C_29_4+C_29_11,C_29_5+C_29_12,C_29_6+C_29_13],[C_30_1+C_30_8,C_30_2+C_30_9,C_30_3+C_30_10,C_30_4+C_30_11,C_30_5+C_30_12,C_30_6+C_30_13]])))+Trace(Mul(Matrix(7, 12, [[A_7_5,A_7_6,A_7_1,A_7_2,A_7_3,A_7_15,A_7_16,A_7_17,A_7_18,A_7_19,A_7_20,A_7_21],[A_8_5,A_8_6,A_8_1,A_8_2,A_8_3,A_8_15,A_8_16,A_8_17,A_8_18,A_8_19,A_8_20,A_8_21],[A_9_5,A_9_6,A_9_1,A_9_2,A_9_3,A_9_15,A_9_16,A_9_17,A_9_18,A_9_19,A_9_20,A_9_21],[A_10_5,A_10_6,A_10_1,A_10_2,A_10_3,A_10_15,A_10_16,A_10_17,A_10_18,A_10_19,A_10_20,A_10_21],[A_11_5,A_11_6,A_11_1,A_11_2,A_11_3,A_11_15,A_11_16,A_11_17,A_11_18,A_11_19,A_11_20,A_11_21],[A_12_5,A_12_6,A_12_1,A_12_2,A_12_3,A_12_15,A_12_16,A_12_17,A_12_18,A_12_19,A_12_20,A_12_21],[A_13_5,A_13_6,A_13_1,A_13_2,A_13_3,A_13_15,A_13_16,A_13_17,A_13_18,A_13_19,A_13_20,A_13_21]]),Matrix(12, 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_25,B_5_26,B_5_27,B_5_13],[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_25,B_6_26,B_6_27,B_6_13],[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_25,B_1_26,B_1_27,B_1_13],[B_2_1-B_7_1,B_2_2-B_7_2,B_2_3-B_7_3,B_2_4-B_7_4,B_2_5-B_7_5,B_2_6-B_7_6,B_2_7-B_7_7,B_2_8-B_7_8,B_2_25-B_7_25,B_2_26-B_7_26,-B_7_27+B_2_27,B_2_13-B_7_13],[B_3_1-B_8_1,B_3_2-B_8_2,B_3_3-B_8_3,B_3_4-B_8_4,B_3_5-B_8_5,B_3_6-B_8_6,B_3_7-B_8_7,B_3_8-B_8_8,B_3_25-B_8_25,B_3_26-B_8_26,-B_8_27+B_3_27,B_3_13-B_8_13],[-B_9_1+B_15_1,-B_9_2+B_15_2,-B_9_3+B_15_3,-B_9_4+B_15_4,-B_9_5+B_15_5,-B_9_6+B_15_6,-B_9_7+B_15_7,-B_9_8+B_15_8,-B_9_25+B_15_25,-B_9_26+B_15_26,-B_9_27+B_15_27,-B_9_13+B_15_13],[-B_10_1+B_16_1,-B_10_2+B_16_2,-B_10_3+B_16_3,-B_10_4+B_16_4,-B_10_5+B_16_5,-B_10_6+B_16_6,-B_10_7+B_16_7,-B_10_8+B_16_8,-B_10_25+B_16_25,-B_10_26+B_16_26,-B_10_27+B_16_27,-B_10_13+B_16_13],[-B_11_1+B_17_1,-B_11_2+B_17_2,-B_11_3+B_17_3,-B_11_4+B_17_4,-B_11_5+B_17_5,-B_11_6+B_17_6,-B_11_7+B_17_7,-B_11_8+B_17_8,-B_11_25+B_17_25,-B_11_26+B_17_26,-B_11_27+B_17_27,-B_11_13+B_17_13],[-B_12_1+B_18_1,-B_12_2+B_18_2,-B_12_3+B_18_3,-B_12_4+B_18_4,-B_12_5+B_18_5,-B_12_6+B_18_6,-B_12_7+B_18_7,-B_12_8+B_18_8,-B_12_25+B_18_25,-B_12_26+B_18_26,-B_12_27+B_18_27,-B_12_13+B_18_13],[-B_13_1+B_19_1,-B_13_2+B_19_2,-B_13_3+B_19_3,-B_13_4+B_19_4,-B_13_5+B_19_5,-B_13_6+B_19_6,-B_13_7+B_19_7,-B_13_8+B_19_8,-B_13_25+B_19_25,-B_13_26+B_19_26,-B_13_27+B_19_27,-B_13_13+B_19_13],[-B_14_1+B_20_1,-B_14_2+B_20_2,-B_14_3+B_20_3,-B_14_4+B_20_4,-B_14_5+B_20_5,-B_14_6+B_20_6,-B_14_7+B_20_7,-B_14_8+B_20_8,-B_14_25+B_20_25,-B_14_26+B_20_26,-B_14_27+B_20_27,-B_14_13+B_20_13],[-B_4_1+B_21_1,-B_4_2+B_21_2,-B_4_3+B_21_3,-B_4_4+B_21_4,-B_4_5+B_21_5,-B_4_6+B_21_6,-B_4_7+B_21_7,-B_4_8+B_21_8,-B_4_25+B_21_25,-B_4_26+B_21_26,-B_4_27+B_21_27,-B_4_13+B_21_13]]),Matrix(12, 7, [[C_1_7,C_1_1+C_1_8,C_1_2+C_1_9,C_1_3+C_1_10,C_1_4+C_1_11,C_1_5+C_1_12,C_1_6+C_1_13],[C_2_7,C_2_1+C_2_8,C_2_2+C_2_9,C_2_3+C_2_10,C_2_4+C_2_11,C_2_5+C_2_12,C_2_6+C_2_13],[C_3_7,C_3_1+C_3_8,C_3_2+C_3_9,C_3_3+C_3_10,C_3_4+C_3_11,C_3_5+C_3_12,C_3_6+C_3_13],[C_4_7,C_4_1+C_4_8,C_4_2+C_4_9,C_4_3+C_4_10,C_4_4+C_4_11,C_4_5+C_4_12,C_4_6+C_4_13],[C_5_7,C_5_1+C_5_8,C_5_2+C_5_9,C_5_3+C_5_10,C_5_4+C_5_11,C_5_5+C_5_12,C_5_6+C_5_13],[C_6_7,C_6_1+C_6_8,C_6_2+C_6_9,C_6_3+C_6_10,C_6_4+C_6_11,C_6_5+C_6_12,C_6_6+C_6_13],[C_7_7,C_7_1+C_7_8,C_7_2+C_7_9,C_7_3+C_7_10,C_7_4+C_7_11,C_7_5+C_7_12,C_7_6+C_7_13],[C_8_7,C_8_1+C_8_8,C_8_2+C_8_9,C_8_3+C_8_10,C_8_4+C_8_11,C_8_5+C_8_12,C_8_6+C_8_13],[C_25_7,C_25_1+C_25_8,C_25_2+C_25_9,C_25_3+C_25_10,C_25_4+C_25_11,C_25_5+C_25_12,C_25_6+C_25_13],[C_26_7,C_26_1+C_26_8,C_26_2+C_26_9,C_26_3+C_26_10,C_26_4+C_26_11,C_26_5+C_26_12,C_26_6+C_26_13],[C_27_7,C_27_1+C_27_8,C_27_2+C_27_9,C_27_3+C_27_10,C_27_4+C_27_11,C_27_5+C_27_12,C_27_6+C_27_13],[C_13_7,C_13_1+C_13_8,C_13_2+C_13_9,C_13_3+C_13_10,C_13_4+C_13_11,C_13_5+C_13_12,C_13_6+C_13_13]])))+Trace(Mul(Matrix(7, 9, [[A_7_2+A_7_7,A_7_3+A_7_8,A_7_9+A_7_15,A_7_10+A_7_16,A_7_11+A_7_17,A_7_12+A_7_18,A_7_13+A_7_19,A_7_14+A_7_20,A_7_4+A_7_21],[A_8_2+A_8_7,A_8_3+A_8_8,A_8_9+A_8_15,A_8_10+A_8_16,A_8_11+A_8_17,A_8_12+A_8_18,A_8_13+A_8_19,A_8_14+A_8_20,A_8_4+A_8_21],[A_9_2+A_9_7,A_9_3+A_9_8,A_9_9+A_9_15,A_9_10+A_9_16,A_9_11+A_9_17,A_9_12+A_9_18,A_9_13+A_9_19,A_9_14+A_9_20,A_9_4+A_9_21],[A_10_2+A_10_7,A_10_3+A_10_8,A_10_9+A_10_15,A_10_10+A_10_16,A_10_11+A_10_17,A_10_12+A_10_18,A_10_13+A_10_19,A_10_14+A_10_20,A_10_4+A_10_21],[A_11_2+A_11_7,A_11_3+A_11_8,A_11_9+A_11_15,A_11_10+A_11_16,A_11_11+A_11_17,A_11_12+A_11_18,A_11_13+A_11_19,A_11_14+A_11_20,A_11_4+A_11_21],[A_12_2+A_12_7,A_12_3+A_12_8,A_12_9+A_12_15,A_12_10+A_12_16,A_12_11+A_12_17,A_12_12+A_12_18,A_12_13+A_12_19,A_12_14+A_12_20,A_12_4+A_12_21],[A_13_2+A_13_7,A_13_3+A_13_8,A_13_9+A_13_15,A_13_10+A_13_16,A_13_11+A_13_17,A_13_12+A_13_18,A_13_13+A_13_19,A_13_14+A_13_20,A_13_4+A_13_21]]),Matrix(9, 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_25,B_7_26,B_7_27,B_7_13],[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_25,B_8_26,B_8_27,B_8_13],[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_25,B_9_26,B_9_27,B_9_13],[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_25,B_10_26,B_10_27,B_10_13],[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_25,B_11_26,B_11_27,B_11_13],[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_25,B_12_26,B_12_27,B_12_13],[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_25,B_13_26,B_13_27,B_13_13],[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_25,B_14_26,B_14_27,B_14_13],[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_25,B_4_26,B_4_27,B_4_13]]),Matrix(12, 7, [[C_1_7-C_20_7,C_1_8-C_20_8,C_1_9-C_20_9,C_1_10-C_20_10,C_1_11-C_20_11,C_1_12-C_20_12,C_1_13-C_20_13],[C_2_7-C_21_7,C_2_8-C_21_8,C_2_9-C_21_9,C_2_10-C_21_10,C_2_11-C_21_11,C_2_12-C_21_12,C_2_13-C_21_13],[C_3_7-C_22_7,C_3_8-C_22_8,C_3_9-C_22_9,C_3_10-C_22_10,C_3_11-C_22_11,C_3_12-C_22_12,C_3_13-C_22_13],[C_4_7-C_23_7,C_4_8-C_23_8,C_4_9-C_23_9,C_4_10-C_23_10,C_4_11-C_23_11,C_4_12-C_23_12,C_4_13-C_23_13],[C_5_7-C_24_7,C_5_8-C_24_8,C_5_9-C_24_9,C_5_10-C_24_10,C_5_11-C_24_11,C_5_12-C_24_12,C_5_13-C_24_13],[C_6_7-C_9_7,C_6_8-C_9_8,C_6_9-C_9_9,C_6_10-C_9_10,C_6_11-C_9_11,C_6_12-C_9_12,C_6_13-C_9_13],[C_7_7-C_10_7,C_7_8-C_10_8,C_7_9-C_10_9,C_7_10-C_10_10,C_7_11-C_10_11,C_7_12-C_10_12,C_7_13-C_10_13],[C_8_7-C_11_7,C_8_8-C_11_8,C_8_9-C_11_9,C_8_10-C_11_10,C_8_11-C_11_11,C_8_12-C_11_12,C_8_13-C_11_13],[-C_12_7+C_25_7,-C_12_8+C_25_8,-C_12_9+C_25_9,-C_12_10+C_25_10,-C_12_11+C_25_11,-C_12_12+C_25_12,-C_12_13+C_25_13],[C_26_7-C_28_7,C_26_8-C_28_8,C_26_9-C_28_9,C_26_10-C_28_10,C_26_11-C_28_11,C_26_12-C_28_12,C_26_13-C_28_13],[C_27_7-C_29_7,C_27_8-C_29_8,C_27_9-C_29_9,C_27_10-C_29_10,C_27_11-C_29_11,C_27_12-C_29_12,C_27_13-C_29_13],[C_13_7-C_30_7,C_13_8-C_30_8,C_13_9-C_30_9,C_13_10-C_30_10,C_13_11-C_30_11,C_13_12-C_30_12,C_13_13-C_30_13]])))

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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