Description of fast matrix multiplication algorithm: ⟨25×28×31:11750⟩

Algorithm type

8⁢X9⁢Y⁢Z+40⁢X6⁢Y2⁢Z2+100⁢X4⁢Y3⁢Z3+10⁢X6⁢Y2⁢Z+4094⁢X3⁢Y3⁢Z3+50⁢X6⁢Y⁢Z+100⁢X4⁢Y2⁢Z2+64⁢X3⁢Y2⁢Z3+10⁢X4⁢Y2⁢Z+30⁢X4⁢Y⁢Z2+1156⁢X3⁢Y3⁢Z+253⁢X3⁢Y2⁢Z2+96⁢X3⁢Y⁢Z3+1876⁢X2⁢Y3⁢Z2+253⁢X2⁢Y2⁢Z3+60⁢X4⁢Y⁢Z+22⁢X3⁢Y2⁢Z+169⁢X2⁢Y3⁢Z+618⁢X2⁢Y2⁢Z2+114⁢X3⁢Y⁢Z+116⁢X2⁢Y2⁢Z+10⁢X2⁢Y⁢Z2+216⁢X⁢Y3⁢Z+33⁢X⁢Y2⁢Z2+1178⁢X⁢Y⁢Z3+325⁢X2⁢Y⁢Z+84⁢X⁢Y2⁢Z+222⁢X⁢Y⁢Z2+443⁢X⁢Y⁢Z8X9YZ40X6Y2Z2100X4Y3Z310X6Y2Z4094X3Y3Z350X6YZ100X4Y2Z264X3Y2Z310X4Y2Z30X4YZ21156X3Y3Z253X3Y2Z296X3YZ31876X2Y3Z2253X2Y2Z360X4YZ22X3Y2Z169X2Y3Z618X2Y2Z2114X3YZ116X2Y2Z10X2YZ2216XY3Z33XY2Z21178XYZ3325X2YZ84XY2Z222XYZ2443XYZ8*X^9*Y*Z+40*X^6*Y^2*Z^2+100*X^4*Y^3*Z^3+10*X^6*Y^2*Z+4094*X^3*Y^3*Z^3+50*X^6*Y*Z+100*X^4*Y^2*Z^2+64*X^3*Y^2*Z^3+10*X^4*Y^2*Z+30*X^4*Y*Z^2+1156*X^3*Y^3*Z+253*X^3*Y^2*Z^2+96*X^3*Y*Z^3+1876*X^2*Y^3*Z^2+253*X^2*Y^2*Z^3+60*X^4*Y*Z+22*X^3*Y^2*Z+169*X^2*Y^3*Z+618*X^2*Y^2*Z^2+114*X^3*Y*Z+116*X^2*Y^2*Z+10*X^2*Y*Z^2+216*X*Y^3*Z+33*X*Y^2*Z^2+1178*X*Y*Z^3+325*X^2*Y*Z+84*X*Y^2*Z+222*X*Y*Z^2+443*X*Y*Z

Algorithm definition

The algorithm ⟨25×28×31:11750⟩ could be constructed using the following decomposition:

⟨25×28×31:11750⟩ = ⟨25×28×3:1544⟩ + ⟨25×28×28:10206⟩.

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_1_20A_1_21A_1_22A_1_23A_1_24A_1_25A_1_26A_1_27A_1_28A_2_1A_2_2A_2_3A_2_4A_2_5A_2_6A_2_7A_2_8A_2_9A_2_10A_2_11A_2_12A_2_13A_2_14A_2_15A_2_16A_2_17A_2_18A_2_19A_2_20A_2_21A_2_22A_2_23A_2_24A_2_25A_2_26A_2_27A_2_28A_3_1A_3_2A_3_3A_3_4A_3_5A_3_6A_3_7A_3_8A_3_9A_3_10A_3_11A_3_12A_3_13A_3_14A_3_15A_3_16A_3_17A_3_18A_3_19A_3_20A_3_21A_3_22A_3_23A_3_24A_3_25A_3_26A_3_27A_3_28A_4_1A_4_2A_4_3A_4_4A_4_5A_4_6A_4_7A_4_8A_4_9A_4_10A_4_11A_4_12A_4_13A_4_14A_4_15A_4_16A_4_17A_4_18A_4_19A_4_20A_4_21A_4_22A_4_23A_4_24A_4_25A_4_26A_4_27A_4_28A_5_1A_5_2A_5_3A_5_4A_5_5A_5_6A_5_7A_5_8A_5_9A_5_10A_5_11A_5_12A_5_13A_5_14A_5_15A_5_16A_5_17A_5_18A_5_19A_5_20A_5_21A_5_22A_5_23A_5_24A_5_25A_5_26A_5_27A_5_28A_6_1A_6_2A_6_3A_6_4A_6_5A_6_6A_6_7A_6_8A_6_9A_6_10A_6_11A_6_12A_6_13A_6_14A_6_15A_6_16A_6_17A_6_18A_6_19A_6_20A_6_21A_6_22A_6_23A_6_24A_6_25A_6_26A_6_27A_6_28A_7_1A_7_2A_7_3A_7_4A_7_5A_7_6A_7_7A_7_8A_7_9A_7_10A_7_11A_7_12A_7_13A_7_14A_7_15A_7_16A_7_17A_7_18A_7_19A_7_20A_7_21A_7_22A_7_23A_7_24A_7_25A_7_26A_7_27A_7_28A_8_1A_8_2A_8_3A_8_4A_8_5A_8_6A_8_7A_8_8A_8_9A_8_10A_8_11A_8_12A_8_13A_8_14A_8_15A_8_16A_8_17A_8_18A_8_19A_8_20A_8_21A_8_22A_8_23A_8_24A_8_25A_8_26A_8_27A_8_28A_9_1A_9_2A_9_3A_9_4A_9_5A_9_6A_9_7A_9_8A_9_9A_9_10A_9_11A_9_12A_9_13A_9_14A_9_15A_9_16A_9_17A_9_18A_9_19A_9_20A_9_21A_9_22A_9_23A_9_24A_9_25A_9_26A_9_27A_9_28A_10_1A_10_2A_10_3A_10_4A_10_5A_10_6A_10_7A_10_8A_10_9A_10_10A_10_11A_10_12A_10_13A_10_14A_10_15A_10_16A_10_17A_10_18A_10_19A_10_20A_10_21A_10_22A_10_23A_10_24A_10_25A_10_26A_10_27A_10_28A_11_1A_11_2A_11_3A_11_4A_11_5A_11_6A_11_7A_11_8A_11_9A_11_10A_11_11A_11_12A_11_13A_11_14A_11_15A_11_16A_11_17A_11_18A_11_19A_11_20A_11_21A_11_22A_11_23A_11_24A_11_25A_11_26A_11_27A_11_28A_12_1A_12_2A_12_3A_12_4A_12_5A_12_6A_12_7A_12_8A_12_9A_12_10A_12_11A_12_12A_12_13A_12_14A_12_15A_12_16A_12_17A_12_18A_12_19A_12_20A_12_21A_12_22A_12_23A_12_24A_12_25A_12_26A_12_27A_12_28A_13_1A_13_2A_13_3A_13_4A_13_5A_13_6A_13_7A_13_8A_13_9A_13_10A_13_11A_13_12A_13_13A_13_14A_13_15A_13_16A_13_17A_13_18A_13_19A_13_20A_13_21A_13_22A_13_23A_13_24A_13_25A_13_26A_13_27A_13_28A_14_1A_14_2A_14_3A_14_4A_14_5A_14_6A_14_7A_14_8A_14_9A_14_10A_14_11A_14_12A_14_13A_14_14A_14_15A_14_16A_14_17A_14_18A_14_19A_14_20A_14_21A_14_22A_14_23A_14_24A_14_25A_14_26A_14_27A_14_28A_15_1A_15_2A_15_3A_15_4A_15_5A_15_6A_15_7A_15_8A_15_9A_15_10A_15_11A_15_12A_15_13A_15_14A_15_15A_15_16A_15_17A_15_18A_15_19A_15_20A_15_21A_15_22A_15_23A_15_24A_15_25A_15_26A_15_27A_15_28A_16_1A_16_2A_16_3A_16_4A_16_5A_16_6A_16_7A_16_8A_16_9A_16_10A_16_11A_16_12A_16_13A_16_14A_16_15A_16_16A_16_17A_16_18A_16_19A_16_20A_16_21A_16_22A_16_23A_16_24A_16_25A_16_26A_16_27A_16_28A_17_1A_17_2A_17_3A_17_4A_17_5A_17_6A_17_7A_17_8A_17_9A_17_10A_17_11A_17_12A_17_13A_17_14A_17_15A_17_16A_17_17A_17_18A_17_19A_17_20A_17_21A_17_22A_17_23A_17_24A_17_25A_17_26A_17_27A_17_28A_18_1A_18_2A_18_3A_18_4A_18_5A_18_6A_18_7A_18_8A_18_9A_18_10A_18_11A_18_12A_18_13A_18_14A_18_15A_18_16A_18_17A_18_18A_18_19A_18_20A_18_21A_18_22A_18_23A_18_24A_18_25A_18_26A_18_27A_18_28A_19_1A_19_2A_19_3A_19_4A_19_5A_19_6A_19_7A_19_8A_19_9A_19_10A_19_11A_19_12A_19_13A_19_14A_19_15A_19_16A_19_17A_19_18A_19_19A_19_20A_19_21A_19_22A_19_23A_19_24A_19_25A_19_26A_19_27A_19_28A_20_1A_20_2A_20_3A_20_4A_20_5A_20_6A_20_7A_20_8A_20_9A_20_10A_20_11A_20_12A_20_13A_20_14A_20_15A_20_16A_20_17A_20_18A_20_19A_20_20A_20_21A_20_22A_20_23A_20_24A_20_25A_20_26A_20_27A_20_28A_21_1A_21_2A_21_3A_21_4A_21_5A_21_6A_21_7A_21_8A_21_9A_21_10A_21_11A_21_12A_21_13A_21_14A_21_15A_21_16A_21_17A_21_18A_21_19A_21_20A_21_21A_21_22A_21_23A_21_24A_21_25A_21_26A_21_27A_21_28A_22_1A_22_2A_22_3A_22_4A_22_5A_22_6A_22_7A_22_8A_22_9A_22_10A_22_11A_22_12A_22_13A_22_14A_22_15A_22_16A_22_17A_22_18A_22_19A_22_20A_22_21A_22_22A_22_23A_22_24A_22_25A_22_26A_22_27A_22_28A_23_1A_23_2A_23_3A_23_4A_23_5A_23_6A_23_7A_23_8A_23_9A_23_10A_23_11A_23_12A_23_13A_23_14A_23_15A_23_16A_23_17A_23_18A_23_19A_23_20A_23_21A_23_22A_23_23A_23_24A_23_25A_23_26A_23_27A_23_28A_24_1A_24_2A_24_3A_24_4A_24_5A_24_6A_24_7A_24_8A_24_9A_24_10A_24_11A_24_12A_24_13A_24_14A_24_15A_24_16A_24_17A_24_18A_24_19A_24_20A_24_21A_24_22A_24_23A_24_24A_24_25A_24_26A_24_27A_24_28A_25_1A_25_2A_25_3A_25_4A_25_5A_25_6A_25_7A_25_8A_25_9A_25_10A_25_11A_25_12A_25_13A_25_14A_25_15A_25_16A_25_17A_25_18A_25_19A_25_20A_25_21A_25_22A_25_23A_25_24A_25_25A_25_26A_25_27A_25_28B_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_1_31B_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_2_31B_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_3_31B_4_1B_4_2B_4_3B_4_4B_4_5B_4_6B_4_7B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28, [[A_1_1,A_1_2,A_1_3,A_1_4,A_1_5,A_1_6,A_1_7,A_1_8,A_1_9,A_1_10,A_1_11,A_1_12,A_1_13,A_1_14,A_1_15,A_1_16,A_1_17,A_1_18,A_1_19,A_1_20,A_1_21,A_1_22,A_1_23,A_1_24,A_1_25,A_1_26,A_1_27,A_1_28],[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6,A_2_7,A_2_8,A_2_9,A_2_10,A_2_11,A_2_12,A_2_13,A_2_14,A_2_15,A_2_16,A_2_17,A_2_18,A_2_19,A_2_20,A_2_21,A_2_22,A_2_23,A_2_24,A_2_25,A_2_26,A_2_27,A_2_28],[A_3_1,A_3_2,A_3_3,A_3_4,A_3_5,A_3_6,A_3_7,A_3_8,A_3_9,A_3_10,A_3_11,A_3_12,A_3_13,A_3_14,A_3_15,A_3_16,A_3_17,A_3_18,A_3_19,A_3_20,A_3_21,A_3_22,A_3_23,A_3_24,A_3_25,A_3_26,A_3_27,A_3_28],[A_4_1,A_4_2,A_4_3,A_4_4,A_4_5,A_4_6,A_4_7,A_4_8,A_4_9,A_4_10,A_4_11,A_4_12,A_4_13,A_4_14,A_4_15,A_4_16,A_4_17,A_4_18,A_4_19,A_4_20,A_4_21,A_4_22,A_4_23,A_4_24,A_4_25,A_4_26,A_4_27,A_4_28],[A_5_1,A_5_2,A_5_3,A_5_4,A_5_5,A_5_6,A_5_7,A_5_8,A_5_9,A_5_10,A_5_11,A_5_12,A_5_13,A_5_14,A_5_15,A_5_16,A_5_17,A_5_18,A_5_19,A_5_20,A_5_21,A_5_22,A_5_23,A_5_24,A_5_25,A_5_26,A_5_27,A_5_28],[A_6_1,A_6_2,A_6_3,A_6_4,A_6_5,A_6_6,A_6_7,A_6_8,A_6_9,A_6_10,A_6_11,A_6_12,A_6_13,A_6_14,A_6_15,A_6_16,A_6_17,A_6_18,A_6_19,A_6_20,A_6_21,A_6_22,A_6_23,A_6_24,A_6_25,A_6_26,A_6_27,A_6_28],[A_7_1,A_7_2,A_7_3,A_7_4,A_7_5,A_7_6,A_7_7,A_7_8,A_7_9,A_7_10,A_7_11,A_7_12,A_7_13,A_7_14,A_7_15,A_7_16,A_7_17,A_7_18,A_7_19,A_7_20,A_7_21,A_7_22,A_7_23,A_7_24,A_7_25,A_7_26,A_7_27,A_7_28],[A_8_1,A_8_2,A_8_3,A_8_4,A_8_5,A_8_6,A_8_7,A_8_8,A_8_9,A_8_10,A_8_11,A_8_12,A_8_13,A_8_14,A_8_15,A_8_16,A_8_17,A_8_18,A_8_19,A_8_20,A_8_21,A_8_22,A_8_23,A_8_24,A_8_25,A_8_26,A_8_27,A_8_28],[A_9_1,A_9_2,A_9_3,A_9_4,A_9_5,A_9_6,A_9_7,A_9_8,A_9_9,A_9_10,A_9_11,A_9_12,A_9_13,A_9_14,A_9_15,A_9_16,A_9_17,A_9_18,A_9_19,A_9_20,A_9_21,A_9_22,A_9_23,A_9_24,A_9_25,A_9_26,A_9_27,A_9_28],[A_10_1,A_10_2,A_10_3,A_10_4,A_10_5,A_10_6,A_10_7,A_10_8,A_10_9,A_10_10,A_10_11,A_10_12,A_10_13,A_10_14,A_10_15,A_10_16,A_10_17,A_10_18,A_10_19,A_10_20,A_10_21,A_10_22,A_10_23,A_10_24,A_10_25,A_10_26,A_10_27,A_10_28],[A_11_1,A_11_2,A_11_3,A_11_4,A_11_5,A_11_6,A_11_7,A_11_8,A_11_9,A_11_10,A_11_11,A_11_12,A_11_13,A_11_14,A_11_15,A_11_16,A_11_17,A_11_18,A_11_19,A_11_20,A_11_21,A_11_22,A_11_23,A_11_24,A_11_25,A_11_26,A_11_27,A_11_28],[A_12_1,A_12_2,A_12_3,A_12_4,A_12_5,A_12_6,A_12_7,A_12_8,A_12_9,A_12_10,A_12_11,A_12_12,A_12_13,A_12_14,A_12_15,A_12_16,A_12_17,A_12_18,A_12_19,A_12_20,A_12_21,A_12_22,A_12_23,A_12_24,A_12_25,A_12_26,A_12_27,A_12_28],[A_13_1,A_13_2,A_13_3,A_13_4,A_13_5,A_13_6,A_13_7,A_13_8,A_13_9,A_13_10,A_13_11,A_13_12,A_13_13,A_13_14,A_13_15,A_13_16,A_13_17,A_13_18,A_13_19,A_13_20,A_13_21,A_13_22,A_13_23,A_13_24,A_13_25,A_13_26,A_13_27,A_13_28],[A_14_1,A_14_2,A_14_3,A_14_4,A_14_5,A_14_6,A_14_7,A_14_8,A_14_9,A_14_10,A_14_11,A_14_12,A_14_13,A_14_14,A_14_15,A_14_16,A_14_17,A_14_18,A_14_19,A_14_20,A_14_21,A_14_22,A_14_23,A_14_24,A_14_25,A_14_26,A_14_27,A_14_28],[A_15_1,A_15_2,A_15_3,A_15_4,A_15_5,A_15_6,A_15_7,A_15_8,A_15_9,A_15_10,A_15_11,A_15_12,A_15_13,A_15_14,A_15_15,A_15_16,A_15_17,A_15_18,A_15_19,A_15_20,A_15_21,A_15_22,A_15_23,A_15_24,A_15_25,A_15_26,A_15_27,A_15_28],[A_16_1,A_16_2,A_16_3,A_16_4,A_16_5,A_16_6,A_16_7,A_16_8,A_16_9,A_16_10,A_16_11,A_16_12,A_16_13,A_16_14,A_16_15,A_16_16,A_16_17,A_16_18,A_16_19,A_16_20,A_16_21,A_16_22,A_16_23,A_16_24,A_16_25,A_16_26,A_16_27,A_16_28],[A_17_1,A_17_2,A_17_3,A_17_4,A_17_5,A_17_6,A_17_7,A_17_8,A_17_9,A_17_10,A_17_11,A_17_12,A_17_13,A_17_14,A_17_15,A_17_16,A_17_17,A_17_18,A_17_19,A_17_20,A_17_21,A_17_22,A_17_23,A_17_24,A_17_25,A_17_26,A_17_27,A_17_28],[A_18_1,A_18_2,A_18_3,A_18_4,A_18_5,A_18_6,A_18_7,A_18_8,A_18_9,A_18_10,A_18_11,A_18_12,A_18_13,A_18_14,A_18_15,A_18_16,A_18_17,A_18_18,A_18_19,A_18_20,A_18_21,A_18_22,A_18_23,A_18_24,A_18_25,A_18_26,A_18_27,A_18_28],[A_19_1,A_19_2,A_19_3,A_19_4,A_19_5,A_19_6,A_19_7,A_19_8,A_19_9,A_19_10,A_19_11,A_19_12,A_19_13,A_19_14,A_19_15,A_19_16,A_19_17,A_19_18,A_19_19,A_19_20,A_19_21,A_19_22,A_19_23,A_19_24,A_19_25,A_19_26,A_19_27,A_19_28],[A_20_1,A_20_2,A_20_3,A_20_4,A_20_5,A_20_6,A_20_7,A_20_8,A_20_9,A_20_10,A_20_11,A_20_12,A_20_13,A_20_14,A_20_15,A_20_16,A_20_17,A_20_18,A_20_19,A_20_20,A_20_21,A_20_22,A_20_23,A_20_24,A_20_25,A_20_26,A_20_27,A_20_28],[A_21_1,A_21_2,A_21_3,A_21_4,A_21_5,A_21_6,A_21_7,A_21_8,A_21_9,A_21_10,A_21_11,A_21_12,A_21_13,A_21_14,A_21_15,A_21_16,A_21_17,A_21_18,A_21_19,A_21_20,A_21_21,A_21_22,A_21_23,A_21_24,A_21_25,A_21_26,A_21_27,A_21_28],[A_22_1,A_22_2,A_22_3,A_22_4,A_22_5,A_22_6,A_22_7,A_22_8,A_22_9,A_22_10,A_22_11,A_22_12,A_22_13,A_22_14,A_22_15,A_22_16,A_22_17,A_22_18,A_22_19,A_22_20,A_22_21,A_22_22,A_22_23,A_22_24,A_22_25,A_22_26,A_22_27,A_22_28],[A_23_1,A_23_2,A_23_3,A_23_4,A_23_5,A_23_6,A_23_7,A_23_8,A_23_9,A_23_10,A_23_11,A_23_12,A_23_13,A_23_14,A_23_15,A_23_16,A_23_17,A_23_18,A_23_19,A_23_20,A_23_21,A_23_22,A_23_23,A_23_24,A_23_25,A_23_26,A_23_27,A_23_28],[A_24_1,A_24_2,A_24_3,A_24_4,A_24_5,A_24_6,A_24_7,A_24_8,A_24_9,A_24_10,A_24_11,A_24_12,A_24_13,A_24_14,A_24_15,A_24_16,A_24_17,A_24_18,A_24_19,A_24_20,A_24_21,A_24_22,A_24_23,A_24_24,A_24_25,A_24_26,A_24_27,A_24_28],[A_25_1,A_25_2,A_25_3,A_25_4,A_25_5,A_25_6,A_25_7,A_25_8,A_25_9,A_25_10,A_25_11,A_25_12,A_25_13,A_25_14,A_25_15,A_25_16,A_25_17,A_25_18,A_25_19,A_25_20,A_25_21,A_25_22,A_25_23,A_25_24,A_25_25,A_25_26,A_25_27,A_25_28]]),Matrix(28, 31, 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_22_29,B_22_30,B_22_31],[B_23_1,B_23_2,B_23_3,B_23_4,B_23_5,B_23_6,B_23_7,B_23_8,B_23_9,B_23_10,B_23_11,B_23_12,B_23_13,B_23_14,B_23_15,B_23_16,B_23_17,B_23_18,B_23_19,B_23_20,B_23_21,B_23_22,B_23_23,B_23_24,B_23_25,B_23_26,B_23_27,B_23_28,B_23_29,B_23_30,B_23_31],[B_24_1,B_24_2,B_24_3,B_24_4,B_24_5,B_24_6,B_24_7,B_24_8,B_24_9,B_24_10,B_24_11,B_24_12,B_24_13,B_24_14,B_24_15,B_24_16,B_24_17,B_24_18,B_24_19,B_24_20,B_24_21,B_24_22,B_24_23,B_24_24,B_24_25,B_24_26,B_24_27,B_24_28,B_24_29,B_24_30,B_24_31],[B_25_1,B_25_2,B_25_3,B_25_4,B_25_5,B_25_6,B_25_7,B_25_8,B_25_9,B_25_10,B_25_11,B_25_12,B_25_13,B_25_14,B_25_15,B_25_16,B_25_17,B_25_18,B_25_19,B_25_20,B_25_21,B_25_22,B_25_23,B_25_24,B_25_25,B_25_26,B_25_27,B_25_28,B_25_29,B_25_30,B_25_31],[B_26_1,B_26_2,B_26_3,B_26_4,B_26_5,B_26_6,B_26_7,B_26_8,B_26_9,B_26_10,B_26_11,B_26_12,B_26_13,B_26_14,B_26_15,B_26_16,B_26_17,B_26_18,B_26_19,B_26_20,B_26_21,B_26_22,B_26_23,B_26_24,B_26_25,B_26_26,B_26_27,B_26_28,B_26_29,B_26_30,B_26_31],[B_27_1,B_27_2,B_27_3,B_27_4,B_27_5,B_27_6,B_27_7,B_27_8,B_27_9,B_27_10,B_27_11,B_27_12,B_27_13,B_27_14,B_27_15,B_27_16,B_27_17,B_27_18,B_27_19,B_27_20,B_27_21,B_27_22,B_27_23,B_27_24,B_27_25,B_27_26,B_27_27,B_27_28,B_27_29,B_27_30,B_27_31],[B_28_1,B_28_2,B_28_3,B_28_4,B_28_5,B_28_6,B_28_7,B_28_8,B_28_9,B_28_10,B_28_11,B_28_12,B_28_13,B_28_14,B_28_15,B_28_16,B_28_17,B_28_18,B_28_19,B_28_20,B_28_21,B_28_22,B_28_23,B_28_24,B_28_25,B_28_26,B_28_27,B_28_28,B_28_29,B_28_30,B_28_31]]),Matrix(31, 25, [[C_1_1,C_1_2,C_1_3,C_1_4,C_1_5,C_1_6,C_1_7,C_1_8,C_1_9,C_1_10,C_1_11,C_1_12,C_1_13,C_1_14,C_1_15,C_1_16,C_1_17,C_1_18,C_1_19,C_1_20,C_1_21,C_1_22,C_1_23,C_1_24,C_1_25],[C_2_1,C_2_2,C_2_3,C_2_4,C_2_5,C_2_6,C_2_7,C_2_8,C_2_9,C_2_10,C_2_11,C_2_12,C_2_13,C_2_14,C_2_15,C_2_16,C_2_17,C_2_18,C_2_19,C_2_20,C_2_21,C_2_22,C_2_23,C_2_24,C_2_25],[C_3_1,C_3_2,C_3_3,C_3_4,C_3_5,C_3_6,C_3_7,C_3_8,C_3_9,C_3_10,C_3_11,C_3_12,C_3_13,C_3_14,C_3_15,C_3_16,C_3_17,C_3_18,C_3_19,C_3_20,C_3_21,C_3_22,C_3_23,C_3_24,C_3_25],[C_4_1,C_4_2,C_4_3,C_4_4,C_4_5,C_4_6,C_4_7,C_4_8,C_4_9,C_4_10,C_4_11,C_4_12,C_4_13,C_4_14,C_4_15,C_4_16,C_4_17,C_4_18,C_4_19,C_4_20,C_4_21,C_4_22,C_4_23,C_4_24,C_4_25],[C_5_1,C_5_2,C_5_3,C_5_4,C_5_5,C_5_6,C_5_7,C_5_8,C_5_9,C_5_10,C_5_11,C_5_12,C_5_13,C_5_14,C_5_15,C_5_16,C_5_17,C_5_18,C_5_19,C_5_20,C_5_21,C_5_22,C_5_23,C_5_24,C_5_25],[C_6_1,C_6_2,C_6_3,C_6_4,C_6_5,C_6_6,C_6_7,C_6_8,C_6_9,C_6_10,C_6_11,C_6_12,C_6_13,C_6_14,C_6_15,C_6_16,C_6_17,C_6_18,C_6_19,C_6_20,C_6_21,C_6_22,C_6_23,C_6_24,C_6_25],[C_7_1,C_7_2,C_7_3,C_7_4,C_7_5,C_7_6,C_7_7,C_7_8,C_7_9,C_7_10,C_7_11,C_7_12,C_7_13,C_7_14,C_7_15,C_7_16,C_7_17,C_7_18,C_7_19,C_7_20,C_7_21,C_7_22,C_7_23,C_7_24,C_7_25],[C_8_1,C_8_2,C_8_3,C_8_4,C_8_5,C_8_6,C_8_7,C_8_8,C_8_9,C_8_10,C_8_11,C_8_12,C_8_13,C_8_14,C_8_15,C_8_16,C_8_17,C_8_18,C_8_19,C_8_20,C_8_21,C_8_22,C_8_23,C_8_24,C_8_25],[C_9_1,C_9_2,C_9_3,C_9_4,C_9_5,C_9_6,C_9_7,C_9_8,C_9_9,C_9_10,C_9_11,C_9_12,C_9_13,C_9_14,C_9_15,C_9_16,C_9_17,C_9_18,C_9_19,C_9_20,C_9_21,C_9_22,C_9_23,C_9_24,C_9_25],[C_10_1,C_10_2,C_10_3,C_10_4,C_10_5,C_10_6,C_10_7,C_10_8,C_10_9,C_10_10,C_10_11,C_10_12,C_10_13,C_10_14,C_10_15,C_10_16,C_10_17,C_10_18,C_10_19,C_10_20,C_10_21,C_10_22,C_10_23,C_10_24,C_10_25],[C_11_1,C_11_2,C_11_3,C_11_4,C_11_5,C_11_6,C_11_7,C_11_8,C_11_9,C_11_10,C_11_11,C_11_12,C_11_13,C_11_14,C_11_15,C_11_16,C_11_17,C_11_18,C_11_19,C_11_20,C_11_21,C_11_22,C_11_23,C_11_24,C_11_25],[C_12_1,C_12_2,C_12_3,C_12_4,C_12_5,C_12_6,C_12_7,C_12_8,C_12_9,C_12_10,C_12_11,C_12_12,C_12_13,C_12_14,C_12_15,C_12_16,C_12_17,C_12_18,C_12_19,C_12_20,C_12_21,C_12_22,C_12_23,C_12_24,C_12_25],[C_13_1,C_13_2,C_13_3,C_13_4,C_13_5,C_13_6,C_13_7,C_13_8,C_13_9,C_13_10,C_13_11,C_13_12,C_13_13,C_13_14,C_13_15,C_13_16,C_13_17,C_13_18,C_13_19,C_13_20,C_13_21,C_13_22,C_13_23,C_13_24,C_13_25],[C_14_1,C_14_2,C_14_3,C_14_4,C_14_5,C_14_6,C_14_7,C_14_8,C_14_9,C_14_10,C_14_11,C_14_12,C_14_13,C_14_14,C_14_15,C_14_16,C_14_17,C_14_18,C_14_19,C_14_20,C_14_21,C_14_22,C_14_23,C_14_24,C_14_25],[C_15_1,C_15_2,C_15_3,C_15_4,C_15_5,C_15_6,C_15_7,C_15_8,C_15_9,C_15_10,C_15_11,C_15_12,C_15_13,C_15_14,C_15_15,C_15_16,C_15_17,C_15_18,C_15_19,C_15_20,C_15_21,C_15_22,C_15_23,C_15_24,C_15_25],[C_16_1,C_16_2,C_16_3,C_16_4,C_16_5,C_16_6,C_16_7,C_16_8,C_16_9,C_16_10,C_16_11,C_16_12,C_16_13,C_16_14,C_16_15,C_16_16,C_16_17,C_16_18,C_16_19,C_16_20,C_16_21,C_16_22,C_16_23,C_16_24,C_16_25],[C_17_1,C_17_2,C_17_3,C_17_4,C_17_5,C_17_6,C_17_7,C_17_8,C_17_9,C_17_10,C_17_11,C_17_12,C_17_13,C_17_14,C_17_15,C_17_16,C_17_17,C_17_18,C_17_19,C_17_20,C_17_21,C_17_22,C_17_23,C_17_24,C_17_25],[C_18_1,C_18_2,C_18_3,C_18_4,C_18_5,C_18_6,C_18_7,C_18_8,C_18_9,C_18_10,C_18_11,C_18_12,C_18_13,C_18_14,C_18_15,C_18_16,C_18_17,C_18_18,C_18_19,C_18_20,C_18_21,C_18_22,C_18_23,C_18_24,C_18_25],[C_19_1,C_19_2,C_19_3,C_19_4,C_19_5,C_19_6,C_19_7,C_19_8,C_19_9,C_19_10,C_19_11,C_19_12,C_19_13,C_19_14,C_19_15,C_19_16,C_19_17,C_19_18,C_19_19,C_19_20,C_19_21,C_19_22,C_19_23,C_19_24,C_19_25],[C_20_1,C_20_2,C_20_3,C_20_4,C_20_5,C_20_6,C_20_7,C_20_8,C_20_9,C_20_10,C_20_11,C_20_12,C_20_13,C_20_14,C_20_15,C_20_16,C_20_17,C_20_18,C_20_19,C_20_20,C_20_21,C_20_22,C_20_23,C_20_24,C_20_25],[C_21_1,C_21_2,C_21_3,C_21_4,C_21_5,C_21_6,C_21_7,C_21_8,C_21_9,C_21_10,C_21_11,C_21_12,C_21_13,C_21_14,C_21_15,C_21_16,C_21_17,C_21_18,C_21_19,C_21_20,C_21_21,C_21_22,C_21_23,C_21_24,C_21_25],[C_22_1,C_22_2,C_22_3,C_22_4,C_22_5,C_22_6,C_22_7,C_22_8,C_22_9,C_22_10,C_22_11,C_22_12,C_22_13,C_22_14,C_22_15,C_22_16,C_22_17,C_22_18,C_22_19,C_22_20,C_22_21,C_22_22,C_22_23,C_22_24,C_22_25],[C_23_1,C_23_2,C_23_3,C_23_4,C_23_5,C_23_6,C_23_7,C_23_8,C_23_9,C_23_10,C_23_11,C_23_12,C_23_13,C_23_14,C_23_15,C_23_16,C_23_17,C_23_18,C_23_19,C_23_20,C_23_21,C_23_22,C_23_23,C_23_24,C_23_25],[C_24_1,C_24_2,C_24_3,C_24_4,C_24_5,C_24_6,C_24_7,C_24_8,C_24_9,C_24_10,C_24_11,C_24_12,C_24_13,C_24_14,C_24_15,C_24_16,C_24_17,C_24_18,C_24_19,C_24_20,C_24_21,C_24_22,C_24_23,C_24_24,C_24_25],[C_25_1,C_25_2,C_25_3,C_25_4,C_25_5,C_25_6,C_25_7,C_25_8,C_25_9,C_25_10,C_25_11,C_25_12,C_25_13,C_25_14,C_25_15,C_25_16,C_25_17,C_25_18,C_25_19,C_25_20,C_25_21,C_25_22,C_25_23,C_25_24,C_25_25],[C_26_1,C_26_2,C_26_3,C_26_4,C_26_5,C_26_6,C_26_7,C_26_8,C_26_9,C_26_10,C_26_11,C_26_12,C_26_13,C_26_14,C_26_15,C_26_16,C_26_17,C_26_18,C_26_19,C_26_20,C_26_21,C_26_22,C_26_23,C_26_24,C_26_25],[C_27_1,C_27_2,C_27_3,C_27_4,C_27_5,C_27_6,C_27_7,C_27_8,C_27_9,C_27_10,C_27_11,C_27_12,C_27_13,C_27_14,C_27_15,C_27_16,C_27_17,C_27_18,C_27_19,C_27_20,C_27_21,C_27_22,C_27_23,C_27_24,C_27_25],[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_28_14,C_28_15,C_28_16,C_28_17,C_28_18,C_28_19,C_28_20,C_28_21,C_28_22,C_28_23,C_28_24,C_28_25],[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_29_14,C_29_15,C_29_16,C_29_17,C_29_18,C_29_19,C_29_20,C_29_21,C_29_22,C_29_23,C_29_24,C_29_25],[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,C_30_14,C_30_15,C_30_16,C_30_17,C_30_18,C_30_19,C_30_20,C_30_21,C_30_22,C_30_23,C_30_24,C_30_25],[C_31_1,C_31_2,C_31_3,C_31_4,C_31_5,C_31_6,C_31_7,C_31_8,C_31_9,C_31_10,C_31_11,C_31_12,C_31_13,C_31_14,C_31_15,C_31_16,C_31_17,C_31_18,C_31_19,C_31_20,C_31_21,C_31_22,C_31_23,C_31_24,C_31_25]]))) = Trace(Mul(Matrix(25, 28, [[A_1_1,A_1_2,A_1_3,A_1_4,A_1_5,A_1_6,A_1_7,A_1_8,A_1_9,A_1_10,A_1_11,A_1_12,A_1_13,A_1_14,A_1_15,A_1_16,A_1_17,A_1_18,A_1_19,A_1_20,A_1_21,A_1_22,A_1_23,A_1_24,A_1_25,A_1_26,A_1_27,A_1_28],[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6,A_2_7,A_2_8,A_2_9,A_2_10,A_2_11,A_2_12,A_2_13,A_2_14,A_2_15,A_2_16,A_2_17,A_2_18,A_2_19,A_2_20,A_2_21,A_2_22,A_2_23,A_2_24,A_2_25,A_2_26,A_2_27,A_2_28],[A_3_1,A_3_2,A_3_3,A_3_4,A_3_5,A_3_6,A_3_7,A_3_8,A_3_9,A_3_10,A_3_11,A_3_12,A_3_13,A_3_14,A_3_15,A_3_16,A_3_17,A_3_18,A_3_19,A_3_20,A_3_21,A_3_22,A_3_23,A_3_24,A_3_25,A_3_26,A_3_27,A_3_28],[A_4_1,A_4_2,A_4_3,A_4_4,A_4_5,A_4_6,A_4_7,A_4_8,A_4_9,A_4_10,A_4_11,A_4_12,A_4_13,A_4_14,A_4_15,A_4_16,A_4_17,A_4_18,A_4_19,A_4_20,A_4_21,A_4_22,A_4_23,A_4_24,A_4_25,A_4_26,A_4_27,A_4_28],[A_5_1,A_5_2,A_5_3,A_5_4,A_5_5,A_5_6,A_5_7,A_5_8,A_5_9,A_5_10,A_5_11,A_5_12,A_5_13,A_5_14,A_5_15,A_5_16,A_5_17,A_5_18,A_5_19,A_5_20,A_5_21,A_5_22,A_5_23,A_5_24,A_5_25,A_5_26,A_5_27,A_5_28],[A_6_1,A_6_2,A_6_3,A_6_4,A_6_5,A_6_6,A_6_7,A_6_8,A_6_9,A_6_10,A_6_11,A_6_12,A_6_13,A_6_14,A_6_15,A_6_16,A_6_17,A_6_18,A_6_19,A_6_20,A_6_21,A_6_22,A_6_23,A_6_24,A_6_25,A_6_26,A_6_27,A_6_28],[A_7_1,A_7_2,A_7_3,A_7_4,A_7_5,A_7_6,A_7_7,A_7_8,A_7_9,A_7_10,A_7_11,A_7_12,A_7_13,A_7_14,A_7_15,A_7_16,A_7_17,A_7_18,A_7_19,A_7_20,A_7_21,A_7_22,A_7_23,A_7_24,A_7_25,A_7_26,A_7_27,A_7_28],[A_8_1,A_8_2,A_8_3,A_8_4,A_8_5,A_8_6,A_8_7,A_8_8,A_8_9,A_8_10,A_8_11,A_8_12,A_8_13,A_8_14,A_8_15,A_8_16,A_8_17,A_8_18,A_8_19,A_8_20,A_8_21,A_8_22,A_8_23,A_8_24,A_8_25,A_8_26,A_8_27,A_8_28],[A_9_1,A_9_2,A_9_3,A_9_4,A_9_5,A_9_6,A_9_7,A_9_8,A_9_9,A_9_10,A_9_11,A_9_12,A_9_13,A_9_14,A_9_15,A_9_16,A_9_17,A_9_18,A_9_19,A_9_20,A_9_21,A_9_22,A_9_23,A_9_24,A_9_25,A_9_26,A_9_27,A_9_28],[A_10_1,A_10_2,A_10_3,A_10_4,A_10_5,A_10_6,A_10_7,A_10_8,A_10_9,A_10_10,A_10_11,A_10_12,A_10_13,A_10_14,A_10_15,A_10_16,A_10_17,A_10_18,A_10_19,A_10_20,A_10_21,A_10_22,A_10_23,A_10_24,A_10_25,A_10_26,A_10_27,A_10_28],[A_11_1,A_11_2,A_11_3,A_11_4,A_11_5,A_11_6,A_11_7,A_11_8,A_11_9,A_11_10,A_11_11,A_11_12,A_11_13,A_11_14,A_11_15,A_11_16,A_11_17,A_11_18,A_11_19,A_11_20,A_11_21,A_11_22,A_11_23,A_11_24,A_11_25,A_11_26,A_11_27,A_11_28],[A_12_1,A_12_2,A_12_3,A_12_4,A_12_5,A_12_6,A_12_7,A_12_8,A_12_9,A_12_10,A_12_11,A_12_12,A_12_13,A_12_14,A_12_15,A_12_16,A_12_17,A_12_18,A_12_19,A_12_20,A_12_21,A_12_22,A_12_23,A_12_24,A_12_25,A_12_26,A_12_27,A_12_28],[A_13_1,A_13_2,A_13_3,A_13_4,A_13_5,A_13_6,A_13_7,A_13_8,A_13_9,A_13_10,A_13_11,A_13_12,A_13_13,A_13_14,A_13_15,A_13_16,A_13_17,A_13_18,A_13_19,A_13_20,A_13_21,A_13_22,A_13_23,A_13_24,A_13_25,A_13_26,A_13_27,A_13_28],[A_14_1,A_14_2,A_14_3,A_14_4,A_14_5,A_14_6,A_14_7,A_14_8,A_14_9,A_14_10,A_14_11,A_14_12,A_14_13,A_14_14,A_14_15,A_14_16,A_14_17,A_14_18,A_14_19,A_14_20,A_14_21,A_14_22,A_14_23,A_14_24,A_14_25,A_14_26,A_14_27,A_14_28],[A_15_1,A_15_2,A_15_3,A_15_4,A_15_5,A_15_6,A_15_7,A_15_8,A_15_9,A_15_10,A_15_11,A_15_12,A_15_13,A_15_14,A_15_15,A_15_16,A_15_17,A_15_18,A_15_19,A_15_20,A_15_21,A_15_22,A_15_23,A_15_24,A_15_25,A_15_26,A_15_27,A_15_28],[A_16_1,A_16_2,A_16_3,A_16_4,A_16_5,A_16_6,A_16_7,A_16_8,A_16_9,A_16_10,A_16_11,A_16_12,A_16_13,A_16_14,A_16_15,A_16_16,A_16_17,A_16_18,A_16_19,A_16_20,A_16_21,A_16_22,A_16_23,A_16_24,A_16_25,A_16_26,A_16_27,A_16_28],[A_17_1,A_17_2,A_17_3,A_17_4,A_17_5,A_17_6,A_17_7,A_17_8,A_17_9,A_17_10,A_17_11,A_17_12,A_17_13,A_17_14,A_17_15,A_17_16,A_17_17,A_17_18,A_17_19,A_17_20,A_17_21,A_17_22,A_17_23,A_17_24,A_17_25,A_17_26,A_17_27,A_17_28],[A_18_1,A_18_2,A_18_3,A_18_4,A_18_5,A_18_6,A_18_7,A_18_8,A_18_9,A_18_10,A_18_11,A_18_12,A_18_13,A_18_14,A_18_15,A_18_16,A_18_17,A_18_18,A_18_19,A_18_20,A_18_21,A_18_22,A_18_23,A_18_24,A_18_25,A_18_26,A_18_27,A_18_28],[A_19_1,A_19_2,A_19_3,A_19_4,A_19_5,A_19_6,A_19_7,A_19_8,A_19_9,A_19_10,A_19_11,A_19_12,A_19_13,A_19_14,A_19_15,A_19_16,A_19_17,A_19_18,A_19_19,A_19_20,A_19_21,A_19_22,A_19_23,A_19_24,A_19_25,A_19_26,A_19_27,A_19_28],[A_20_1,A_20_2,A_20_3,A_20_4,A_20_5,A_20_6,A_20_7,A_20_8,A_20_9,A_20_10,A_20_11,A_20_12,A_20_13,A_20_14,A_20_15,A_20_16,A_20_17,A_20_18,A_20_19,A_20_20,A_20_21,A_20_22,A_20_23,A_20_24,A_20_25,A_20_26,A_20_27,A_20_28],[A_21_1,A_21_2,A_21_3,A_21_4,A_21_5,A_21_6,A_21_7,A_21_8,A_21_9,A_21_10,A_21_11,A_21_12,A_21_13,A_21_14,A_21_15,A_21_16,A_21_17,A_21_18,A_21_19,A_21_20,A_21_21,A_21_22,A_21_23,A_21_24,A_21_25,A_21_26,A_21_27,A_21_28],[A_22_1,A_22_2,A_22_3,A_22_4,A_22_5,A_22_6,A_22_7,A_22_8,A_22_9,A_22_10,A_22_11,A_22_12,A_22_13,A_22_14,A_22_15,A_22_16,A_22_17,A_22_18,A_22_19,A_22_20,A_22_21,A_22_22,A_22_23,A_22_24,A_22_25,A_22_26,A_22_27,A_22_28],[A_23_1,A_23_2,A_23_3,A_23_4,A_23_5,A_23_6,A_23_7,A_23_8,A_23_9,A_23_10,A_23_11,A_23_12,A_23_13,A_23_14,A_23_15,A_23_16,A_23_17,A_23_18,A_23_19,A_23_20,A_23_21,A_23_22,A_23_23,A_23_24,A_23_25,A_23_26,A_23_27,A_23_28],[A_24_1,A_24_2,A_24_3,A_24_4,A_24_5,A_24_6,A_24_7,A_24_8,A_24_9,A_24_10,A_24_11,A_24_12,A_24_13,A_24_14,A_24_15,A_24_16,A_24_17,A_24_18,A_24_19,A_24_20,A_24_21,A_24_22,A_24_23,A_24_24,A_24_25,A_24_26,A_24_27,A_24_28],[A_25_1,A_25_2,A_25_3,A_25_4,A_25_5,A_25_6,A_25_7,A_25_8,A_25_9,A_25_10,A_25_11,A_25_12,A_25_13,A_25_14,A_25_15,A_25_16,A_25_17,A_25_18,A_25_19,A_25_20,A_25_21,A_25_22,A_25_23,A_25_24,A_25_25,A_25_26,A_25_27,A_25_28]]),Matrix(28, 3, [[B_1_1,B_1_2,B_1_3],[B_2_1,B_2_2,B_2_3],[B_3_1,B_3_2,B_3_3],[B_4_1,B_4_2,B_4_3],[B_5_1,B_5_2,B_5_3],[B_6_1,B_6_2,B_6_3],[B_7_1,B_7_2,B_7_3],[B_8_1,B_8_2,B_8_3],[B_9_1,B_9_2,B_9_3],[B_10_1,B_10_2,B_10_3],[B_11_1,B_11_2,B_11_3],[B_12_1,B_12_2,B_12_3],[B_13_1,B_13_2,B_13_3],[B_14_1,B_14_2,B_14_3],[B_15_1,B_15_2,B_15_3],[B_16_1,B_16_2,B_16_3],[B_17_1,B_17_2,B_17_3],[B_18_1,B_18_2,B_18_3],[B_19_1,B_19_2,B_19_3],[B_20_1,B_20_2,B_20_3],[B_21_1,B_21_2,B_21_3],[B_22_1,B_22_2,B_22_3],[B_23_1,B_23_2,B_23_3],[B_24_1,B_24_2,B_24_3],[B_25_1,B_25_2,B_25_3],[B_26_1,B_26_2,B_26_3],[B_27_1,B_27_2,B_27_3],[B_28_1,B_28_2,B_28_3]]),Matrix(3, 25, [[C_1_1,C_1_2,C_1_3,C_1_4,C_1_5,C_1_6,C_1_7,C_1_8,C_1_9,C_1_10,C_1_11,C_1_12,C_1_13,C_1_14,C_1_15,C_1_16,C_1_17,C_1_18,C_1_19,C_1_20,C_1_21,C_1_22,C_1_23,C_1_24,C_1_25],[C_2_1,C_2_2,C_2_3,C_2_4,C_2_5,C_2_6,C_2_7,C_2_8,C_2_9,C_2_10,C_2_11,C_2_12,C_2_13,C_2_14,C_2_15,C_2_16,C_2_17,C_2_18,C_2_19,C_2_20,C_2_21,C_2_22,C_2_23,C_2_24,C_2_25],[C_3_1,C_3_2,C_3_3,C_3_4,C_3_5,C_3_6,C_3_7,C_3_8,C_3_9,C_3_10,C_3_11,C_3_12,C_3_13,C_3_14,C_3_15,C_3_16,C_3_17,C_3_18,C_3_19,C_3_20,C_3_21,C_3_22,C_3_23,C_3_24,C_3_25]])))+Trace(Mul(Matrix(25, 28, [[A_1_1,A_1_2,A_1_3,A_1_4,A_1_5,A_1_6,A_1_7,A_1_8,A_1_9,A_1_10,A_1_11,A_1_12,A_1_13,A_1_14,A_1_15,A_1_16,A_1_17,A_1_18,A_1_19,A_1_20,A_1_21,A_1_22,A_1_23,A_1_24,A_1_25,A_1_26,A_1_27,A_1_28],[A_2_1,A_2_2,A_2_3,A_2_4,A_2_5,A_2_6,A_2_7,A_2_8,A_2_9,A_2_10,A_2_11,A_2_12,A_2_13,A_2_14,A_2_15,A_2_16,A_2_17,A_2_18,A_2_19,A_2_20,A_2_21,A_2_22,A_2_23,A_2_24,A_2_25,A_2_26,A_2_27,A_2_28],[A_3_1,A_3_2,A_3_3,A_3_4,A_3_5,A_3_6,A_3_7,A_3_8,A_3_9,A_3_10,A_3_11,A_3_12,A_3_13,A_3_14,A_3_15,A_3_16,A_3_17,A_3_18,A_3_19,A_3_20,A_3_21,A_3_22,A_3_23,A_3_24,A_3_25,A_3_26,A_3_27,A_3_28],[A_4_1,A_4_2,A_4_3,A_4_4,A_4_5,A_4_6,A_4_7,A_4_8,A_4_9,A_4_10,A_4_11,A_4_12,A_4_13,A_4_14,A_4_15,A_4_16,A_4_17,A_4_18,A_4_19,A_4_20,A_4_21,A_4_22,A_4_23,A_4_24,A_4_25,A_4_26,A_4_27,A_4_28],[A_5_1,A_5_2,A_5_3,A_5_4,A_5_5,A_5_6,A_5_7,A_5_8,A_5_9,A_5_10,A_5_11,A_5_12,A_5_13,A_5_14,A_5_15,A_5_16,A_5_17,A_5_18,A_5_19,A_5_20,A_5_21,A_5_22,A_5_23,A_5_24,A_5_25,A_5_26,A_5_27,A_5_28],[A_6_1,A_6_2,A_6_3,A_6_4,A_6_5,A_6_6,A_6_7,A_6_8,A_6_9,A_6_10,A_6_11,A_6_12,A_6_13,A_6_14,A_6_15,A_6_16,A_6_17,A_6_18,A_6_19,A_6_20,A_6_21,A_6_22,A_6_23,A_6_24,A_6_25,A_6_26,A_6_27,A_6_28],[A_7_1,A_7_2,A_7_3,A_7_4,A_7_5,A_7_6,A_7_7,A_7_8,A_7_9,A_7_10,A_7_11,A_7_12,A_7_13,A_7_14,A_7_15,A_7_16,A_7_17,A_7_18,A_7_19,A_7_20,A_7_21,A_7_22,A_7_23,A_7_24,A_7_25,A_7_26,A_7_27,A_7_28],[A_8_1,A_8_2,A_8_3,A_8_4,A_8_5,A_8_6,A_8_7,A_8_8,A_8_9,A_8_10,A_8_11,A_8_12,A_8_13,A_8_14,A_8_15,A_8_16,A_8_17,A_8_18,A_8_19,A_8_20,A_8_21,A_8_22,A_8_23,A_8_24,A_8_25,A_8_26,A_8_27,A_8_28],[A_9_1,A_9_2,A_9_3,A_9_4,A_9_5,A_9_6,A_9_7,A_9_8,A_9_9,A_9_10,A_9_11,A_9_12,A_9_13,A_9_14,A_9_15,A_9_16,A_9_17,A_9_18,A_9_19,A_9_20,A_9_21,A_9_22,A_9_23,A_9_24,A_9_25,A_9_26,A_9_27,A_9_28],[A_10_1,A_10_2,A_10_3,A_10_4,A_10_5,A_10_6,A_10_7,A_10_8,A_10_9,A_10_10,A_10_11,A_10_12,A_10_13,A_10_14,A_10_15,A_10_16,A_10_17,A_10_18,A_10_19,A_10_20,A_10_21,A_10_22,A_10_23,A_10_24,A_10_25,A_10_26,A_10_27,A_10_28],[A_11_1,A_11_2,A_11_3,A_11_4,A_11_5,A_11_6,A_11_7,A_11_8,A_11_9,A_11_10,A_11_11,A_11_12,A_11_13,A_11_14,A_11_15,A_11_16,A_11_17,A_11_18,A_11_19,A_11_20,A_11_21,A_11_22,A_11_23,A_11_24,A_11_25,A_11_26,A_11_27,A_11_28],[A_12_1,A_12_2,A_12_3,A_12_4,A_12_5,A_12_6,A_12_7,A_12_8,A_12_9,A_12_10,A_12_11,A_12_12,A_12_13,A_12_14,A_12_15,A_12_16,A_12_17,A_12_18,A_12_19,A_12_20,A_12_21,A_12_22,A_12_23,A_12_24,A_12_25,A_12_26,A_12_27,A_12_28],[A_13_1,A_13_2,A_13_3,A_13_4,A_13_5,A_13_6,A_13_7,A_13_8,A_13_9,A_13_10,A_13_11,A_13_12,A_13_13,A_13_14,A_13_15,A_13_16,A_13_17,A_13_18,A_13_19,A_13_20,A_13_21,A_13_22,A_13_23,A_13_24,A_13_25,A_13_26,A_13_27,A_13_28],[A_14_1,A_14_2,A_14_3,A_14_4,A_14_5,A_14_6,A_14_7,A_14_8,A_14_9,A_14_10,A_14_11,A_14_12,A_14_13,A_14_14,A_14_15,A_14_16,A_14_17,A_14_18,A_14_19,A_14_20,A_14_21,A_14_22,A_14_23,A_14_24,A_14_25,A_14_26,A_14_27,A_14_28],[A_15_1,A_15_2,A_15_3,A_15_4,A_15_5,A_15_6,A_15_7,A_15_8,A_15_9,A_15_10,A_15_11,A_15_12,A_15_13,A_15_14,A_15_15,A_15_16,A_15_17,A_15_18,A_15_19,A_15_20,A_15_21,A_15_22,A_15_23,A_15_24,A_15_25,A_15_26,A_15_27,A_15_28],[A_16_1,A_16_2,A_16_3,A_16_4,A_16_5,A_16_6,A_16_7,A_16_8,A_16_9,A_16_10,A_16_11,A_16_12,A_16_13,A_16_14,A_16_15,A_16_16,A_16_17,A_16_18,A_16_19,A_16_20,A_16_21,A_16_22,A_16_23,A_16_24,A_16_25,A_16_26,A_16_27,A_16_28],[A_17_1,A_17_2,A_17_3,A_17_4,A_17_5,A_17_6,A_17_7,A_17_8,A_17_9,A_17_10,A_17_11,A_17_12,A_17_13,A_17_14,A_17_15,A_17_16,A_17_17,A_17_18,A_17_19,A_17_20,A_17_21,A_17_22,A_17_23,A_17_24,A_17_25,A_17_26,A_17_27,A_17_28],[A_18_1,A_18_2,A_18_3,A_18_4,A_18_5,A_18_6,A_18_7,A_18_8,A_18_9,A_18_10,A_18_11,A_18_12,A_18_13,A_18_14,A_18_15,A_18_16,A_18_17,A_18_18,A_18_19,A_18_20,A_18_21,A_18_22,A_18_23,A_18_24,A_18_25,A_18_26,A_18_27,A_18_28],[A_19_1,A_19_2,A_19_3,A_19_4,A_19_5,A_19_6,A_19_7,A_19_8,A_19_9,A_19_10,A_19_11,A_19_12,A_19_13,A_19_14,A_19_15,A_19_16,A_19_17,A_19_18,A_19_19,A_19_20,A_19_21,A_19_22,A_19_23,A_19_24,A_19_25,A_19_26,A_19_27,A_19_28],[A_20_1,A_20_2,A_20_3,A_20_4,A_20_5,A_20_6,A_20_7,A_20_8,A_20_9,A_20_10,A_20_11,A_20_12,A_20_13,A_20_14,A_20_15,A_20_16,A_20_17,A_20_18,A_20_19,A_20_20,A_20_21,A_20_22,A_20_23,A_20_24,A_20_25,A_20_26,A_20_27,A_20_28],[A_21_1,A_21_2,A_21_3,A_21_4,A_21_5,A_21_6,A_21_7,A_21_8,A_21_9,A_21_10,A_21_11,A_21_12,A_21_13,A_21_14,A_21_15,A_21_16,A_21_17,A_21_18,A_21_19,A_21_20,A_21_21,A_21_22,A_21_23,A_21_24,A_21_25,A_21_26,A_21_27,A_21_28],[A_22_1,A_22_2,A_22_3,A_22_4,A_22_5,A_22_6,A_22_7,A_22_8,A_22_9,A_22_10,A_22_11,A_22_12,A_22_13,A_22_14,A_22_15,A_22_16,A_22_17,A_22_18,A_22_19,A_22_20,A_22_21,A_22_22,A_22_23,A_22_24,A_22_25,A_22_26,A_22_27,A_22_28],[A_23_1,A_23_2,A_23_3,A_23_4,A_23_5,A_23_6,A_23_7,A_23_8,A_23_9,A_23_10,A_23_11,A_23_12,A_23_13,A_23_14,A_23_15,A_23_16,A_23_17,A_23_18,A_23_19,A_23_20,A_23_21,A_23_22,A_23_23,A_23_24,A_23_25,A_23_26,A_23_27,A_23_28],[A_24_1,A_24_2,A_24_3,A_24_4,A_24_5,A_24_6,A_24_7,A_24_8,A_24_9,A_24_10,A_24_11,A_24_12,A_24_13,A_24_14,A_24_15,A_24_16,A_24_17,A_24_18,A_24_19,A_24_20,A_24_21,A_24_22,A_24_23,A_24_24,A_24_25,A_24_26,A_24_27,A_24_28],[A_25_1,A_25_2,A_25_3,A_25_4,A_25_5,A_25_6,A_25_7,A_25_8,A_25_9,A_25_10,A_25_11,A_25_12,A_25_13,A_25_14,A_25_15,A_25_16,A_25_17,A_25_18,A_25_19,A_25_20,A_25_21,A_25_22,A_25_23,A_25_24,A_25_25,A_25_26,A_25_27,A_25_28]]),Matrix(28, 28, [[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_1_31],[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_2_31],[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_3_31],[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_4_31],[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_5_31],[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_6_31],[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_7_31],[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_8_31],[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_9_31],[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_10_31],[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_11_31],[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_12_31],[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_13_31],[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_14_31],[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_15_31],[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_16_31],[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_17_31],[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_18_31],[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_19_31],[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_20_31],[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,B_21_31],[B_22_4,B_22_5,B_22_6,B_22_7,B_22_8,B_22_9,B_22_10,B_22_11,B_22_12,B_22_13,B_22_14,B_22_15,B_22_16,B_22_17,B_22_18,B_22_19,B_22_20,B_22_21,B_22_22,B_22_23,B_22_24,B_22_25,B_22_26,B_22_27,B_22_28,B_22_29,B_22_30,B_22_31],[B_23_4,B_23_5,B_23_6,B_23_7,B_23_8,B_23_9,B_23_10,B_23_11,B_23_12,B_23_13,B_23_14,B_23_15,B_23_16,B_23_17,B_23_18,B_23_19,B_23_20,B_23_21,B_23_22,B_23_23,B_23_24,B_23_25,B_23_26,B_23_27,B_23_28,B_23_29,B_23_30,B_23_31],[B_24_4,B_24_5,B_24_6,B_24_7,B_24_8,B_24_9,B_24_10,B_24_11,B_24_12,B_24_13,B_24_14,B_24_15,B_24_16,B_24_17,B_24_18,B_24_19,B_24_20,B_24_21,B_24_22,B_24_23,B_24_24,B_24_25,B_24_26,B_24_27,B_24_28,B_24_29,B_24_30,B_24_31],[B_25_4,B_25_5,B_25_6,B_25_7,B_25_8,B_25_9,B_25_10,B_25_11,B_25_12,B_25_13,B_25_14,B_25_15,B_25_16,B_25_17,B_25_18,B_25_19,B_25_20,B_25_21,B_25_22,B_25_23,B_25_24,B_25_25,B_25_26,B_25_27,B_25_28,B_25_29,B_25_30,B_25_31],[B_26_4,B_26_5,B_26_6,B_26_7,B_26_8,B_26_9,B_26_10,B_26_11,B_26_12,B_26_13,B_26_14,B_26_15,B_26_16,B_26_17,B_26_18,B_26_19,B_26_20,B_26_21,B_26_22,B_26_23,B_26_24,B_26_25,B_26_26,B_26_27,B_26_28,B_26_29,B_26_30,B_26_31],[B_27_4,B_27_5,B_27_6,B_27_7,B_27_8,B_27_9,B_27_10,B_27_11,B_27_12,B_27_13,B_27_14,B_27_15,B_27_16,B_27_17,B_27_18,B_27_19,B_27_20,B_27_21,B_27_22,B_27_23,B_27_24,B_27_25,B_27_26,B_27_27,B_27_28,B_27_29,B_27_30,B_27_31],[B_28_4,B_28_5,B_28_6,B_28_7,B_28_8,B_28_9,B_28_10,B_28_11,B_28_12,B_28_13,B_28_14,B_28_15,B_28_16,B_28_17,B_28_18,B_28_19,B_28_20,B_28_21,B_28_22,B_28_23,B_28_24,B_28_25,B_28_26,B_28_27,B_28_28,B_28_29,B_28_30,B_28_31]]),Matrix(28, 25, [[C_4_1,C_4_2,C_4_3,C_4_4,C_4_5,C_4_6,C_4_7,C_4_8,C_4_9,C_4_10,C_4_11,C_4_12,C_4_13,C_4_14,C_4_15,C_4_16,C_4_17,C_4_18,C_4_19,C_4_20,C_4_21,C_4_22,C_4_23,C_4_24,C_4_25],[C_5_1,C_5_2,C_5_3,C_5_4,C_5_5,C_5_6,C_5_7,C_5_8,C_5_9,C_5_10,C_5_11,C_5_12,C_5_13,C_5_14,C_5_15,C_5_16,C_5_17,C_5_18,C_5_19,C_5_20,C_5_21,C_5_22,C_5_23,C_5_24,C_5_25],[C_6_1,C_6_2,C_6_3,C_6_4,C_6_5,C_6_6,C_6_7,C_6_8,C_6_9,C_6_10,C_6_11,C_6_12,C_6_13,C_6_14,C_6_15,C_6_16,C_6_17,C_6_18,C_6_19,C_6_20,C_6_21,C_6_22,C_6_23,C_6_24,C_6_25],[C_7_1,C_7_2,C_7_3,C_7_4,C_7_5,C_7_6,C_7_7,C_7_8,C_7_9,C_7_10,C_7_11,C_7_12,C_7_13,C_7_14,C_7_15,C_7_16,C_7_17,C_7_18,C_7_19,C_7_20,C_7_21,C_7_22,C_7_23,C_7_24,C_7_25],[C_8_1,C_8_2,C_8_3,C_8_4,C_8_5,C_8_6,C_8_7,C_8_8,C_8_9,C_8_10,C_8_11,C_8_12,C_8_13,C_8_14,C_8_15,C_8_16,C_8_17,C_8_18,C_8_19,C_8_20,C_8_21,C_8_22,C_8_23,C_8_24,C_8_25],[C_9_1,C_9_2,C_9_3,C_9_4,C_9_5,C_9_6,C_9_7,C_9_8,C_9_9,C_9_10,C_9_11,C_9_12,C_9_13,C_9_14,C_9_15,C_9_16,C_9_17,C_9_18,C_9_19,C_9_20,C_9_21,C_9_22,C_9_23,C_9_24,C_9_25],[C_10_1,C_10_2,C_10_3,C_10_4,C_10_5,C_10_6,C_10_7,C_10_8,C_10_9,C_10_10,C_10_11,C_10_12,C_10_13,C_10_14,C_10_15,C_10_16,C_10_17,C_10_18,C_10_19,C_10_20,C_10_21,C_10_22,C_10_23,C_10_24,C_10_25],[C_11_1,C_11_2,C_11_3,C_11_4,C_11_5,C_11_6,C_11_7,C_11_8,C_11_9,C_11_10,C_11_11,C_11_12,C_11_13,C_11_14,C_11_15,C_11_16,C_11_17,C_11_18,C_11_19,C_11_20,C_11_21,C_11_22,C_11_23,C_11_24,C_11_25],[C_12_1,C_12_2,C_12_3,C_12_4,C_12_5,C_12_6,C_12_7,C_12_8,C_12_9,C_12_10,C_12_11,C_12_12,C_12_13,C_12_14,C_12_15,C_12_16,C_12_17,C_12_18,C_12_19,C_12_20,C_12_21,C_12_22,C_12_23,C_12_24,C_12_25],[C_13_1,C_13_2,C_13_3,C_13_4,C_13_5,C_13_6,C_13_7,C_13_8,C_13_9,C_13_10,C_13_11,C_13_12,C_13_13,C_13_14,C_13_15,C_13_16,C_13_17,C_13_18,C_13_19,C_13_20,C_13_21,C_13_22,C_13_23,C_13_24,C_13_25],[C_14_1,C_14_2,C_14_3,C_14_4,C_14_5,C_14_6,C_14_7,C_14_8,C_14_9,C_14_10,C_14_11,C_14_12,C_14_13,C_14_14,C_14_15,C_14_16,C_14_17,C_14_18,C_14_19,C_14_20,C_14_21,C_14_22,C_14_23,C_14_24,C_14_25],[C_15_1,C_15_2,C_15_3,C_15_4,C_15_5,C_15_6,C_15_7,C_15_8,C_15_9,C_15_10,C_15_11,C_15_12,C_15_13,C_15_14,C_15_15,C_15_16,C_15_17,C_15_18,C_15_19,C_15_20,C_15_21,C_15_22,C_15_23,C_15_24,C_15_25],[C_16_1,C_16_2,C_16_3,C_16_4,C_16_5,C_16_6,C_16_7,C_16_8,C_16_9,C_16_10,C_16_11,C_16_12,C_16_13,C_16_14,C_16_15,C_16_16,C_16_17,C_16_18,C_16_19,C_16_20,C_16_21,C_16_22,C_16_23,C_16_24,C_16_25],[C_17_1,C_17_2,C_17_3,C_17_4,C_17_5,C_17_6,C_17_7,C_17_8,C_17_9,C_17_10,C_17_11,C_17_12,C_17_13,C_17_14,C_17_15,C_17_16,C_17_17,C_17_18,C_17_19,C_17_20,C_17_21,C_17_22,C_17_23,C_17_24,C_17_25],[C_18_1,C_18_2,C_18_3,C_18_4,C_18_5,C_18_6,C_18_7,C_18_8,C_18_9,C_18_10,C_18_11,C_18_12,C_18_13,C_18_14,C_18_15,C_18_16,C_18_17,C_18_18,C_18_19,C_18_20,C_18_21,C_18_22,C_18_23,C_18_24,C_18_25],[C_19_1,C_19_2,C_19_3,C_19_4,C_19_5,C_19_6,C_19_7,C_19_8,C_19_9,C_19_10,C_19_11,C_19_12,C_19_13,C_19_14,C_19_15,C_19_16,C_19_17,C_19_18,C_19_19,C_19_20,C_19_21,C_19_22,C_19_23,C_19_24,C_19_25],[C_20_1,C_20_2,C_20_3,C_20_4,C_20_5,C_20_6,C_20_7,C_20_8,C_20_9,C_20_10,C_20_11,C_20_12,C_20_13,C_20_14,C_20_15,C_20_16,C_20_17,C_20_18,C_20_19,C_20_20,C_20_21,C_20_22,C_20_23,C_20_24,C_20_25],[C_21_1,C_21_2,C_21_3,C_21_4,C_21_5,C_21_6,C_21_7,C_21_8,C_21_9,C_21_10,C_21_11,C_21_12,C_21_13,C_21_14,C_21_15,C_21_16,C_21_17,C_21_18,C_21_19,C_21_20,C_21_21,C_21_22,C_21_23,C_21_24,C_21_25],[C_22_1,C_22_2,C_22_3,C_22_4,C_22_5,C_22_6,C_22_7,C_22_8,C_22_9,C_22_10,C_22_11,C_22_12,C_22_13,C_22_14,C_22_15,C_22_16,C_22_17,C_22_18,C_22_19,C_22_20,C_22_21,C_22_22,C_22_23,C_22_24,C_22_25],[C_23_1,C_23_2,C_23_3,C_23_4,C_23_5,C_23_6,C_23_7,C_23_8,C_23_9,C_23_10,C_23_11,C_23_12,C_23_13,C_23_14,C_23_15,C_23_16,C_23_17,C_23_18,C_23_19,C_23_20,C_23_21,C_23_22,C_23_23,C_23_24,C_23_25],[C_24_1,C_24_2,C_24_3,C_24_4,C_24_5,C_24_6,C_24_7,C_24_8,C_24_9,C_24_10,C_24_11,C_24_12,C_24_13,C_24_14,C_24_15,C_24_16,C_24_17,C_24_18,C_24_19,C_24_20,C_24_21,C_24_22,C_24_23,C_24_24,C_24_25],[C_25_1,C_25_2,C_25_3,C_25_4,C_25_5,C_25_6,C_25_7,C_25_8,C_25_9,C_25_10,C_25_11,C_25_12,C_25_13,C_25_14,C_25_15,C_25_16,C_25_17,C_25_18,C_25_19,C_25_20,C_25_21,C_25_22,C_25_23,C_25_24,C_25_25],[C_26_1,C_26_2,C_26_3,C_26_4,C_26_5,C_26_6,C_26_7,C_26_8,C_26_9,C_26_10,C_26_11,C_26_12,C_26_13,C_26_14,C_26_15,C_26_16,C_26_17,C_26_18,C_26_19,C_26_20,C_26_21,C_26_22,C_26_23,C_26_24,C_26_25],[C_27_1,C_27_2,C_27_3,C_27_4,C_27_5,C_27_6,C_27_7,C_27_8,C_27_9,C_27_10,C_27_11,C_27_12,C_27_13,C_27_14,C_27_15,C_27_16,C_27_17,C_27_18,C_27_19,C_27_20,C_27_21,C_27_22,C_27_23,C_27_24,C_27_25],[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_28_14,C_28_15,C_28_16,C_28_17,C_28_18,C_28_19,C_28_20,C_28_21,C_28_22,C_28_23,C_28_24,C_28_25],[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_29_14,C_29_15,C_29_16,C_29_17,C_29_18,C_29_19,C_29_20,C_29_21,C_29_22,C_29_23,C_29_24,C_29_25],[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,C_30_14,C_30_15,C_30_16,C_30_17,C_30_18,C_30_19,C_30_20,C_30_21,C_30_22,C_30_23,C_30_24,C_30_25],[C_31_1,C_31_2,C_31_3,C_31_4,C_31_5,C_31_6,C_31_7,C_31_8,C_31_9,C_31_10,C_31_11,C_31_12,C_31_13,C_31_14,C_31_15,C_31_16,C_31_17,C_31_18,C_31_19,C_31_20,C_31_21,C_31_22,C_31_23,C_31_24,C_31_25]])))

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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