Description of fast matrix multiplication algorithm: ⟨23×24×25:7454⟩

Algorithm type

3080⁢X3⁢Y3⁢Z3+968⁢X3⁢Y3⁢Z+231⁢X3⁢Y2⁢Z2+682⁢X2⁢Y3⁢Z2+231⁢X2⁢Y2⁢Z3+22⁢X3⁢Y2⁢Z+67⁢X2⁢Y3⁢Z+308⁢X2⁢Y2⁢Z2+58⁢X2⁢Y2⁢Z+22⁢X⁢Y3⁢Z+11⁢X⁢Y2⁢Z2+990⁢X⁢Y⁢Z3+24⁢X⁢Y2⁢Z+114⁢X⁢Y⁢Z2+646⁢X⁢Y⁢Z3080X3Y3Z3968X3Y3Z231X3Y2Z2682X2Y3Z2231X2Y2Z322X3Y2Z67X2Y3Z308X2Y2Z258X2Y2Z22XY3Z11XY2Z2990XYZ324XY2Z114XYZ2646XYZ3080*X^3*Y^3*Z^3+968*X^3*Y^3*Z+231*X^3*Y^2*Z^2+682*X^2*Y^3*Z^2+231*X^2*Y^2*Z^3+22*X^3*Y^2*Z+67*X^2*Y^3*Z+308*X^2*Y^2*Z^2+58*X^2*Y^2*Z+22*X*Y^3*Z+11*X*Y^2*Z^2+990*X*Y*Z^3+24*X*Y^2*Z+114*X*Y*Z^2+646*X*Y*Z

Algorithm definition

The algorithm ⟨23×24×25:7454⟩ could be constructed using the following decomposition:

⟨23×24×25:7454⟩ = ⟨23×24×1:552⟩ + ⟨23×24×24:6902⟩.

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_24B_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_20_1B_20_2B_20_3B_20_4B_20_5B_20_6B_20_7B_20_8B_20_9B_20_10B_20_11B_20_12B_20_13B_20_14B_20_15B_20_16B_20_17B_20_18B_20_19B_20_20B_20_21B_20_22B_20_23B_20_24B_20_25B_21_1B_21_2B_21_3B_21_4B_21_5B_21_6B_21_7B_21_8B_21_9B_21_10B_21_11B_21_12B_21_13B_21_14B_21_15B_21_16B_21_17B_21_18B_21_19B_21_20B_21_21B_21_22B_21_23B_21_24B_21_25B_22_1B_22_2B_22_3B_22_4B_22_5B_22_6B_22_7B_22_8B_22_9B_22_10B_22_11B_22_12B_22_13B_22_14B_22_15B_22_16B_22_17B_22_18B_22_19B_22_20B_22_21B_22_22B_22_23B_22_24B_22_25B_23_1B_23_2B_23_3B_23_4B_23_5B_23_6B_23_7B_23_8B_23_9B_23_10B_23_11B_23_12B_23_13B_23_14B_23_15B_23_16B_23_17B_23_18B_23_19B_23_20B_23_21B_23_22B_23_23B_23_24B_23_25B_24_1B_24_2B_24_3B_24_4B_24_5B_24_6B_24_7B_24_8B_24_9B_24_10B_24_11B_24_12B_24_13B_24_14B_24_15B_24_16B_24_17B_24_18B_24_19B_24_20B_24_21B_24_22B_24_23B_24_24B_24_25C_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_1_15C_1_16C_1_17C_1_18C_1_19C_1_20C_1_21C_1_22C_1_23C_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_2_15C_2_16C_2_17C_2_18C_2_19C_2_20C_2_21C_2_22C_2_23C_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_3_15C_3_16C_3_17C_3_18C_3_19C_3_20C_3_21C_3_22C_3_23C_4_1C_4_2C_4_3C_4_4C_4_5C_4_6C_4_7C_4_8C_4_9C_4_10C_4_11C_4_12C_4_13C_4_14C_4_15C_4_16C_4_17C_4_18C_4_19C_4_20C_4_21C_4_22C_4_23C_5_1C_5_2C_5_3C_5_4C_5_5C_5_6C_5_7C_5_8C_5_9C_5_10C_5_11C_5_12C_5_13C_5_14C_5_15C_5_16C_5_17C_5_18C_5_19C_5_20C_5_21C_5_22C_5_23C_6_1C_6_2C_6_3C_6_4C_6_5C_6_6C_6_7C_6_8C_6_9C_6_10C_6_11C_6_12C_6_13C_6_14C_6_15C_6_16C_6_17C_6_18C_6_19C_6_20C_6_21C_6_22C_6_23C_7_1C_7_2C_7_3C_7_4C_7_5C_7_6C_7_7C_7_8C_7_9C_7_10C_7_11C_7_12C_7_13C_7_14C_7_15C_7_16C_7_17C_7_18C_7_19C_7_20C_7_21C_7_22C_7_23C_8_1C_8_2C_8_3C_8_4C_8_5C_8_6C_8_7C_8_8C_8_9C_8_10C_8_11C_8_12C_8_13C_8_14C_8_15C_8_16C_8_17C_8_18C_8_19C_8_20C_8_21C_8_22C_8_23C_9_1C_9_2C_9_3C_9_4C_9_5C_9_6C_9_7C_9_8C_9_9C_9_10C_9_11C_9_12C_9_13C_9_14C_9_15C_9_16C_9_17C_9_18C_9_19C_9_20C_9_21C_9_22C_9_23C_10_1C_10_2C_10_3C_10_4C_10_5C_10_6C_10_7C_10_8C_10_9C_10_10C_10_11C_10_12C_10_13C_10_14C_10_15C_10_16C_10_17C_10_18C_10_19C_10_20C_10_21C_10_22C_10_23C_11_1C_11_2C_11_3C_11_4C_11_5C_11_6C_11_7C_11_8C_11_9C_11_10C_11_11C_11_12C_11_13C_11_14C_11_15C_11_16C_11_17C_11_18C_11_19C_11_20C_11_21C_11_22C_11_23C_12_1C_12_2C_12_3C_12_4C_12_5C_12_6C_12_7C_12_8C_12_9C_12_10C_12_11C_12_12C_12_13C_12_14C_12_15C_12_16C_12_17C_12_18C_12_19C_12_20C_12_21C_12_22C_12_23C_13_1C_13_2C_13_3C_13_4C_13_5C_13_6C_13_7C_13_8C_13_9C_13_10C_13_11C_13_12C_13_13C_13_14C_13_15C_13_16C_13_17C_13_18C_13_19C_13_20C_13_21C_13_22C_13_23C_14_1C_14_2C_14_3C_14_4C_14_5C_14_6C_14_7C_14_8C_14_9C_14_10C_14_11C_14_12C_14_13C_14_14C_14_15C_14_16C_14_17C_14_18C_14_19C_14_20C_14_21C_14_22C_14_23C_15_1C_15_2C_15_3C_15_4C_15_5C_15_6C_15_7C_15_8C_15_9C_15_10C_15_11C_15_12C_15_13C_15_14C_15_15C_15_16C_15_17C_15_18C_15_19C_15_20C_15_21C_15_22C_15_23C_16_1C_16_2C_16_3C_16_4C_16_5C_16_6C_16_7C_16_8C_16_9C_16_10C_16_11C_16_12C_16_13C_16_14C_16_15C_16_16C_16_17C_16_18C_16_19C_16_20C_16_21C_16_22C_16_23C_17_1C_17_2C_17_3C_17_4C_17_5C_17_6C_17_7C_17_8C_17_9C_17_10C_17_11C_17_12C_17_13C_17_14C_17_15C_17_16C_17_17C_17_18C_17_19C_17_20C_17_21C_17_22C_17_23C_18_1C_18_2C_18_3C_18_4C_18_5C_18_6C_18_7C_18_8C_18_9C_18_10C_18_11C_18_12C_18_13C_18_14C_18_15C_18_16C_18_17C_18_18C_18_19C_18_20C_18_21C_18_22C_18_23C_19_1C_19_2C_19_3C_19_4C_19_5C_19_6C_19_7C_19_8C_19_9C_19_10C_19_11C_19_12C_19_13C_19_14C_19_15C_19_16C_19_17C_19_18C_19_19C_19_20C_19_21C_19_22C_19_23C_20_1C_20_2C_20_3C_20_4C_20_5C_20_6C_20_7C_20_8C_20_9C_20_10C_20_11C_20_12C_20_13C_20_14C_20_15C_20_16C_20_17C_20_18C_20_19C_20_20C_20_21C_20_22C_20_23C_21_1C_21_2C_21_3C_21_4C_21_5C_21_6C_21_7C_21_8C_21_9C_21_10C_21_11C_21_12C_21_13C_21_14C_21_15C_21_16C_21_17C_21_18C_21_19C_21_20C_21_21C_21_22C_21_23C_22_1C_22_2C_22_3C_22_4C_22_5C_22_6C_22_7C_22_8C_22_9C_22_10C_22_11C_22_12C_22_13C_22_14C_22_15C_22_16C_22_17C_22_18C_22_19C_22_20C_22_21C_22_22C_22_23C_23_1C_23_2C_23_3C_23_4C_23_5C_23_6C_23_7C_23_8C_23_9C_23_10C_23_11C_23_12C_23_13C_23_14C_23_15C_23_16C_23_17C_23_18C_23_19C_23_20C_23_21C_23_22C_23_23C_24_1C_24_2C_24_3C_24_4C_24_5C_24_6C_24_7C_24_8C_24_9C_24_10C_24_11C_24_12C_24_13C_24_14C_24_15C_24_16C_24_17C_24_18C_24_19C_24_20C_24_21C_24_22C_24_23C_25_1C_25_2C_25_3C_25_4C_25_5C_25_6C_25_7C_25_8C_25_9C_25_10C_25_11C_25_12C_25_13C_25_14C_25_15C_25_16C_25_17C_25_18C_25_19C_25_20C_25_21C_25_22C_25_23=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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_24B_1_1B_2_1B_3_1B_4_1B_5_1B_6_1B_7_1B_8_1B_9_1B_10_1B_11_1B_12_1B_13_1B_14_1B_15_1B_16_1B_17_1B_18_1B_19_1B_20_1B_21_1B_22_1B_23_1B_24_1C_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_1_15C_1_16C_1_17C_1_18C_1_19C_1_20C_1_21C_1_22C_1_23+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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_24B_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_20_2B_20_3B_20_4B_20_5B_20_6B_20_7B_20_8B_20_9B_20_10B_20_11B_20_12B_20_13B_20_14B_20_15B_20_16B_20_17B_20_18B_20_19B_20_20B_20_21B_20_22B_20_23B_20_24B_20_25B_21_2B_21_3B_21_4B_21_5B_21_6B_21_7B_21_8B_21_9B_21_10B_21_11B_21_12B_21_13B_21_14B_21_15B_21_16B_21_17B_21_18B_21_19B_21_20B_21_21B_21_22B_21_23B_21_24B_21_25B_22_2B_22_3B_22_4B_22_5B_22_6B_22_7B_22_8B_22_9B_22_10B_22_11B_22_12B_22_13B_22_14B_22_15B_22_16B_22_17B_22_18B_22_19B_22_20B_22_21B_22_22B_22_23B_22_24B_22_25B_23_2B_23_3B_23_4B_23_5B_23_6B_23_7B_23_8B_23_9B_23_10B_23_11B_23_12B_23_13B_23_14B_23_15B_23_16B_23_17B_23_18B_23_19B_23_20B_23_21B_23_22B_23_23B_23_24B_23_25B_24_2B_24_3B_24_4B_24_5B_24_6B_24_7B_24_8B_24_9B_24_10B_24_11B_24_12B_24_13B_24_14B_24_15B_24_16B_24_17B_24_18B_24_19B_24_20B_24_21B_24_22B_24_23B_24_24B_24_25C_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_2_15C_2_16C_2_17C_2_18C_2_19C_2_20C_2_21C_2_22C_2_23C_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_3_15C_3_16C_3_17C_3_18C_3_19C_3_20C_3_21C_3_22C_3_23C_4_1C_4_2C_4_3C_4_4C_4_5C_4_6C_4_7C_4_8C_4_9C_4_10C_4_11C_4_12C_4_13C_4_14C_4_15C_4_16C_4_17C_4_18C_4_19C_4_20C_4_21C_4_22C_4_23C_5_1C_5_2C_5_3C_5_4C_5_5C_5_6C_5_7C_5_8C_5_9C_5_10C_5_11C_5_12C_5_13C_5_14C_5_15C_5_16C_5_17C_5_18C_5_19C_5_20C_5_21C_5_22C_5_23C_6_1C_6_2C_6_3C_6_4C_6_5C_6_6C_6_7C_6_8C_6_9C_6_10C_6_11C_6_12C_6_13C_6_14C_6_15C_6_16C_6_17C_6_18C_6_19C_6_20C_6_21C_6_22C_6_23C_7_1C_7_2C_7_3C_7_4C_7_5C_7_6C_7_7C_7_8C_7_9C_7_10C_7_11C_7_12C_7_13C_7_14C_7_15C_7_16C_7_17C_7_18C_7_19C_7_20C_7_21C_7_22C_7_23C_8_1C_8_2C_8_3C_8_4C_8_5C_8_6C_8_7C_8_8C_8_9C_8_10C_8_11C_8_12C_8_13C_8_14C_8_15C_8_16C_8_17C_8_18C_8_19C_8_20C_8_21C_8_22C_8_23C_9_1C_9_2C_9_3C_9_4C_9_5C_9_6C_9_7C_9_8C_9_9C_9_10C_9_11C_9_12C_9_13C_9_14C_9_15C_9_16C_9_17C_9_18C_9_19C_9_20C_9_21C_9_22C_9_23C_10_1C_10_2C_10_3C_10_4C_10_5C_10_6C_10_7C_10_8C_10_9C_10_10C_10_11C_10_12C_10_13C_10_14C_10_15C_10_16C_10_17C_10_18C_10_19C_10_20C_10_21C_10_22C_10_23C_11_1C_11_2C_11_3C_11_4C_11_5C_11_6C_11_7C_11_8C_11_9C_11_10C_11_11C_11_12C_11_13C_11_14C_11_15C_11_16C_11_17C_11_18C_11_19C_11_20C_11_21C_11_22C_11_23C_12_1C_12_2C_12_3C_12_4C_12_5C_12_6C_12_7C_12_8C_12_9C_12_10C_12_11C_12_12C_12_13C_12_14C_12_15C_12_16C_12_17C_12_18C_12_19C_12_20C_12_21C_12_22C_12_23C_13_1C_13_2C_13_3C_13_4C_13_5C_13_6C_13_7C_13_8C_13_9C_13_10C_13_11C_13_12C_13_13C_13_14C_13_15C_13_16C_13_17C_13_18C_13_19C_13_20C_13_21C_13_22C_13_23C_14_1C_14_2C_14_3C_14_4C_14_5C_14_6C_14_7C_14_8C_14_9C_14_10C_14_11C_14_12C_14_13C_14_14C_14_15C_14_16C_14_17C_14_18C_14_19C_14_20C_14_21C_14_22C_14_23C_15_1C_15_2C_15_3C_15_4C_15_5C_15_6C_15_7C_15_8C_15_9C_15_10C_15_11C_15_12C_15_13C_15_14C_15_15C_15_16C_15_17C_15_18C_15_19C_15_20C_15_21C_15_22C_15_23C_16_1C_16_2C_16_3C_16_4C_16_5C_16_6C_16_7C_16_8C_16_9C_16_10C_16_11C_16_12C_16_13C_16_14C_16_15C_16_16C_16_17C_16_18C_16_19C_16_20C_16_21C_16_22C_16_23C_17_1C_17_2C_17_3C_17_4C_17_5C_17_6C_17_7C_17_8C_17_9C_17_10C_17_11C_17_12C_17_13C_17_14C_17_15C_17_16C_17_17C_17_18C_17_19C_17_20C_17_21C_17_22C_17_23C_18_1C_18_2C_18_3C_18_4C_18_5C_18_6C_18_7C_18_8C_18_9C_18_10C_18_11C_18_12C_18_13C_18_14C_18_15C_18_16C_18_17C_18_18C_18_19C_18_20C_18_21C_18_22C_18_23C_19_1C_19_2C_19_3C_19_4C_19_5C_19_6C_19_7C_19_8C_19_9C_19_10C_19_11C_19_12C_19_13C_19_14C_19_15C_19_16C_19_17C_19_18C_19_19C_19_20C_19_21C_19_22C_19_23C_20_1C_20_2C_20_3C_20_4C_20_5C_20_6C_20_7C_20_8C_20_9C_20_10C_20_11C_20_12C_20_13C_20_14C_20_15C_20_16C_20_17C_20_18C_20_19C_20_20C_20_21C_20_22C_20_23C_21_1C_21_2C_21_3C_21_4C_21_5C_21_6C_21_7C_21_8C_21_9C_21_10C_21_11C_21_12C_21_13C_21_14C_21_15C_21_16C_21_17C_21_18C_21_19C_21_20C_21_21C_21_22C_21_23C_22_1C_22_2C_22_3C_22_4C_22_5C_22_6C_22_7C_22_8C_22_9C_22_10C_22_11C_22_12C_22_13C_22_14C_22_15C_22_16C_22_17C_22_18C_22_19C_22_20C_22_21C_22_22C_22_23C_23_1C_23_2C_23_3C_23_4C_23_5C_23_6C_23_7C_23_8C_23_9C_23_10C_23_11C_23_12C_23_13C_23_14C_23_15C_23_16C_23_17C_23_18C_23_19C_23_20C_23_21C_23_22C_23_23C_24_1C_24_2C_24_3C_24_4C_24_5C_24_6C_24_7C_24_8C_24_9C_24_10C_24_11C_24_12C_24_13C_24_14C_24_15C_24_16C_24_17C_24_18C_24_19C_24_20C_24_21C_24_22C_24_23C_25_1C_25_2C_25_3C_25_4C_25_5C_25_6C_25_7C_25_8C_25_9C_25_10C_25_11C_25_12C_25_13C_25_14C_25_15C_25_16C_25_17C_25_18C_25_19C_25_20C_25_21C_25_22C_25_23

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.

Back to main table