Description of fast matrix multiplication algorithm: ⟨5×25×28:2285⟩

Algorithm type

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Algorithm definition

The algorithm ⟨5×25×28:2285⟩ could be constructed using the following decomposition:

⟨5×25×28:2285⟩ = ⟨3×5×4:47⟩ + ⟨2×5×4:32⟩ + ⟨2×5×4:32⟩ + ⟨2×5×4:32⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨2×5×4:32⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨2×5×4:32⟩ + ⟨3×5×4:47⟩ + ⟨2×5×4:32⟩ + ⟨2×5×4:32⟩ + ⟨2×5×4:32⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨2×5×4:32⟩ + ⟨3×5×4:47⟩ + ⟨2×5×4:32⟩ + ⟨2×5×4:32⟩ + ⟨3×5×4:47⟩ + ⟨2×5×4:32⟩ + ⟨2×5×4:32⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨2×5×4:32⟩ + ⟨3×5×4:47⟩ + ⟨2×5×4:32⟩ + ⟨2×5×4:32⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨2×5×4:32⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨2×5×4:32⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨3×5×4:47⟩ + ⟨2×5×4:32⟩ + ⟨2×5×4:32⟩.

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_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_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_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_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_25B_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_19_1B_19_2B_19_3B_19_4B_19_5B_19_6B_19_7B_19_8B_19_9B_19_10B_19_11B_19_12B_19_13B_19_14B_19_15B_19_16B_19_17B_19_18B_19_19B_19_20B_19_21B_19_22B_19_23B_19_24B_19_25B_19_26B_19_27B_19_28B_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_20_26B_20_27B_20_28B_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_21_26B_21_27B_21_28B_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_22_26B_22_27B_22_28B_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_23_26B_23_27B_23_28B_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_25B_24_26B_24_27B_24_28B_25_1B_25_2B_25_3B_25_4B_25_5B_25_6B_25_7B_25_8B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⁢B_13_5-B_18_5-B_3_17-B_8_17-B_13_17+B_18_17+3⁢B_3_25+2⁢B_8_25+B_13_25+B_18_254⁢B_3_2+3⁢B_8_2+2⁢B_13_2+5⁢B_3_6+4⁢B_8_6+3⁢B_13_6-B_18_6-B_3_18-B_8_18-B_13_18+B_18_18+3⁢B_3_26+2⁢B_8_26+B_13_26+B_18_264⁢B_3_3+3⁢B_8_3+2⁢B_13_3+5⁢B_3_7+4⁢B_8_7+3⁢B_13_7-B_18_7-B_3_19-B_8_19-B_13_19+B_18_19+3⁢B_3_27+2⁢B_8_27+B_13_27+B_18_274⁢B_3_4+3⁢B_8_4+2⁢B_13_4+5⁢B_3_8+4⁢B_8_8+3⁢B_13_8-B_18_8-B_3_20-B_8_20-B_13_20+B_18_20+3⁢B_3_28+2⁢B_8_28+B_13_28+B_18_284⁢B_4_1+3⁢B_9_1+2⁢B_14_1+5⁢B_4_5+4⁢B_9_5+3⁢B_14_5-B_19_5-B_4_17-B_9_17-B_14_17+B_19_17+3⁢B_4_25+2⁢B_9_25+B_14_25+B_19_254⁢B_4_2+3⁢B_9_2+2⁢B_14_2+5⁢B_4_6+4⁢B_9_6+3⁢B_14_6-B_19_6-B_4_18-B_9_18-B_14_18+B_19_18+3⁢B_4_26+2⁢B_9_26+B_14_26+B_19_264⁢B_4_3+3⁢B_9_3+2⁢B_14_3+5⁢B_4_7+4⁢B_9_7+3⁢B_14_7-B_19_7-B_4_19-B_9_19-B_14_19+B_19_19+3⁢B_4_27+2⁢B_9_27+B_14_27+B_19_274⁢B_4_4+3⁢B_9_4+2⁢B_14_4+5⁢B_4_8+4⁢B_9_8+3⁢B_14_8-B_19_8-B_4_20-B_9_20-B_14_20+B_19_20+3⁢B_4_28+2⁢B_9_28+B_14_28+B_19_284⁢B_5_1+3⁢B_10_1+2⁢B_15_1+5⁢B_5_5+4⁢B_10_5+3⁢B_15_5-B_20_5-B_5_17-B_10_17-B_15_17+B_20_17+3⁢B_5_25+2⁢B_10_25+B_15_25+B_20_254⁢B_5_2+3⁢B_10_2+2⁢B_15_2+5⁢B_5_6+4⁢B_10_6+3⁢B_15_6-B_20_6-B_5_18-B_10_18-B_15_18+B_20_18+3⁢B_5_26+2⁢B_10_26+B_15_26+B_20_264⁢B_5_3+3⁢B_10_3+2⁢B_15_3+5⁢B_5_7+4⁢B_10_7+3⁢B_15_7-B_20_7-B_5_19-B_10_19-B_15_19+B_20_19+3⁢B_5_27+2⁢B_10_27+B_15_27+B_20_274⁢B_5_4+3⁢B_10_4+2⁢B_15_4+5⁢B_5_8+4⁢B_10_8+3⁢B_15_8-B_20_8-B_5_20-B_10_20-B_15_20+B_20_20+3⁢B_5_28+2⁢B_10_28+B_15_28+B_20_28C_25_3-C_17_1+C_21_1+C_25_4-C_17_2+C_21_2+C_25_5C_26_3-C_18_1+C_22_1+C_26_4-C_18_2+C_22_2+C_26_5C_27_3-C_19_1+C_23_1+C_27_4-C_19_2+C_23_2+C_27_5C_28_3-C_20_1+C_24_1+C_28_4-C_20_2+C_24_2+C_28_5+Trace⁡Mul⁡A_1_1-A_1_6-A_1_11-A_1_16A_1_2-A_1_7-A_1_12-A_1_17A_1_3-A_1_8-A_1_13-A_1_18A_1_4-A_1_9-A_1_14-A_1_19-A_1_10+A_1_5-A_1_15-A_1_20A_2_1-A_2_6-A_2_11-A_2_16A_2_2-A_2_7-A_2_12-A_2_17A_2_3-A_2_8-A_2_13-A_2_18A_2_4-A_2_9-A_2_14-A_2_19-A_2_10+A_2_5-A_2_15-A_2_202⁢B_1_1+B_6_1+B_11_1+B_16_1+2⁢B_1_5+B_6_5+B_11_5+B_16_5-B_21_9+2⁢B_1_13+B_6_13+B_11_13+B_16_13+B_21_132⁢B_1_2+B_6_2+B_11_2+B_16_2+2⁢B_1_6+B_6_6+B_11_6+B_16_6-B_21_10+2⁢B_1_14+B_6_14+B_11_14+B_16_14+B_21_142⁢B_1_3+B_6_3+B_11_3+B_16_3+2⁢B_1_7+B_6_7+B_11_7+B_16_7-B_21_11+2⁢B_1_15+B_6_15+B_11_15+B_16_15+B_21_152⁢B_1_4+B_6_4+B_11_4+B_16_4+2⁢B_1_8+B_6_8+B_11_8+B_16_8-B_21_12+2⁢B_1_16+B_6_16+B_11_16+B_16_16+B_21_162⁢B_2_1+B_7_1+B_12_1+B_17_1+2⁢B_2_5+B_7_5+B_12_5+B_17_5-B_22_9+2⁢B_2_13+B_7_13+B_12_13+B_17_13+B_22_132⁢B_2_2+B_7_2+B_12_2+B_17_2+2⁢B_2_6+B_7_6+B_12_6+B_17_6-B_22_10+2⁢B_2_14+B_7_14+B_12_14+B_17_14+B_22_142⁢B_2_3+B_7_3+B_12_3+B_17_3+2⁢B_2_7+B_7_7+B_12_7+B_17_7-B_22_11+2⁢B_2_15+B_7_15+B_12_15+B_17_15+B_22_152⁢B_2_4+B_7_4+B_12_4+B_17_4+2⁢B_2_8+B_7_8+B_12_8+B_17_8-B_22_12+2⁢B_2_16+B_7_16+B_12_16+B_17_16+B_22_162⁢B_3_1+B_8_1+B_13_1+B_18_1+2⁢B_3_5+B_8_5+B_13_5+B_18_5-B_23_9+2⁢B_3_13+B_8_13+B_13_13+B_18_13+B_23_132⁢B_3_2+B_8_2+B_13_2+B_18_2+2⁢B_3_6+B_8_6+B_13_6+B_18_6-B_23_10+2⁢B_3_14+B_8_14+B_13_14+B_18_14+B_23_142⁢B_3_3+B_8_3+B_13_3+B_18_3+2⁢B_3_7+B_8_7+B_13_7+B_18_7-B_23_11+2⁢B_3_15+B_8_15+B_13_15+B_18_15+B_23_152⁢B_3_4+B_8_4+B_13_4+B_18_4+2⁢B_3_8+B_8_8+B_13_8+B_18_8-B_23_12+2⁢B_3_16+B_8_16+B_13_16+B_18_16+B_23_162⁢B_4_1+B_9_1+B_14_1+B_19_1+2⁢B_4_5+B_9_5+B_14_5+B_19_5-B_24_9+2⁢B_4_13+B_9_13+B_14_13+B_19_13+B_24_132⁢B_4_2+B_9_2+B_14_2+B_19_2+2⁢B_4_6+B_9_6+B_14_6+B_19_6-B_24_10+2⁢B_4_14+B_9_14+B_14_14+B_19_14+B_24_142⁢B_4_3+B_9_3+B_14_3+B_19_3+2⁢B_4_7+B_9_7+B_14_7+B_19_7-B_24_11+2⁢B_4_15+B_9_15+B_14_15+B_19_15+B_24_152⁢B_4_4+B_9_4+B_14_4+B_19_4+2⁢B_4_8+B_9_8+B_14_8+B_19_8-B_24_12+2⁢B_4_16+B_9_16+B_14_16+B_19_16+B_24_162⁢B_5_1+B_10_1+B_15_1+B_20_1+2⁢B_5_5+B_10_5+B_15_5+B_20_5-B_25_9+2⁢B_5_13+B_10_13+B_15_13+B_20_13+B_25_132⁢B_5_2+B_10_2+B_15_2+B_20_2+2⁢B_5_6+B_10_6+B_15_6+B_20_6-B_25_10+2⁢B_5_14+B_10_14+B_15_14+B_20_14+B_25_142⁢B_5_3+B_10_3+B_15_3+B_20_3+2⁢B_5_7+B_10_7+B_15_7+B_20_7-B_25_11+2⁢B_5_15+B_10_15+B_15_15+B_20_15+B_25_152⁢B_5_4+B_10_4+B_15_4+B_20_4+2⁢B_5_8+B_10_8+B_15_8+B_20_8-B_25_12+2⁢B_5_16+B_10_16+B_15_16+B_20_16+B_25_16-C_13_1+C_21_1-C_13_2+C_21_2-C_14_1+C_22_1-C_14_2+C_22_2-C_15_1+C_23_1-C_15_2+C_23_2-C_16_1+C_24_1-C_16_2+C_24_2+Trace⁡Mul⁡-A_3_1+A_3_6-A_3_2+A_3_7-A_3_3+A_3_8-A_3_4+A_3_9-A_3_5+A_3_10-A_4_1+A_4_6-A_4_2+A_4_7-A_4_3+A_4_8-A_4_4+A_4_9-A_4_5+A_4_10-A_5_1+A_5_6A_5_7-A_5_2-A_5_3+A_5_8-A_5_4+A_5_9-A_5_5+A_5_10-B_1_9-B_16_9+B_1_13+B_16_13-B_1_10-B_16_10+B_1_14+B_16_14-B_1_11-B_16_11+B_1_15+B_16_15-B_1_12-B_16_12+B_1_16+B_16_16-B_2_9-B_17_9+B_2_13+B_17_13-B_2_10-B_17_10+B_2_14+B_17_14-B_2_11-B_17_11+B_2_15+B_17_15-B_2_12-B_17_12+B_2_16+B_17_16-B_3_9-B_18_9+B_3_13+B_18_13-B_3_10-B_18_10+B_3_14+B_18_14-B_3_11-B_18_11+B_3_15+B_18_15-B_3_12-B_18_12+B_3_16+B_18_16-B_4_9-B_19_9+B_4_13+B_19_13-B_4_10-B_19_10+B_4_14+B_19_14-B_4_11-B_19_11+B_4_15+B_19_15-B_4_12-B_19_12+B_4_16+B_19_16-B_5_9-B_20_9+B_5_13+B_20_13-B_5_10-B_20_10+B_5_14+B_20_14-B_5_11-B_20_11+B_5_15+B_20_15-B_5_12-B_20_12+B_5_16+B_20_16C_9_3+C_21_3C_9_1+C_21_1+C_9_4+C_21_4C_9_2+C_21_2+C_9_5+C_21_5C_10_3+C_22_3C_10_1+C_22_1+C_10_4+C_22_4C_10_2+C_22_2+C_10_5+C_22_5C_11_3+C_23_3C_11_1+C_23_1+C_11_4+C_23_4C_11_2+C_23_2+C_11_5+C_23_5C_12_3+C_24_3C_12_1+C_24_1+C_12_4+C_24_4C_12_2+C_24_2+C_12_5+C_24_5+Trace⁡Mul⁡-A_1_6+A_1_11+A_1_16-A_1_7+A_1_12+A_1_17-A_1_8+A_1_13+A_1_18-A_1_9+A_1_14+A_1_19-A_1_10+A_1_15+A_1_20-A_2_6+A_2_11+A_2_16-A_2_7+A_2_12+A_2_17-A_2_8+A_2_13+A_2_18-A_2_9+A_2_14+A_2_19-A_2_10+A_2_15+A_2_20-B_6_1-B_11_1+B_16_1-B_1_5-2⁢B_6_5-2⁢B_11_5+B_16_5-B_1_9-B_16_9+B_1_13+B_16_13+B_1_21+B_16_21+2⁢B_1_25+B_6_25+B_11_25+B_16_25-B_6_2-B_11_2+B_16_2-B_1_6-2⁢B_6_6-2⁢B_11_6+B_16_6-B_1_10-B_16_10+B_1_14+B_16_14+B_1_22+B_16_22+2⁢B_1_26+B_6_26+B_11_26+B_16_26-B_6_3-B_11_3+B_16_3-B_1_7-2⁢B_6_7-2⁢B_11_7+B_16_7-B_1_11-B_16_11+B_1_15+B_16_15+B_1_23+B_16_23+2⁢B_1_27+B_6_27+B_11_27+B_16_27-B_6_4-B_11_4+B_16_4-B_1_8-2⁢B_6_8-2⁢B_11_8+B_16_8-B_1_12-B_16_12+B_1_16+B_16_16+B_1_24+B_16_24+2⁢B_1_28+B_6_28+B_11_28+B_16_28-B_7_1-B_12_1+B_17_1-B_2_5-2⁢B_7_5-2⁢B_12_5+B_17_5-B_2_9-B_17_9+B_2_13+B_17_13+B_2_21+B_17_21+2⁢B_2_25+B_7_25+B_12_25+B_17_25-B_7_2-B_12_2+B_17_2-B_2_6-2⁢B_7_6-2⁢B_12_6+B_17_6-B_2_10-B_17_10+B_2_14+B_17_14+B_2_22+B_17_22+2⁢B_2_26+B_7_26+B_12_26+B_17_26-B_7_3-B_12_3+B_17_3-B_2_7-2⁢B_7_7-2⁢B_12_7+B_17_7-B_2_11-B_17_11+B_2_15+B_17_15+B_2_23+B_17_23+2⁢B_2_27+B_7_27+B_12_27+B_17_27-B_7_4-B_12_4+B_17_4-B_2_8-2⁢B_7_8-2⁢B_12_8+B_17_8-B_2_12-B_17_12+B_2_16+B_17_16+B_2_24+B_17_24+2⁢B_2_28+B_7_28+B_12_28+B_17_28-B_8_1-B_13_1+B_18_1-B_3_5-2⁢B_8_5-2⁢B_13_5+B_18_5-B_3_9-B_18_9+B_3_13+B_18_13+B_3_21+B_18_21+2⁢B_3_25+B_8_25+B_13_25+B_18_25-B_8_2-B_13_2+B_18_2-B_3_6-2⁢B_8_6-2⁢B_13_6+B_18_6-B_3_10-B_18_10+B_3_14+B_18_14+B_3_22+B_18_22+2⁢B_3_26+B_8_26+B_13_26+B_18_26-B_8_3-B_13_3+B_18_3-B_3_7-2⁢B_8_7-2⁢B_13_7+B_18_7-B_3_11-B_18_11+B_3_15+B_18_15+B_3_23+B_18_23+2⁢B_3_27+B_8_27+B_13_27+B_18_27-B_8_4-B_13_4+B_18_4-B_3_8-2⁢B_8_8-2⁢B_13_8+B_18_8-B_3_12-B_18_12+B_3_16+B_18_16+B_3_24+B_18_24+2⁢B_3_28+B_8_28+B_13_28+B_18_28-B_9_1-B_14_1+B_19_1-B_4_5-2⁢B_9_5-2⁢B_14_5+B_19_5-B_4_9-B_19_9+B_4_13+B_19_13+B_4_21+B_19_21+2⁢B_4_25+B_9_25+B_14_25+B_19_25-B_9_2-B_14_2+B_19_2-B_4_6-2⁢B_9_6-2⁢B_14_6+B_19_6-B_4_10-B_19_10+B_4_14+B_19_14+B_4_22+B_19_22+2⁢B_4_26+B_9_26+B_14_26+B_19_26-B_9_3-B_14_3+B_19_3-B_4_7-2⁢B_9_7-2⁢B_14_7+B_19_7-B_4_11-B_19_11+B_4_15+B_19_15+B_4_23+B_19_23+2⁢B_4_27+B_9_27+B_14_27+B_19_27-B_9_4-B_14_4+B_19_4-B_4_8-2⁢B_9_8-2⁢B_14_8+B_19_8-B_4_12-B_19_12+B_4_16+B_19_16+B_4_24+B_19_24+2⁢B_4_28+B_9_28+B_14_28+B_19_28-B_10_1-B_15_1+B_20_1-B_5_5-2⁢B_10_5-2⁢B_15_5+B_20_5-B_5_9-B_20_9+B_5_13+B_20_13+B_5_21+B_20_21+2⁢B_5_25+B_10_25+B_15_25+B_20_25-B_10_2-B_15_2+B_20_2-B_5_6-2⁢B_10_6-2⁢B_15_6+B_20_6-B_5_10-B_20_10+B_5_14+B_20_14+B_5_22+B_20_22+2⁢B_5_26+B_10_26+B_15_26+B_20_26-B_10_3-B_15_3+B_20_3-B_5_7-2⁢B_10_7-2⁢B_15_7+B_20_7-B_5_11-B_20_11+B_5_15+B_20_15+B_5_23+B_20_23+2⁢B_5_27+B_10_27+B_15_27+B_20_27-B_10_4-B_15_4+B_20_4-B_5_8-2⁢B_10_8-2⁢B_15_8+B_20_8-B_5_12-B_20_12+B_5_16+B_20_16+B_5_24+B_20_24+2⁢B_5_28+B_10_28+B_15_28+B_20_28C_1_1-C_5_1-C_17_1+C_21_1+C_1_4-C_5_4-C_17_4+C_21_4C_1_2-C_5_2-C_17_2+C_21_2+C_1_5-C_5_5-C_17_5+C_21_5C_2_1-C_6_1-C_18_1+C_22_1+C_2_4-C_6_4-C_18_4+C_22_4C_2_2-C_6_2-C_18_2+C_22_2+C_2_5-C_6_5-C_18_5+C_22_5-C_7_1+C_3_1-C_19_1+C_23_1+C_3_4-C_7_4-C_19_4+C_23_4-C_7_2+C_3_2-C_19_2+C_23_2+C_3_5-C_7_5-C_19_5+C_23_5-C_8_1+C_4_1-C_20_1+C_24_1+C_4_4-C_8_4-C_20_4+C_24_4C_4_2-C_8_2-C_20_2+C_24_2+C_4_5-C_8_5-C_20_5+C_24_5

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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