Description of fast matrix multiplication algorithm: ⟨15×20×26:4464⟩

Algorithm type

2 X^{4} Y^{7} Z^{5} + X^{4} Y^{7} Z^{4} + X^{4} Y^{4} Z^{7} + 14 X^{4} Y^{6} Z^{4} + 4 X^{4} Y^{4} Z^{6} + 8 X^{4} Y^{5} Z^{4} + 5 X^{4} Y^{4} Z^{5} + 4 X^{6} Y^{2} Z^{4} + X^{4} Y^{5} Z^{3} + 326 X^{4} Y^{4} Z^{4} + 2 X^{2} Y^{8} Z^{2} + 2 X^{2} Y^{7} Z^{3} + X^{2} Y^{6} Z^{4} + 13 X^{6} Y^{3} Z^{2} + 7 X^{6} Y^{2} Z^{3} + 2 X^{6} Y Z^{4} + X^{4} Y^{5} Z^{2} + 2 X^{4} Y^{4} Z^{3} + 18 X^{4} Y^{3} Z^{4} + 4 X^{2} Y^{7} Z^{2} + X^{2} Y^{5} Z^{4} + 2 X^{2} Y^{4} Z^{5} + 3 X^{2} Y^{3} Z^{6} + 2 X^{2} Y^{2} Z^{7} + 271 X^{6} Y^{2} Z^{2} + 2 X^{6} Y Z^{3} + 11 X^{4} Y^{4} Z^{2} + 2 X^{4} Y^{3} Z^{3} + 26 X^{4} Y^{2} Z^{4} + 13 X^{2} Y^{6} Z^{2} + 29 X^{2} Y^{4} Z^{4} + 2 X^{2} Y^{3} Z^{5} + 40 X^{2} Y^{2} Z^{6} + 2 X^{4} Y^{3} Z^{2} + 15 X^{4} Y^{2} Z^{3} + 17 X^{2} Y^{5} Z^{2} + 13 X^{2} Y^{4} Z^{3} + 3 X^{2} Y^{3} Z^{4} + 10 X^{2} Y^{2} Z^{5} + X Y^{2} Z^{6} + 5 X^{4} Y^{2} Z^{2} + 2 X^{3} Y Z^{4} + X^{2} Y^{5} Z + 215 X^{2} Y^{4} Z^{2} + X^{2} Y^{3} Z^{3} + 144 X^{2} Y^{2} Z^{4} + 2 X Y^{6} Z + 6 X Y^{4} Z^{3} + 4 X Y^{2} Z^{5} + 6 X Y Z^{6} + 4 X^{3} Y^{3} Z + 10 X^{3} Y^{2} Z^{2} + 8 X^{3} Y Z^{3} + X^{2} Y^{4} Z + 61 X^{2} Y^{3} Z^{2} + 42 X^{2} Y^{2} Z^{3} + 21 X^{2} Y Z^{4} + 8 X Y^{4} Z^{2} + 14 X Y^{2} Z^{4} + 6 X Y Z^{5} + 130 X^{3} Y^{2} Z + 108 X^{3} Y Z^{2} + 970 X^{2} Y^{2} Z^{2} + 44 X^{2} Y Z^{3} + 20 X Y^{4} Z + 2 X Y^{3} Z^{2} + 16 X Y^{2} Z^{3} + 20 X Y Z^{4} + 137 X^{3} Y Z + 2 X^{2} Y^{2} Z + 32 X^{2} Y Z^{2} + 12 X Y^{3} Z + 68 X Y^{2} Z^{2} + 44 X Y Z^{3} + 6 X^{2} Y Z + 414 X Y^{2} Z + 354 X Y Z^{2} + 452 X Y Z

Algorithm definition

The algorithm ⟨15×20×26:4464⟩ is serendipitous tensor product (⟨5×5×13:227⟩ - 64) ⊗ ⟨3×4×2:20⟩ +4⟨3×4×6:54⟩ +26⟨3×4×4:38⟩.

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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