Description of fast matrix multiplication algorithm: ⟨15×25×32:6728⟩

Algorithm type

6 X^{2} Y^{9} Z^{4} + 2 X^{2} Y^{8} Z^{4} + 4 X^{2} Y^{6} Z^{6} + X Y^{4} Z^{9} + X^{3} Y Z^{9} + X^{2} Y^{8} Z^{3} + X^{2} Y^{5} Z^{6} + 2 X Y^{6} Z^{6} + 728 X^{4} Y^{4} Z^{4} + X^{3} Y^{2} Z^{7} + 57 X^{2} Y^{6} Z^{4} + 29 X^{2} Y^{4} Z^{6} + 13 X Y^{9} Z^{2} + 6 X Y^{2} Z^{9} + 4 X^{9} Y Z + 2 X^{3} Y^{2} Z^{6} + 5 X^{2} Y^{6} Z^{3} + 11 X^{2} Y^{5} Z^{4} + X^{2} Y^{4} Z^{5} + 17 X^{2} Y^{3} Z^{6} + 17 X Y^{6} Z^{4} + 11 X Y^{4} Z^{6} + X Y^{2} Z^{8} + 2 X Y Z^{9} + 237 X^{6} Y^{2} Z^{2} + 112 X^{4} Y^{4} Z^{2} + 2 X^{3} Y^{2} Z^{5} + X^{3} Y Z^{6} + 116 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{5} Z^{3} + 107 X^{2} Y^{4} Z^{4} + 168 X^{2} Y^{2} Z^{6} + X Y^{7} Z^{2} + 12 X Y^{6} Z^{3} + 2 X Y^{4} Z^{5} + 13 X Y^{3} Z^{6} + 8 X Y^{2} Z^{7} + X Y Z^{8} + 2 X^{6} Y^{2} Z + X^{3} Y Z^{5} + 3 X^{2} Y^{5} Z^{2} + 8 X^{2} Y^{4} Z^{3} + 30 X^{2} Y^{3} Z^{4} + 41 X Y^{6} Z^{2} + X Y^{5} Z^{3} + 18 X Y^{4} Z^{4} + 6 X Y^{3} Z^{5} + 32 X Y^{2} Z^{6} + 2 X Y Z^{7} + 58 X^{6} Y Z + 505 X^{4} Y^{2} Z^{2} + 2 X^{3} Y^{3} Z^{2} + X^{3} Y^{2} Z^{3} + 728 X^{2} Y^{4} Z^{2} + 7 X^{2} Y^{3} Z^{3} + 429 X^{2} Y^{2} Z^{4} + 46 X Y^{6} Z + 12 X Y^{5} Z^{2} + 28 X Y^{4} Z^{3} + 35 X Y^{3} Z^{4} + 18 X Y^{2} Z^{5} + 66 X Y Z^{6} + 26 X^{4} Y^{2} Z + 3 X^{3} Y^{3} Z + 2 X^{3} Y^{2} Z^{2} + 5 X^{3} Y Z^{3} + 36 X^{2} Y^{4} Z + 10 X^{2} Y^{3} Z^{2} + 2 X^{2} Y^{2} Z^{3} + 2 X Y^{5} Z + 64 X Y^{4} Z^{2} + 15 X Y^{3} Z^{3} + 55 X Y^{2} Z^{4} + 9 X Y Z^{5} + 78 X^{4} Y Z + 85 X^{3} Y^{2} Z + 83 X^{3} Y Z^{2} + 26 X^{2} Y^{3} Z + 544 X^{2} Y^{2} Z^{2} + 40 X^{2} Y Z^{3} + 173 X Y^{4} Z + 65 X Y^{3} Z^{2} + 73 X Y^{2} Z^{3} + 71 X Y Z^{4} + 69 X^{3} Y Z + 247 X^{2} Y^{2} Z + 160 X^{2} Y Z^{2} + 44 X Y^{3} Z + 266 X Y^{2} Z^{2} + 55 X Y Z^{3} + 164 X^{2} Y Z + 236 X Y^{2} Z + 152 X Y Z^{2} + 83 X Y Z

Algorithm definition

The algorithm ⟨15×25×32:6728⟩ is serendipitous tensor product (⟨5×5×8:144⟩ - 20) ⊗ ⟨3×5×4:47⟩ +10⟨3×5×8:90⟩.

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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