Description of fast matrix multiplication algorithm: ⟨15×21×28:4975⟩

Algorithm type

12 X^{4} Y^{6} Z^{6} + X Y^{13} Z + 144 X^{4} Y^{6} Z^{4} + 30 X^{4} Y^{4} Z^{6} + 16 X^{2} Y^{9} Z^{3} + 8 X Y^{12} Z + 25 X^{2} Y^{9} Z^{2} + 4 X^{2} Y^{8} Z^{3} + 12 X^{2} Y^{3} Z^{8} + X Y^{11} Z + 16 X Y^{9} Z^{3} + 360 X^{4} Y^{4} Z^{4} + 12 X^{4} Y^{2} Z^{6} + 48 X^{2} Y^{8} Z^{2} + 36 X^{2} Y^{6} Z^{4} + 30 X^{2} Y^{2} Z^{8} + 4 X Y^{10} Z + X Y^{9} Z^{2} + 8 X Y^{8} Z^{3} + 12 X^{6} Y^{3} Z^{2} + 4 X^{2} Y^{7} Z^{2} + 24 X^{2} Y^{6} Z^{3} + 24 X^{2} Y^{3} Z^{6} + 12 X^{2} Y Z^{8} + 49 X Y^{9} Z + 13 X Y^{8} Z^{2} + 30 X^{6} Y^{2} Z^{2} + 144 X^{4} Y^{2} Z^{4} + X^{2} Y^{7} Z + 453 X^{2} Y^{6} Z^{2} + 90 X^{2} Y^{4} Z^{4} + 60 X^{2} Y^{2} Z^{6} + 31 X Y^{8} Z + 12 X^{6} Y Z^{2} + 12 X^{4} Y^{3} Z^{2} + 5 X^{2} Y^{6} Z + 4 X^{2} Y^{5} Z^{2} + 24 X^{2} Y^{4} Z^{3} + 84 X^{2} Y^{3} Z^{4} + 24 X^{2} Y Z^{6} + 3 X Y^{7} Z + 77 X Y^{6} Z^{2} + 4 X Y^{4} Z^{4} + 30 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{4} Z + 505 X^{2} Y^{4} Z^{2} + 246 X^{2} Y^{2} Z^{4} + 214 X Y^{6} Z + 8 X Y^{4} Z^{3} + 24 X Y^{3} Z^{4} + 12 X^{4} Y Z^{2} + 31 X^{3} Y^{3} Z + 16 X^{2} Y^{4} Z + 38 X^{2} Y^{3} Z^{2} + 20 X^{2} Y^{2} Z^{3} + 84 X^{2} Y Z^{4} + 13 X Y^{5} Z + 102 X Y^{4} Z^{2} + 49 X Y^{3} Z^{3} + 24 X Y^{2} Z^{4} + 24 X^{3} Y^{2} Z + 48 X^{2} Y^{3} Z + 355 X^{2} Y^{2} Z^{2} + 164 X Y^{4} Z + 184 X Y^{3} Z^{2} + 50 X Y^{2} Z^{3} + 20 X Y Z^{4} + 23 X^{3} Y Z + 26 X^{2} Y^{2} Z + 12 X^{2} Y Z^{2} + 65 X Y^{3} Z + 231 X Y^{2} Z^{2} + 48 X Y Z^{3} + 31 X^{2} Y Z + 147 X Y^{2} Z + 140 X Y Z^{2} + 23 X Y Z

Algorithm definition

The algorithm ⟨15×21×28:4975⟩ is serendipitous tensor product (⟨5×3×7:79⟩ - 5) ⊗ ⟨3×7×4:63⟩ +⟨3×7×20:313⟩.

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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