Description of fast matrix multiplication algorithm: ⟨8×15×27:1978⟩

Algorithm type

144 X^{4} Y^{4} Z^{4} + 6 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{4} Z^{4} + 9 X^{2} Y^{2} Z^{6} + 25 X^{4} Y^{2} Z^{2} + 354 X^{2} Y^{4} Z^{2} + 54 X^{2} Y^{2} Z^{4} + 12 X Y^{6} Z + X^{4} Y Z^{2} + 3 X^{3} Y^{2} Z^{2} + 2 X^{2} Y^{2} Z^{3} + 12 X Y^{4} Z^{2} + 2 X^{4} Y Z + X^{2} Y^{3} Z + 371 X^{2} Y^{2} Z^{2} + 2 X^{2} Y Z^{3} + 132 X Y^{4} Z + 18 X Y^{2} Z^{3} + 5 X^{3} Y Z + 48 X^{2} Y^{2} Z + 6 X^{2} Y Z^{2} + 13 X Y^{3} Z + 120 X Y^{2} Z^{2} + 20 X Y Z^{3} + 54 X^{2} Y Z + 282 X Y^{2} Z + 118 X Y Z^{2} + 158 X Y Z

Algorithm definition

The algorithm ⟨8×15×27:1978⟩ is serendipitous tensor product (⟨4×5×9:132⟩ - 4) ⊗ ⟨2×3×3:15⟩ +2⟨4×3×3:29⟩.

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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