Description of fast matrix multiplication algorithm: ⟨15×18×28:4264⟩

Algorithm type

36 X^{4} Y^{4} Z^{6} + 48 X^{3} Y^{9} Z^{2} + 72 X^{3} Y^{9} Z + 432 X^{4} Y^{4} Z^{4} + 36 X^{2} Y^{2} Z^{8} + 36 X^{6} Y^{2} Z^{2} + 16 X^{3} Y^{5} Z^{2} + 83 X^{2} Y^{6} Z^{2} + 108 X^{2} Y^{4} Z^{4} + 72 X^{2} Y^{2} Z^{6} + 36 X^{4} Y^{2} Z^{3} + 24 X^{3} Y^{5} Z + 36 X^{2} Y^{4} Z^{3} + 36 X^{6} Y Z + 468 X^{4} Y^{2} Z^{2} + 655 X^{2} Y^{4} Z^{2} + 252 X^{2} Y^{2} Z^{4} + 84 X Y^{6} Z + 36 X^{2} Y Z^{4} + 108 X Y^{4} Z^{2} + 36 X Y^{2} Z^{4} + 36 X^{4} Y Z + 36 X^{3} Y^{2} Z + 88 X^{2} Y^{3} Z + 162 X^{2} Y^{2} Z^{2} + 72 X^{2} Y Z^{3} + 222 X Y^{4} Z + 72 X Y^{2} Z^{3} + 252 X^{2} Y^{2} Z + 252 X^{2} Y Z^{2} + 252 X Y^{2} Z^{2} + 56 X^{2} Y Z + 54 X Y^{2} Z

Algorithm definition

The algorithm ⟨15×18×28:4264⟩ is serendipitous tensor product (⟨5×3×7:79⟩ - 5) ⊗ ⟨3×6×4:54⟩ +⟨3×6×20:268⟩.

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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