Description of fast matrix multiplication algorithm: ⟨9×10×28:1578⟩

Algorithm type

8 X^{4} Y^{6} Z^{4} + 96 X^{4} Y^{4} Z^{4} + 8 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{3} Z^{6} + 28 X Y Z^{9} + 8 X^{6} Y^{2} Z^{2} + 16 X^{2} Y^{6} Z^{2} + 24 X^{2} Y^{4} Z^{4} + 124 X^{2} Y^{2} Z^{6} + 24 X Y^{2} Z^{6} + 8 X^{4} Y^{2} Z^{2} + 55 X^{2} Y^{4} Z^{2} + 48 X^{2} Y^{2} Z^{4} + 8 X Y^{4} Z^{3} + 48 X Y Z^{6} + 8 X^{3} Y Z^{3} + 29 X^{2} Y^{3} Z^{2} + 2 X^{2} Y^{2} Z^{3} + X Y^{5} Z + X Y^{4} Z^{2} + 16 X Y^{3} Z^{3} + X^{2} Y^{3} Z + 303 X^{2} Y^{2} Z^{2} + 8 X^{2} Y Z^{3} + 27 X Y^{4} Z + X Y^{3} Z^{2} + 52 X Y^{2} Z^{3} + 27 X^{3} Y Z + 2 X^{2} Y^{2} Z + 56 X Y^{3} Z + 72 X Y^{2} Z^{2} + 97 X Y Z^{3} + 25 X^{2} Y Z + 159 X Y^{2} Z + 144 X Y Z^{2} + 36 X Y Z

Algorithm definition

The algorithm ⟨9×10×28:1578⟩ is serendipitous tensor product (⟨3×5×7:79⟩ - 2) ⊗ ⟨3×2×4:20⟩ +⟨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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