Description of fast matrix multiplication algorithm: ⟨8×8×15:628⟩

Algorithm type

32 X^{4} Y^{4} Z^{8} + 32 X^{2} Y^{6} Z^{4} + 32 X^{2} Y^{2} Z^{8} + 16 X^{2} Y^{4} Z^{2} + 32 X^{2} Y^{2} Z^{4} + 32 X Y^{3} Z^{4} + 24 X^{3} Y^{2} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 8 X Y^{4} Z^{2} + 4 X Y^{2} Z^{4} + 8 X^{3} Y^{2} Z + 88 X^{2} Y^{2} Z^{2} + 4 X Y^{2} Z^{3} + 32 X Y Z^{4} + 32 X^{3} Y Z + 28 X^{2} Y^{2} Z + 12 X^{2} Y Z^{2} + 76 X Y^{3} Z + 8 X Y^{2} Z^{2} + 12 X^{2} Y Z + 40 X Y^{2} Z + 64 X Y Z

Algorithm definition

The algorithm ⟨8×8×15:628⟩ is serendipitous tensor product (⟨2×8×3:40⟩ - 40) ⊗ ⟨4×1×5:20⟩ +4⟨4×4×5:61⟩ +12⟨4×2×5:32⟩.

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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