Description of fast matrix multiplication algorithm: ⟨8×16×27:2072⟩

Algorithm type

16 X^{6} Y^{8} Z^{6} + 16 X^{3} Y^{12} Z^{3} + 32 X^{4} Y^{8} Z^{4} + 16 X Y^{12} Z + 128 X^{4} Y^{4} Z^{4} + 80 X^{2} Y^{8} Z^{2} + 16 X^{3} Y^{4} Z^{3} + 128 X^{2} Y^{6} Z^{2} + 32 X Y^{8} Z + 88 X^{2} Y^{4} Z^{2} + 8 X Y^{6} Z + 480 X^{2} Y^{2} Z^{2} + 112 X Y^{4} Z + 16 X^{2} Y Z^{2} + 272 X Y^{3} Z + 168 X Y^{2} Z + 464 X Y Z

Algorithm definition

The algorithm ⟨8×16×27:2072⟩ is serendipitous tensor product (⟨2×4×3:20⟩ - 8) ⊗ ⟨4×4×9:104⟩ +4⟨4×8×9:206⟩.

Algorithm description

maple tensor representation (compressed by bzip2);
maple LRP representation (compressed by bzip2);
maple evaluation scheme (compressed by bzip2).

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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