Description of fast matrix multiplication algorithm: ⟨8×12×18:1068⟩

Algorithm type

84 X^{4} Y^{4} Z^{4} + 72 X^{2} Y^{6} Z^{2} + 120 X^{2} Y^{4} Z^{2} + 72 X^{2} Y^{2} Z^{4} + 72 X Y^{6} Z + 144 X^{2} Y^{2} Z^{2} + 48 X Y^{4} Z + 72 X Y^{3} Z^{2} + 216 X Y^{2} Z + 72 X Y Z^{2} + 96 X Y Z

Algorithm definition

The algorithm ⟨8×12×18:1068⟩ is serendipitous tensor product (⟨2×4×3:20⟩ - 8) ⊗ ⟨4×3×6:54⟩ +4⟨4×6×6:105⟩.

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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