Description of fast matrix multiplication algorithm: ⟨12×16×32:3501⟩

Algorithm type

32 X^{4} Y^{8} Z^{4} + 32 X^{2} Y^{8} Z^{6} + 64 X^{4} Y^{6} Z^{4} + 112 X^{4} Y^{4} Z^{6} + 160 X^{4} Y^{4} Z^{4} + 48 X^{2} Y^{8} Z^{2} + 64 X^{2} Y^{6} Z^{4} + 78 X^{2} Y^{4} Z^{6} + 16 X^{4} Y^{4} Z^{2} + 18 X^{2} Y^{4} Z^{4} + 224 X^{2} Y^{2} Z^{6} + 17 X Y^{2} Z^{6} + 2 X^{3} Y^{2} Z^{3} + 83 X^{2} Y^{4} Z^{2} + 112 X^{2} Y^{2} Z^{4} + 89 X Y^{4} Z^{3} + 128 X^{2} Y^{3} Z^{2} + 232 X^{2} Y^{2} Z^{3} + 13 X Y^{2} Z^{4} + 512 X^{2} Y^{2} Z^{2} + 101 X Y^{4} Z + 128 X Y^{3} Z^{2} + 115 X Y^{2} Z^{3} + 32 X^{2} Y^{2} Z + 448 X Y Z^{3} + 33 X Y^{2} Z + 224 X Y Z^{2} + 384 X Y Z

Algorithm definition

The algorithm ⟨12×16×32:3501⟩ is serendipitous tensor product (⟨3×4×8:73⟩ - 13) ⊗ ⟨4×4×4:48⟩ +⟨4×4×12:141⟩ +5⟨4×4×8:96⟩.

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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