Description of fast matrix multiplication algorithm: ⟨8×12×21:1248⟩

Algorithm type

24 X^{4} Y^{4} Z^{6} + 60 X^{4} Y^{4} Z^{4} + 8 X^{2} Y^{2} Z^{8} + 24 X^{2} Y^{6} Z^{3} + 24 X^{4} Y^{4} Z^{2} + 60 X^{2} Y^{6} Z^{2} + 48 X^{2} Y^{2} Z^{6} + 24 X^{2} Y^{6} Z + 36 X^{2} Y^{4} Z^{2} + 48 X^{2} Y^{2} Z^{4} + 8 X Y^{3} Z^{4} + 76 X^{2} Y^{3} Z^{2} + 24 X^{2} Y^{2} Z^{3} + 4 X Y^{4} Z^{2} + 48 X Y^{3} Z^{3} + 168 X^{2} Y^{2} Z^{2} + 20 X Y^{4} Z + 56 X Y^{3} Z^{2} + 8 X Y Z^{4} + 4 X^{3} Y Z + 60 X^{2} Y^{2} Z + 8 X^{2} Y Z^{2} + 92 X Y^{3} Z + 20 X Y^{2} Z^{2} + 48 X Y Z^{3} + 4 X^{2} Y Z + 88 X Y^{2} Z + 76 X Y Z^{2} + 80 X Y Z

Algorithm definition

The algorithm ⟨8×12×21:1248⟩ is serendipitous tensor product (⟨2×4×3:20⟩ - 8) ⊗ ⟨4×3×7:63⟩ +4⟨4×6×7:123⟩.

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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