Description of fast matrix multiplication algorithm: ⟨4×18×21:989⟩

Algorithm type

15 X^{4} Y^{8} Z^{4} + 9 X^{2} Y^{12} Z^{2} + 12 X^{2} Y^{10} Z^{2} + 18 X Y^{12} Z + 39 X^{4} Y^{4} Z^{4} + 57 X^{2} Y^{8} Z^{2} + 24 X Y^{10} Z + 6 X^{4} Y^{2} Z^{4} + 21 X^{2} Y^{6} Z^{2} + 54 X Y^{8} Z + 126 X^{2} Y^{4} Z^{2} + 60 X Y^{6} Z + 24 X Y^{5} Z + X^{2} Y^{3} Z + 142 X^{2} Y^{2} Z^{2} + 90 X Y^{4} Z + 2 X^{3} Y Z + 14 X^{2} Y Z^{2} + 42 X Y^{3} Z + 2 X Y Z^{3} + 5 X^{2} Y Z + 126 X Y^{2} Z + 4 X Y Z^{2} + 96 X Y Z

Algorithm definition

The algorithm ⟨4×18×21:989⟩ is serendipitous tensor product (⟨2×6×7:66⟩ - 2) ⊗ ⟨2×3×3:15⟩ +⟨4×3×3:29⟩.

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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