Description of fast matrix multiplication algorithm: ⟨4×18×24:1119⟩

Algorithm type

2 X^{4} Y^{12} Z^{2} + X^{3} Y^{12} Z^{2} + 4 X Y^{15} Z + 12 X^{4} Y^{8} Z^{4} + 12 X^{2} Y^{12} Z^{2} + 8 X^{2} Y^{12} Z + X^{4} Y^{8} Z^{2} + 4 X^{2} Y^{10} Z^{2} + 30 X Y^{12} Z + 3 X^{3} Y^{8} Z^{2} + 52 X^{4} Y^{4} Z^{4} + 30 X^{2} Y^{8} Z^{2} + 5 X^{2} Y^{8} Z + 36 X Y^{9} Z + 88 X^{2} Y^{6} Z^{2} + 3 X Y^{8} Z + 52 X^{2} Y^{4} Z^{2} + 16 X Y^{6} Z + 7 X^{2} Y^{4} Z + 12 X Y^{5} Z + 224 X^{2} Y^{2} Z^{2} + 89 X Y^{4} Z + 176 X Y^{3} Z + 48 X Y^{2} Z + 204 X Y Z

Algorithm definition

The algorithm ⟨4×18×24:1119⟩ is serendipitous tensor product (⟨2×6×6:56⟩ - 2) ⊗ ⟨2×3×4:20⟩ +⟨2×6×4:39⟩.

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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