Description of fast matrix multiplication algorithm: ⟨4×21×28:1518⟩

Algorithm type

X^{2} Y^{21} Z^{2} + X^{2} Y^{19} Z^{2} + 10 X Y^{21} Z + 8 X^{2} Y^{18} Z^{2} + X^{2} Y^{17} Z^{2} + 5 X Y^{19} Z + 8 X^{4} Y^{12} Z^{4} + X^{2} Y^{16} Z^{2} + 4 X Y^{18} Z + 18 X^{2} Y^{15} Z^{2} + 2 X Y^{17} Z + 16 X^{4} Y^{10} Z^{4} + 9 X^{2} Y^{14} Z^{2} + 4 X Y^{16} Z + 63 X Y^{15} Z + 16 X^{4} Y^{8} Z^{4} + 22 X^{2} Y^{12} Z^{2} + X Y^{14} Z + 2 X^{2} Y^{11} Z^{2} + 12 X^{4} Y^{6} Z^{4} + 63 X^{2} Y^{10} Z^{2} + 28 X Y^{12} Z + 12 X^{2} Y^{9} Z^{2} + 2 X Y^{11} Z + 36 X^{4} Y^{4} Z^{4} + 24 X^{2} Y^{8} Z^{2} + 9 X Y^{10} Z + 36 X Y^{9} Z + 4 X^{4} Y^{2} Z^{4} + 96 X^{2} Y^{6} Z^{2} + 48 X^{2} Y^{5} Z^{2} + 28 X Y^{7} Z + 68 X^{2} Y^{4} Z^{2} + 32 X Y^{6} Z + 40 X^{2} Y^{3} Z^{2} + 188 X Y^{5} Z + 156 X^{2} Y^{2} Z^{2} + 72 X Y^{4} Z + 12 X^{2} Y Z^{2} + 156 X Y^{3} Z + 60 X Y^{2} Z + 144 X Y Z

Algorithm definition

The algorithm ⟨4×21×28:1518⟩ is serendipitous tensor product (⟨2×7×7:76⟩ - 4) ⊗ ⟨2×3×4:20⟩ +2⟨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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