Description of fast matrix multiplication algorithm: ⟨16×27×32:7570⟩

Algorithm type

8 X^{4} Y^{16} Z^{12} + 8 X^{4} Y^{20} Z^{4} + 8 X^{6} Y^{8} Z^{12} + 28 X^{6} Y^{12} Z^{6} + 8 X^{2} Y^{20} Z^{2} + 8 X^{2} Y^{16} Z^{6} + 16 X^{6} Y^{8} Z^{9} + 24 X^{2} Y^{12} Z^{8} + 4 X^{3} Y^{12} Z^{6} + 40 X^{6} Y^{8} Z^{6} + 28 X^{4} Y^{8} Z^{8} + 8 X^{3} Y^{8} Z^{9} + 4 X^{3} Y^{4} Z^{12} + 56 X^{3} Y^{12} Z^{3} + 36 X^{2} Y^{12} Z^{4} + 24 X Y^{12} Z^{4} + 4 X^{6} Y^{4} Z^{6} + 8 X^{4} Y^{8} Z^{4} + 64 X^{4} Y^{4} Z^{8} + 28 X^{2} Y^{12} Z^{2} + 24 X^{2} Y^{8} Z^{6} + 18 X^{2} Y^{6} Z^{8} + 52 X Y^{12} Z^{2} + 224 X^{4} Y^{6} Z^{4} + 128 X^{4} Y^{4} Z^{6} + 20 X^{3} Y^{8} Z^{3} + 48 X^{2} Y^{8} Z^{4} + 24 X^{2} Y^{4} Z^{8} + 56 X Y^{12} Z + 6 X Y^{9} Z^{4} + 4 X^{3} Y^{4} Z^{6} + 16 X^{2} Y^{8} Z^{3} + 320 X^{4} Y^{4} Z^{4} + 64 X^{2} Y^{8} Z^{2} + 66 X^{2} Y^{6} Z^{4} + 94 X^{2} Y^{4} Z^{6} + 50 X^{2} Y^{2} Z^{8} + 22 X Y^{9} Z^{2} + 32 X Y^{8} Z^{3} + 4 X^{2} Y^{3} Z^{6} + 24 X Y^{6} Z^{4} + 32 X^{4} Y^{2} Z^{4} + 48 X^{3} Y^{4} Z^{3} + 448 X^{2} Y^{6} Z^{2} + 36 X^{2} Y^{4} Z^{4} + 36 X Y^{8} Z + 6 X Y^{6} Z^{3} + 12 X^{2} Y^{5} Z^{2} + 24 X Y^{6} Z^{2} + 28 X Y^{4} Z^{4} + 184 X^{2} Y^{4} Z^{2} + 196 X^{2} Y^{2} Z^{4} + 4 X Y^{6} Z + 24 X Y^{4} Z^{3} + 84 X Y^{3} Z^{4} + 452 X^{2} Y^{3} Z^{2} + 256 X^{2} Y^{2} Z^{3} + 4 X^{2} Y Z^{4} + 76 X Y^{4} Z^{2} + 24 X Y^{2} Z^{4} + 1046 X^{2} Y^{2} Z^{2} + 72 X Y^{4} Z + 198 X Y^{3} Z^{2} + 206 X Y^{2} Z^{3} + 142 X Y Z^{4} + 64 X^{2} Y Z^{2} + 898 X Y^{3} Z + 380 X Y^{2} Z + 88 X Y Z^{2} + 794 X Y Z

Algorithm definition

The algorithm ⟨16×27×32:7570⟩ is serendipitous tensor product (⟨4×3×8:73⟩ - 13) ⊗ ⟨4×9×4:104⟩ +⟨4×9×12:300⟩ +5⟨4×9×8:206⟩.

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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