Description of fast matrix multiplication algorithm: ⟨16×20×27:4884⟩

Algorithm type

52 X^{6} Y^{8} Z^{6} + 16 X^{4} Y^{4} Z^{12} + 16 X^{3} Y^{12} Z^{3} + 8 X^{6} Y^{8} Z^{3} + 8 X^{9} Y^{4} Z^{3} + 8 X^{3} Y^{4} Z^{9} + 32 X^{2} Y^{2} Z^{12} + 16 X^{4} Y^{2} Z^{8} + 24 X^{3} Y^{8} Z^{3} + 16 X Y^{12} Z + 16 X Y Z^{12} + 32 X^{6} Y^{4} Z^{3} + 8 X^{3} Y^{4} Z^{6} + 416 X^{4} Y^{4} Z^{4} + 52 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{8} Z + 16 X^{2} Y Z^{8} + 4 X Y Z^{9} + 64 X^{6} Y^{2} Z^{2} + 64 X^{4} Y^{4} Z^{2} + 8 X^{4} Y^{2} Z^{4} + 16 X^{3} Y^{4} Z^{3} + 128 X^{2} Y^{6} Z^{2} + 76 X^{2} Y^{2} Z^{6} + 24 X Y^{8} Z + 262 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{4} Z + 192 X^{2} Y^{4} Z^{2} + 84 X^{2} Y^{2} Z^{4} + 8 X Y^{4} Z^{3} + 20 X Y Z^{6} + 32 X^{2} Y^{4} Z + 28 X^{2} Y^{2} Z^{3} + 8 X^{2} Y Z^{4} + 8 X Y^{4} Z^{2} + 970 X^{2} Y^{2} Z^{2} + 2 X^{2} Y Z^{3} + 16 X Y^{4} Z + 24 X Y Z^{4} + 128 X^{3} Y Z + 128 X^{2} Y^{2} Z + 40 X^{2} Y Z^{2} + 256 X Y^{3} Z + 182 X Y Z^{3} + 538 X^{2} Y Z + 384 X Y^{2} Z + 156 X Y Z^{2} + 282 X Y Z

Algorithm definition

The algorithm ⟨16×20×27:4884⟩ is serendipitous tensor product (⟨4×5×3:47⟩ - 4) ⊗ ⟨4×4×9:104⟩ +2⟨8×4×9:206⟩.

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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