Description of fast matrix multiplication algorithm: ⟨16×16×27:3946⟩

Algorithm type

40 X^{6} Y^{8} Z^{6} + 24 X^{6} Y^{4} Z^{8} + 12 X^{3} Y^{12} Z^{3} + 8 X^{6} Y^{8} Z^{3} + 8 X^{9} Y^{4} Z^{3} + 8 X^{6} Y^{4} Z^{6} + 12 X^{3} Y^{4} Z^{9} + 16 X^{4} Y^{2} Z^{8} + 4 X^{3} Y^{8} Z^{3} + 12 X Y^{12} Z + 24 X^{6} Y^{4} Z^{3} + 4 X^{3} Y^{4} Z^{6} + 24 X^{3} Y^{2} Z^{8} + 8 X^{6} Y^{2} Z^{4} + 320 X^{4} Y^{4} Z^{4} + 40 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{8} Z + 16 X^{2} Y Z^{8} + 70 X^{6} Y^{2} Z^{2} + 64 X^{4} Y^{4} Z^{2} + 100 X^{4} Y^{2} Z^{4} + 8 X^{3} Y^{4} Z^{3} + 96 X^{2} Y^{6} Z^{2} + 96 X^{2} Y^{2} Z^{6} + 4 X Y^{8} Z + 4 X^{2} Y Z^{6} + 222 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{4} Z + 8 X^{3} Y Z^{4} + 40 X^{2} Y^{4} Z^{2} + 56 X^{2} Y^{2} Z^{4} + 12 X Y^{4} Z^{3} + 36 X^{3} Y^{2} Z^{2} + 2 X^{3} Y Z^{3} + 24 X^{2} Y^{4} Z + 40 X^{2} Y Z^{4} + 4 X Y^{4} Z^{2} + 12 X^{3} Y^{2} Z + 8 X^{3} Y Z^{2} + 710 X^{2} Y^{2} Z^{2} + 10 X^{2} Y Z^{3} + 8 X Y^{4} Z + 24 X Y Z^{4} + 154 X^{3} Y Z + 128 X^{2} Y^{2} Z + 220 X^{2} Y Z^{2} + 192 X Y^{3} Z + 194 X Y Z^{3} + 482 X^{2} Y Z + 64 X Y^{2} Z + 72 X Y Z^{2} + 186 X Y Z

Algorithm definition

The algorithm ⟨16×16×27:3946⟩ is serendipitous tensor product (⟨4×4×3:38⟩ - 6) ⊗ ⟨4×4×9:104⟩ +3⟨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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