Description of fast matrix multiplication algorithm: ⟨16×28×28:6902⟩

Algorithm type

12 X^{4} Y^{10} Z^{2} + 13 X^{4} Y^{9} Z^{2} + 16 X^{4} Y^{8} Z^{2} + 128 X^{4} Y^{6} Z^{4} + 14 X^{4} Y^{7} Z^{2} + 2 X^{3} Y^{8} Z^{2} + 7 X^{2} Y^{10} Z + 15 X^{4} Y^{6} Z^{2} + 704 X^{4} Y^{4} Z^{4} + 18 X^{2} Y^{9} Z + 16 X^{2} Y^{8} Z^{2} + 16 X^{2} Y^{6} Z^{4} + 10 X^{4} Y^{5} Z^{2} + 2 X^{3} Y^{6} Z^{2} + 8 X^{2} Y^{8} Z + 23 X^{4} Y^{5} Z + 16 X^{4} Y^{4} Z^{2} + 16 X^{4} Y^{2} Z^{4} + 6 X^{2} Y^{7} Z + 96 X^{2} Y^{6} Z^{2} + 16 X^{2} Y^{4} Z^{4} + 16 X^{2} Y^{2} Z^{6} + 21 X^{4} Y^{4} Z + X^{3} Y^{5} Z + 12 X^{2} Y^{6} Z + 6 X^{4} Y^{3} Z + 182 X^{4} Y^{2} Z^{2} + 2 X^{3} Y^{4} Z + 16 X^{2} Y^{5} Z + 336 X^{2} Y^{4} Z^{2} + 208 X^{2} Y^{2} Z^{4} + X^{3} Y^{3} Z + 8 X^{2} Y^{4} Z + 256 X^{2} Y^{3} Z^{2} + 4 X^{4} Y Z + 2 X^{2} Y^{3} Z + 1888 X^{2} Y^{2} Z^{2} + 32 X Y^{4} Z + 32 X Y^{3} Z^{2} + 2 X^{3} Y Z + 32 X^{2} Y^{2} Z + 32 X^{2} Y Z^{2} + 192 X Y^{3} Z + 32 X Y^{2} Z^{2} + 32 X Y Z^{3} + 355 X^{2} Y Z + 672 X Y^{2} Z + 416 X Y Z^{2} + 960 X Y Z

Algorithm definition

The algorithm ⟨16×28×28:6902⟩ is serendipitous tensor product (⟨4×7×7:144⟩ - 15) ⊗ ⟨4×4×4:48⟩ +⟨4×20×4:230⟩ +5⟨4×8×4:96⟩.

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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