Description of fast matrix multiplication algorithm: ⟨20×28×28:8438⟩

Algorithm type

16 X^{6} Y^{4} Z^{4} + 160 X^{4} Y^{6} Z^{4} + 11 X^{2} Y^{2} Z^{10} + 31 X^{2} Y^{2} Z^{9} + 928 X^{4} Y^{4} Z^{4} + 25 X^{2} Y^{2} Z^{8} + 11 X Y Z^{10} + 4 X^{2} Y^{2} Z^{7} + 23 X Y Z^{9} + 64 X^{6} Y^{2} Z^{2} + 16 X^{4} Y^{4} Z^{2} + 128 X^{2} Y^{6} Z^{2} + 112 X^{2} Y^{4} Z^{4} + 28 X^{2} Y^{2} Z^{6} + 10 X Y Z^{8} + 2 X^{2} Y^{2} Z^{5} + 2 X Y Z^{7} + 304 X^{4} Y^{2} Z^{2} + 400 X^{2} Y^{4} Z^{2} + 229 X^{2} Y^{2} Z^{4} + 31 X Y^{2} Z^{5} + 8 X Y Z^{6} + 32 X^{3} Y^{2} Z^{2} + 320 X^{2} Y^{3} Z^{2} + 24 X Y^{2} Z^{4} + 15 X Y Z^{5} + 2224 X^{2} Y^{2} Z^{2} + 10 X Y Z^{4} + 128 X^{3} Y Z + 32 X^{2} Y^{2} Z + 256 X Y^{3} Z + 229 X Y^{2} Z^{2} + 32 X Y Z^{3} + 608 X^{2} Y Z + 800 X Y^{2} Z + 449 X Y Z^{2} + 736 X Y Z

Algorithm definition

The algorithm ⟨20×28×28:8438⟩ is serendipitous tensor product (⟨5×7×7:176⟩ - 5) ⊗ ⟨4×4×4:48⟩ +⟨4×4×20:230⟩.

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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