Description of fast matrix multiplication algorithm: ⟨10×20×20:2407⟩

Algorithm type

X^{2} Y^{12} Z^{3} + X^{2} Y^{9} Z^{4} + X Y^{12} Z^{2} + 2 X^{5} Y^{3} Z^{6} + 8 X^{2} Y^{9} Z^{3} + X Y^{11} Z^{2} + X Y^{10} Z^{2} + 6 X^{6} Y^{4} Z^{2} + 192 X^{4} Y^{4} Z^{4} + 8 X^{4} Y^{2} Z^{6} + X^{2} Y^{6} Z^{4} + 2 X Y^{9} Z^{2} + 5 X^{4} Y^{2} Z^{5} + X^{3} Y^{2} Z^{6} + X^{2} Y^{7} Z^{2} + 5 X^{2} Y^{5} Z^{4} + 9 X Y^{8} Z^{2} + 6 X^{4} Y^{4} Z^{2} + 9 X^{4} Y^{2} Z^{4} + 2 X^{3} Y^{6} Z + X^{3} Y^{2} Z^{5} + 64 X^{2} Y^{6} Z^{2} + X^{2} Y^{5} Z^{3} + 2 X Y^{7} Z^{2} + 2 X^{4} Y^{2} Z^{3} + 2 X^{2} Y^{6} Z + X^{2} Y^{3} Z^{4} + X Y^{7} Z + 3 X Y^{6} Z^{2} + 66 X^{4} Y^{2} Z^{2} + 3 X^{4} Y Z^{3} + 8 X^{3} Y^{4} Z + 318 X^{2} Y^{4} Z^{2} + X^{2} Y^{3} Z^{3} + 63 X^{2} Y^{2} Z^{4} + 21 X Y^{6} Z + X Y^{5} Z^{2} + X Y Z^{6} + X^{3} Y Z^{3} + 8 X^{2} Y^{4} Z + X^{2} Y^{2} Z^{3} + X Y^{4} Z^{2} + 10 X^{3} Y^{2} Z + X^{3} Y Z^{2} + 22 X^{2} Y^{3} Z + 443 X^{2} Y^{2} Z^{2} + 34 X^{2} Y Z^{3} + 83 X Y^{4} Z + 39 X Y^{3} Z^{2} + 98 X^{2} Y^{2} Z + 24 X^{2} Y Z^{2} + 40 X Y^{3} Z + 93 X Y^{2} Z^{2} + 2 X Y Z^{3} + 126 X^{2} Y Z + 260 X Y^{2} Z + 113 X Y Z^{2} + 187 X Y Z

Algorithm definition

The algorithm ⟨10×20×20:2407⟩ is serendipitous tensor product (⟨5×5×5:93⟩ - 10) ⊗ ⟨2×4×4:26⟩ +⟨2×4×12:77⟩ +⟨2×4×8:51⟩ +⟨6×4×4:73⟩ +⟨4×4×4:48⟩.

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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