Description of fast matrix multiplication algorithm: ⟨10×25×25:3703⟩

Algorithm type

X^{2} Y^{15} Z^{4} + 5 X Y^{15} Z^{2} + 2 X^{2} Y^{11} Z^{4} + X Y^{14} Z^{2} + X^{2} Y^{11} Z^{3} + 3 X^{2} Y^{9} Z^{4} + 2 X Y^{12} Z^{2} + 2 X^{2} Y^{9} Z^{3} + 4 X Y^{11} Z^{2} + X^{2} Y^{7} Z^{4} + X Y^{11} Z + 4 X Y^{10} Z^{2} + 10 X^{6} Y^{4} Z^{2} + 320 X^{4} Y^{4} Z^{4} + 6 X^{4} Y^{2} Z^{6} + 6 X^{2} Y^{6} Z^{4} + 9 X Y^{9} Z^{2} + 7 X^{4} Y^{2} Z^{5} + 4 X^{3} Y^{2} Z^{6} + 7 X^{2} Y^{5} Z^{4} + 2 X Y^{9} Z + X Y^{8} Z^{2} + 10 X^{4} Y^{4} Z^{2} + 4 X^{3} Y^{6} Z + 9 X^{3} Y^{2} Z^{5} + X^{3} Y Z^{6} + 128 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{5} Z^{3} + 3 X^{2} Y^{4} Z^{4} + 8 X Y^{7} Z^{2} + X^{5} Y Z^{3} + 7 X^{4} Y^{2} Z^{3} + 4 X^{3} Y^{2} Z^{4} + 4 X^{2} Y^{6} Z + X^{2} Y^{5} Z^{2} + 2 X^{2} Y^{4} Z^{3} + X^{2} Y^{3} Z^{4} + 4 X^{2} Y^{2} Z^{5} + 7 X^{2} Y Z^{6} + 4 X Y^{6} Z^{2} + 110 X^{4} Y^{2} Z^{2} + 5 X^{4} Y Z^{3} + 10 X^{3} Y^{4} Z + 430 X^{2} Y^{4} Z^{2} + 100 X^{2} Y^{2} Z^{4} + 6 X^{2} Y Z^{5} + 40 X Y^{6} Z + 10 X Y^{5} Z^{2} + 2 X^{4} Y Z^{2} + 6 X^{3} Y Z^{3} + 10 X^{2} Y^{4} Z + 5 X^{2} Y^{3} Z^{2} + 9 X^{2} Y^{2} Z^{3} + X^{2} Y Z^{4} + 2 X Y^{4} Z^{2} + X Y^{3} Z^{3} + X Y Z^{5} + 4 X^{4} Y Z + 16 X^{3} Y^{2} Z + 3 X^{3} Y Z^{2} + 52 X^{2} Y^{3} Z + 722 X^{2} Y^{2} Z^{2} + 8 X^{2} Y Z^{3} + 115 X Y^{4} Z + 61 X Y^{3} Z^{2} + 4 X Y^{2} Z^{3} + 4 X Y Z^{4} + 126 X^{2} Y^{2} Z + 8 X^{2} Y Z^{2} + 79 X Y^{3} Z + 122 X Y^{2} Z^{2} + 5 X Y Z^{3} + 184 X^{2} Y Z + 352 X Y^{2} Z + 173 X Y Z^{2} + 317 X Y Z

Algorithm definition

The algorithm ⟨10×25×25:3703⟩ is serendipitous tensor product (⟨5×5×5:93⟩ - 10) ⊗ ⟨2×5×5:40⟩ +⟨2×5×15:118⟩ +⟨2×5×10:79⟩ +⟨6×5×5:110⟩ +⟨4×5×5:76⟩.

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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