Description of fast matrix multiplication algorithm: ⟨10×24×30:4146⟩

Algorithm type

X^{3} Y^{13} Z^{2} + 400 X^{4} Y^{8} Z^{4} + 5 X^{2} Y^{13} Z + 5 X^{2} Y^{12} Z^{2} + 2 X^{4} Y^{9} Z^{2} + X^{3} Y^{10} Z^{2} + X^{2} Y^{12} Z + X Y^{13} Z + 8 X^{2} Y^{8} Z^{4} + 10 X Y^{12} Z + 2 X^{6} Y^{5} Z^{2} + 3 X^{3} Y^{8} Z^{2} + 2 X^{2} Y^{9} Z^{2} + 3 X Y^{11} Z + 7 X^{6} Y^{4} Z^{2} + 2 X^{4} Y^{2} Z^{6} + X^{3} Y^{7} Z^{2} + X^{2} Y^{9} Z + 520 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{4} Z^{6} + X Y^{10} Z + X^{6} Y^{3} Z^{2} + X^{5} Y^{4} Z^{2} + 6 X^{4} Y^{5} Z^{2} + 4 X^{4} Y^{2} Z^{5} + 3 X^{3} Y^{6} Z^{2} + 3 X^{3} Y^{2} Z^{6} + 18 X^{2} Y^{8} Z + 10 X Y^{9} Z + 8 X Y^{8} Z^{2} + 16 X^{6} Y^{2} Z^{2} + X^{5} Y^{3} Z^{2} + 99 X^{4} Y^{4} Z^{2} + 3 X^{4} Y^{2} Z^{4} + 6 X^{3} Y^{5} Z^{2} + 2 X^{3} Y^{2} Z^{5} + 5 X^{2} Y^{7} Z + 11 X^{2} Y^{6} Z^{2} + 128 X^{2} Y^{4} Z^{4} + 123 X Y^{8} Z + 5 X^{5} Y^{2} Z^{2} + 4 X^{4} Y^{3} Z^{2} + 14 X^{3} Y^{5} Z + 8 X^{3} Y^{4} Z^{2} + 9 X^{3} Y^{2} Z^{4} + 5 X^{2} Y^{6} Z + 3 X^{2} Y^{5} Z^{2} + X^{2} Y^{2} Z^{5} + 4 X^{2} Y Z^{6} + 3 X Y^{7} Z + 11 X^{4} Y^{2} Z^{2} + 3 X^{4} Y Z^{3} + 11 X^{3} Y^{4} Z + 11 X^{3} Y^{3} Z^{2} + 5 X^{3} Y^{2} Z^{3} + 13 X^{2} Y^{5} Z + 133 X^{2} Y^{4} Z^{2} + X^{2} Y^{3} Z^{3} + 2 X^{2} Y^{2} Z^{4} + 7 X^{2} Y Z^{5} + 13 X Y^{6} Z + 8 X Y^{4} Z^{3} + X^{4} Y Z^{2} + 14 X^{3} Y^{3} Z + 10 X^{3} Y^{2} Z^{2} + 6 X^{3} Y Z^{3} + 122 X^{2} Y^{4} Z + 2 X^{2} Y^{3} Z^{2} + 2 X^{2} Y^{2} Z^{3} + X^{2} Y Z^{4} + 7 X Y^{5} Z + 128 X Y^{4} Z^{2} + X Y Z^{5} + 14 X^{3} Y^{2} Z + 2 X^{3} Y Z^{2} + 31 X^{2} Y^{3} Z + 811 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 134 X Y^{4} Z + 2 X Y^{2} Z^{3} + 3 X Y Z^{4} + 32 X^{3} Y Z + 43 X^{2} Y^{2} Z + 6 X^{2} Y Z^{2} + 24 X Y^{3} Z + 16 X Y^{2} Z^{2} + 20 X Y Z^{3} + 229 X^{2} Y Z + 248 X Y^{2} Z + 256 X Y Z^{2} + 269 X Y Z

Algorithm definition

The algorithm ⟨10×24×30:4146⟩ is serendipitous tensor product (⟨5×6×6:130⟩ - 19) ⊗ ⟨2×4×5:32⟩ +⟨6×4×5:90⟩ +8⟨2×8×5:63⟩.

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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