Description of fast matrix multiplication algorithm: ⟨10×20×24:2837⟩

Algorithm type

X^{2} Y^{12} Z^{2} + X Y^{12} Z + 240 X^{4} Y^{4} Z^{4} + 3 X^{2} Y^{8} Z^{2} + 3 X^{2} Y^{7} Z^{2} + X^{2} Y^{6} Z^{3} + X^{2} Y^{5} Z^{4} + 5 X Y^{9} Z + X Y^{8} Z^{2} + 12 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{2} Z^{4} + 8 X^{3} Y^{2} Z^{5} + 92 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{5} Z^{3} + 2 X^{2} Y^{4} Z^{4} + 14 X^{2} Y^{2} Z^{6} + 5 X Y^{8} Z + X Y^{7} Z^{2} + 2 X^{2} Y^{4} Z^{3} + 3 X^{2} Y^{3} Z^{4} + 3 X Y^{7} Z + X Y^{6} Z^{2} + 70 X^{4} Y^{2} Z^{2} + 394 X^{2} Y^{4} Z^{2} + 13 X^{2} Y^{3} Z^{3} + 82 X^{2} Y^{2} Z^{4} + 45 X Y^{6} Z + 7 X Y^{5} Z^{2} + 4 X^{3} Y^{2} Z^{2} + 3 X^{2} Y^{3} Z^{2} + 6 X^{2} Y^{2} Z^{3} + 6 X Y^{5} Z + 9 X Y^{4} Z^{2} + 4 X Y^{3} Z^{3} + 20 X^{2} Y^{3} Z + 524 X^{2} Y^{2} Z^{2} + 10 X^{2} Y Z^{3} + 100 X Y^{4} Z + 51 X Y^{3} Z^{2} + 16 X Y^{2} Z^{3} + 32 X^{3} Y Z + 80 X^{2} Y^{2} Z + 14 X^{2} Y Z^{2} + 59 X Y^{3} Z + 119 X Y^{2} Z^{2} + 26 X Y Z^{3} + 124 X^{2} Y Z + 257 X Y^{2} Z + 163 X Y Z^{2} + 195 X Y Z

Algorithm definition

The algorithm ⟨10×20×24:2837⟩ is serendipitous tensor product (⟨5×5×6:110⟩ - 22) ⊗ ⟨2×4×4:26⟩ +7⟨2×4×8:51⟩ +4⟨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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