Description of fast matrix multiplication algorithm: ⟨9×10×32:1797⟩

Algorithm type

X^{4} Y^{2} Z^{9} + 3 X^{6} Y^{2} Z^{6} + 12 X^{4} Y^{6} Z^{4} + 3 X^{3} Y Z^{9} + 3 X^{2} Y^{2} Z^{9} + 108 X^{4} Y^{4} Z^{4} + 2 X^{4} Y^{2} Z^{6} + 4 X^{2} Y^{4} Z^{6} + 4 X Y^{2} Z^{9} + X^{4} Y^{2} Z^{5} + 12 X^{2} Y^{3} Z^{6} + X^{2} Y^{2} Z^{7} + 41 X Y Z^{9} + 3 X^{6} Y^{2} Z^{2} + 4 X^{4} Y^{2} Z^{4} + X^{3} Y^{2} Z^{5} + 5 X^{3} Y Z^{6} + 20 X^{2} Y^{6} Z^{2} + 28 X^{2} Y^{4} Z^{4} + 142 X^{2} Y^{2} Z^{6} + X^{4} Y^{2} Z^{3} + 2 X^{3} Y^{2} Z^{4} + 2 X^{3} Y Z^{5} + 2 X^{2} Y Z^{6} + 28 X Y^{2} Z^{6} + 5 X Y Z^{7} + X^{3} Y^{2} Z^{3} + 2 X^{3} Y Z^{4} + 64 X^{2} Y^{4} Z^{2} + 54 X^{2} Y^{2} Z^{4} + X^{2} Y Z^{5} + 57 X Y Z^{6} + 13 X^{3} Y Z^{3} + 36 X^{2} Y^{3} Z^{2} + 7 X^{2} Y Z^{4} + 20 X Y^{3} Z^{3} + X Y Z^{5} + 3 X^{3} Y Z^{2} + 340 X^{2} Y^{2} Z^{2} + 3 X^{2} Y Z^{3} + 76 X Y^{2} Z^{3} + 4 X Y Z^{4} + 8 X^{3} Y Z + 3 X^{2} Y Z^{2} + 60 X Y^{3} Z + 84 X Y^{2} Z^{2} + 117 X Y Z^{3} + 4 X^{2} Y Z + 192 X Y^{2} Z + 161 X Y Z^{2} + 48 X Y Z

Algorithm definition

The algorithm ⟨9×10×32:1797⟩ is serendipitous tensor product (⟨3×5×8:90⟩ - 6) ⊗ ⟨3×2×4:20⟩ +3⟨6×2×4:39⟩.

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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