Description of fast matrix multiplication algorithm: ⟨10×18×21:2245⟩

Algorithm type

3 X^{6} Y^{4} Z^{4} + 177 X^{4} Y^{4} Z^{4} + 4 X^{6} Y^{2} Z^{2} + 6 X^{4} Y^{4} Z^{2} + 3 X^{4} Y^{2} Z^{4} + X^{6} Y Z^{2} + 3 X^{5} Y^{2} Z^{2} + X^{4} Y^{2} Z^{3} + 6 X^{3} Y^{4} Z^{2} + 2 X^{6} Y Z + 39 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{2} Z^{3} + 435 X^{2} Y^{4} Z^{2} + 59 X^{2} Y^{2} Z^{4} + 5 X^{5} Y Z + 4 X^{4} Y Z^{2} + 3 X^{3} Y^{3} Z + 17 X^{3} Y^{2} Z^{2} + 2 X^{3} Y Z^{3} + 12 X^{2} Y^{4} Z + 3 X^{2} Y^{2} Z^{3} + 2 X^{2} Y Z^{4} + 3 X^{4} Y Z + 6 X^{3} Y^{2} Z + 7 X^{3} Y Z^{2} + 2 X^{2} Y^{3} Z + 421 X^{2} Y^{2} Z^{2} + 4 X^{2} Y Z^{3} + 162 X Y^{4} Z + X Y Z^{4} + 20 X^{3} Y Z + 84 X^{2} Y^{2} Z + 23 X^{2} Y Z^{2} + 114 X Y^{2} Z^{2} + 5 X Y Z^{3} + 85 X^{2} Y Z + 270 X Y^{2} Z + 131 X Y Z^{2} + 116 X Y Z

Algorithm definition

The algorithm ⟨10×18×21:2245⟩ is serendipitous tensor product (⟨5×6×7:150⟩ - 10) ⊗ ⟨2×3×3:15⟩ +5⟨4×3×3:29⟩.

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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