Description of fast matrix multiplication algorithm: ⟨10×20×25:2967⟩

Algorithm type

8 X^{2} Y^{12} Z^{4} + 8 X^{6} Y^{8} Z^{2} + 256 X^{4} Y^{8} Z^{4} + 8 X Y^{12} Z^{2} + 8 X^{4} Y^{8} Z^{2} + 8 X^{2} Y^{8} Z^{4} + 9 X^{4} Y^{2} Z^{6} + 8 X^{3} Y^{8} Z + 344 X^{2} Y^{8} Z^{2} + 6 X^{4} Y^{2} Z^{5} + X^{3} Y^{2} Z^{6} + 8 X^{2} Y^{8} Z + 8 X Y^{8} Z^{2} + 88 X^{4} Y^{4} Z^{2} + 5 X^{3} Y^{2} Z^{5} + 80 X^{2} Y^{4} Z^{4} + 3 X^{2} Y^{2} Z^{6} + 88 X Y^{8} Z + 2 X^{4} Y^{2} Z^{3} + 10 X^{2} Y Z^{6} + 7 X^{4} Y Z^{3} + 6 X^{3} Y^{2} Z^{3} + 160 X^{2} Y^{4} Z^{2} + X^{2} Y^{3} Z^{3} + X^{2} Y^{2} Z^{4} + 4 X^{2} Y Z^{5} + 2 X Y^{2} Z^{5} + 2 X Y Z^{6} + X^{4} Y Z^{2} + 6 X^{3} Y^{2} Z^{2} + 5 X^{3} Y Z^{3} + 88 X^{2} Y^{4} Z + 6 X^{2} Y^{2} Z^{3} + X^{2} Y Z^{4} + 80 X Y^{4} Z^{2} + 3 X Y^{2} Z^{4} + 18 X^{3} Y^{2} Z + 2 X^{3} Y Z^{2} + 519 X^{2} Y^{2} Z^{2} + 14 X^{2} Y Z^{3} + 160 X Y^{4} Z + 16 X Y^{3} Z^{2} + 6 X Y^{2} Z^{3} + 8 X^{3} Y Z + 16 X^{2} Y^{2} Z + 14 X^{2} Y Z^{2} + 2 X Y^{3} Z + 18 X Y^{2} Z^{2} + 3 X Y Z^{3} + 177 X^{2} Y Z + 176 X Y^{2} Z + 161 X Y Z^{2} + 328 X Y Z

Algorithm definition

The algorithm ⟨10×20×25:2967⟩ is serendipitous tensor product (⟨5×5×5:93⟩ - 5) ⊗ ⟨2×4×5:32⟩ +⟨6×4×5:90⟩ +⟨4×4×5:61⟩.

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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