Description of fast matrix multiplication algorithm: ⟨10×20×30:3508⟩

Algorithm type

320 X^{4} Y^{8} Z^{4} + 24 X^{2} Y^{12} Z^{2} + 8 X^{2} Y^{8} Z^{4} + 24 X Y^{12} Z + X^{3} Y^{2} Z^{7} + 432 X^{2} Y^{8} Z^{2} + 16 X^{2} Y^{4} Z^{6} + X^{2} Y^{2} Z^{8} + 6 X^{7} Y^{2} Z^{2} + X^{6} Y^{2} Z^{3} + 2 X^{4} Y^{2} Z^{5} + X^{3} Y^{2} Z^{6} + 8 X Y^{8} Z^{2} + 2 X^{7} Y^{2} Z + 5 X^{6} Y^{2} Z^{2} + 80 X^{4} Y^{4} Z^{2} + 3 X^{4} Y^{2} Z^{4} + 2 X^{3} Y^{2} Z^{5} + 104 X^{2} Y^{4} Z^{4} + 2 X^{2} Y^{2} Z^{6} + X^{2} Y Z^{7} + 112 X Y^{8} Z + X Y^{2} Z^{7} + 8 X^{7} Y Z + 4 X^{6} Y Z^{2} + X^{4} Y^{2} Z^{3} + X^{4} Y Z^{4} + 2 X^{3} Y^{2} Z^{4} + X^{3} Y Z^{5} + X^{2} Y^{2} Z^{5} + 2 X^{2} Y Z^{6} + X Y^{2} Z^{6} + 10 X^{6} Y Z + 16 X^{4} Y^{2} Z^{2} + 5 X^{4} Y Z^{3} + 2 X^{3} Y^{2} Z^{3} + X^{3} Y Z^{4} + 152 X^{2} Y^{4} Z^{2} + 6 X^{2} Y^{2} Z^{4} + 16 X Y^{4} Z^{3} + 2 X^{4} Y^{2} Z + 8 X^{4} Y Z^{2} + 2 X^{3} Y^{3} Z + 10 X^{3} Y^{2} Z^{2} + 2 X^{3} Y Z^{3} + 80 X^{2} Y^{4} Z + X^{2} Y^{3} Z^{2} + 2 X^{2} Y^{2} Z^{3} + 104 X Y^{4} Z^{2} + X Y^{3} Z^{3} + 2 X Y^{2} Z^{4} + 18 X^{4} Y Z + 4 X^{3} Y^{2} Z + 6 X^{3} Y Z^{2} + 2 X^{2} Y^{3} Z + 657 X^{2} Y^{2} Z^{2} + 5 X^{2} Y Z^{3} + 152 X Y^{4} Z + X Y^{2} Z^{3} + 17 X^{3} Y Z + 2 X^{2} Y^{2} Z + 11 X^{2} Y Z^{2} + 50 X Y^{3} Z + 22 X Y^{2} Z^{2} + 36 X Y Z^{3} + 179 X^{2} Y Z + 226 X Y^{2} Z + 208 X Y Z^{2} + 313 X Y Z

Algorithm definition

The algorithm ⟨10×20×30:3508⟩ is serendipitous tensor product (⟨5×5×6:110⟩ - 8) ⊗ ⟨2×4×5:32⟩ +4⟨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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