Description of fast matrix multiplication algorithm: ⟨20×25×30:8072⟩

Algorithm type

8 X^{12} Y Z + 41 X^{4} Y^{6} Z^{4} + 12 X Y Z^{12} + 167 X^{4} Y^{5} Z^{4} + 160 X^{8} Y^{2} Z^{2} + 848 X^{4} Y^{4} Z^{4} + 160 X^{2} Y^{2} Z^{8} + 4 X^{8} Y Z^{2} + 4 X^{2} Y Z^{8} + 4 X Y^{2} Z^{8} + 48 X^{8} Y Z + 24 X^{6} Y^{2} Z^{2} + 320 X^{4} Y^{4} Z^{2} + 12 X^{4} Y^{2} Z^{4} + 558 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{4} Z^{4} + 36 X^{2} Y^{2} Z^{6} + 52 X Y Z^{8} + 16 X^{6} Y^{2} Z + 24 X^{2} Y^{6} Z + 88 X^{2} Y^{5} Z^{2} + 89 X^{2} Y^{3} Z^{4} + 8 X^{6} Y Z + 12 X^{4} Y^{3} Z + 316 X^{4} Y^{2} Z^{2} + 12 X^{4} Y Z^{3} + 8 X^{3} Y Z^{4} + 822 X^{2} Y^{4} Z^{2} + 283 X^{2} Y^{2} Z^{4} + 186 X Y^{6} Z + 12 X Y^{3} Z^{4} + 152 X^{4} Y^{2} Z + 56 X^{4} Y Z^{2} + 112 X^{2} Y^{4} Z + 94 X^{2} Y^{3} Z^{2} + 24 X^{2} Y^{2} Z^{3} + 48 X^{2} Y Z^{4} + 4 X Y^{4} Z^{2} + 56 X Y^{2} Z^{4} + 132 X^{4} Y Z + 8 X^{3} Y^{2} Z + 12 X^{2} Y^{3} Z + 918 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 256 X Y^{4} Z + 303 X Y^{3} Z^{2} + 12 X Y^{2} Z^{3} + 84 X Y Z^{4} + 8 X^{3} Y Z + 272 X^{2} Y^{2} Z + 56 X^{2} Y Z^{2} + 320 X Y^{3} Z + 56 X Y^{2} Z^{2} + 12 X Y Z^{3} + 132 X^{2} Y Z + 198 X Y^{2} Z + 181 X Y Z^{2} + 208 X Y Z

Algorithm definition

The algorithm ⟨20×25×30:8072⟩ is serendipitous tensor product (⟨4×5×5:76⟩ - 36) ⊗ ⟨5×6×5:110⟩ +18⟨5×12×5:204⟩.

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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