Description of fast matrix multiplication algorithm: ⟨20×25×26:7171⟩

Algorithm type

8 X^{12} Y^{4} Z^{6} + 40 X^{8} Y^{6} Z^{4} + 8 X^{12} Y^{2} Z^{3} + 736 X^{8} Y^{4} Z^{4} + 8 X^{8} Y^{2} Z^{4} + 40 X^{8} Y^{3} Z^{2} + 736 X^{8} Y^{2} Z^{2} + 8 X^{4} Y^{6} Z^{2} + 16 X^{4} Y^{4} Z^{4} + 24 X^{4} Y^{2} Z^{6} + 8 X^{8} Y Z^{2} + 288 X^{4} Y^{4} Z^{2} + 240 X^{4} Y^{2} Z^{4} + 16 X^{2} Y^{6} Z^{2} + X^{4} Y^{3} Z^{2} + 2 X^{3} Y^{4} Z^{2} + X^{3} Y^{3} Z^{3} + 2 X^{3} Y^{2} Z^{4} + 8 X^{2} Y^{6} Z + 14 X^{2} Y^{4} Z^{3} + 6 X^{2} Y^{3} Z^{4} + 18 X^{2} Y^{2} Z^{5} + 11 X^{4} Y^{3} Z + 30 X^{4} Y^{2} Z^{2} + 24 X^{4} Y Z^{3} + X^{3} Y^{4} Z + 10 X^{3} Y^{3} Z^{2} + 29 X^{3} Y^{2} Z^{3} + 2 X^{3} Y Z^{4} + 59 X^{2} Y^{4} Z^{2} + 54 X^{2} Y^{3} Z^{3} + 49 X^{2} Y^{2} Z^{4} + 2 X Y^{6} Z + 2 X Y^{5} Z^{2} + X Y^{4} Z^{3} + 6 X Y^{2} Z^{5} + 289 X^{4} Y^{2} Z + 240 X^{4} Y Z^{2} + 2 X^{3} Y^{3} Z + 37 X^{3} Y^{2} Z^{2} + 6 X^{3} Y Z^{3} + 25 X^{2} Y^{4} Z + 112 X^{2} Y^{3} Z^{2} + 199 X^{2} Y^{2} Z^{3} + 6 X^{2} Y Z^{4} + 2 X Y^{5} Z + 7 X Y^{4} Z^{2} + 15 X Y^{3} Z^{3} + 10 X Y^{2} Z^{4} + 26 X Y Z^{5} + 5 X^{3} Y Z^{2} + 15 X^{2} Y^{3} Z + 1554 X^{2} Y^{2} Z^{2} + 49 X^{2} Y Z^{3} + 19 X Y^{4} Z + 86 X Y^{3} Z^{2} + 75 X Y^{2} Z^{3} + 37 X Y Z^{4} + X^{3} Y Z + 26 X^{2} Y^{2} Z + 22 X^{2} Y Z^{2} + 80 X Y^{3} Z + 173 X Y^{2} Z^{2} + 231 X Y Z^{3} + 19 X^{2} Y Z + 725 X Y^{2} Z + 548 X Y Z^{2} + 22 X Y Z

Algorithm definition

The algorithm ⟨20×25×26:7171⟩ is serendipitous tensor product (⟨5×5×13:227⟩ - 56) ⊗ ⟨4×5×2:32⟩ +6⟨4×5×6:90⟩ +19⟨4×5×4:61⟩.

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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