Description of fast matrix multiplication algorithm: ⟨16×18×32:5260⟩

Algorithm type

40 X^{8} Y^{8} Z^{8} + 12 X^{2} Y^{18} Z^{2} + 12 X^{12} Y^{4} Z^{4} + 8 X^{8} Y^{4} Z^{8} + 52 X^{4} Y^{12} Z^{4} + 8 X^{4} Y^{8} Z^{8} + 8 X^{4} Y^{4} Z^{12} + 64 X^{4} Y^{8} Z^{6} + 8 X^{2} Y^{12} Z^{4} + 64 X^{4} Y^{8} Z^{5} + 4 X^{8} Y^{4} Z^{4} + 4 X^{4} Y^{8} Z^{4} + 44 X^{4} Y^{4} Z^{8} + 4 X^{2} Y^{12} Z^{2} + 96 X^{2} Y^{8} Z^{6} + 64 X^{4} Y^{6} Z^{5} + 96 X^{2} Y^{8} Z^{5} + 12 X^{6} Y^{6} Z^{2} + 8 X^{4} Y^{6} Z^{4} + 8 X^{2} Y^{6} Z^{6} + 96 X^{2} Y^{6} Z^{5} + 64 X^{2} Y^{5} Z^{6} + 4 X^{4} Y^{6} Z^{2} + 292 X^{4} Y^{4} Z^{4} + 44 X^{2} Y^{6} Z^{4} + 64 X^{2} Y^{5} Z^{5} + 96 X Y^{5} Z^{6} + 128 X^{2} Y^{6} Z^{3} + 72 X Y^{9} Z + 96 X Y^{5} Z^{5} + 84 X^{6} Y^{2} Z^{2} + 56 X^{4} Y^{2} Z^{4} + 336 X^{2} Y^{6} Z^{2} + 64 X^{2} Y^{5} Z^{3} + 56 X^{2} Y^{4} Z^{4} + 56 X^{2} Y^{2} Z^{6} + 192 X Y^{6} Z^{3} + 48 X Y^{6} Z^{2} + 96 X Y^{5} Z^{3} + 28 X^{4} Y^{2} Z^{2} + 56 X^{2} Y^{4} Z^{2} + 376 X^{2} Y^{2} Z^{4} + 40 X Y^{6} Z + 8 X Y Z^{6} + 72 X^{3} Y^{3} Z + 84 X^{2} Y^{3} Z^{2} + 36 X^{2} Y^{2} Z^{3} + 4 X Y^{5} Z + 48 X Y^{3} Z^{3} + 8 X Y^{2} Z^{4} + 8 X Y Z^{5} + 4 X^{3} Y^{2} Z + 8 X^{3} Y Z^{2} + 24 X^{2} Y^{3} Z + 328 X^{2} Y^{2} Z^{2} + 20 X Y^{4} Z + 280 X Y^{3} Z^{2} + 8 X Y^{2} Z^{3} + 24 X Y Z^{4} + 72 X^{3} Y Z + 48 X^{2} Y Z^{2} + 192 X Y^{3} Z + 168 X Y^{2} Z^{2} + 64 X Y Z^{3} + 24 X^{2} Y Z + 152 X Y^{2} Z + 416 X Y Z^{2} + 100 X Y Z

Algorithm definition

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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