Description of fast matrix multiplication algorithm: ⟨16×18×26:4305⟩

Algorithm type

31 X^{8} Y^{8} Z^{8} + 3 X^{8} Y^{6} Z^{10} + 2 X^{2} Y^{18} Z^{2} + 2 X^{2} Y^{14} Z^{6} + 10 X^{12} Y^{4} Z^{4} + X^{8} Y^{6} Z^{6} + 3 X^{8} Y^{4} Z^{8} + 9 X^{4} Y^{12} Z^{4} + 2 X^{4} Y^{10} Z^{6} + 3 X^{4} Y^{8} Z^{8} + 4 X^{4} Y^{4} Z^{12} + 19 X^{8} Y^{4} Z^{6} + 4 X^{4} Y^{10} Z^{4} + X^{4} Y^{8} Z^{6} + 3 X^{4} Y^{4} Z^{10} + 4 X^{2} Y^{14} Z^{2} + 8 X^{8} Y^{4} Z^{4} + 36 X^{4} Y^{8} Z^{4} + 23 X^{4} Y^{4} Z^{8} + 6 X^{2} Y^{12} Z^{2} + 4 X^{6} Y^{6} Z^{2} + 32 X^{4} Y^{4} Z^{6} + 7 X^{2} Y^{6} Z^{6} + 12 X^{6} Y^{4} Z^{2} + 262 X^{4} Y^{4} Z^{4} + 18 X^{4} Y^{3} Z^{5} + 5 X^{4} Y^{2} Z^{6} + 3 X^{2} Y^{6} Z^{4} + 5 X^{2} Y^{4} Z^{6} + 12 X Y^{9} Z + 12 X Y^{7} Z^{3} + 84 X^{6} Y^{2} Z^{2} + 13 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{3} Z^{3} + 84 X^{4} Y^{2} Z^{4} + 76 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{5} Z^{3} + 40 X^{2} Y^{4} Z^{4} + 88 X^{2} Y^{2} Z^{6} + 114 X^{4} Y^{2} Z^{3} + 24 X^{2} Y^{5} Z^{2} + 6 X^{2} Y^{4} Z^{3} + 18 X^{2} Y^{2} Z^{5} + 24 X Y^{7} Z + 79 X^{4} Y^{2} Z^{2} + 223 X^{2} Y^{4} Z^{2} + 171 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 24 X^{3} Y^{3} Z + 192 X^{2} Y^{2} Z^{3} + 42 X Y^{3} Z^{3} + 72 X^{3} Y^{2} Z + 471 X^{2} Y^{2} Z^{2} + 30 X^{2} Y Z^{3} + 18 X Y^{3} Z^{2} + 30 X Y^{2} Z^{3} + 144 X^{3} Y Z + 78 X^{2} Y^{2} Z + 396 X^{2} Y Z^{2} + 132 X Y^{3} Z + 132 X Y^{2} Z^{2} + 384 X Y Z^{3} + 186 X^{2} Y Z + 42 X Y^{2} Z + 198 X Y Z^{2} + 90 X Y Z

Algorithm definition

The algorithm ⟨16×18×26:4305⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×9×13:615⟩.

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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