Description of fast matrix multiplication algorithm: ⟨16×21×27:5205⟩

Algorithm type

24 X^{8} Y^{8} Z^{8} + 24 X^{8} Y^{6} Z^{8} + 48 X^{4} Y^{4} Z^{12} + 24 X^{4} Y^{10} Z^{4} + 96 X^{4} Y^{8} Z^{4} + 3 X^{6} Y^{6} Z^{2} + 132 X^{4} Y^{6} Z^{4} + 51 X^{2} Y^{10} Z^{2} + 27 X^{2} Y^{6} Z^{6} + 9 X^{6} Y^{4} Z^{2} + 3 X^{4} Y^{6} Z^{2} + 183 X^{4} Y^{4} Z^{4} + 99 X^{2} Y^{8} Z^{2} + 18 X^{2} Y^{6} Z^{4} + 126 X^{2} Y^{4} Z^{6} + 6 X Y^{10} Z + 48 X^{4} Y^{3} Z^{4} + 6 X^{6} Y^{2} Z^{2} + 15 X^{4} Y^{4} Z^{2} + 42 X^{4} Y^{2} Z^{4} + 6 X^{3} Y^{6} Z + 291 X^{2} Y^{6} Z^{2} + 15 X^{2} Y^{4} Z^{4} + 165 X^{2} Y^{2} Z^{6} + 6 X Y^{8} Z + 54 X Y^{6} Z^{3} + 6 X^{2} Y^{6} Z + 48 X^{2} Y^{5} Z^{2} + 36 X Y^{6} Z^{2} + 21 X^{4} Y^{2} Z^{2} + 18 X^{3} Y^{4} Z + 513 X^{2} Y^{4} Z^{2} + 6 X^{2} Y^{2} Z^{4} + 246 X Y^{6} Z + 60 X Y^{4} Z^{3} + 6 X^{3} Y^{3} Z + 30 X^{2} Y^{4} Z + 168 X^{2} Y^{3} Z^{2} + 6 X Y^{5} Z + 30 X Y^{4} Z^{2} + 54 X Y^{3} Z^{3} + 30 X^{3} Y^{2} Z + 6 X^{2} Y^{3} Z + 468 X^{2} Y^{2} Z^{2} + 300 X Y^{4} Z + 36 X Y^{3} Z^{2} + 198 X Y^{2} Z^{3} + 12 X^{3} Y Z + 72 X^{2} Y^{2} Z + 84 X^{2} Y Z^{2} + 246 X Y^{3} Z + 42 X Y^{2} Z^{2} + 138 X Y Z^{3} + 42 X^{2} Y Z + 522 X Y^{2} Z + 12 X Y Z^{2} + 228 X Y Z

Algorithm definition

The algorithm ⟨16×21×27:5205⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨8×7×9:347⟩.

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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