Description of fast matrix multiplication algorithm: ⟨14×18×27:3960⟩

Algorithm type

18 X^{8} Y^{8} Z^{8} + 18 X^{8} Y^{8} Z^{6} + 12 X^{4} Y^{8} Z^{6} + 18 X^{4} Y^{4} Z^{10} + 84 X^{4} Y^{8} Z^{4} + 24 X^{4} Y^{4} Z^{8} + 36 X^{4} Y^{8} Z^{3} + 12 X^{4} Y^{8} Z^{2} + 45 X^{4} Y^{4} Z^{6} + 24 X^{2} Y^{8} Z^{3} + 126 X^{4} Y^{4} Z^{4} + 96 X^{2} Y^{8} Z^{2} + 54 X^{2} Y^{4} Z^{6} + 3 X^{2} Y^{2} Z^{8} + 36 X^{4} Y^{4} Z^{3} + 24 X^{2} Y^{8} Z + 36 X^{2} Y^{4} Z^{5} + 12 X^{4} Y^{4} Z^{2} + 3 X^{4} Y^{2} Z^{4} + 108 X^{2} Y^{4} Z^{4} + 84 X^{2} Y^{2} Z^{6} + 114 X^{2} Y^{4} Z^{3} + 36 X^{2} Y^{2} Z^{5} + 6 X^{4} Y^{2} Z^{2} + 333 X^{2} Y^{4} Z^{2} + 165 X^{2} Y^{2} Z^{4} + 108 X Y^{4} Z^{3} + 48 X^{2} Y^{4} Z + 90 X^{2} Y^{2} Z^{3} + 120 X Y^{4} Z^{2} + 6 X Y^{2} Z^{4} + 297 X^{2} Y^{2} Z^{2} + 114 X Y^{4} Z + 276 X Y^{2} Z^{3} + 6 X Y Z^{4} + 36 X^{2} Y^{2} Z + 6 X^{2} Y Z^{2} + 354 X Y^{2} Z^{2} + 168 X Y Z^{3} + 12 X^{2} Y Z + 336 X Y^{2} Z + 234 X Y Z^{2} + 222 X Y Z

Algorithm definition

The algorithm ⟨14×18×27:3960⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨7×6×9:264⟩.

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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