Description of fast matrix multiplication algorithm: ⟨18×18×28:5040⟩

Algorithm type

48 X^{8} Y^{12} Z^{12} + 72 X^{4} Y^{12} Z^{12} + 96 X^{8} Y^{6} Z^{6} + 9 X^{8} Y^{4} Z^{4} + 528 X^{4} Y^{6} Z^{6} + 3 X^{10} Y^{2} Z^{2} + 3 X^{8} Y^{4} Z^{2} + 576 X^{2} Y^{6} Z^{6} + 6 X^{10} Y Z + 42 X^{8} Y^{2} Z^{2} + 39 X^{4} Y^{4} Z^{4} + 6 X^{8} Y^{2} Z + 48 X^{8} Y Z + 27 X^{6} Y^{2} Z^{2} + 576 X^{4} Y^{3} Z^{3} + 54 X^{6} Y Z + 108 X^{4} Y^{2} Z^{2} + 1440 X^{2} Y^{3} Z^{3} + 6 X^{5} Y Z + 6 X^{4} Y^{2} Z + 864 X Y^{3} Z^{3} + 72 X^{4} Y Z + 129 X^{2} Y^{2} Z^{2} + 54 X^{3} Y Z + 126 X^{2} Y Z + 102 X Y Z

Algorithm definition

The algorithm ⟨18×18×28:5040⟩ is the (Kronecker) tensor product of ⟨3×3×2:15⟩ with ⟨6×6×14:336⟩.

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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