Description of fast matrix multiplication algorithm: ⟨8×18×22:1925⟩

Algorithm type

5 X^{8} Y^{10} Z^{8} + 5 X^{8} Y^{8} Z^{8} + 2 X^{8} Y^{6} Z^{8} + X^{4} Y^{12} Z^{4} + 19 X^{4} Y^{10} Z^{4} + 28 X^{4} Y^{8} Z^{4} + 8 X^{2} Y^{12} Z^{2} + 23 X^{4} Y^{6} Z^{4} + 28 X^{2} Y^{10} Z^{2} + 30 X^{4} Y^{5} Z^{4} + 46 X^{4} Y^{4} Z^{4} + 17 X^{2} Y^{8} Z^{2} + X^{2} Y^{6} Z^{4} + 12 X^{4} Y^{3} Z^{4} + 5 X^{4} Y^{2} Z^{4} + 56 X^{2} Y^{6} Z^{2} + 114 X^{2} Y^{5} Z^{2} + 204 X^{2} Y^{4} Z^{2} + X^{2} Y^{2} Z^{4} + 48 X Y^{6} Z + 138 X^{2} Y^{3} Z^{2} + 168 X Y^{5} Z + 126 X^{2} Y^{2} Z^{2} + 102 X Y^{4} Z + 6 X Y^{3} Z^{2} + 30 X^{2} Y Z^{2} + 300 X Y^{3} Z + 216 X Y^{2} Z + 6 X Y Z^{2} + 180 X Y Z

Algorithm definition

The algorithm ⟨8×18×22:1925⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨4×9×11:275⟩.

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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