Description of fast matrix multiplication algorithm: ⟨12×22×27:4125⟩

Algorithm type

15 X^{8} Y^{10} Z^{8} + 15 X^{8} Y^{8} Z^{8} + 6 X^{8} Y^{6} Z^{8} + 3 X^{4} Y^{12} Z^{4} + 57 X^{4} Y^{10} Z^{4} + 30 X^{4} Y^{5} Z^{8} + 84 X^{4} Y^{8} Z^{4} + 30 X^{4} Y^{4} Z^{8} + 24 X^{2} Y^{12} Z^{2} + 12 X^{4} Y^{3} Z^{8} + 69 X^{4} Y^{6} Z^{4} + 84 X^{2} Y^{10} Z^{2} + 30 X^{4} Y^{5} Z^{4} + 3 X^{4} Y^{6} Z^{2} + 78 X^{4} Y^{4} Z^{4} + 51 X^{2} Y^{8} Z^{2} + 6 X^{2} Y^{6} Z^{4} + 12 X^{4} Y^{3} Z^{4} + 114 X^{2} Y^{5} Z^{4} + 15 X^{4} Y^{2} Z^{4} + 156 X^{2} Y^{6} Z^{2} + 168 X^{2} Y^{4} Z^{4} + 114 X^{2} Y^{5} Z^{2} + 138 X^{2} Y^{3} Z^{4} + 48 X Y^{6} Z^{2} + 3 X^{4} Y^{2} Z^{2} + 276 X^{2} Y^{4} Z^{2} + 96 X^{2} Y^{2} Z^{4} + 48 X Y^{6} Z + 168 X Y^{5} Z^{2} + 144 X^{2} Y^{3} Z^{2} + 30 X^{2} Y Z^{4} + 168 X Y^{5} Z + 102 X Y^{4} Z^{2} + 6 X^{2} Y^{3} Z + 186 X^{2} Y^{2} Z^{2} + 102 X Y^{4} Z + 300 X Y^{3} Z^{2} + 36 X^{2} Y Z^{2} + 300 X Y^{3} Z + 216 X Y^{2} Z^{2} + 6 X^{2} Y Z + 216 X Y^{2} Z + 180 X Y Z^{2} + 180 X Y Z

Algorithm definition

The algorithm ⟨12×22×27:4125⟩ is the (Kronecker) tensor product of ⟨3×2×3:15⟩ with ⟨4×11×9:275⟩.

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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