Description of fast matrix multiplication algorithm: ⟨12×22×22:3430⟩

Algorithm type

16 X^{8} Y^{12} Z^{12} + 16 X^{8} Y^{10} Z^{12} + 24 X^{4} Y^{12} Z^{12} + 24 X^{4} Y^{10} Z^{12} + 128 X^{4} Y^{6} Z^{6} + 96 X^{4} Y^{5} Z^{6} + 8 X^{4} Y^{6} Z^{4} + 192 X^{2} Y^{6} Z^{6} + 144 X^{2} Y^{5} Z^{6} + 7 X^{6} Y^{4} Z^{2} + 8 X^{6} Y^{2} Z^{4} + 89 X^{4} Y^{4} Z^{4} + 8 X^{4} Y^{2} Z^{6} + 10 X^{2} Y^{8} Z^{2} + 7 X^{2} Y^{4} Z^{6} + 25 X^{6} Y^{2} Z^{2} + 10 X^{4} Y^{4} Z^{2} + 21 X^{2} Y^{6} Z^{2} + 10 X^{2} Y^{4} Z^{4} + 25 X^{2} Y^{2} Z^{6} + 17 X^{4} Y^{2} Z^{2} + 45 X^{2} Y^{4} Z^{2} + 192 X^{2} Y^{3} Z^{3} + 17 X^{2} Y^{2} Z^{4} + 48 X^{2} Y^{3} Z^{2} + 288 X Y^{3} Z^{3} + 42 X^{3} Y^{2} Z + 48 X^{3} Y Z^{2} + 557 X^{2} Y^{2} Z^{2} + 48 X^{2} Y Z^{3} + 60 X Y^{4} Z + 42 X Y^{2} Z^{3} + 150 X^{3} Y Z + 60 X^{2} Y^{2} Z + 126 X Y^{3} Z + 60 X Y^{2} Z^{2} + 150 X Y Z^{3} + 102 X^{2} Y Z + 270 X Y^{2} Z + 102 X Y Z^{2} + 138 X Y Z

Algorithm definition

The algorithm ⟨12×22×22:3430⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×11×11:490⟩.

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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