Description of fast matrix multiplication algorithm: ⟨12×22×26:4018⟩

Algorithm type

16 X^{12} Y^{10} Z^{8} + 24 X^{12} Y^{10} Z^{4} + 12 X^{8} Y^{8} Z^{8} + X^{8} Y^{6} Z^{8} + X^{6} Y^{8} Z^{8} + 4 X^{6} Y^{6} Z^{8} + 13 X^{8} Y^{4} Z^{4} + 16 X^{6} Y^{6} Z^{4} + 13 X^{4} Y^{8} Z^{4} + 64 X^{4} Y^{6} Z^{6} + 96 X^{6} Y^{5} Z^{4} + X^{8} Y^{2} Z^{4} + 24 X^{6} Y^{6} Z^{2} + 3 X^{6} Y^{4} Z^{4} + 9 X^{4} Y^{6} Z^{4} + X^{2} Y^{8} Z^{4} + 96 X^{2} Y^{6} Z^{6} + 144 X^{6} Y^{5} Z^{2} + 3 X^{6} Y^{2} Z^{4} + 156 X^{4} Y^{4} Z^{4} + 2 X^{4} Y^{2} Z^{6} + 6 X^{2} Y^{8} Z^{2} + X^{2} Y^{6} Z^{4} + 3 X^{2} Y^{4} Z^{6} + 6 X^{4} Y^{3} Z^{4} + 6 X^{3} Y^{4} Z^{4} + 10 X^{6} Y^{2} Z^{2} + 4 X^{4} Y^{4} Z^{2} + 24 X^{3} Y^{3} Z^{4} + 13 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{4} Z^{4} + 18 X^{2} Y^{2} Z^{6} + 108 X^{4} Y^{2} Z^{2} + 96 X^{3} Y^{3} Z^{2} + 132 X^{2} Y^{4} Z^{2} + 384 X^{2} Y^{3} Z^{3} + 24 X^{2} Y^{2} Z^{4} + 6 X^{4} Y Z^{2} + 144 X^{3} Y^{3} Z + 18 X^{3} Y^{2} Z^{2} + 54 X^{2} Y^{3} Z^{2} + 6 X Y^{4} Z^{2} + 576 X Y^{3} Z^{3} + 18 X^{3} Y Z^{2} + 516 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 36 X Y^{4} Z + 6 X Y^{3} Z^{2} + 18 X Y^{2} Z^{3} + 60 X^{3} Y Z + 24 X^{2} Y^{2} Z + 78 X Y^{3} Z + 72 X Y^{2} Z^{2} + 108 X Y Z^{3} + 180 X^{2} Y Z + 324 X Y^{2} Z + 144 X Y Z^{2} + 72 X Y Z

Algorithm definition

The algorithm ⟨12×22×26:4018⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×11×13:574⟩.

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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