Description of fast matrix multiplication algorithm: ⟨12×18×32:3864⟩

Algorithm type

64 X^{4} Y^{16} Z^{6} + 28 X^{8} Y^{8} Z^{8} + 96 X^{2} Y^{16} Z^{6} + 4 X^{12} Y^{6} Z^{4} + 64 X^{4} Y^{12} Z^{6} + 12 X^{4} Y^{12} Z^{4} + 8 X^{4} Y^{8} Z^{8} + 8 X^{4} Y^{4} Z^{12} + 96 X^{2} Y^{12} Z^{6} + 3 X^{4} Y^{10} Z^{4} + 4 X^{2} Y^{14} Z^{2} + 2 X^{2} Y^{12} Z^{4} + 34 X^{4} Y^{8} Z^{4} + 16 X^{4} Y^{4} Z^{8} + 3 X^{2} Y^{12} Z^{2} + 4 X^{6} Y^{6} Z^{2} + 4 X^{4} Y^{6} Z^{4} + 5 X^{2} Y^{10} Z^{2} + 5 X^{2} Y^{8} Z^{4} + 4 X^{2} Y^{6} Z^{6} + 384 X^{2} Y^{8} Z^{3} + 195 X^{4} Y^{4} Z^{4} + 11 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{6} Z^{4} + 2 X^{2} Y^{4} Z^{6} + 576 X Y^{8} Z^{3} + 24 X^{6} Y^{3} Z^{2} + 384 X^{2} Y^{6} Z^{3} + 87 X^{2} Y^{6} Z^{2} + 50 X^{2} Y^{4} Z^{4} + 50 X^{2} Y^{2} Z^{6} + 576 X Y^{6} Z^{3} + 18 X^{2} Y^{5} Z^{2} + 24 X Y^{7} Z + 12 X Y^{6} Z^{2} + 208 X^{2} Y^{4} Z^{2} + 103 X^{2} Y^{2} Z^{4} + 18 X Y^{6} Z + 24 X^{3} Y^{3} Z + 24 X^{2} Y^{3} Z^{2} + 30 X Y^{5} Z + 30 X Y^{4} Z^{2} + 24 X Y^{3} Z^{3} + 172 X^{2} Y^{2} Z^{2} + 66 X Y^{4} Z + 48 X Y^{3} Z^{2} + 12 X Y^{2} Z^{3} + 90 X Y^{3} Z + 12 X Y^{2} Z^{2} + 12 X Y Z^{3} + 24 X Y^{2} Z + 42 X Y Z^{2} + 60 X Y Z

Algorithm definition

The algorithm ⟨12×18×32:3864⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×9×16:552⟩.

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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