Description of fast matrix multiplication algorithm: ⟨12×18×32:3892⟩

Algorithm type

48 X^{8} Y^{12} Z^{12} + 72 X^{4} Y^{12} Z^{12} + 64 X^{4} Y^{12} Z^{6} + 96 X^{2} Y^{12} Z^{6} + 14 X^{4} Y^{8} Z^{4} + 352 X^{4} Y^{6} Z^{6} + 4 X^{2} Y^{12} Z^{2} + 4 X^{2} Y^{8} Z^{4} + 528 X^{2} Y^{6} Z^{6} + 2 X^{6} Y^{4} Z^{2} + 14 X^{4} Y^{4} Z^{4} + 8 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{4} Z^{6} + 384 X^{2} Y^{6} Z^{3} + 2 X^{6} Y^{2} Z^{2} + 4 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{4} Z^{4} + 4 X^{2} Y^{2} Z^{6} + 576 X Y^{6} Z^{3} + 106 X^{2} Y^{4} Z^{2} + 384 X^{2} Y^{3} Z^{3} + 8 X^{2} Y^{2} Z^{4} + 24 X Y^{6} Z + 24 X Y^{4} Z^{2} + 576 X Y^{3} Z^{3} + 12 X^{3} Y^{2} Z + 98 X^{2} Y^{2} Z^{2} + 48 X Y^{4} Z + 24 X Y^{2} Z^{3} + 12 X^{3} Y Z + 24 X Y^{3} Z + 72 X Y^{2} Z^{2} + 24 X Y Z^{3} + 132 X Y^{2} Z + 48 X Y Z^{2} + 84 X Y Z

Algorithm definition

The algorithm ⟨12×18×32:3892⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×9×16:556⟩.

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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