Description of fast matrix multiplication algorithm: ⟨12×12×20:1729⟩

Algorithm type

16 X^{8} Y^{12} Z^{12} + 24 X^{4} Y^{12} Z^{12} + 144 X^{4} Y^{6} Z^{6} + 216 X^{2} Y^{6} Z^{6} + 21 X^{4} Y^{4} Z^{4} + 3 X^{6} Y^{2} Z^{2} + 6 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{4} Z^{4} + 6 X^{2} Y^{2} Z^{6} + 12 X^{2} Y^{4} Z^{2} + 288 X^{2} Y^{3} Z^{3} + 12 X^{2} Y^{2} Z^{4} + 432 X Y^{3} Z^{3} + 147 X^{2} Y^{2} Z^{2} + 18 X^{3} Y Z + 36 X Y^{3} Z + 36 X Y^{2} Z^{2} + 36 X Y Z^{3} + 72 X Y^{2} Z + 72 X Y Z^{2} + 126 X Y Z

Algorithm definition

The algorithm ⟨12×12×20:1729⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×6×10:247⟩.

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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