Description of fast matrix multiplication algorithm: ⟨12×18×30:3705⟩

Algorithm type

48 X^{8} Y^{12} Z^{12} + 72 X^{4} Y^{12} Z^{12} + 96 X^{4} Y^{12} Z^{6} + 144 X^{2} Y^{12} Z^{6} + 240 X^{4} Y^{6} Z^{6} + 360 X^{2} Y^{6} Z^{6} + 63 X^{4} Y^{4} Z^{4} + 288 X^{2} Y^{6} Z^{3} + 9 X^{6} Y^{2} Z^{2} + 18 X^{2} Y^{6} Z^{2} + 18 X^{2} Y^{4} Z^{4} + 18 X^{2} Y^{2} Z^{6} + 432 X Y^{6} Z^{3} + 162 X^{2} Y^{4} Z^{2} + 288 X^{2} Y^{3} Z^{3} + 36 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 36 X Y^{4} Z^{2} + 432 X Y^{3} Z^{3} + 18 X^{3} Y^{2} Z + 189 X^{2} Y^{2} Z^{2} + 72 X Y^{4} Z + 36 X Y^{2} Z^{3} + 18 X^{3} Y Z + 36 X Y^{3} Z + 108 X Y^{2} Z^{2} + 36 X Y Z^{3} + 198 X Y^{2} Z + 72 X Y Z^{2} + 126 X Y Z

Algorithm definition

The algorithm ⟨12×18×30:3705⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ 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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