Description of fast matrix multiplication algorithm: ⟨12×18×28:3500⟩

Algorithm type

16 X^{8} Y^{12} Z^{12} + 32 X^{8} Y^{10} Z^{10} + 24 X^{4} Y^{12} Z^{12} + 48 X^{4} Y^{10} Z^{10} + 32 X^{4} Y^{12} Z^{6} + 32 X^{4} Y^{10} Z^{6} + 48 X^{2} Y^{12} Z^{6} + 48 X^{2} Y^{10} Z^{6} + 6 X^{4} Y^{8} Z^{4} + 160 X^{4} Y^{6} Z^{6} + 192 X^{4} Y^{5} Z^{5} + 240 X^{2} Y^{6} Z^{6} + 6 X^{4} Y^{4} Z^{4} + 288 X^{2} Y^{5} Z^{5} + 192 X^{2} Y^{6} Z^{3} + 12 X^{4} Y^{4} Z^{2} + 192 X^{2} Y^{5} Z^{3} + 288 X Y^{6} Z^{3} + 288 X Y^{5} Z^{3} + 12 X^{4} Y^{2} Z^{2} + 48 X^{2} Y^{4} Z^{2} + 384 X^{2} Y^{3} Z^{3} + 576 X Y^{3} Z^{3} + 48 X^{2} Y^{2} Z^{2} + 72 X^{2} Y^{2} Z + 72 X^{2} Y Z + 72 X Y^{2} Z + 72 X Y Z

Algorithm definition

The algorithm ⟨12×18×28:3500⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×9×14:500⟩.

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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