Description of fast matrix multiplication algorithm: ⟨8×21×32:3280⟩

Algorithm type

12 X^{8} Y^{8} Z^{8} + 4 X^{8} Y^{6} Z^{8} + 8 X^{6} Y^{6} Z^{8} + 12 X^{4} Y^{12} Z^{4} + 8 X^{2} Y^{15} Z^{2} + 8 X^{4} Y^{10} Z^{4} + 4 X^{4} Y^{9} Z^{4} + 16 X^{4} Y^{8} Z^{4} + 8 X^{3} Y^{9} Z^{4} + 16 X^{2} Y^{12} Z^{2} + 8 X^{4} Y^{6} Z^{4} + 8 X^{2} Y^{9} Z^{2} + 188 X^{4} Y^{4} Z^{4} + 8 X^{2} Y^{6} Z^{4} + 8 X Y^{9} Z^{2} + 12 X^{4} Y^{3} Z^{4} + 72 X Y^{9} Z + 8 X^{4} Y^{2} Z^{4} + 24 X^{3} Y^{3} Z^{4} + 224 X^{2} Y^{6} Z^{2} + 24 X^{2} Y^{5} Z^{2} + 144 X^{2} Y^{4} Z^{2} + 96 X Y^{6} Z + 32 X^{2} Y^{3} Z^{2} + 720 X^{2} Y^{2} Z^{2} + 24 X Y^{3} Z^{2} + 24 X^{2} Y Z^{2} + 480 X Y^{3} Z + 288 X Y^{2} Z + 792 X Y Z

Algorithm definition

The algorithm ⟨8×21×32:3280⟩ is the (Kronecker) tensor product of ⟨2×3×4:20⟩ with ⟨4×7×8:164⟩.

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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