Description of fast matrix multiplication algorithm: ⟨8×15×32:2336⟩

Algorithm type

16 X^{2} Y^{12} Z^{8} + 56 X^{4} Y^{12} Z^{4} + 16 X^{4} Y^{8} Z^{8} + 32 X^{4} Y^{8} Z^{6} + 40 X^{2} Y^{12} Z^{4} + 16 X Y^{12} Z^{4} + 80 X^{4} Y^{8} Z^{4} + 168 X^{2} Y^{12} Z^{2} + 32 X^{2} Y^{8} Z^{6} + 40 X Y^{12} Z^{2} + 16 X^{2} Y^{8} Z^{4} + 24 X^{2} Y^{4} Z^{8} + 112 X Y^{12} Z + 32 X^{2} Y^{8} Z^{3} + 8 X^{4} Y^{4} Z^{4} + 136 X^{2} Y^{8} Z^{2} + 32 X Y^{8} Z^{3} + 16 X^{2} Y^{4} Z^{4} + 56 X Y^{8} Z + 24 X Y^{4} Z^{4} + 104 X^{2} Y^{4} Z^{2} + 32 X^{2} Y^{2} Z^{4} + 32 X Y^{3} Z^{4} + 112 X^{2} Y^{3} Z^{2} + 64 X^{2} Y^{2} Z^{3} + 16 X Y^{4} Z^{2} + 160 X^{2} Y^{2} Z^{2} + 96 X Y^{4} Z + 80 X Y^{3} Z^{2} + 64 X Y^{2} Z^{3} + 48 X Y Z^{4} + 16 X^{2} Y Z^{2} + 224 X Y^{3} Z + 112 X Y^{2} Z + 32 X Y Z^{2} + 192 X Y Z

Algorithm definition

The algorithm ⟨8×15×32:2336⟩ is the (Kronecker) tensor product of ⟨2×5×4:32⟩ with ⟨4×3×8:73⟩.

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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