Description of fast matrix multiplication algorithm: ⟨8×28×32:4264⟩

Algorithm type

18 X^{8} Y^{8} Z^{8} + 6 X^{8} Y^{6} Z^{8} + 12 X^{6} Y^{6} Z^{8} + 6 X^{4} Y^{12} Z^{4} + 4 X^{2} Y^{15} Z^{2} + 12 X^{4} Y^{10} Z^{4} + 2 X^{4} Y^{9} Z^{4} + 48 X^{4} Y^{8} Z^{4} + 4 X^{3} Y^{9} Z^{4} + 8 X^{2} Y^{12} Z^{2} + 20 X^{4} Y^{6} Z^{4} + 16 X^{2} Y^{10} Z^{2} + 16 X^{3} Y^{6} Z^{4} + 4 X^{2} Y^{9} Z^{2} + 258 X^{4} Y^{4} Z^{4} + 32 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{6} Z^{4} + 4 X Y^{9} Z^{2} + 10 X^{4} Y^{3} Z^{4} + 36 X Y^{9} Z + 12 X^{4} Y^{2} Z^{4} + 20 X^{3} Y^{3} Z^{4} + 200 X^{2} Y^{6} Z^{2} + 20 X^{2} Y^{5} Z^{2} + 16 X Y^{6} Z^{2} + 488 X^{2} Y^{4} Z^{2} + 192 X Y^{6} Z + 24 X^{2} Y^{3} Z^{2} + 792 X^{2} Y^{2} Z^{2} + 192 X Y^{4} Z + 20 X Y^{3} Z^{2} + 20 X^{2} Y Z^{2} + 312 X Y^{3} Z + 768 X Y^{2} Z + 660 X Y Z

Algorithm definition

The algorithm ⟨8×28×32:4264⟩ is the (Kronecker) tensor product of ⟨2×4×4:26⟩ 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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