Description of fast matrix multiplication algorithm: ⟨16×20×32:5936⟩

Algorithm type

2 X^{14} Y^{14} Z^{16} + 2 X^{8} Y^{20} Z^{8} + 36 X^{8} Y^{8} Z^{8} + 4 X^{8} Y^{6} Z^{8} + 12 X^{7} Y^{7} Z^{8} + 4 X^{6} Y^{8} Z^{8} + 6 X^{2} Y^{18} Z^{2} + 6 X^{12} Y^{4} Z^{4} + 4 X^{8} Y^{4} Z^{8} + 4 X^{6} Y^{6} Z^{8} + 42 X^{4} Y^{12} Z^{4} + 4 X^{4} Y^{8} Z^{8} + 4 X^{4} Y^{4} Z^{12} + 12 X^{4} Y^{10} Z^{4} + 4 X^{2} Y^{12} Z^{4} + 2 X^{8} Y^{4} Z^{4} + 10 X^{4} Y^{8} Z^{4} + 22 X^{4} Y^{4} Z^{8} + 2 X^{2} Y^{12} Z^{2} + 6 X^{6} Y^{6} Z^{2} + 4 X^{4} Y^{6} Z^{4} + 4 X^{2} Y^{6} Z^{6} + 2 X^{4} Y^{6} Z^{2} + 408 X^{4} Y^{4} Z^{4} + 22 X^{2} Y^{6} Z^{4} + 24 X^{4} Y^{3} Z^{4} + 24 X^{3} Y^{4} Z^{4} + 36 X Y^{9} Z + 60 X^{6} Y^{2} Z^{2} + 46 X^{4} Y^{2} Z^{4} + 24 X^{3} Y^{3} Z^{4} + 346 X^{2} Y^{6} Z^{2} + 46 X^{2} Y^{4} Z^{4} + 40 X^{2} Y^{2} Z^{6} + 24 X Y^{6} Z^{2} + 20 X^{4} Y^{2} Z^{2} + 68 X^{2} Y^{4} Z^{2} + 222 X^{2} Y^{2} Z^{4} + 12 X Y^{6} Z + 36 X^{3} Y^{3} Z + 24 X^{2} Y^{3} Z^{2} + 24 X Y^{3} Z^{3} + 12 X^{2} Y^{3} Z + 1328 X^{2} Y^{2} Z^{2} + 132 X Y^{3} Z^{2} + 144 X^{3} Y Z + 132 X^{2} Y Z^{2} + 564 X Y^{3} Z + 132 X Y^{2} Z^{2} + 96 X Y Z^{3} + 48 X^{2} Y Z + 48 X Y^{2} Z + 540 X Y Z^{2} + 1056 X Y Z

Algorithm definition

The algorithm ⟨16×20×32:5936⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×10×16:848⟩.

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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