Description of fast matrix multiplication algorithm: ⟨15×16×25:3572⟩

Algorithm type

12 X^{12} Y Z + 13 X^{4} Y^{4} Z^{6} + 8 X Y^{12} Z + 4 X^{2} Y^{2} Z^{9} + 52 X^{8} Y^{2} Z^{2} + 299 X^{4} Y^{4} Z^{4} + 52 X^{2} Y^{8} Z^{2} + 2 X^{2} Y^{4} Z^{6} + 4 X^{8} Y^{2} Z + 3 X^{6} Y^{2} Z^{3} + X^{4} Y^{4} Z^{3} + 4 X^{2} Y^{8} Z + 2 X^{2} Y^{6} Z^{3} + 8 X Y^{8} Z^{2} + 52 X Y Z^{9} + 12 X^{8} Y Z + 69 X^{6} Y^{2} Z^{2} + 23 X^{4} Y^{4} Z^{2} + 46 X^{2} Y^{6} Z^{2} + 150 X^{2} Y^{4} Z^{4} + 267 X^{2} Y^{2} Z^{6} + 32 X Y^{8} Z + 3 X^{4} Y^{2} Z^{3} + 8 X^{2} Y^{4} Z^{3} + 16 X Y^{6} Z^{2} + 16 X Y^{4} Z^{4} + 58 X Y^{2} Z^{6} + 8 X^{4} Y^{3} Z + 77 X^{4} Y^{2} Z^{2} + 16 X^{4} Y Z^{3} + 12 X^{3} Y^{4} Z + 244 X^{2} Y^{4} Z^{2} + 190 X^{2} Y^{2} Z^{4} + 8 X Y^{6} Z + 16 X Y^{4} Z^{3} + 94 X Y Z^{6} + 32 X^{4} Y^{2} Z + 24 X^{4} Y Z^{2} + 24 X^{3} Y^{2} Z^{2} + 39 X^{3} Y Z^{3} + 16 X^{2} Y^{4} Z + 18 X^{2} Y^{2} Z^{3} + 96 X Y^{4} Z^{2} + 26 X Y^{3} Z^{3} + 56 X Y^{2} Z^{4} + 20 X^{4} Y Z + 12 X^{3} Y^{2} Z + 12 X^{3} Y Z^{2} + 338 X^{2} Y^{2} Z^{2} + 39 X^{2} Y Z^{3} + 52 X Y^{4} Z + 8 X Y^{3} Z^{2} + 120 X Y^{2} Z^{3} + 24 X Y Z^{4} + 45 X^{3} Y Z + 27 X^{2} Y^{2} Z + 12 X^{2} Y Z^{2} + 30 X Y^{3} Z + 126 X Y^{2} Z^{2} + 125 X Y Z^{3} + 45 X^{2} Y Z + 140 X Y^{2} Z + 110 X Y Z^{2} + 75 X Y Z

Algorithm definition

The algorithm ⟨15×16×25:3572⟩ is the (Kronecker) tensor product of ⟨3×4×5:47⟩ with ⟨5×4×5:76⟩.

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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