Description of fast matrix multiplication algorithm: ⟨14×20×22:3682⟩

Algorithm type

12 X^{8} Y^{8} Z^{8} + 4 X^{8} Y^{8} Z^{6} + 3 X^{6} Y^{8} Z^{8} + X^{12} Y^{4} Z^{4} + 2 X^{8} Y^{4} Z^{8} + 10 X^{6} Y^{8} Z^{6} + X^{4} Y^{12} Z^{4} + X^{4} Y^{8} Z^{8} + 2 X^{8} Y^{8} Z^{2} + X^{6} Y^{8} Z^{4} + 3 X^{8} Y^{4} Z^{4} + 11 X^{4} Y^{8} Z^{4} + 7 X^{4} Y^{4} Z^{8} + X^{8} Y^{4} Z^{2} + 2 X^{6} Y^{4} Z^{4} + X^{4} Y^{8} Z^{2} + 6 X^{4} Y^{6} Z^{4} + 6 X^{4} Y^{4} Z^{6} + 4 X^{2} Y^{8} Z^{4} + X^{2} Y^{4} Z^{8} + 8 X^{8} Y^{2} Z^{2} + 2 X^{6} Y^{4} Z^{2} + 4 X^{6} Y^{2} Z^{4} + 211 X^{4} Y^{4} Z^{4} + 4 X^{4} Y^{2} Z^{6} + 6 X^{2} Y^{8} Z^{2} + 7 X^{2} Y^{4} Z^{6} + 8 X^{2} Y^{2} Z^{8} + 24 X^{4} Y^{4} Z^{3} + 18 X^{3} Y^{4} Z^{4} + 24 X^{6} Y^{2} Z^{2} + 14 X^{4} Y^{4} Z^{2} + 14 X^{4} Y^{2} Z^{4} + 60 X^{3} Y^{4} Z^{3} + 44 X^{2} Y^{6} Z^{2} + 29 X^{2} Y^{4} Z^{4} + 13 X^{2} Y^{2} Z^{6} + 12 X^{4} Y^{4} Z + 6 X^{3} Y^{4} Z^{2} + 42 X^{4} Y^{2} Z^{2} + 119 X^{2} Y^{4} Z^{2} + 65 X^{2} Y^{2} Z^{4} + 6 X^{4} Y^{2} Z + 12 X^{3} Y^{2} Z^{2} + 6 X^{2} Y^{4} Z + 36 X^{2} Y^{3} Z^{2} + 36 X^{2} Y^{2} Z^{3} + 24 X Y^{4} Z^{2} + 6 X Y^{2} Z^{4} + 48 X^{4} Y Z + 12 X^{3} Y^{2} Z + 24 X^{3} Y Z^{2} + 895 X^{2} Y^{2} Z^{2} + 24 X^{2} Y Z^{3} + 36 X Y^{4} Z + 42 X Y^{2} Z^{3} + 48 X Y Z^{4} + 108 X^{3} Y Z + 84 X^{2} Y^{2} Z + 12 X^{2} Y Z^{2} + 228 X Y^{3} Z + 138 X Y^{2} Z^{2} + 78 X Y Z^{3} + 144 X^{2} Y Z + 318 X Y^{2} Z + 138 X Y Z^{2} + 366 X Y Z

Algorithm definition

The algorithm ⟨14×20×22:3682⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨7×10×11:526⟩.

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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