Description of fast matrix multiplication algorithm: ⟨14×20×20:3346⟩

Algorithm type

X^{8} Y^{12} Z^{8} + 11 X^{8} Y^{8} Z^{8} + 3 X^{14} Y^{4} Z^{4} + 3 X^{4} Y^{4} Z^{14} + X^{14} Y^{4} Z^{2} + 12 X^{6} Y^{8} Z^{6} + 10 X^{4} Y^{12} Z^{4} + 4 X^{4} Y^{8} Z^{8} + X^{2} Y^{4} Z^{14} + 3 X^{4} Y^{12} Z^{2} + 2 X^{4} Y^{8} Z^{6} + 3 X^{4} Y^{8} Z^{4} + 2 X^{4} Y^{4} Z^{8} + 2 X^{2} Y^{8} Z^{6} + 9 X^{4} Y^{6} Z^{4} + X^{4} Y^{4} Z^{6} + 12 X^{8} Y^{2} Z^{2} + 3 X^{6} Y^{4} Z^{2} + 197 X^{4} Y^{4} Z^{4} + 7 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{4} Z^{6} + 12 X^{2} Y^{2} Z^{8} + 18 X^{7} Y^{2} Z^{2} + 18 X^{2} Y^{2} Z^{7} + 6 X^{7} Y^{2} Z + 15 X^{6} Y^{2} Z^{2} + 9 X^{4} Y^{4} Z^{2} + 72 X^{3} Y^{4} Z^{3} + 102 X^{2} Y^{6} Z^{2} + 55 X^{2} Y^{4} Z^{4} + 15 X^{2} Y^{2} Z^{6} + 6 X Y^{2} Z^{7} + 18 X^{2} Y^{6} Z + 12 X^{2} Y^{4} Z^{3} + 3 X^{4} Y^{2} Z^{2} + 69 X^{2} Y^{4} Z^{2} + 27 X^{2} Y^{2} Z^{4} + 12 X Y^{4} Z^{3} + 18 X^{2} Y^{3} Z^{2} + 6 X^{2} Y^{2} Z^{3} + 72 X^{4} Y Z + 18 X^{3} Y^{2} Z + 852 X^{2} Y^{2} Z^{2} + 42 X Y^{4} Z + 24 X Y^{2} Z^{3} + 72 X Y Z^{4} + 90 X^{3} Y Z + 54 X^{2} Y^{2} Z + 252 X Y^{3} Z + 186 X Y^{2} Z^{2} + 90 X Y Z^{3} + 18 X^{2} Y Z + 306 X Y^{2} Z + 90 X Y Z^{2} + 396 X Y Z

Algorithm definition

The algorithm ⟨14×20×20:3346⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨7×10×10:478⟩.

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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