Description of fast matrix multiplication algorithm: ⟨10×20×22:2702⟩

Algorithm type

7 X^{8} Y^{8} Z^{8} + 2 X^{6} Y^{12} Z^{6} + X^{4} Y^{14} Z^{4} + 2 X^{10} Y^{4} Z^{6} + 2 X^{8} Y^{8} Z^{4} + X^{8} Y^{6} Z^{6} + 4 X^{6} Y^{8} Z^{6} + 5 X^{4} Y^{12} Z^{4} + 2 X^{4} Y^{8} Z^{8} + 4 X^{10} Y^{4} Z^{4} + 2 X^{6} Y^{4} Z^{8} + X^{2} Y^{14} Z^{2} + X^{2} Y^{8} Z^{8} + 2 X^{8} Y^{4} Z^{4} + 6 X^{6} Y^{6} Z^{4} + 9 X^{4} Y^{8} Z^{4} + 2 X^{4} Y^{4} Z^{8} + 2 X^{2} Y^{4} Z^{10} + 2 X^{10} Y^{2} Z^{2} + 2 X^{6} Y^{6} Z^{2} + 2 X^{6} Y^{4} Z^{4} + 2 X^{4} Y^{6} Z^{4} + 4 X^{6} Y^{4} Z^{2} + 2 X^{6} Y^{2} Z^{4} + 127 X^{4} Y^{4} Z^{4} + 2 X^{4} Y^{2} Z^{6} + 12 X^{3} Y^{6} Z^{3} + 14 X^{2} Y^{8} Z^{2} + 5 X^{2} Y^{4} Z^{6} + 6 X^{2} Y^{7} Z^{2} + 18 X^{6} Y^{2} Z^{2} + 12 X^{5} Y^{2} Z^{3} + 20 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{3} Z^{3} + X^{4} Y^{2} Z^{4} + 24 X^{3} Y^{4} Z^{3} + 60 X^{2} Y^{6} Z^{2} + 18 X^{2} Y^{4} Z^{4} + 14 X^{2} Y^{2} Z^{6} + 24 X^{5} Y^{2} Z^{2} + 12 X^{3} Y^{2} Z^{4} + 6 X Y^{7} Z + 6 X Y^{4} Z^{4} + 22 X^{4} Y^{2} Z^{2} + 36 X^{3} Y^{3} Z^{2} + 106 X^{2} Y^{4} Z^{2} + 14 X^{2} Y^{2} Z^{4} + 12 X Y^{2} Z^{5} + 12 X^{5} Y Z + 12 X^{3} Y^{3} Z + 12 X^{3} Y^{2} Z^{2} + 12 X^{2} Y^{3} Z^{2} + 24 X^{3} Y^{2} Z + 12 X^{3} Y Z^{2} + 580 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 84 X Y^{4} Z + 30 X Y^{2} Z^{3} + 108 X^{3} Y Z + 48 X^{2} Y^{2} Z + 6 X^{2} Y Z^{2} + 180 X Y^{3} Z + 36 X Y^{2} Z^{2} + 84 X Y Z^{3} + 60 X^{2} Y Z + 312 X Y^{2} Z + 12 X Y Z^{2} + 420 X Y Z

Algorithm definition

The algorithm ⟨10×20×22:2702⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨5×10×11:386⟩.

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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