Description of fast matrix multiplication algorithm: ⟨20×24×28:7588⟩

Algorithm type

2 X^{8} Y^{16} Z^{8} + 3 X^{8} Y^{8} Z^{12} + 10 X^{16} Y^{4} Z^{4} + 53 X^{8} Y^{8} Z^{8} + 6 X^{4} Y^{16} Z^{4} + 2 X^{16} Y^{4} Z^{2} + 6 X^{8} Y^{6} Z^{8} + 6 X^{4} Y^{14} Z^{4} + 12 X^{8} Y^{6} Z^{6} + 20 X^{4} Y^{8} Z^{8} + 27 X^{4} Y^{4} Z^{12} + 10 X^{2} Y^{16} Z^{2} + 2 X^{6} Y^{8} Z^{4} + 4 X^{4} Y^{8} Z^{6} + 6 X^{4} Y^{4} Z^{10} + 6 X^{2} Y^{14} Z^{2} + 124 X^{4} Y^{8} Z^{4} + 4 X^{4} Y^{6} Z^{6} + 10 X^{4} Y^{4} Z^{8} + 6 X^{4} Y^{2} Z^{10} + 16 X^{8} Y^{4} Z^{2} + 2 X^{6} Y^{4} Z^{4} + 2 X^{4} Y^{8} Z^{2} + 20 X^{4} Y^{6} Z^{4} + 24 X^{4} Y^{4} Z^{6} + 32 X^{2} Y^{8} Z^{4} + 76 X^{8} Y^{2} Z^{2} + 4 X^{6} Y^{4} Z^{2} + 475 X^{4} Y^{4} Z^{4} + 72 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{6} Z^{4} + 48 X^{2} Y^{4} Z^{6} + 12 X^{8} Y^{2} Z + 36 X^{4} Y^{3} Z^{4} + 36 X^{2} Y^{7} Z^{2} + 4 X^{6} Y^{2} Z^{2} + 18 X^{4} Y^{4} Z^{2} + 72 X^{4} Y^{3} Z^{3} + 6 X^{4} Y^{2} Z^{4} + 2 X^{2} Y^{6} Z^{2} + 176 X^{2} Y^{4} Z^{4} + 222 X^{2} Y^{2} Z^{6} + 60 X Y^{8} Z + 12 X^{3} Y^{4} Z^{2} + 24 X^{2} Y^{4} Z^{3} + 36 X^{2} Y^{2} Z^{5} + 36 X Y^{7} Z + 18 X^{4} Y^{2} Z^{2} + 800 X^{2} Y^{4} Z^{2} + 24 X^{2} Y^{3} Z^{3} + 80 X^{2} Y^{2} Z^{4} + 36 X^{2} Y Z^{5} + 96 X^{4} Y^{2} Z + 12 X^{3} Y^{2} Z^{2} + 12 X^{2} Y^{4} Z + 120 X^{2} Y^{3} Z^{2} + 36 X^{2} Y^{2} Z^{3} + 192 X Y^{4} Z^{2} + 96 X^{4} Y Z + 24 X^{3} Y^{2} Z + 1064 X^{2} Y^{2} Z^{2} + 216 X Y^{4} Z + 24 X Y^{3} Z^{2} + 288 X Y^{2} Z^{3} + 24 X^{3} Y Z + 108 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 12 X Y^{3} Z + 336 X Y^{2} Z^{2} + 360 X Y Z^{3} + 108 X^{2} Y Z + 768 X Y^{2} Z + 120 X Y Z^{2} + 732 X Y Z

Algorithm definition

The algorithm ⟨20×24×28:7588⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨10×12×14:1084⟩.

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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