Description of fast matrix multiplication algorithm: ⟨16×22×30:6090⟩

Algorithm type

X^{16} Y^{16} Z^{16} + 2 X^{14} Y^{14} Z^{16} + 2 X^{8} Y^{16} Z^{8} + 2 X^{8} Y^{14} Z^{8} + X^{8} Y^{12} Z^{8} + 2 X^{8} Y^{10} Z^{8} + 38 X^{8} Y^{8} Z^{8} + 2 X^{8} Y^{6} Z^{8} + 12 X^{7} Y^{7} Z^{8} + 8 X^{6} Y^{8} Z^{8} + 3 X^{8} Y^{8} Z^{4} + 6 X^{8} Y^{4} Z^{8} + 4 X^{6} Y^{6} Z^{8} + 6 X^{4} Y^{12} Z^{4} + 3 X^{4} Y^{4} Z^{12} + 4 X^{4} Y^{10} Z^{4} + 5 X^{8} Y^{4} Z^{4} + 108 X^{4} Y^{8} Z^{4} + 6 X^{4} Y^{4} Z^{8} + 14 X^{2} Y^{12} Z^{2} + 12 X^{4} Y^{7} Z^{4} + 4 X^{6} Y^{4} Z^{4} + 4 X^{4} Y^{8} Z^{2} + 20 X^{4} Y^{6} Z^{4} + 2 X^{2} Y^{10} Z^{2} + 4 X^{2} Y^{8} Z^{4} + 12 X^{4} Y^{5} Z^{4} + 6 X^{6} Y^{4} Z^{2} + 353 X^{4} Y^{4} Z^{4} + 40 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{4} Z^{6} + 12 X^{4} Y^{3} Z^{4} + 48 X^{3} Y^{4} Z^{4} + 6 X^{6} Y^{2} Z^{2} + 40 X^{4} Y^{4} Z^{2} + 46 X^{4} Y^{2} Z^{4} + 24 X^{3} Y^{3} Z^{4} + 56 X^{2} Y^{6} Z^{2} + 38 X^{2} Y^{4} Z^{4} + 26 X^{2} Y^{2} Z^{6} + 24 X^{2} Y^{5} Z^{2} + 48 X^{4} Y^{2} Z^{2} + 736 X^{2} Y^{4} Z^{2} + 62 X^{2} Y^{2} Z^{4} + 84 X Y^{6} Z + 24 X^{3} Y^{2} Z^{2} + 24 X^{2} Y^{4} Z + 84 X^{2} Y^{3} Z^{2} + 12 X Y^{5} Z + 24 X Y^{4} Z^{2} + 36 X^{3} Y^{2} Z + 1086 X^{2} Y^{2} Z^{2} + 240 X Y^{4} Z + 48 X Y^{2} Z^{3} + 36 X^{3} Y Z + 132 X^{2} Y^{2} Z + 60 X^{2} Y Z^{2} + 120 X Y^{3} Z + 228 X Y^{2} Z^{2} + 48 X Y Z^{3} + 108 X^{2} Y Z + 960 X Y^{2} Z + 156 X Y Z^{2} + 720 X Y Z

Algorithm definition

The algorithm ⟨16×22×30:6090⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×11×15:870⟩.

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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