Description of fast matrix multiplication algorithm: ⟨16×16×25:3721⟩

Algorithm type

X Y^{4} Z^{16} + 2 X^{2} Y^{4} Z^{12} + 36 X^{9} Y^{4} Z^{4} + X^{4} Y^{4} Z^{9} + 2 X Y^{4} Z^{12} + 12 X^{6} Y^{4} Z^{6} + 4 X^{2} Y^{2} Z^{12} + 24 X^{9} Y^{4} Z^{2} + 4 X^{4} Y^{2} Z^{9} + 12 X^{3} Y^{4} Z^{8} + 2 X^{2} Y^{4} Z^{9} + 4 X^{9} Y^{4} Z + 108 X^{6} Y^{4} Z^{4} + 24 X^{6} Y^{2} Z^{6} + 18 X^{4} Y^{4} Z^{6} + 4 X^{4} Y Z^{9} + 18 X^{2} Y^{4} Z^{8} + X Y^{4} Z^{9} + 96 X^{9} Y^{2} Z^{2} + 4 X^{6} Y^{4} Z^{3} + 12 X^{3} Y^{4} Z^{6} + 4 X^{2} Y^{2} Z^{9} + 8 X Y^{4} Z^{8} + 32 X^{9} Y^{2} Z + 36 X^{6} Y^{4} Z^{2} + 48 X^{6} Y^{2} Z^{4} + 81 X^{4} Y^{4} Z^{4} + 44 X^{4} Y^{2} Z^{6} + 26 X^{2} Y^{4} Z^{6} + 8 X^{2} Y^{2} Z^{8} + 64 X^{9} Y Z + 24 X^{6} Y^{2} Z^{3} + 16 X^{4} Y Z^{6} + 24 X^{3} Y^{6} Z^{2} + 52 X^{3} Y^{4} Z^{4} + 4 X^{2} Y^{6} Z^{3} + 4 X Y^{9} Z + 4 X Y^{6} Z^{4} + 8 X Y^{4} Z^{6} + 280 X^{6} Y^{2} Z^{2} + 32 X^{6} Y Z^{3} + 72 X^{4} Y^{2} Z^{4} + 8 X^{3} Y^{6} Z + 4 X^{3} Y^{4} Z^{3} + 36 X^{2} Y^{6} Z^{2} + 72 X^{2} Y^{4} Z^{4} + 24 X^{2} Y^{2} Z^{6} + 4 X Y^{6} Z^{3} + 40 X^{6} Y^{2} Z + 64 X^{6} Y Z^{2} + 20 X^{4} Y^{2} Z^{3} + 16 X^{4} Y Z^{4} + 40 X^{3} Y^{4} Z^{2} + 16 X^{3} Y^{2} Z^{4} + 4 X^{2} Y^{4} Z^{3} + 16 X Y^{6} Z^{2} + 20 X Y^{4} Z^{4} + 160 X^{6} Y Z + 180 X^{4} Y^{2} Z^{2} + 40 X^{4} Y Z^{3} + 8 X^{3} Y^{4} Z + 16 X^{3} Y^{2} Z^{3} + 36 X^{2} Y^{4} Z^{2} + 8 X^{2} Y^{3} Z^{3} + 52 X^{2} Y^{2} Z^{4} + 8 X Y^{6} Z + 4 X Y^{4} Z^{3} + 80 X^{4} Y Z^{2} + 32 X^{3} Y^{3} Z + 172 X^{3} Y^{2} Z^{2} + 16 X^{2} Y^{3} Z^{2} + 46 X^{2} Y^{2} Z^{3} + 16 X Y^{4} Z^{2} + 18 X Y^{2} Z^{4} + 100 X^{4} Y Z + 68 X^{3} Y^{2} Z + 40 X^{2} Y^{3} Z + 258 X^{2} Y^{2} Z^{2} + 36 X^{2} Y Z^{3} + 4 X Y^{4} Z + 18 X Y^{2} Z^{3} + 144 X^{3} Y Z + 40 X^{2} Y^{2} Z + 72 X^{2} Y Z^{2} + 36 X Y^{3} Z + 72 X Y^{2} Z^{2} + 180 X^{2} Y Z + 36 X Y^{2} Z + 81 X Y Z

Algorithm definition

The algorithm ⟨16×16×25:3721⟩ is the (Kronecker) tensor product of ⟨4×4×5:61⟩ with ⟨4×4×5:61⟩.

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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