Description of fast matrix multiplication algorithm: ⟨9×25×25:3364⟩

Algorithm type

4 X Y^{16} Z + X^{9} Y^{4} Z + 4 X Y^{12} Z + X Y^{4} Z^{9} + 10 X^{9} Y^{2} Z + 34 X^{6} Y^{4} Z^{2} + 289 X^{4} Y^{4} Z^{4} + 4 X^{3} Y^{8} Z + 68 X^{2} Y^{8} Z^{2} + 34 X^{2} Y^{4} Z^{6} + 4 X Y^{8} Z^{3} + 10 X Y^{2} Z^{9} + 25 X^{9} Y Z + 4 X^{6} Y^{4} Z + 8 X^{2} Y^{8} Z + X Y^{9} Z + 8 X Y^{8} Z^{2} + 4 X Y^{4} Z^{6} + 25 X Y Z^{9} + 170 X^{6} Y^{2} Z^{2} + 68 X^{4} Y^{4} Z^{2} + 2 X^{3} Y^{6} Z + 2 X^{3} Y^{4} Z^{3} + 34 X^{2} Y^{6} Z^{2} + 68 X^{2} Y^{4} Z^{4} + 170 X^{2} Y^{2} Z^{6} + 52 X Y^{8} Z + 2 X Y^{6} Z^{3} + 22 X^{6} Y^{2} Z + 4 X^{4} Y^{4} Z + 4 X^{3} Y^{4} Z^{2} + 4 X^{2} Y^{6} Z + 4 X^{2} Y^{4} Z^{3} + 4 X Y^{6} Z^{2} + 4 X Y^{4} Z^{4} + 22 X Y^{2} Z^{6} + 10 X^{6} Y Z + 34 X^{4} Y^{2} Z^{2} + 46 X^{3} Y^{4} Z + 20 X^{3} Y^{2} Z^{3} + 450 X^{2} Y^{4} Z^{2} + 34 X^{2} Y^{2} Z^{4} + 26 X Y^{6} Z + 46 X Y^{4} Z^{3} + 10 X Y Z^{6} + 4 X^{4} Y^{2} Z + 10 X^{3} Y^{3} Z + 22 X^{3} Y^{2} Z^{2} + 50 X^{3} Y Z^{3} + 56 X^{2} Y^{4} Z + 22 X^{2} Y^{2} Z^{3} + 56 X Y^{4} Z^{2} + 10 X Y^{3} Z^{3} + 4 X Y^{2} Z^{4} + X^{4} Y Z + 144 X^{3} Y^{2} Z + 10 X^{3} Y Z^{2} + 2 X^{2} Y^{3} Z + 246 X^{2} Y^{2} Z^{2} + 10 X^{2} Y Z^{3} + 197 X Y^{4} Z + 2 X Y^{3} Z^{2} + 144 X Y^{2} Z^{3} + X Y Z^{4} + 70 X^{3} Y Z + 54 X^{2} Y^{2} Z + 2 X^{2} Y Z^{2} + 14 X Y^{3} Z + 54 X Y^{2} Z^{2} + 70 X Y Z^{3} + 14 X^{2} Y Z + 182 X Y^{2} Z + 14 X Y Z^{2} + 49 X Y Z

Algorithm definition

The algorithm ⟨9×25×25:3364⟩ is the (Kronecker) tensor product of ⟨3×5×5:58⟩ with ⟨3×5×5:58⟩.

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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