Description of fast matrix multiplication algorithm: ⟨15×20×28:4788⟩

Algorithm type

8 X Y^{16} Z + 6 X^{6} Y^{6} Z^{4} + 24 X^{2} Y^{12} Z^{2} + 15 X^{6} Y^{4} Z^{4} + 138 X^{4} Y^{6} Z^{4} + 48 X Y^{12} Z + 2 X^{3} Y^{8} Z^{2} + 24 X^{2} Y^{3} Z^{8} + 6 X^{6} Y^{2} Z^{4} + 345 X^{4} Y^{4} Z^{4} + 106 X^{2} Y^{8} Z^{2} + 60 X^{2} Y^{2} Z^{8} + 78 X^{6} Y^{3} Z^{2} + 48 X^{4} Y^{3} Z^{4} + 12 X^{3} Y^{6} Z^{2} + 24 X^{2} Y Z^{8} + 195 X^{6} Y^{2} Z^{2} + 258 X^{4} Y^{2} Z^{4} + 276 X^{2} Y^{6} Z^{2} + 48 X Y^{8} Z + 78 X^{6} Y Z^{2} + 24 X^{4} Y^{3} Z^{2} + 48 X^{4} Y Z^{4} + 12 X^{3} Y^{4} Z^{2} + 24 X^{2} Y^{3} Z^{4} + 8 X Y^{4} Z^{4} + 60 X^{4} Y^{2} Z^{2} + 26 X^{3} Y^{4} Z + 316 X^{2} Y^{4} Z^{2} + 60 X^{2} Y^{2} Z^{4} + 48 X Y^{3} Z^{4} + 24 X^{4} Y Z^{2} + 156 X^{3} Y^{3} Z + 10 X^{3} Y^{2} Z^{2} + 8 X^{2} Y^{4} Z + 186 X^{2} Y^{3} Z^{2} + 24 X^{2} Y Z^{4} + 8 X Y^{4} Z^{2} + 48 X Y^{2} Z^{4} + 156 X^{3} Y^{2} Z + 48 X^{2} Y^{3} Z + 551 X^{2} Y^{2} Z^{2} + 70 X Y^{4} Z + 48 X Y^{3} Z^{2} + 40 X Y Z^{4} + 130 X^{3} Y Z + 48 X^{2} Y^{2} Z + 170 X^{2} Y Z^{2} + 180 X Y^{3} Z + 48 X Y^{2} Z^{2} + 40 X^{2} Y Z + 180 X Y^{2} Z + 40 X Y Z^{2} + 150 X Y Z

Algorithm definition

The algorithm ⟨15×20×28:4788⟩ is the (Kronecker) tensor product of ⟨3×4×7:63⟩ with ⟨5×5×4:76⟩.

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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