Description of fast matrix multiplication algorithm: ⟨15×15×15:2088⟩

Algorithm type

18 X^{8} Y^{2} Z^{2} + 9 X^{4} Y^{6} Z^{2} + 153 X^{4} Y^{4} Z^{4} + 9 X^{4} Y^{2} Z^{6} + 2 X^{2} Y Z^{9} + 10 X Y Z^{9} + 9 X^{6} Y^{2} Z^{2} + 18 X^{4} Y^{4} Z^{2} + 18 X^{4} Y^{2} Z^{4} + 45 X^{2} Y^{6} Z^{2} + 79 X^{2} Y^{2} Z^{6} + 6 X^{2} Y^{6} Z + 10 X^{2} Y Z^{6} + 117 X^{4} Y^{2} Z^{2} + 4 X^{4} Y Z^{3} + 111 X^{2} Y^{4} Z^{2} + 2 X^{2} Y^{3} Z^{3} + 111 X^{2} Y^{2} Z^{4} + 30 X Y^{6} Z + 32 X Y Z^{6} + 12 X^{4} Y^{2} Z + 12 X^{4} Y Z^{2} + 2 X^{3} Y Z^{3} + 12 X^{2} Y^{4} Z + 6 X^{2} Y^{3} Z^{2} + 10 X^{2} Y^{2} Z^{3} + 12 X^{2} Y Z^{4} + 10 X Y^{3} Z^{3} + 26 X^{4} Y Z + 6 X^{3} Y^{2} Z + 6 X^{3} Y Z^{2} + 13 X^{2} Y^{3} Z + 308 X^{2} Y^{2} Z^{2} + 39 X^{2} Y Z^{3} + 6 X Y^{4} Z + 30 X Y^{3} Z^{2} + 32 X Y^{2} Z^{3} + 6 X Y Z^{4} + 13 X^{3} Y Z + 104 X^{2} Y^{2} Z + 104 X^{2} Y Z^{2} + 65 X Y^{3} Z + 12 X Y^{2} Z^{2} + 79 X Y Z^{3} + 169 X^{2} Y Z + 55 X Y^{2} Z + 55 X Y Z^{2} + 91 X Y Z

Algorithm definition

The algorithm ⟨15×15×15:2088⟩ is the (Kronecker) tensor product of ⟨3×3×5:36⟩ with ⟨5×5×3:58⟩.

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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