Description of fast matrix multiplication algorithm: ⟨9×15×16:1350⟩

Algorithm type

3 X^{6} Y^{2} Z^{6} + 9 X^{4} Y^{6} Z^{4} + 81 X^{4} Y^{4} Z^{4} + 3 X^{2} Y^{4} Z^{6} + 3 X^{6} Y^{2} Z^{2} + 6 X^{6} Y Z^{3} + 15 X^{2} Y^{6} Z^{2} + 21 X^{2} Y^{4} Z^{4} + 30 X^{2} Y^{2} Z^{6} + 18 X^{4} Y^{3} Z^{2} + 6 X^{6} Y Z + 165 X^{4} Y^{2} Z^{2} + 48 X^{2} Y^{4} Z^{2} + 42 X^{2} Y^{2} Z^{4} + 6 X^{3} Y Z^{3} + 18 X^{2} Y^{3} Z^{2} + 6 X^{2} Y^{2} Z^{3} + 6 X^{4} Y Z + 30 X^{2} Y^{3} Z + 216 X^{2} Y^{2} Z^{2} + 60 X^{2} Y Z^{3} + 6 X Y^{2} Z^{3} + 6 X^{3} Y Z + 96 X^{2} Y^{2} Z + 84 X^{2} Y Z^{2} + 30 X Y^{3} Z + 42 X Y^{2} Z^{2} + 60 X Y Z^{3} + 30 X^{2} Y Z + 96 X Y^{2} Z + 84 X Y Z^{2} + 24 X Y Z

Algorithm definition

The algorithm ⟨9×15×16:1350⟩ is the (Kronecker) tensor product of ⟨3×3×2:15⟩ with ⟨3×5×8:90⟩.

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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