Description of fast matrix multiplication algorithm: ⟨9×15×16:1363⟩

Algorithm type

91 X^{4} Y^{4} Z^{4} + 4 X^{9} Y Z + 4 X Y^{9} Z + 6 X Y Z^{9} + 41 X^{6} Y^{2} Z^{2} + 14 X^{4} Y^{4} Z^{2} + 40 X^{2} Y^{6} Z^{2} + 33 X^{2} Y^{4} Z^{4} + 47 X^{2} Y^{2} Z^{6} + 2 X^{6} Y^{2} Z + 4 X^{2} Y^{6} Z + 6 X Y^{6} Z^{2} + 2 X Y^{4} Z^{4} + 8 X Y^{2} Z^{6} + 6 X^{6} Y Z + 42 X^{4} Y^{2} Z^{2} + 112 X^{2} Y^{4} Z^{2} + 73 X^{2} Y^{2} Z^{4} + 24 X Y^{6} Z + 18 X Y Z^{6} + 10 X^{3} Y^{3} Z + 9 X^{3} Y^{2} Z^{2} + 11 X^{3} Y Z^{3} + 8 X^{2} Y^{4} Z + 4 X^{2} Y^{2} Z^{3} + 20 X Y^{4} Z^{2} + 10 X Y^{3} Z^{3} + 10 X Y^{2} Z^{4} + 24 X^{3} Y^{2} Z + 19 X^{3} Y Z^{2} + 12 X^{2} Y^{3} Z + 146 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 32 X Y^{4} Z + 14 X Y^{3} Z^{2} + 28 X Y^{2} Z^{3} + 12 X Y Z^{4} + 33 X^{3} Y Z + 38 X^{2} Y^{2} Z + 24 X^{2} Y Z^{2} + 24 X Y^{3} Z + 61 X Y^{2} Z^{2} + 31 X Y Z^{3} + 42 X^{2} Y Z + 76 X Y^{2} Z + 41 X Y Z^{2} + 35 X Y Z

Algorithm definition

The algorithm ⟨9×15×16:1363⟩ is the (Kronecker) tensor product of ⟨3×3×4:29⟩ with ⟨3×5×4:47⟩.

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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