Description of fast matrix multiplication algorithm: ⟨9×16×16:1444⟩

Algorithm type

100 X^{4} Y^{4} Z^{4} + 9 X^{9} Y Z + 4 X Y^{9} Z + 9 X Y Z^{9} + 60 X^{6} Y^{2} Z^{2} + 40 X^{4} Y^{4} Z^{2} + 40 X^{2} Y^{6} Z^{2} + 40 X^{2} Y^{4} Z^{4} + 60 X^{2} Y^{2} Z^{6} + 12 X^{6} Y^{2} Z + 4 X^{4} Y^{4} Z + 8 X^{2} Y^{6} Z + 8 X Y^{6} Z^{2} + 4 X Y^{4} Z^{4} + 12 X Y^{2} Z^{6} + 6 X^{6} Y Z + 20 X^{4} Y^{2} Z^{2} + 228 X^{2} Y^{4} Z^{2} + 20 X^{2} Y^{2} Z^{4} + 44 X Y^{6} Z + 6 X Y Z^{6} + 4 X^{4} Y^{2} Z + 12 X^{3} Y^{3} Z + 12 X^{3} Y^{2} Z^{2} + 18 X^{3} Y Z^{3} + 44 X^{2} Y^{4} Z + 12 X^{2} Y^{2} Z^{3} + 44 X Y^{4} Z^{2} + 12 X Y^{3} Z^{3} + 4 X Y^{2} Z^{4} + X^{4} Y Z + 66 X^{3} Y^{2} Z + 6 X^{3} Y Z^{2} + 4 X^{2} Y^{3} Z + 68 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 121 X Y^{4} Z + 4 X Y^{3} Z^{2} + 66 X Y^{2} Z^{3} + X Y Z^{4} + 18 X^{3} Y Z + 34 X^{2} Y^{2} Z + 2 X^{2} Y Z^{2} + 12 X Y^{3} Z + 34 X Y^{2} Z^{2} + 18 X Y Z^{3} + 6 X^{2} Y Z + 66 X Y^{2} Z + 6 X Y Z^{2} + 9 X Y Z

Algorithm definition

The algorithm ⟨9×16×16:1444⟩ is the (Kronecker) tensor product of ⟨3×4×4:38⟩ with ⟨3×4×4:38⟩.

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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