Description of fast matrix multiplication algorithm: ⟨6×21×21:1665⟩

Algorithm type

6 X^{4} Y^{8} Z^{4} + 6 X^{4} Y^{6} Z^{4} + 12 X^{2} Y^{10} Z^{2} + 96 X^{4} Y^{4} Z^{4} + 24 X^{2} Y^{8} Z^{2} + 9 X^{2} Y^{6} Z^{4} + 24 X Y^{10} Z + 18 X^{6} Y^{2} Z^{2} + 3 X^{4} Y^{2} Z^{4} + 30 X^{2} Y^{6} Z^{2} + 27 X^{2} Y^{4} Z^{4} + 18 X^{2} Y^{2} Z^{6} + 24 X Y^{8} Z + 18 X Y^{6} Z^{2} + 252 X^{2} Y^{4} Z^{2} + 51 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 12 X^{2} Y^{3} Z^{2} + 24 X Y^{5} Z + 54 X Y^{4} Z^{2} + 36 X^{3} Y^{2} Z + 207 X^{2} Y^{2} Z^{2} + 120 X Y^{4} Z + 18 X Y^{3} Z^{2} + 36 X Y^{2} Z^{3} + 36 X^{3} Y Z + 6 X^{2} Y Z^{2} + 36 X Y^{3} Z + 156 X Y^{2} Z^{2} + 36 X Y Z^{3} + 114 X Y^{2} Z + 102 X Y Z^{2} + 18 X Y Z

Algorithm definition

The algorithm ⟨6×21×21:1665⟩ is the (Kronecker) tensor product of ⟨3×7×7:111⟩ with ⟨2×3×3:15⟩.

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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