Description of fast matrix multiplication algorithm: ⟨16×21×21:3969⟩

Algorithm type

36 X^{6} Y^{4} Z^{6} + 90 X^{6} Y^{4} Z^{4} + 90 X^{4} Y^{4} Z^{6} + 12 X^{8} Y^{2} Z^{3} + 12 X^{3} Y^{2} Z^{8} + 30 X^{8} Y^{2} Z^{2} + 36 X^{6} Y^{4} Z^{2} + 225 X^{4} Y^{4} Z^{4} + 36 X^{2} Y^{4} Z^{6} + 30 X^{2} Y^{2} Z^{8} + 12 X^{8} Y^{2} Z + 72 X^{6} Y^{2} Z^{3} + 72 X^{3} Y^{2} Z^{6} + 12 X Y^{2} Z^{8} + 180 X^{6} Y^{2} Z^{2} + 90 X^{4} Y^{4} Z^{2} + 90 X^{2} Y^{4} Z^{4} + 180 X^{2} Y^{2} Z^{6} + 72 X^{6} Y^{2} Z + 72 X^{4} Y^{2} Z^{3} + 4 X^{4} Y Z^{4} + 72 X^{3} Y^{2} Z^{4} + 72 X Y^{2} Z^{6} + 180 X^{4} Y^{2} Z^{2} + 24 X^{4} Y Z^{3} + 24 X^{3} Y Z^{4} + 36 X^{2} Y^{4} Z^{2} + 180 X^{2} Y^{2} Z^{4} + 72 X^{4} Y^{2} Z + 24 X^{4} Y Z^{2} + 60 X^{3} Y^{2} Z^{2} + 144 X^{3} Y Z^{3} + 60 X^{2} Y^{2} Z^{3} + 24 X^{2} Y Z^{4} + 72 X Y^{2} Z^{4} + 20 X^{4} Y Z + 144 X^{3} Y Z^{2} + 300 X^{2} Y^{2} Z^{2} + 144 X^{2} Y Z^{3} + 20 X Y Z^{4} + 120 X^{3} Y Z + 60 X^{2} Y^{2} Z + 144 X^{2} Y Z^{2} + 60 X Y^{2} Z^{2} + 120 X Y Z^{3} + 120 X^{2} Y Z + 120 X Y Z^{2} + 100 X Y Z

Algorithm definition

The algorithm ⟨16×21×21:3969⟩ is the (Kronecker) tensor product of ⟨4×3×7:63⟩ with ⟨4×7×3:63⟩.

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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