Description of fast matrix multiplication algorithm: ⟨20×21×21:5040⟩

Algorithm type

12 X^{8} Y^{4} Z^{6} + 30 X^{8} Y^{4} Z^{4} + 24 X^{6} Y^{4} Z^{6} + 12 X^{8} Y^{4} Z^{2} + 60 X^{6} Y^{4} Z^{4} + 120 X^{4} Y^{4} Z^{6} + 4 X^{4} Y^{2} Z^{8} + 18 X^{8} Y^{2} Z^{3} + 6 X^{6} Y^{4} Z^{3} + 8 X^{3} Y^{2} Z^{8} + 45 X^{8} Y^{2} Z^{2} + 39 X^{6} Y^{4} Z^{2} + 300 X^{4} Y^{4} Z^{4} + 24 X^{4} Y^{2} Z^{6} + 40 X^{2} Y^{2} Z^{8} + 18 X^{8} Y^{2} Z + 6 X^{6} Y^{4} Z + 42 X^{6} Y^{2} Z^{3} + 24 X^{4} Y^{4} Z^{3} + 48 X^{3} Y^{2} Z^{6} + 12 X^{2} Y^{6} Z^{3} + 105 X^{6} Y^{2} Z^{2} + 180 X^{4} Y^{4} Z^{2} + 24 X^{4} Y^{2} Z^{4} + 30 X^{2} Y^{6} Z^{2} + 240 X^{2} Y^{2} Z^{6} + 42 X^{6} Y^{2} Z + 24 X^{4} Y^{4} Z + 54 X^{4} Y^{2} Z^{3} + 6 X^{4} Y Z^{4} + 50 X^{3} Y^{2} Z^{4} + 12 X^{2} Y^{6} Z + 54 X^{2} Y^{4} Z^{3} + 155 X^{4} Y^{2} Z^{2} + 36 X^{4} Y Z^{3} + 12 X^{3} Y^{2} Z^{3} + 14 X^{3} Y Z^{4} + 135 X^{2} Y^{4} Z^{2} + 248 X^{2} Y^{2} Z^{4} + 4 X Y^{3} Z^{4} + 54 X^{4} Y^{2} Z + 36 X^{4} Y Z^{2} + 52 X^{3} Y^{2} Z^{2} + 84 X^{3} Y Z^{3} + 54 X^{2} Y^{4} Z + 162 X^{2} Y^{2} Z^{3} + 18 X^{2} Y Z^{4} + 24 X Y^{3} Z^{3} + 18 X Y^{2} Z^{4} + 30 X^{4} Y Z + 10 X^{3} Y^{2} Z + 84 X^{3} Y Z^{2} + 533 X^{2} Y^{2} Z^{2} + 108 X^{2} Y Z^{3} + 24 X Y^{3} Z^{2} + 108 X Y^{2} Z^{3} + 38 X Y Z^{4} + 70 X^{3} Y Z + 154 X^{2} Y^{2} Z + 108 X^{2} Y Z^{2} + 20 X Y^{3} Z + 108 X Y^{2} Z^{2} + 228 X Y Z^{3} + 90 X^{2} Y Z + 90 X Y^{2} Z + 228 X Y Z^{2} + 190 X Y Z

Algorithm definition

The algorithm ⟨20×21×21:5040⟩ is the (Kronecker) tensor product of ⟨4×3×7:63⟩ with ⟨5×7×3:80⟩.

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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