Description of fast matrix multiplication algorithm: ⟨18×20×21:4284⟩

Algorithm type

12 X^{6} Y^{6} Z^{4} + 12 X^{2} Y^{9} Z^{4} + 4 X Y^{12} Z^{2} + 30 X^{6} Y^{4} Z^{4} + 108 X^{4} Y^{6} Z^{4} + 12 X^{2} Y^{6} Z^{6} + 12 X Y^{12} Z + 12 X^{8} Y^{3} Z^{2} + 18 X^{4} Y^{3} Z^{6} + 4 X^{3} Y^{8} Z^{2} + 36 X^{2} Y^{9} Z^{2} + 30 X^{8} Y^{2} Z^{2} + 12 X^{6} Y^{2} Z^{4} + 24 X^{4} Y^{6} Z^{2} + 270 X^{4} Y^{4} Z^{4} + 45 X^{4} Y^{2} Z^{6} + 36 X^{2} Y^{8} Z^{2} + 30 X^{2} Y^{6} Z^{4} + 30 X^{2} Y^{4} Z^{6} + 24 X Y^{9} Z^{2} + 4 X Y^{8} Z^{3} + 12 X^{8} Y Z^{2} + 30 X^{6} Y^{3} Z^{2} + 18 X^{4} Y Z^{6} + 24 X^{3} Y^{6} Z^{2} + 8 X^{2} Y^{8} Z + 24 X^{2} Y^{3} Z^{6} + 72 X Y^{9} Z + 75 X^{6} Y^{2} Z^{2} + 60 X^{4} Y^{4} Z^{2} + 108 X^{4} Y^{2} Z^{4} + 354 X^{2} Y^{6} Z^{2} + 72 X^{2} Y^{2} Z^{6} + 16 X Y^{8} Z + 24 X Y^{6} Z^{3} + 30 X^{6} Y Z^{2} + 4 X^{4} Y^{4} Z + 48 X^{4} Y^{3} Z^{2} + 24 X^{3} Y^{4} Z^{2} + 48 X^{2} Y^{6} Z + 6 X^{2} Y^{4} Z^{3} + 12 X^{2} Y^{3} Z^{4} + 24 X^{2} Y Z^{6} + 24 X Y^{6} Z^{2} + 24 X^{4} Y^{3} Z + 144 X^{4} Y^{2} Z^{2} + 10 X^{3} Y^{4} Z + 336 X^{2} Y^{4} Z^{2} + 36 X^{2} Y^{3} Z^{3} + 168 X Y^{6} Z + 32 X Y^{4} Z^{3} + 24 X^{4} Y^{2} Z + 48 X^{4} Y Z^{2} + 60 X^{3} Y^{3} Z + 20 X^{3} Y^{2} Z^{2} + 64 X^{2} Y^{4} Z + 60 X^{2} Y^{3} Z^{2} + 36 X^{2} Y^{2} Z^{3} + 48 X Y^{3} Z^{3} + 20 X^{4} Y Z + 60 X^{3} Y^{2} Z + 96 X^{2} Y^{3} Z + 288 X^{2} Y^{2} Z^{2} + 30 X^{2} Y Z^{3} + 104 X Y^{4} Z + 20 X Y^{3} Z^{2} + 68 X Y^{2} Z^{3} + 50 X^{3} Y Z + 136 X^{2} Y^{2} Z + 24 X^{2} Y Z^{2} + 108 X Y^{3} Z + 40 X Y Z^{3} + 80 X^{2} Y Z + 128 X Y^{2} Z + 40 X Y Z

Algorithm definition

The algorithm ⟨18×20×21:4284⟩ is the (Kronecker) tensor product of ⟨3×4×7:63⟩ with ⟨6×5×3:68⟩.

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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