Description of fast matrix multiplication algorithm: ⟨12×16×21:2394⟩

Algorithm type

60 X^{4} Y^{6} Z^{4} + 6 X Y^{12} Z + 18 X^{2} Y^{9} Z^{2} + 12 X^{4} Y^{6} Z^{2} + 150 X^{4} Y^{4} Z^{4} + 20 X^{2} Y^{8} Z^{2} + 12 X^{6} Y^{3} Z^{2} + 12 X^{4} Y^{3} Z^{4} + 4 X^{2} Y^{8} Z + 18 X^{2} Y^{3} Z^{6} + 36 X Y^{9} Z + 30 X^{6} Y^{2} Z^{2} + 30 X^{4} Y^{4} Z^{2} + 90 X^{4} Y^{2} Z^{4} + 171 X^{2} Y^{6} Z^{2} + 45 X^{2} Y^{2} Z^{6} + 2 X Y^{8} Z + 12 X^{6} Y Z^{2} + 66 X^{4} Y^{3} Z^{2} + 12 X^{4} Y Z^{4} + 24 X^{2} Y^{6} Z + 6 X^{2} Y^{3} Z^{4} + 18 X^{2} Y Z^{6} + 177 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{4} Z + 139 X^{2} Y^{4} Z^{2} + 15 X^{2} Y^{2} Z^{4} + 48 X Y^{6} Z + 6 X Y^{4} Z^{3} + 66 X^{4} Y Z^{2} + 24 X^{3} Y^{3} Z + 46 X^{2} Y^{4} Z + 60 X^{2} Y^{3} Z^{2} + 6 X^{2} Y Z^{4} + 2 X Y^{4} Z^{2} + 36 X Y^{3} Z^{3} + 24 X^{3} Y^{2} Z + 132 X^{2} Y^{3} Z + 175 X^{2} Y^{2} Z^{2} + 18 X Y^{4} Z + 12 X Y^{3} Z^{2} + 36 X Y^{2} Z^{3} + 20 X^{3} Y Z + 152 X^{2} Y^{2} Z + 38 X^{2} Y Z^{2} + 66 X Y^{3} Z + 12 X Y^{2} Z^{2} + 30 X Y Z^{3} + 110 X^{2} Y Z + 46 X Y^{2} Z + 10 X Y Z^{2} + 30 X Y Z

Algorithm definition

The algorithm ⟨12×16×21:2394⟩ is the (Kronecker) tensor product of ⟨3×4×7:63⟩ with ⟨4×4×3:38⟩.

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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