Description of fast matrix multiplication algorithm: ⟨12×21×28:3969⟩

Algorithm type

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

Algorithm definition

The algorithm ⟨12×21×28:3969⟩ is the (Kronecker) tensor product of ⟨3×7×4:63⟩ with ⟨4×3×7:63⟩.

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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