Description of fast matrix multiplication algorithm: ⟨8×21×21:2160⟩

Algorithm type

3 X^{4} Y^{10} Z^{2} + 6 X^{4} Y^{8} Z^{2} + 24 X^{4} Y^{6} Z^{4} + 6 X^{2} Y^{10} Z + 3 X^{4} Y^{6} Z^{2} + 132 X^{4} Y^{4} Z^{4} + 3 X^{2} Y^{8} Z^{2} + 3 X^{2} Y^{6} Z^{4} + 12 X^{2} Y^{8} Z + 3 X^{4} Y^{4} Z^{2} + 3 X^{4} Y^{2} Z^{4} + 66 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{4} Z^{4} + 3 X^{2} Y^{2} Z^{6} + 6 X Y^{8} Z + 6 X^{2} Y^{6} Z + 6 X Y^{6} Z^{2} + 36 X^{4} Y^{2} Z^{2} + 6 X^{2} Y^{5} Z + 327 X^{2} Y^{4} Z^{2} + 39 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 18 X^{2} Y^{4} Z + 48 X^{2} Y^{3} Z^{2} + 6 X Y^{4} Z^{2} + 6 X^{2} Y^{3} Z + 360 X^{2} Y^{2} Z^{2} + 132 X Y^{4} Z + 6 X Y^{3} Z^{2} + 6 X Y^{2} Z^{3} + 78 X^{2} Y^{2} Z + 6 X^{2} Y Z^{2} + 36 X Y^{3} Z + 84 X Y^{2} Z^{2} + 6 X Y Z^{3} + 72 X^{2} Y Z + 306 X Y^{2} Z + 78 X Y Z^{2} + 180 X Y Z

Algorithm definition

The algorithm ⟨8×21×21:2160⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨4×7×7:144⟩.

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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