Description of fast matrix multiplication algorithm: ⟨8×21×21:2205⟩

Algorithm type

9 X^{8} Y^{8} Z^{8} + 3 X^{8} Y^{4} Z^{8} + 6 X^{4} Y^{10} Z^{4} + 6 X^{6} Y^{4} Z^{6} + 30 X^{4} Y^{8} Z^{4} + 12 X^{2} Y^{10} Z^{2} + 123 X^{4} Y^{4} Z^{4} + 24 X^{2} Y^{8} Z^{2} + 18 X^{4} Y^{2} Z^{4} + 12 X^{3} Y^{4} Z^{3} + 54 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{5} Z^{2} + 12 X^{3} Y^{2} Z^{3} + 270 X^{2} Y^{4} Z^{2} + 108 X Y^{6} Z + 414 X^{2} Y^{2} Z^{2} + 96 X Y^{4} Z + 24 X^{2} Y Z^{2} + 108 X Y^{3} Z + 480 X Y^{2} Z + 384 X Y Z

Algorithm definition

The algorithm ⟨8×21×21:2205⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨4×7×7:147⟩.

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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