Description of fast matrix multiplication algorithm: ⟨8×16×20:1612⟩

Algorithm type

6 X^{8} Y^{8} Z^{8} + 2 X^{4} Y^{12} Z^{4} + 8 X^{4} Y^{8} Z^{4} + 6 X^{4} Y^{6} Z^{4} + 2 X^{2} Y^{9} Z^{2} + 94 X^{4} Y^{4} Z^{4} + 4 X Y^{9} Z + 6 X^{4} Y^{4} Z^{2} + 12 X^{4} Y^{2} Z^{4} + 48 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{2} Z^{6} + 2 X^{2} Y^{6} Z + 18 X^{4} Y^{2} Z^{2} + 160 X^{2} Y^{4} Z^{2} + 12 X^{2} Y^{2} Z^{4} + 32 X Y^{6} Z + 8 X^{2} Y^{4} Z + 14 X^{2} Y^{3} Z^{2} + 2 X Y^{3} Z^{3} + 6 X^{2} Y^{3} Z + 318 X^{2} Y^{2} Z^{2} + 64 X Y^{4} Z + 4 X Y^{3} Z^{2} + 8 X Y^{2} Z^{3} + 34 X^{2} Y^{2} Z + 20 X^{2} Y Z^{2} + 74 X Y^{3} Z + 16 X Y^{2} Z^{2} + 10 X Y Z^{3} + 30 X^{2} Y Z + 296 X Y^{2} Z + 20 X Y Z^{2} + 270 X Y Z

Algorithm definition

The algorithm ⟨8×16×20:1612⟩ is the (Kronecker) tensor product of ⟨2×4×4:26⟩ with ⟨4×4×5:62⟩.

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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