Description of fast matrix multiplication algorithm: ⟨12×16×20:2303⟩

Algorithm type

13 X^{8} Y^{8} Z^{8} + 3 X^{12} Y^{4} Z^{4} + X^{8} Y^{8} Z^{4} + 2 X^{4} Y^{12} Z^{4} + 2 X^{4} Y^{8} Z^{8} + 4 X^{4} Y^{4} Z^{12} + 3 X^{8} Y^{4} Z^{4} + 8 X^{4} Y^{8} Z^{4} + 6 X^{4} Y^{4} Z^{8} + 161 X^{4} Y^{4} Z^{4} + 36 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{4} Z^{2} + 24 X^{2} Y^{6} Z^{2} + 24 X^{2} Y^{4} Z^{4} + 48 X^{2} Y^{2} Z^{6} + 36 X^{4} Y^{2} Z^{2} + 96 X^{2} Y^{4} Z^{2} + 72 X^{2} Y^{2} Z^{4} + 528 X^{2} Y^{2} Z^{2} + 108 X^{3} Y Z + 36 X^{2} Y^{2} Z + 72 X Y^{3} Z + 72 X Y^{2} Z^{2} + 144 X Y Z^{3} + 108 X^{2} Y Z + 288 X Y^{2} Z + 216 X Y Z^{2} + 180 X Y Z

Algorithm definition

The algorithm ⟨12×16×20:2303⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×8×10:329⟩.

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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