Description of fast matrix multiplication algorithm: ⟨8×22×28:3003⟩

Algorithm type

8 X^{8} Y^{16} Z^{8} + 16 X^{8} Y^{14} Z^{8} + 16 X^{4} Y^{16} Z^{4} + 24 X^{4} Y^{14} Z^{4} + 8 X^{2} Y^{16} Z^{2} + 8 X^{2} Y^{14} Z^{2} + 89 X^{4} Y^{8} Z^{4} + 5 X^{2} Y^{12} Z^{2} + 96 X^{4} Y^{7} Z^{4} + 5 X^{4} Y^{6} Z^{4} + 3 X^{2} Y^{10} Z^{2} + 51 X^{4} Y^{4} Z^{4} + 141 X^{2} Y^{8} Z^{2} + 144 X^{2} Y^{7} Z^{2} + 12 X^{4} Y^{2} Z^{4} + 15 X^{2} Y^{6} Z^{2} + 48 X Y^{8} Z + 48 X Y^{7} Z + 326 X^{2} Y^{4} Z^{2} + 30 X Y^{6} Z + 30 X^{2} Y^{3} Z^{2} + 18 X Y^{5} Z + 398 X^{2} Y^{2} Z^{2} + 270 X Y^{4} Z + 72 X^{2} Y Z^{2} + 90 X Y^{3} Z + 480 X Y^{2} Z + 552 X Y Z

Algorithm definition

The algorithm ⟨8×22×28:3003⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨4×11×14:429⟩.

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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