Description of fast matrix multiplication algorithm: ⟨8×22×24:2534⟩

Algorithm type

14 X^{8} Y^{8} Z^{8} + 32 X^{4} Y^{12} Z^{4} + 8 X^{2} Y^{16} Z^{2} + 22 X^{4} Y^{10} Z^{4} + 8 X^{2} Y^{14} Z^{2} + 6 X^{4} Y^{8} Z^{4} + 16 X^{2} Y^{12} Z^{2} + 18 X^{4} Y^{6} Z^{4} + 16 X^{2} Y^{10} Z^{2} + 130 X^{4} Y^{4} Z^{4} + 8 X^{2} Y^{8} Z^{2} + 248 X^{2} Y^{6} Z^{2} + 48 X Y^{8} Z + 132 X^{2} Y^{5} Z^{2} + 48 X Y^{7} Z + 86 X^{2} Y^{4} Z^{2} + 96 X Y^{6} Z + 108 X^{2} Y^{3} Z^{2} + 96 X Y^{5} Z + 338 X^{2} Y^{2} Z^{2} + 48 X Y^{4} Z + 336 X Y^{3} Z + 300 X Y^{2} Z + 372 X Y Z

Algorithm definition

The algorithm ⟨8×22×24:2534⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨4×11×12:362⟩.

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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