Description of fast matrix multiplication algorithm: ⟨8×20×32:3136⟩

Algorithm type

X^{8} Y^{16} Z^{8} + 8 X^{8} Y^{12} Z^{8} + X^{4} Y^{20} Z^{4} + 7 X^{8} Y^{8} Z^{8} + 10 X^{4} Y^{16} Z^{4} + 11 X^{4} Y^{12} Z^{4} + 21 X^{4} Y^{8} Z^{4} + 96 X^{4} Y^{6} Z^{4} + 12 X^{2} Y^{10} Z^{2} + 101 X^{4} Y^{4} Z^{4} + 120 X^{2} Y^{8} Z^{2} + 132 X^{2} Y^{6} Z^{2} + 144 X^{2} Y^{4} Z^{2} + 288 X^{2} Y^{3} Z^{2} + 36 X Y^{5} Z + 456 X^{2} Y^{2} Z^{2} + 360 X Y^{4} Z + 396 X Y^{3} Z + 324 X Y^{2} Z + 612 X Y Z

Algorithm definition

The algorithm ⟨8×20×32:3136⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨4×10×16:448⟩.

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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