Description of fast matrix multiplication algorithm: ⟨8×32×32:4662⟩

Algorithm type

3 X^{8} Y^{16} Z^{8} + 9 X^{8} Y^{12} Z^{8} + 27 X^{8} Y^{8} Z^{8} + 20 X^{4} Y^{16} Z^{4} + 2 X^{4} Y^{14} Z^{4} + 6 X^{2} Y^{18} Z^{2} + 9 X^{8} Y^{4} Z^{8} + 57 X^{4} Y^{12} Z^{4} + 15 X^{2} Y^{16} Z^{2} + 7 X^{4} Y^{10} Z^{4} + 23 X^{2} Y^{14} Z^{2} + 82 X^{4} Y^{8} Z^{4} + 14 X^{2} Y^{12} Z^{2} + 62 X^{4} Y^{6} Z^{4} + 23 X^{2} Y^{10} Z^{2} + 239 X^{4} Y^{4} Z^{4} + 179 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{7} Z^{2} + 36 X Y^{9} Z + 81 X^{4} Y^{2} Z^{4} + 417 X^{2} Y^{6} Z^{2} + 90 X Y^{8} Z + 42 X^{2} Y^{5} Z^{2} + 138 X Y^{7} Z + 438 X^{2} Y^{4} Z^{2} + 84 X Y^{6} Z + 48 X^{2} Y^{3} Z^{2} + 138 X Y^{5} Z + 549 X^{2} Y^{2} Z^{2} + 354 X Y^{4} Z + 162 X^{2} Y Z^{2} + 450 X Y^{3} Z + 324 X Y^{2} Z + 522 X Y Z

Algorithm definition

The algorithm ⟨8×32×32:4662⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨4×16×16:666⟩.

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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