Description of fast matrix multiplication algorithm: ⟨8×30×32:4522⟩

Algorithm type

27 X^{8} Y^{8} Z^{8} + 3 X^{8} Y^{6} Z^{8} + 2 X^{2} Y^{18} Z^{2} + 6 X^{6} Y^{6} Z^{8} + 15 X^{4} Y^{12} Z^{4} + 2 X^{2} Y^{16} Z^{2} + 9 X^{4} Y^{10} Z^{4} + 77 X^{4} Y^{8} Z^{4} + 30 X^{2} Y^{12} Z^{2} + 9 X^{4} Y^{6} Z^{4} + 6 X^{2} Y^{10} Z^{2} + 270 X^{4} Y^{4} Z^{4} + 44 X^{2} Y^{8} Z^{2} + 6 X^{2} Y^{6} Z^{4} + 18 X^{4} Y^{3} Z^{4} + 12 X Y^{9} Z + 6 X^{4} Y^{2} Z^{4} + 36 X^{3} Y^{3} Z^{4} + 138 X^{2} Y^{6} Z^{2} + 12 X Y^{8} Z + 54 X^{2} Y^{5} Z^{2} + 602 X^{2} Y^{4} Z^{2} + 180 X Y^{6} Z + 54 X^{2} Y^{3} Z^{2} + 36 X Y^{5} Z + 756 X^{2} Y^{2} Z^{2} + 264 X Y^{4} Z + 36 X Y^{3} Z^{2} + 36 X^{2} Y Z^{2} + 288 X Y^{3} Z + 840 X Y^{2} Z + 648 X Y Z

Algorithm definition

The algorithm ⟨8×30×32:4522⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨4×15×16:646⟩.

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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