Description of fast matrix multiplication algorithm: ⟨8×15×32:2329⟩

Algorithm type

X^{2} Y^{13} Z^{8} + 4 X^{2} Y^{12} Z^{8} + 56 X^{4} Y^{12} Z^{4} + 16 X^{4} Y^{8} Z^{8} + X^{2} Y^{14} Z^{4} + X^{2} Y^{9} Z^{8} + 32 X^{4} Y^{8} Z^{6} + 12 X^{2} Y^{12} Z^{4} + 7 X Y^{13} Z^{4} + 7 X Y^{14} Z^{2} + 6 X Y^{12} Z^{4} + 80 X^{4} Y^{8} Z^{4} + 168 X^{2} Y^{12} Z^{2} + 21 X^{2} Y^{8} Z^{6} + 11 X^{2} Y^{6} Z^{8} + X^{2} Y^{9} Z^{4} + X^{2} Y^{5} Z^{8} + 14 X Y^{12} Z^{2} + 18 X^{2} Y^{8} Z^{4} + X^{2} Y^{6} Z^{6} + 12 X^{2} Y^{4} Z^{8} + 112 X Y^{12} Z + 8 X Y^{9} Z^{4} + 34 X^{2} Y^{8} Z^{3} + 5 X^{2} Y^{5} Z^{6} + X^{2} Y^{3} Z^{8} + 8 X^{4} Y^{4} Z^{4} + 125 X^{2} Y^{8} Z^{2} + 15 X^{2} Y^{6} Z^{4} + 6 X^{2} Y^{4} Z^{6} + 11 X^{2} Y^{2} Z^{8} + 8 X Y^{9} Z^{2} + 29 X Y^{8} Z^{3} + 4 X Y^{8} Z^{2} + 4 X Y^{7} Z^{3} + 8 X Y^{6} Z^{4} + X^{2} Y^{6} Z^{2} + 26 X^{2} Y^{4} Z^{4} + 53 X Y^{8} Z + 16 X Y^{7} Z^{2} + 4 X Y^{6} Z^{3} + 7 X Y^{5} Z^{4} + 5 X^{2} Y^{5} Z^{2} + 4 X Y^{7} Z + 10 X Y^{6} Z^{2} + 5 X Y^{5} Z^{3} + 14 X Y^{4} Z^{4} + 110 X^{2} Y^{4} Z^{2} + 32 X^{2} Y^{2} Z^{4} + 4 X Y^{6} Z + 3 X Y^{4} Z^{3} + 25 X Y^{3} Z^{4} + 112 X^{2} Y^{3} Z^{2} + 64 X^{2} Y^{2} Z^{3} + 5 X Y^{5} Z + 18 X Y^{4} Z^{2} + 6 X Y^{3} Z^{3} + 8 X Y^{2} Z^{4} + 160 X^{2} Y^{2} Z^{2} + 99 X Y^{4} Z + 57 X Y^{3} Z^{2} + 43 X Y^{2} Z^{3} + 33 X Y Z^{4} + 16 X^{2} Y Z^{2} + 230 X Y^{3} Z + 91 X Y^{2} Z + 28 X Y Z^{2} + 192 X Y Z

Algorithm definition

The algorithm ⟨8×15×32:2329⟩ is serendipitous tensor product (⟨4×3×8:73⟩ - 13) ⊗ ⟨2×5×4:32⟩ +⟨2×5×12:94⟩ +5⟨2×5×8:63⟩.

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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