Description of fast matrix multiplication algorithm: ⟨15×20×32:5442⟩

Algorithm type

4 X Y^{12} Z^{5} + 2 X^{2} Y^{11} Z^{4} + 2 X Y^{8} Z^{8} + 2 X^{2} Y^{11} Z^{3} + 4 X^{2} Y^{9} Z^{4} + X^{2} Y^{7} Z^{6} + 4 X^{2} Y^{4} Z^{9} + 2 X^{2} Y^{9} Z^{3} + 2 X^{2} Y^{8} Z^{4} + X^{2} Y^{7} Z^{5} + 10 X^{2} Y^{6} Z^{6} + 3 X^{2} Y^{4} Z^{8} + 6 X Y^{9} Z^{4} + 2 X Y^{8} Z^{5} + 2 X Y^{6} Z^{7} + X^{2} Y^{7} Z^{4} + 8 X^{2} Y^{6} Z^{5} + X^{2} Y^{5} Z^{6} + X^{2} Y^{4} Z^{7} + 2 X Y^{11} Z + 4 X Y^{10} Z^{2} + 4 X Y^{8} Z^{4} + 3 X Y^{6} Z^{6} + 4 X Y^{4} Z^{8} + 560 X^{4} Y^{4} Z^{4} + 3 X^{2} Y^{7} Z^{3} + 22 X^{2} Y^{6} Z^{4} + 13 X^{2} Y^{4} Z^{6} + 4 X Y^{8} Z^{3} + 10 X Y^{6} Z^{5} + X Y^{5} Z^{6} + 3 X Y^{4} Z^{7} + 11 X Y^{2} Z^{9} + 3 X^{9} Y Z + 4 X^{2} Y^{7} Z^{2} + 3 X^{2} Y^{6} Z^{3} + 4 X^{2} Y^{5} Z^{4} + 5 X^{2} Y^{4} Z^{5} + 3 X^{2} Y^{3} Z^{6} + 2 X^{2} Y^{2} Z^{7} + 9 X Y^{6} Z^{4} + 2 X Y^{4} Z^{6} + 5 X Y^{2} Z^{8} + 178 X^{6} Y^{2} Z^{2} + 112 X^{4} Y^{4} Z^{2} + 126 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{5} Z^{3} + 123 X^{2} Y^{4} Z^{4} + 4 X^{2} Y^{3} Z^{5} + 168 X^{2} Y^{2} Z^{6} + 2 X Y^{7} Z^{2} + 5 X Y^{6} Z^{3} + 3 X Y^{5} Z^{4} + 6 X Y^{4} Z^{5} + 18 X Y^{3} Z^{6} + 4 X Y^{2} Z^{7} + 2 X^{6} Y^{2} Z + 5 X^{2} Y^{5} Z^{2} + 22 X^{2} Y^{4} Z^{3} + 17 X^{2} Y^{3} Z^{4} + 4 X^{2} Y^{2} Z^{5} + 4 X Y^{7} Z + 16 X Y^{6} Z^{2} + 8 X Y^{4} Z^{4} + 12 X Y^{3} Z^{5} + 19 X Y^{2} Z^{6} + 40 X^{6} Y Z + 186 X^{4} Y^{2} Z^{2} + 828 X^{2} Y^{4} Z^{2} + 16 X^{2} Y^{3} Z^{3} + 258 X^{2} Y^{2} Z^{4} + 43 X Y^{6} Z + 5 X Y^{5} Z^{2} + 15 X Y^{4} Z^{3} + 17 X Y^{3} Z^{4} + 14 X Y^{2} Z^{5} + 60 X Y Z^{6} + 26 X^{4} Y^{2} Z + 2 X^{3} Y^{3} Z + 2 X^{3} Y^{2} Z^{2} + 3 X^{3} Y Z^{3} + 38 X^{2} Y^{4} Z + 2 X^{2} Y^{3} Z^{2} + 2 X^{2} Y^{2} Z^{3} + X Y^{5} Z + 43 X Y^{4} Z^{2} + 6 X Y^{3} Z^{3} + 55 X Y^{2} Z^{4} + 6 X Y Z^{5} + 13 X^{4} Y Z + 65 X^{3} Y^{2} Z + 61 X^{3} Y Z^{2} + 26 X^{2} Y^{3} Z + 397 X^{2} Y^{2} Z^{2} + 39 X^{2} Y Z^{3} + 204 X Y^{4} Z + 70 X Y^{3} Z^{2} + 112 X Y^{2} Z^{3} + 33 X Y Z^{4} + 51 X^{3} Y Z + 193 X^{2} Y^{2} Z + 33 X^{2} Y Z^{2} + 39 X Y^{3} Z + 312 X Y^{2} Z^{2} + 60 X Y Z^{3} + 55 X^{2} Y Z + 275 X Y^{2} Z + 85 X Y Z^{2} + 48 X Y Z

Algorithm definition

The algorithm ⟨15×20×32:5442⟩ is serendipitous tensor product (⟨5×5×8:144⟩ - 20) ⊗ ⟨3×4×4:38⟩ +10⟨3×4×8:73⟩.

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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