Description of fast matrix multiplication algorithm: ⟨14×25×28:5607⟩

Algorithm type

4 X^{2} Y^{18} Z^{2} + X^{2} Y^{17} Z^{2} + 14 X Y^{18} Z + 8 X^{6} Y^{8} Z^{4} + 80 X^{4} Y^{8} Z^{6} + 3 X^{2} Y^{14} Z^{2} + 2 X Y^{16} Z + X^{2} Y^{13} Z^{2} + 464 X^{4} Y^{8} Z^{4} + 10 X^{2} Y^{12} Z^{2} + 5 X^{2} Y^{8} Z^{6} + 13 X Y^{14} Z + 2 X^{2} Y^{8} Z^{5} + X^{2} Y^{7} Z^{6} + 6 X Y^{13} Z + 8 X^{2} Y^{10} Z^{2} + 31 X^{2} Y^{8} Z^{4} + X^{2} Y^{7} Z^{5} + 12 X Y^{12} Z + 8 X^{3} Y^{8} Z^{2} + 15 X^{2} Y^{9} Z^{2} + 80 X^{2} Y^{8} Z^{3} + 3 X Y^{11} Z + 16 X^{6} Y^{4} Z^{2} + 8 X^{4} Y^{4} Z^{4} + 575 X^{2} Y^{8} Z^{2} + 2 X^{2} Y^{6} Z^{4} + 2 X^{2} Y^{5} Z^{5} + 48 X^{2} Y^{4} Z^{6} + 4 X Y^{10} Z + 12 X Y^{8} Z^{3} + 4 X^{6} Y^{2} Z^{3} + 2 X^{3} Y^{2} Z^{6} + 3 X^{2} Y^{7} Z^{2} + 2 X^{2} Y^{5} Z^{4} + 5 X^{2} Y^{4} Z^{5} + 3 X^{2} Y^{3} Z^{6} + 9 X Y^{9} Z + 41 X Y^{8} Z^{2} + 8 X Y^{7} Z^{3} + 6 X^{6} Y^{2} Z^{2} + 2 X^{6} Y Z^{3} + 136 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{2} Z^{4} + 2 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{5} Z^{3} + 168 X^{2} Y^{4} Z^{4} + 5 X^{2} Y^{3} Z^{5} + 5 X^{2} Y^{2} Z^{6} + 120 X Y^{8} Z + 6 X Y^{7} Z^{2} + 5 X Y^{6} Z^{3} + 5 X^{6} Y^{2} Z + 4 X^{6} Y Z^{2} + 6 X^{4} Y^{2} Z^{3} + 5 X^{3} Y^{2} Z^{4} + 9 X^{2} Y^{5} Z^{2} + 2 X^{2} Y^{4} Z^{3} + 6 X^{2} Y^{3} Z^{4} + 4 X^{2} Y^{2} Z^{5} + 4 X^{2} Y Z^{6} + 4 X Y^{7} Z + 12 X Y^{6} Z^{2} + 4 X Y^{5} Z^{3} + X Y^{2} Z^{6} + 11 X^{4} Y^{2} Z^{2} + 3 X^{4} Y Z^{3} + 16 X^{3} Y^{4} Z + 8 X^{3} Y^{2} Z^{3} + 8 X^{3} Y Z^{4} + 142 X^{2} Y^{4} Z^{2} + 3 X^{2} Y^{3} Z^{3} + 18 X^{2} Y^{2} Z^{4} + 5 X Y^{6} Z + 14 X Y^{5} Z^{2} + 53 X Y^{4} Z^{3} + X Y^{2} Z^{5} + 4 X Y Z^{6} + 7 X^{4} Y^{2} Z + 5 X^{4} Y Z^{2} + 2 X^{3} Y^{3} Z + 28 X^{3} Y^{2} Z^{2} + 13 X^{3} Y Z^{3} + 136 X^{2} Y^{4} Z + 10 X^{2} Y^{3} Z^{2} + 181 X^{2} Y^{2} Z^{3} + 13 X^{2} Y Z^{4} + 41 X Y^{5} Z + 176 X Y^{4} Z^{2} + 11 X Y^{3} Z^{3} + 3 X Y^{2} Z^{4} + 4 X Y Z^{5} + 5 X^{3} Y^{2} Z + 7 X^{3} Y Z^{2} + 2 X^{2} Y^{3} Z + 947 X^{2} Y^{2} Z^{2} + 10 X^{2} Y Z^{3} + 158 X Y^{4} Z + 15 X Y^{3} Z^{2} + 23 X Y^{2} Z^{3} + 13 X Y Z^{4} + 40 X^{3} Y Z + 5 X^{2} Y^{2} Z + 28 X^{2} Y Z^{2} + 36 X Y^{3} Z + 84 X Y^{2} Z^{2} + 117 X Y Z^{3} + 281 X^{2} Y Z + 234 X Y^{2} Z + 354 X Y Z^{2} + 287 X Y Z

Algorithm definition

The algorithm ⟨14×25×28:5607⟩ is serendipitous tensor product (⟨7×5×7:176⟩ - 29) ⊗ ⟨2×5×4:32⟩ +⟨2×5×20:157⟩ +7⟨2×5×8:63⟩ +5⟨4×5×4:61⟩.

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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