Description of fast matrix multiplication algorithm: ⟨20×25×32:8744⟩

Algorithm type

X^{12} Y^{2} Z + 56 X^{8} Y^{4} Z^{2} + 56 X^{6} Y^{4} Z^{4} + 336 X^{4} Y^{4} Z^{6} + X^{9} Y^{2} Z^{2} + X^{9} Y^{2} Z + 2 X^{9} Y Z^{2} + 56 X^{6} Y^{4} Z^{2} + 112 X^{6} Y^{2} Z^{4} + 504 X^{4} Y^{4} Z^{4} + 8 X^{2} Y^{6} Z^{4} + 117 X^{2} Y^{4} Z^{6} + 13 X^{8} Y^{2} Z + 6 X^{6} Y^{2} Z^{3} + 12 X^{2} Y^{6} Z^{3} + 12 X^{2} Y^{5} Z^{4} + 6 X^{2} Y^{4} Z^{5} + 17 X^{2} Y^{3} Z^{6} + 2 X Y^{8} Z^{2} + 22 X^{6} Y^{2} Z^{2} + 224 X^{4} Y^{4} Z^{2} + 224 X^{4} Y^{2} Z^{4} + 131 X^{2} Y^{6} Z^{2} + 26 X^{2} Y^{5} Z^{3} + 31 X^{2} Y^{4} Z^{4} + 11 X^{2} Y^{3} Z^{5} + 581 X^{2} Y^{2} Z^{6} + 17 X^{6} Y^{2} Z + 30 X^{6} Y Z^{2} + 18 X^{4} Y^{4} Z + 78 X^{4} Y^{2} Z^{3} + 18 X^{3} Y^{4} Z^{2} + 20 X^{3} Y^{2} Z^{4} + X^{2} Y^{5} Z^{2} + 122 X^{2} Y^{4} Z^{3} + 27 X^{2} Y^{3} Z^{4} + 10 X Y^{6} Z^{2} + X Y^{5} Z^{3} + 48 X Y^{2} Z^{6} + 137 X^{4} Y^{2} Z^{2} + 18 X^{3} Y^{4} Z + 2 X^{3} Y^{2} Z^{3} + 40 X^{3} Y Z^{4} + 353 X^{2} Y^{4} Z^{2} + 35 X^{2} Y^{3} Z^{3} + 753 X^{2} Y^{2} Z^{4} + 48 X Y^{6} Z + 12 X Y^{5} Z^{2} + 44 X Y^{4} Z^{3} + 10 X Y^{3} Z^{4} + 6 X Y^{2} Z^{5} + 165 X Y Z^{6} + 68 X^{4} Y^{2} Z + 52 X^{4} Y Z^{2} + 4 X^{3} Y^{3} Z + 73 X^{3} Y^{2} Z^{2} + 9 X^{3} Y Z^{3} + 72 X^{2} Y^{4} Z + 46 X^{2} Y^{3} Z^{2} + 134 X^{2} Y^{2} Z^{3} + 80 X^{2} Y Z^{4} + 13 X Y^{5} Z + 19 X Y^{4} Z^{2} + 34 X Y^{3} Z^{3} + 16 X Y^{2} Z^{4} + 21 X^{3} Y^{2} Z + 43 X^{3} Y Z^{2} + 34 X^{2} Y^{3} Z + 843 X^{2} Y^{2} Z^{2} + 111 X^{2} Y Z^{3} + 77 X Y^{4} Z + 97 X Y^{3} Z^{2} + 218 X Y^{2} Z^{3} + 205 X Y Z^{4} + 11 X^{3} Y Z + 111 X^{2} Y^{2} Z + 201 X^{2} Y Z^{2} + 79 X Y^{3} Z + 323 X Y^{2} Z^{2} + 161 X Y Z^{3} + 134 X^{2} Y Z + 291 X Y^{2} Z + 389 X Y Z^{2} + 194 X Y Z

Algorithm definition

The algorithm ⟨20×25×32:8744⟩ is serendipitous tensor product (⟨5×5×8:144⟩ - 20) ⊗ ⟨4×5×4:61⟩ +10⟨4×5×8:118⟩.

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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