Description of fast matrix multiplication algorithm: ⟨20×25×28:7718⟩

Algorithm type

X^{12} Y^{4} Z^{2} + X^{9} Y^{4} Z^{4} + 6 X^{6} Y^{4} Z^{6} + 3 X^{12} Y^{2} Z + X^{9} Y^{4} Z^{2} + 2 X^{9} Y^{2} Z^{4} + 47 X^{8} Y^{4} Z^{2} + 56 X^{6} Y^{4} Z^{4} + 282 X^{4} Y^{4} Z^{6} + 3 X^{9} Y^{2} Z^{2} + 2 X^{3} Y^{4} Z^{6} + 3 X^{9} Y^{2} Z + 6 X^{9} Y Z^{2} + X^{8} Y^{2} Z^{2} + 51 X^{6} Y^{4} Z^{2} + 99 X^{6} Y^{2} Z^{4} + 423 X^{4} Y^{4} Z^{4} + 6 X^{4} Y^{2} Z^{6} + 94 X^{2} Y^{4} Z^{6} + 9 X^{8} Y^{2} Z + 18 X^{6} Y^{2} Z^{3} + 2 X^{6} Y Z^{4} + 2 X^{3} Y^{6} Z^{2} + 8 X^{3} Y^{2} Z^{6} + 2 X^{2} Y^{3} Z^{6} + 37 X^{6} Y^{2} Z^{2} + 188 X^{4} Y^{4} Z^{2} + 197 X^{4} Y^{2} Z^{4} + 94 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{4} Z^{4} + X^{2} Y^{3} Z^{5} + 486 X^{2} Y^{2} Z^{6} + X Y^{4} Z^{5} + 21 X^{6} Y^{2} Z + 30 X^{6} Y Z^{2} + 17 X^{4} Y^{4} Z + 54 X^{4} Y^{2} Z^{3} + 4 X^{4} Y Z^{4} + 19 X^{3} Y^{4} Z^{2} + 26 X^{3} Y^{2} Z^{4} + 111 X^{2} Y^{4} Z^{3} + 33 X^{2} Y^{3} Z^{4} + 8 X^{2} Y Z^{6} + 32 X Y^{2} Z^{6} + 101 X^{4} Y^{2} Z^{2} + 17 X^{3} Y^{4} Z + 6 X^{3} Y^{2} Z^{3} + 32 X^{3} Y Z^{4} + 280 X^{2} Y^{4} Z^{2} + 31 X^{2} Y^{3} Z^{3} + 655 X^{2} Y^{2} Z^{4} + 34 X Y^{6} Z + 37 X Y^{4} Z^{3} + X Y^{3} Z^{4} + 3 X Y^{2} Z^{5} + 133 X Y Z^{6} + 56 X^{4} Y^{2} Z + 36 X^{4} Y Z^{2} + 6 X^{3} Y^{3} Z + 79 X^{3} Y^{2} Z^{2} + 24 X^{3} Y Z^{3} + 68 X^{2} Y^{4} Z + 13 X^{2} Y^{3} Z^{2} + 162 X^{2} Y^{2} Z^{3} + 74 X^{2} Y Z^{4} + X Y^{5} Z + 9 X Y^{4} Z^{2} + 12 X Y^{3} Z^{3} + 19 X Y^{2} Z^{4} + X Y Z^{5} + 26 X^{3} Y^{2} Z + 73 X^{3} Y Z^{2} + 18 X^{2} Y^{3} Z + 814 X^{2} Y^{2} Z^{2} + 72 X^{2} Y Z^{3} + 53 X Y^{4} Z + 63 X Y^{3} Z^{2} + 203 X Y^{2} Z^{3} + 178 X Y Z^{4} + 29 X^{3} Y Z + 106 X^{2} Y^{2} Z + 191 X^{2} Y Z^{2} + 51 X Y^{3} Z + 253 X Y^{2} Z^{2} + 180 X Y Z^{3} + 98 X^{2} Y Z + 269 X Y^{2} Z + 415 X Y Z^{2} + 246 X Y Z

Algorithm definition

The algorithm ⟨20×25×28:7718⟩ is serendipitous tensor product (⟨5×5×7:127⟩ - 13) ⊗ ⟨4×5×4:61⟩ +⟨4×5×12:174⟩ +5⟨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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