Description of fast matrix multiplication algorithm: ⟨16×25×28:6307⟩

Algorithm type

36 X^{8} Y^{4} Z^{2} + 36 X^{6} Y^{4} Z^{4} + 216 X^{4} Y^{4} Z^{6} + 36 X^{6} Y^{4} Z^{2} + 72 X^{6} Y^{2} Z^{4} + 324 X^{4} Y^{4} Z^{4} + 72 X^{2} Y^{4} Z^{6} + 8 X^{8} Y^{2} Z + 8 X^{6} Y^{2} Z^{2} + 144 X^{4} Y^{4} Z^{2} + 144 X^{4} Y^{2} Z^{4} + 75 X^{2} Y^{6} Z^{2} + 8 X^{2} Y^{5} Z^{3} + 47 X^{2} Y^{4} Z^{4} + 360 X^{2} Y^{2} Z^{6} + 8 X^{6} Y^{2} Z + 16 X^{6} Y Z^{2} + 15 X^{4} Y^{4} Z + 48 X^{4} Y^{2} Z^{3} + 15 X^{3} Y^{4} Z^{2} + 12 X^{3} Y^{2} Z^{4} + 6 X^{2} Y^{5} Z^{2} + 109 X^{2} Y^{4} Z^{3} + 17 X^{2} Y^{3} Z^{4} + 2 X Y^{6} Z^{2} + 24 X Y^{2} Z^{6} + 84 X^{4} Y^{2} Z^{2} + 15 X^{3} Y^{4} Z + 24 X^{3} Y Z^{4} + 262 X^{2} Y^{4} Z^{2} + 37 X^{2} Y^{3} Z^{3} + 514 X^{2} Y^{2} Z^{4} + 32 X Y^{6} Z + 5 X Y^{5} Z^{2} + 30 X Y^{4} Z^{3} + 98 X Y Z^{6} + 48 X^{4} Y^{2} Z + 32 X^{4} Y Z^{2} + 59 X^{3} Y^{2} Z^{2} + 60 X^{2} Y^{4} Z + 34 X^{2} Y^{3} Z^{2} + 158 X^{2} Y^{2} Z^{3} + 48 X^{2} Y Z^{4} + 6 X Y^{5} Z + 30 X Y^{4} Z^{2} + 7 X Y^{3} Z^{3} + 25 X Y^{2} Z^{4} + 18 X^{3} Y^{2} Z + 33 X^{3} Y Z^{2} + 16 X^{2} Y^{3} Z + 625 X^{2} Y^{2} Z^{2} + 64 X^{2} Y Z^{3} + 58 X Y^{4} Z + 57 X Y^{3} Z^{2} + 180 X Y^{2} Z^{3} + 146 X Y Z^{4} + 3 X^{3} Y Z + 97 X^{2} Y^{2} Z + 154 X^{2} Y Z^{2} + 68 X Y^{3} Z + 300 X Y^{2} Z^{2} + 146 X Y Z^{3} + 90 X^{2} Y Z + 257 X Y^{2} Z + 345 X Y Z^{2} + 184 X Y Z

Algorithm definition

The algorithm ⟨16×25×28:6307⟩ is serendipitous tensor product (⟨4×5×7:104⟩ - 17) ⊗ ⟨4×5×4:61⟩ +⟨4×5×12:174⟩ +7⟨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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