Description of fast matrix multiplication algorithm: ⟨8×25×28:3319⟩

Algorithm type

X^{2} Y^{12} Z^{3} + 288 X^{4} Y^{8} Z^{4} + X^{2} Y^{10} Z^{3} + 2 X^{2} Y^{9} Z^{4} + 5 X Y^{12} Z^{2} + 8 X^{2} Y^{8} Z^{4} + X Y^{12} Z + X Y^{11} Z^{2} + X^{2} Y^{9} Z^{2} + 4 X^{2} Y^{8} Z^{3} + X^{2} Y^{7} Z^{4} + 412 X^{2} Y^{8} Z^{2} + X^{2} Y^{7} Z^{3} + X^{2} Y^{6} Z^{4} + X Y^{10} Z + X Y^{9} Z^{2} + X^{2} Y^{7} Z^{2} + 3 X^{2} Y^{6} Z^{3} + 6 X^{2} Y^{5} Z^{4} + 2 X Y^{9} Z + 34 X Y^{8} Z^{2} + 64 X^{4} Y^{4} Z^{2} + 6 X^{2} Y^{5} Z^{3} + 108 X^{2} Y^{4} Z^{4} + 129 X Y^{8} Z + 13 X Y^{7} Z^{2} + 4 X^{2} Y^{5} Z^{2} + 13 X^{2} Y^{4} Z^{3} + 6 X^{2} Y^{3} Z^{4} + 7 X Y^{7} Z + 14 X Y^{6} Z^{2} + 138 X^{2} Y^{4} Z^{2} + 13 X^{2} Y^{3} Z^{3} + 12 X^{2} Y^{2} Z^{4} + 11 X Y^{6} Z + 11 X Y^{5} Z^{2} + 64 X^{2} Y^{4} Z + 7 X^{2} Y^{3} Z^{2} + 18 X^{2} Y^{2} Z^{3} + 12 X Y^{5} Z + 134 X Y^{4} Z^{2} + 586 X^{2} Y^{2} Z^{2} + 141 X Y^{4} Z + 41 X Y^{3} Z^{2} + 13 X Y^{3} Z + 65 X Y^{2} Z^{2} + 128 X^{2} Y Z + 263 X Y^{2} Z + 249 X Y Z^{2} + 274 X Y Z

Algorithm definition

The algorithm ⟨8×25×28:3319⟩ is serendipitous tensor product (⟨4×5×7:104⟩ - 17) ⊗ ⟨2×5×4:32⟩ +⟨2×5×12:94⟩ +7⟨2×5×8:63⟩.

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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