Description of fast matrix multiplication algorithm: ⟨10×25×28:4057⟩

Algorithm type

8 X^{6} Y^{8} Z^{4} + 376 X^{4} Y^{8} Z^{4} + 6 X^{2} Y^{8} Z^{4} + 8 X^{3} Y^{8} Z^{2} + 3 X^{2} Y^{8} Z^{3} + 2 X^{2} Y^{7} Z^{4} + 24 X^{6} Y^{4} Z^{2} + 8 X^{4} Y^{4} Z^{4} + 512 X^{2} Y^{8} Z^{2} + X^{2} Y^{6} Z^{3} + 3 X^{2} Y^{5} Z^{4} + 19 X Y^{8} Z^{2} + 72 X^{4} Y^{4} Z^{2} + 2 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{5} Z^{3} + 131 X^{2} Y^{4} Z^{4} + 137 X Y^{8} Z + 9 X Y^{7} Z^{2} + 2 X^{2} Y^{5} Z^{2} + 7 X^{2} Y^{4} Z^{3} + 10 X^{2} Y^{3} Z^{4} + 2 X Y^{7} Z + 10 X Y^{6} Z^{2} + 24 X^{3} Y^{4} Z + 178 X^{2} Y^{4} Z^{2} + 12 X^{2} Y^{3} Z^{3} + 13 X^{2} Y^{2} Z^{4} + 3 X Y^{6} Z + 12 X Y^{5} Z^{2} + 2 X Y^{4} Z^{3} + 16 X^{3} Y^{2} Z^{2} + 72 X^{2} Y^{4} Z + 4 X^{2} Y^{3} Z^{2} + 16 X^{2} Y^{2} Z^{3} + 15 X Y^{5} Z + 150 X Y^{4} Z^{2} + 2 X Y^{3} Z^{3} + 767 X^{2} Y^{2} Z^{2} + 177 X Y^{4} Z + 23 X Y^{3} Z^{2} + 8 X Y^{2} Z^{3} + 48 X^{3} Y Z + 16 X^{2} Y Z^{2} + 15 X Y^{3} Z + 37 X Y^{2} Z^{2} + 12 X Y Z^{3} + 144 X^{2} Y Z + 294 X Y^{2} Z + 296 X Y Z^{2} + 347 X Y Z

Algorithm definition

The algorithm ⟨10×25×28:4057⟩ is serendipitous tensor product (⟨5×5×7:127⟩ - 13) ⊗ ⟨2×5×4:32⟩ +⟨2×5×12:94⟩ +5⟨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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