Description of fast matrix multiplication algorithm: ⟨10×20×28:3296⟩

Algorithm type

6 X^{6} Y^{4} Z^{4} + X^{2} Y^{8} Z^{3} + 282 X^{4} Y^{4} Z^{4} + 2 X^{2} Y^{8} Z^{2} + 2 X^{3} Y^{6} Z^{2} + X^{2} Y^{7} Z^{2} + 2 X^{2} Y^{3} Z^{6} + X Y^{7} Z^{3} + 18 X^{6} Y^{2} Z^{2} + 6 X^{4} Y^{2} Z^{4} + 95 X^{2} Y^{6} Z^{2} + 8 X^{2} Y^{4} Z^{4} + 3 X Y^{8} Z + X Y^{6} Z^{3} + 8 X^{3} Y^{4} Z^{2} + X^{2} Y^{4} Z^{3} + 4 X^{2} Y^{3} Z^{4} + 2 X Y^{7} Z + 54 X^{4} Y^{2} Z^{2} + 485 X^{2} Y^{4} Z^{2} + 9 X^{2} Y^{3} Z^{3} + 110 X^{2} Y^{2} Z^{4} + 38 X Y^{6} Z + 2 X Y^{5} Z^{2} + 11 X Y^{4} Z^{3} + 6 X^{3} Y^{3} Z + 10 X^{3} Y^{2} Z^{2} + 2 X^{2} Y^{3} Z^{2} + 11 X^{2} Y^{2} Z^{3} + 5 X Y^{5} Z + 5 X Y^{4} Z^{2} + 24 X^{3} Y^{2} Z + 18 X^{2} Y^{3} Z + 621 X^{2} Y^{2} Z^{2} + 151 X Y^{4} Z + 50 X Y^{3} Z^{2} + 7 X Y^{2} Z^{3} + 30 X^{3} Y Z + 72 X^{2} Y^{2} Z + 10 X^{2} Y Z^{2} + 53 X Y^{3} Z + 148 X Y^{2} Z^{2} + 16 X Y Z^{3} + 90 X^{2} Y Z + 356 X Y^{2} Z + 209 X Y Z^{2} + 250 X Y Z

Algorithm definition

The algorithm ⟨10×20×28:3296⟩ is serendipitous tensor product (⟨5×5×7:127⟩ - 13) ⊗ ⟨2×4×4:26⟩ +⟨2×4×12:77⟩ +5⟨2×4×8:51⟩.

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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