Description of fast matrix multiplication algorithm: ⟨10×21×28:3508⟩

Algorithm type

4 X^{6} Y^{4} Z^{4} + 40 X^{4} Y^{6} Z^{4} + 4 X^{2} Y^{2} Z^{10} + 40 X^{2} Y^{9} Z^{2} + 248 X^{4} Y^{4} Z^{4} + 4 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{2} Z^{8} + 8 X^{4} Y^{3} Z^{4} + 4 X^{3} Y^{6} Z^{2} + 24 X^{3} Y^{5} Z^{3} + 4 X^{2} Y^{7} Z^{2} + 64 X^{2} Y^{6} Z^{3} + 32 X Y^{9} Z + 16 X^{6} Y^{2} Z^{2} + 4 X^{4} Y^{4} Z^{2} + 8 X^{4} Y^{2} Z^{4} + 28 X^{3} Y^{4} Z^{3} + 276 X^{2} Y^{6} Z^{2} + 28 X^{2} Y^{4} Z^{4} + 4 X^{2} Y^{2} Z^{6} + 16 X Y^{8} Z + 96 X Y^{6} Z^{3} + 8 X^{3} Y^{3} Z^{3} + 4 X^{3} Y^{2} Z^{4} + 12 X^{2} Y^{6} Z + 16 X^{2} Y^{5} Z^{2} + 4 X Y^{7} Z + 28 X Y^{6} Z^{2} + 4 X Y^{3} Z^{5} + 76 X^{4} Y^{2} Z^{2} + 12 X^{3} Y^{2} Z^{3} + 4 X^{2} Y^{5} Z + 164 X^{2} Y^{4} Z^{2} + 64 X^{2} Y^{3} Z^{3} + 60 X^{2} Y^{2} Z^{4} + 124 X Y^{6} Z + 12 X Y^{3} Z^{4} + 16 X^{3} Y^{3} Z + 4 X^{3} Y^{2} Z^{2} + 8 X^{2} Y^{4} Z + 80 X^{2} Y^{3} Z^{2} + 12 X Y^{5} Z + 100 X Y^{3} Z^{3} + 4 X Y Z^{5} + 80 X^{2} Y^{3} Z + 476 X^{2} Y^{2} Z^{2} + 32 X Y^{4} Z + 60 X Y^{3} Z^{2} + 12 X Y Z^{4} + 16 X^{3} Y Z + 4 X^{2} Y^{2} Z + 24 X^{2} Y Z^{2} + 212 X Y^{3} Z + 40 X Y^{2} Z^{2} + 4 X Y Z^{3} + 76 X^{2} Y Z + 304 X Y^{2} Z + 60 X Y Z^{2} + 328 X Y Z

Algorithm definition

The algorithm ⟨10×21×28:3508⟩ is serendipitous tensor product (⟨2×3×4:20⟩ - 8) ⊗ ⟨5×7×7:176⟩ +4⟨5×7×14:349⟩.

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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