Description of fast matrix multiplication algorithm: ⟨6×20×20:1498⟩

Algorithm type

104 X^{4} Y^{8} Z^{4} + 16 X^{2} Y^{12} Z^{2} + 16 X^{4} Y^{8} Z^{2} + 8 X^{2} Y^{8} Z^{4} + 16 X Y^{12} Z + 32 X^{6} Y^{4} Z^{2} + 168 X^{2} Y^{8} Z^{2} + 24 X^{2} Y^{4} Z^{6} + 16 X^{2} Y^{8} Z + 8 X Y^{8} Z^{2} + 48 X^{4} Y^{4} Z^{2} + 16 X^{2} Y^{4} Z^{4} + 64 X Y^{8} Z + X^{3} Y^{2} Z^{4} + 32 X^{3} Y^{4} Z + 2 X^{3} Y^{2} Z^{3} + 16 X^{2} Y^{4} Z^{2} + 3 X^{2} Y^{2} Z^{4} + 24 X Y^{4} Z^{3} + 10 X^{3} Y^{2} Z^{2} + 48 X^{2} Y^{4} Z + 3 X^{2} Y^{2} Z^{3} + 4 X^{2} Y Z^{4} + 16 X Y^{4} Z^{2} + 6 X Y^{2} Z^{4} + 3 X^{3} Y^{2} Z + 4 X^{3} Y Z^{2} + 222 X^{2} Y^{2} Z^{2} + 3 X^{2} Y Z^{3} + 16 X Y^{4} Z + X Y^{3} Z^{2} + 2 X Y^{2} Z^{3} + 76 X^{3} Y Z + 32 X^{2} Y^{2} Z + 14 X^{2} Y Z^{2} + 35 X Y^{3} Z + 22 X Y^{2} Z^{2} + 48 X Y Z^{3} + 107 X^{2} Y Z + 130 X Y^{2} Z + 37 X Y Z^{2} + 45 X Y Z

Algorithm definition

The algorithm ⟨6×20×20:1498⟩ is serendipitous tensor product (⟨3×5×4:47⟩ - 4) ⊗ ⟨2×4×5:32⟩ +2⟨4×4×5:61⟩.

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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