Description of fast matrix multiplication algorithm: ⟨12×14×18:1837⟩

Algorithm type

135 X^{4} Y^{4} Z^{4} + X^{3} Y^{6} Z^{2} + 5 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{2} Z^{4} + 3 X^{3} Y^{5} Z^{2} + 3 X^{2} Y^{2} Z^{6} + X^{4} Y^{3} Z^{2} + 5 X^{3} Y^{4} Z^{2} + 3 X^{2} Y^{6} Z + 2 X^{4} Y^{3} Z + 32 X^{4} Y^{2} Z^{2} + 9 X^{3} Y^{3} Z^{2} + 2 X^{2} Y^{5} Z + 69 X^{2} Y^{4} Z^{2} + 300 X^{2} Y^{2} Z^{4} + 6 X Y Z^{6} + X^{5} Y Z + 6 X^{4} Y^{2} Z + 2 X^{3} Y^{3} Z + 7 X^{3} Y^{2} Z^{2} + 8 X^{2} Y^{4} Z + 4 X^{2} Y^{3} Z^{2} + 2 X^{2} Y^{2} Z^{3} + 12 X^{2} Y Z^{4} + X Y^{5} Z + 2 X Y^{3} Z^{3} + 3 X^{4} Y Z + 10 X^{3} Y^{2} Z + 6 X^{2} Y^{3} Z + 343 X^{2} Y^{2} Z^{2} + 4 X Y^{4} Z + 4 X Y^{2} Z^{3} + 60 X Y Z^{4} + 10 X^{3} Y Z + 47 X^{2} Y^{2} Z + 66 X^{2} Y Z^{2} + 13 X Y^{3} Z + 132 X Y^{2} Z^{2} + 6 X Y Z^{3} + 80 X^{2} Y Z + 151 X Y^{2} Z + 162 X Y Z^{2} + 113 X Y Z

Algorithm definition

The algorithm ⟨12×14×18:1837⟩ is serendipitous tensor product (⟨4×7×6:123⟩ - 16) ⊗ ⟨3×2×3:15⟩ +8⟨3×4×3:29⟩.

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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