Description of fast matrix multiplication algorithm: ⟨12×12×20:1710⟩

Algorithm type

135 X^{4} Y^{4} Z^{4} + 6 X^{2} Y^{4} Z^{3} + 270 X^{4} Y^{2} Z^{2} + 64 X^{2} Y^{4} Z^{2} + 30 X^{2} Y^{3} Z^{3} + 76 X^{2} Y^{2} Z^{4} + 4 X^{3} Y^{2} Z^{2} + 14 X^{2} Y^{2} Z^{3} + 18 X Y^{4} Z^{2} + 12 X Y^{2} Z^{4} + 11 X^{3} Y^{2} Z + 305 X^{2} Y^{2} Z^{2} + 4 X Y^{4} Z + 16 X Y^{3} Z^{2} + 16 X Y^{2} Z^{3} + 10 X Y Z^{4} + 120 X^{2} Y^{2} Z + 120 X^{2} Y Z^{2} + 24 X Y^{3} Z + 66 X Y^{2} Z^{2} + 24 X Y Z^{3} + 151 X Y^{2} Z + 195 X Y Z^{2} + 19 X Y Z

Algorithm definition

The algorithm ⟨12×12×20:1710⟩ is serendipitous tensor product (⟨4×4×10:115⟩ - 30) ⊗ ⟨3×3×2:15⟩ +15⟨3×3×4:29⟩.

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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