Description of fast matrix multiplication algorithm: ⟨15×20×27:4621⟩

Algorithm type

2 X^{9} Y Z^{2} + 7 X^{6} Y^{2} Z^{4} + 448 X^{4} Y^{4} Z^{4} + 7 X^{4} Y^{2} Z^{6} + X^{2} Y Z^{9} + 130 X^{6} Y^{2} Z^{2} + 2 X^{6} Y Z^{3} + 128 X^{4} Y^{4} Z^{2} + X^{3} Y Z^{6} + 128 X^{2} Y^{6} Z^{2} + 64 X^{2} Y^{2} Z^{6} + 4 X^{6} Y Z^{2} + 2 X^{4} Y^{2} Z^{3} + 4 X^{2} Y^{4} Z^{3} + 4 X^{2} Y^{3} Z^{4} + 20 X^{6} Y Z + 326 X^{4} Y^{2} Z^{2} + 4 X^{4} Y Z^{3} + 2 X^{3} Y^{3} Z^{2} + 454 X^{2} Y^{4} Z^{2} + 22 X^{2} Y^{3} Z^{3} + 170 X^{2} Y^{2} Z^{4} + 52 X Y^{6} Z + 22 X Y Z^{6} + 20 X^{4} Y^{2} Z + 4 X^{3} Y^{2} Z^{2} + 52 X^{2} Y^{4} Z + 20 X^{2} Y^{3} Z^{2} + 26 X^{2} Y^{2} Z^{3} + 4 X Y^{4} Z^{2} + 4 X Y^{2} Z^{4} + 40 X^{4} Y Z + 52 X^{3} Y^{2} Z + 51 X^{3} Y Z^{2} + 20 X^{2} Y^{3} Z + 697 X^{2} Y^{2} Z^{2} + 17 X^{2} Y Z^{3} + 116 X Y^{4} Z + 64 X Y^{3} Z^{2} + 50 X Y^{2} Z^{3} + 12 X Y Z^{4} + 26 X^{3} Y Z + 170 X^{2} Y^{2} Z + 88 X^{2} Y Z^{2} + 70 X Y^{3} Z + 146 X Y^{2} Z^{2} + 57 X Y Z^{3} + 122 X^{2} Y Z + 340 X Y^{2} Z + 258 X Y Z^{2} + 91 X Y Z

Algorithm definition

The algorithm ⟨15×20×27:4621⟩ is serendipitous tensor product (⟨5×5×9:161⟩ - 24) ⊗ ⟨3×4×3:29⟩ +12⟨3×4×6:54⟩.

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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