Description of fast matrix multiplication algorithm: ⟨10×12×21:1557⟩

Algorithm type

108 X^{4} Y^{4} Z^{4} + 6 X^{2} Y^{4} Z^{4} + X^{4} Y^{2} Z^{3} + 21 X^{4} Y^{2} Z^{2} + 3 X^{3} Y^{2} Z^{3} + 264 X^{2} Y^{4} Z^{2} + 57 X^{2} Y^{2} Z^{4} + 3 X^{4} Y Z^{2} + 6 X^{2} Y^{2} Z^{3} + 2 X^{2} Y Z^{4} + 12 X Y^{4} Z^{2} + 2 X^{3} Y Z^{2} + 2 X^{2} Y^{3} Z + 281 X^{2} Y^{2} Z^{2} + 2 X^{2} Y Z^{3} + 96 X Y^{4} Z + X Y^{3} Z^{2} + 2 X Y Z^{4} + 5 X^{3} Y Z + 42 X^{2} Y^{2} Z + 11 X^{2} Y Z^{2} + 120 X Y^{2} Z^{2} + 6 X Y Z^{3} + 47 X^{2} Y Z + 210 X Y^{2} Z + 127 X Y Z^{2} + 120 X Y Z

Algorithm definition

The algorithm ⟨10×12×21:1557⟩ is serendipitous tensor product (⟨5×4×7:104⟩ - 6) ⊗ ⟨2×3×3:15⟩ +3⟨4×3×3:29⟩.

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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