Description of fast matrix multiplication algorithm: ⟨10×18×24:2547⟩

Algorithm type

210 X^{4} Y^{4} Z^{4} + 9 X^{2} Y^{6} Z^{2} + 6 X^{2} Y^{4} Z^{4} + X^{2} Y^{2} Z^{6} + 3 X^{3} Y^{2} Z^{4} + 43 X^{4} Y^{2} Z^{2} + 507 X^{2} Y^{4} Z^{2} + X^{2} Y^{3} Z^{3} + 73 X^{2} Y^{2} Z^{4} + 18 X Y^{6} Z + X Y Z^{6} + X^{3} Y Z^{3} + 5 X^{2} Y^{2} Z^{3} + X^{2} Y Z^{4} + 12 X Y^{4} Z^{2} + X^{4} Y Z + X^{2} Y^{3} Z + 496 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 174 X Y^{4} Z + 2 X Y Z^{4} + 6 X^{3} Y Z + 84 X^{2} Y^{2} Z + 10 X^{2} Y Z^{2} + 19 X Y^{3} Z + 156 X Y^{2} Z^{2} + 7 X Y Z^{3} + 91 X^{2} Y Z + 306 X Y^{2} Z + 158 X Y Z^{2} + 139 X Y Z

Algorithm definition

The algorithm ⟨10×18×24:2547⟩ is serendipitous tensor product (⟨5×6×8:170⟩ - 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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