Description of fast matrix multiplication algorithm: ⟨10×15×24:2155⟩

Algorithm type

168 X^{4} Y^{4} Z^{4} + 3 X^{6} Y^{2} Z^{2} + 6 X^{2} Y^{6} Z^{2} + 9 X^{2} Y^{4} Z^{4} + 6 X^{2} Y^{2} Z^{6} + 36 X^{4} Y^{2} Z^{2} + 3 X^{3} Y^{2} Z^{3} + 408 X^{2} Y^{4} Z^{2} + 62 X^{2} Y^{2} Z^{4} + 12 X Y^{6} Z + X^{4} Y Z^{2} + X^{2} Y^{3} Z^{2} + 9 X^{2} Y^{2} Z^{3} + 18 X Y^{4} Z^{2} + 6 X^{4} Y Z + 6 X^{3} Y^{2} Z + X^{3} Y Z^{2} + 3 X^{2} Y^{3} Z + 399 X^{2} Y^{2} Z^{2} + 3 X^{2} Y Z^{3} + 144 X Y^{4} Z + X Y^{3} Z^{2} + 12 X Y^{2} Z^{3} + 2 X Y Z^{4} + 14 X^{3} Y Z + 60 X^{2} Y^{2} Z + 27 X^{2} Y Z^{2} + 12 X Y^{3} Z + 138 X Y^{2} Z^{2} + 21 X Y Z^{3} + 77 X^{2} Y Z + 240 X Y^{2} Z + 143 X Y Z^{2} + 104 X Y Z

Algorithm definition

The algorithm ⟨10×15×24:2155⟩ is serendipitous tensor product (⟨5×5×8:144⟩ - 10) ⊗ ⟨2×3×3:15⟩ +5⟨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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