Description of fast matrix multiplication algorithm: ⟨14×18×30:4387⟩

Algorithm type

12 X^{8} Y^{8} Z^{8} + 6 X^{8} Y^{8} Z^{6} + 9 X^{8} Y^{6} Z^{8} + 3 X^{6} Y^{8} Z^{8} + 9 X^{8} Y^{6} Z^{6} + 3 X^{8} Y^{4} Z^{8} + 6 X^{6} Y^{8} Z^{6} + 6 X^{6} Y^{6} Z^{6} + 48 X^{4} Y^{8} Z^{4} + 96 X^{4} Y^{6} Z^{6} + 18 X^{4} Y^{4} Z^{8} + 12 X^{4} Y^{8} Z^{3} + 6 X^{3} Y^{8} Z^{4} + 6 X^{4} Y^{8} Z^{2} + 27 X^{4} Y^{6} Z^{4} + 18 X^{4} Y^{4} Z^{6} + 9 X^{4} Y^{2} Z^{8} + 12 X^{3} Y^{8} Z^{3} + 3 X^{2} Y^{8} Z^{4} + 144 X^{2} Y^{6} Z^{6} + 3 X^{2} Y^{4} Z^{8} + 18 X^{4} Y^{6} Z^{3} + 3 X^{4} Y^{6} Z^{2} + 171 X^{4} Y^{4} Z^{4} + 3 X^{4} Y^{2} Z^{6} + 12 X^{3} Y^{6} Z^{3} + 51 X^{2} Y^{8} Z^{2} + 3 X^{2} Y^{4} Z^{6} + 12 X^{4} Y^{4} Z^{3} + 18 X^{4} Y^{3} Z^{4} + 6 X^{3} Y^{4} Z^{4} + 12 X^{2} Y^{8} Z + 192 X^{2} Y^{6} Z^{3} + 6 X Y^{8} Z^{2} + 21 X^{6} Y^{2} Z^{2} + 18 X^{4} Y^{3} Z^{3} + 18 X^{4} Y^{2} Z^{4} + 12 X^{3} Y^{4} Z^{3} + 42 X^{2} Y^{6} Z^{2} + 54 X^{2} Y^{4} Z^{4} + 18 X^{2} Y^{2} Z^{6} + 6 X Y^{8} Z + 288 X Y^{6} Z^{3} + 12 X^{3} Y^{3} Z^{3} + 6 X^{2} Y^{6} Z + 36 X^{2} Y^{4} Z^{3} + 2 X^{2} Y^{2} Z^{5} + 6 X Y^{4} Z^{4} + 6 X^{4} Y^{2} Z^{2} + 402 X^{2} Y^{4} Z^{2} + 192 X^{2} Y^{3} Z^{3} + 183 X^{2} Y^{2} Z^{4} + 48 X Y^{6} Z + 6 X Y^{4} Z^{3} + 12 X^{2} Y^{4} Z + 22 X^{2} Y^{3} Z^{2} + 58 X^{2} Y^{2} Z^{3} + 23 X^{2} Y Z^{4} + 42 X Y^{4} Z^{2} + 288 X Y^{3} Z^{3} + 6 X Y^{2} Z^{4} + 10 X Y Z^{5} + 42 X^{3} Y^{2} Z + 10 X^{3} Y Z^{2} + 8 X^{2} Y^{3} Z + 338 X^{2} Y^{2} Z^{2} + 16 X^{2} Y Z^{3} + 150 X Y^{4} Z + X Y^{3} Z^{2} + 42 X Y^{2} Z^{3} + 15 X Y Z^{4} + 48 X^{3} Y Z + 12 X^{2} Y^{2} Z + 55 X^{2} Y Z^{2} + 49 X Y^{3} Z + 240 X Y^{2} Z^{2} + 56 X Y Z^{3} + 20 X^{2} Y Z + 186 X Y^{2} Z + 247 X Y Z^{2} + 52 X Y Z

Algorithm definition

The algorithm ⟨14×18×30:4387⟩ is serendipitous tensor product (⟨7×6×10:293⟩ - 16) ⊗ ⟨2×3×3:15⟩ +8⟨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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