Description of fast matrix multiplication algorithm: ⟨14×15×21:2635⟩

Algorithm type

3 X^{6} Y^{4} Z^{4} + 30 X^{4} Y^{4} Z^{6} + 3 X^{2} Y^{10} Z^{2} + 174 X^{4} Y^{4} Z^{4} + 9 X^{2} Y^{8} Z^{2} + 6 X Y^{10} Z + X^{6} Y^{2} Z^{3} + 7 X^{6} Y^{2} Z^{2} + 3 X^{4} Y^{2} Z^{4} + 3 X^{2} Y^{6} Z^{2} + 21 X^{2} Y^{4} Z^{4} + 22 X^{2} Y^{2} Z^{6} + 18 X Y^{8} Z + 3 X^{6} Y Z^{2} + 6 X^{4} Y^{2} Z^{3} + 6 X^{3} Y^{4} Z^{2} + 4 X^{3} Y^{2} Z^{4} + 60 X^{2} Y^{4} Z^{3} + X^{6} Y Z + 53 X^{4} Y^{2} Z^{2} + X^{3} Y^{3} Z^{2} + X^{3} Y^{2} Z^{3} + 2 X^{3} Y Z^{4} + 393 X^{2} Y^{4} Z^{2} + X^{2} Y^{3} Z^{3} + 71 X^{2} Y^{2} Z^{4} + 6 X Y^{6} Z + X Y Z^{6} + 4 X^{4} Y Z^{2} + X^{3} Y^{3} Z + 11 X^{3} Y^{2} Z^{2} + 4 X^{3} Y Z^{3} + 66 X^{2} Y^{2} Z^{3} + 2 X^{2} Y Z^{4} + 6 X Y^{5} Z + 42 X Y^{4} Z^{2} + X Y Z^{5} + 6 X^{4} Y Z + 12 X^{3} Y^{2} Z + 10 X^{3} Y Z^{2} + 2 X^{2} Y^{3} Z + 420 X^{2} Y^{2} Z^{2} + 9 X^{2} Y Z^{3} + 108 X Y^{4} Z + 42 X Y^{2} Z^{3} + 6 X Y Z^{4} + 21 X^{3} Y Z + 102 X^{2} Y^{2} Z + 16 X^{2} Y Z^{2} + 6 X Y^{3} Z + 174 X Y^{2} Z^{2} + 51 X Y Z^{3} + 109 X^{2} Y Z + 216 X Y^{2} Z + 147 X Y Z^{2} + 132 X Y Z

Algorithm definition

The algorithm ⟨14×15×21:2635⟩ is serendipitous tensor product (⟨7×5×7:176⟩ - 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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