Description of fast matrix multiplication algorithm: ⟨9×14×21:1655⟩

Algorithm type

6 X^{4} Y^{8} Z^{4} + 6 X^{4} Y^{6} Z^{4} + 7 X^{2} Y^{10} Z^{2} + 2 X^{2} Y^{10} Z + 3 X^{2} Y^{9} Z^{2} + 94 X^{4} Y^{4} Z^{4} + 6 X^{2} Y^{8} Z^{2} + 7 X^{2} Y^{6} Z^{4} + 8 X Y^{10} Z + 4 X^{4} Y^{3} Z^{4} + 2 X^{2} Y^{8} Z + 3 X^{2} Y^{7} Z^{2} + 3 X^{2} Y^{5} Z^{4} + 4 X Y^{9} Z + 18 X^{6} Y^{2} Z^{2} + X^{4} Y^{2} Z^{4} + X^{3} Y^{3} Z^{4} + 20 X^{2} Y^{6} Z^{2} + 37 X^{2} Y^{4} Z^{4} + 19 X^{2} Y^{2} Z^{6} + 3 X Y^{8} Z + X Y^{6} Z^{3} + X Y^{3} Z^{6} + X^{4} Y^{3} Z^{2} + 4 X^{3} Y^{5} Z + X^{2} Y^{6} Z + 12 X^{2} Y^{5} Z^{2} + 14 X^{2} Y^{3} Z^{4} + 5 X Y^{7} Z + X Y^{6} Z^{2} + 2 X Y^{5} Z^{3} + X Y^{2} Z^{6} + 2 X^{5} Y Z^{2} + 2 X^{4} Y^{2} Z^{2} + 4 X^{3} Y^{4} Z + 12 X^{2} Y^{5} Z + 61 X^{2} Y^{4} Z^{2} + 238 X^{2} Y^{2} Z^{4} + 8 X Y^{6} Z + 3 X Y^{5} Z^{2} + 2 X Y^{4} Z^{3} + 12 X Y^{3} Z^{4} + 36 X Y Z^{6} + X^{4} Y Z^{2} + 2 X^{3} Y^{3} Z + 4 X^{3} Y^{2} Z^{2} + 8 X^{2} Y^{4} Z + 21 X^{2} Y^{3} Z^{2} + 18 X Y^{5} Z + 7 X Y^{4} Z^{2} + 2 X Y^{3} Z^{3} + 48 X Y^{2} Z^{4} + 2 X^{3} Y^{2} Z + 38 X^{3} Y Z^{2} + 5 X^{2} Y^{3} Z + 202 X^{2} Y^{2} Z^{2} + 20 X Y^{4} Z + 44 X Y^{3} Z^{2} + 90 X Y Z^{4} + 38 X^{3} Y Z + 11 X^{2} Y^{2} Z + 6 X^{2} Y Z^{2} + 36 X Y^{3} Z + 127 X Y^{2} Z^{2} + 36 X Y Z^{3} + X^{2} Y Z + 89 X Y^{2} Z + 108 X Y Z^{2} + 14 X Y Z

Algorithm definition

The algorithm ⟨9×14×21:1655⟩ is serendipitous tensor product (⟨3×7×7:111⟩ - 20) ⊗ ⟨3×2×3:15⟩ +10⟨3×4×3:29⟩.

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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