Description of fast matrix multiplication algorithm: ⟨14×21×25:4313⟩

Algorithm type

4 X^{4} Y^{10} Z^{6} + 4 X^{2} Y^{15} Z^{2} + 48 X^{4} Y^{10} Z^{4} + 4 X^{4} Y^{8} Z^{6} + X^{4} Y^{11} Z^{2} + 10 X Y^{15} Z + 24 X^{4} Y^{10} Z^{2} + 48 X^{4} Y^{8} Z^{4} + 2 X^{4} Y^{6} Z^{6} + 4 X^{2} Y^{12} Z^{2} + 5 X^{3} Y^{10} Z^{2} + 10 X^{2} Y^{10} Z^{3} + 4 X^{2} Y^{5} Z^{8} + 24 X^{4} Y^{6} Z^{4} + 20 X^{4} Y^{4} Z^{6} + 2 X^{3} Y^{10} Z + 2 X^{2} Y^{11} Z + 132 X^{2} Y^{10} Z^{2} + 4 X^{2} Y^{4} Z^{8} + 14 X Y^{12} Z + 14 X^{6} Y^{5} Z^{2} + 12 X^{4} Y^{5} Z^{4} + 12 X^{2} Y^{10} Z + 2 X^{2} Y^{9} Z^{2} + 14 X^{2} Y^{8} Z^{3} + 8 X^{2} Y^{5} Z^{6} + 2 X^{2} Y^{3} Z^{8} + 14 X^{6} Y^{4} Z^{2} + 17 X^{4} Y^{6} Z^{2} + 252 X^{4} Y^{4} Z^{4} + 2 X^{4} Y^{2} Z^{6} + 172 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{4} Z^{6} + 20 X^{2} Y^{2} Z^{8} + 10 X Y^{10} Z + 7 X^{6} Y^{3} Z^{2} + 24 X^{4} Y^{5} Z^{2} + 6 X^{4} Y^{3} Z^{4} + 5 X^{3} Y^{6} Z^{2} + 8 X^{2} Y^{6} Z^{3} + 28 X^{2} Y^{5} Z^{4} + 4 X^{2} Y^{3} Z^{6} + 2 X^{2} Y Z^{8} + 8 X Y^{9} Z + 70 X^{6} Y^{2} Z^{2} + 18 X^{4} Y^{5} Z + 32 X^{4} Y^{4} Z^{2} + 84 X^{4} Y^{2} Z^{4} + X^{3} Y^{5} Z^{2} + 119 X^{2} Y^{6} Z^{2} + 28 X^{2} Y^{4} Z^{4} + 40 X^{2} Y^{2} Z^{6} + 14 X Y^{8} Z + 10 X Y^{5} Z^{4} + 7 X^{6} Y Z^{2} + 31 X^{4} Y^{3} Z^{2} + 6 X^{4} Y Z^{4} + 38 X^{3} Y^{5} Z + 10 X^{3} Y^{4} Z^{2} + 4 X^{2} Y^{6} Z + 53 X^{2} Y^{5} Z^{2} + 8 X^{2} Y^{4} Z^{3} + 14 X^{2} Y^{3} Z^{4} + 4 X^{2} Y Z^{6} + 20 X Y^{5} Z^{3} + 14 X Y^{4} Z^{4} + 120 X^{4} Y^{2} Z^{2} + 51 X^{3} Y^{4} Z + 10 X^{3} Y^{3} Z^{2} + 81 X^{2} Y^{5} Z + 213 X^{2} Y^{4} Z^{2} + 140 X^{2} Y^{2} Z^{4} + 16 X Y^{6} Z + 73 X Y^{5} Z^{2} + 28 X Y^{4} Z^{3} + 8 X Y^{3} Z^{4} + 10 X^{4} Y^{2} Z + 12 X^{4} Y Z^{2} + 28 X^{3} Y^{3} Z + 94 X^{2} Y^{4} Z + 99 X^{2} Y^{3} Z^{2} + 22 X^{2} Y^{2} Z^{3} + 14 X^{2} Y Z^{4} + 25 X Y^{5} Z + 98 X Y^{4} Z^{2} + 16 X Y^{3} Z^{3} + 8 X Y^{2} Z^{4} + 6 X^{4} Y Z + 38 X^{3} Y^{2} Z + 56 X^{2} Y^{3} Z + 358 X^{2} Y^{2} Z^{2} + 53 X Y^{4} Z + 57 X Y^{3} Z^{2} + 16 X Y^{2} Z^{3} + 22 X Y Z^{4} + 77 X^{3} Y Z + 107 X^{2} Y^{2} Z + 79 X^{2} Y Z^{2} + 56 X Y^{3} Z + 84 X Y^{2} Z^{2} + 44 X Y Z^{3} + 150 X^{2} Y Z + 80 X Y^{2} Z + 169 X Y Z^{2} + 53 X Y Z

Algorithm definition

The algorithm ⟨14×21×25:4313⟩ is serendipitous tensor product (⟨2×7×5:55⟩ - 8) ⊗ ⟨7×3×5:79⟩ +4⟨7×6×5:150⟩.

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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