Description of fast matrix multiplication algorithm: ⟨14×20×21:3453⟩

Algorithm type

12 X^{6} Y^{10} Z^{4} + 12 X^{6} Y^{8} Z^{4} + 30 X^{4} Y^{10} Z^{4} + 6 X^{6} Y^{6} Z^{4} + 30 X^{4} Y^{8} Z^{4} + 16 X^{2} Y^{10} Z^{4} + 4 X^{8} Y^{5} Z^{2} + 30 X^{3} Y^{10} Z^{2} + 14 X^{2} Y^{10} Z^{3} + 4 X^{8} Y^{4} Z^{2} + 60 X^{6} Y^{4} Z^{4} + 15 X^{4} Y^{6} Z^{4} + 80 X^{2} Y^{10} Z^{2} + 12 X^{2} Y^{8} Z^{4} + 2 X^{8} Y^{3} Z^{2} + 24 X^{6} Y^{5} Z^{2} + 42 X^{3} Y^{8} Z^{2} + 38 X Y^{10} Z^{2} + 20 X^{8} Y^{2} Z^{2} + 24 X^{6} Y^{4} Z^{2} + 6 X^{6} Y^{2} Z^{4} + 150 X^{4} Y^{4} Z^{4} + 105 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{6} Z^{4} + 2 X^{8} Y Z^{2} + 12 X^{6} Y^{3} Z^{2} + 24 X^{4} Y^{5} Z^{2} + 24 X^{3} Y^{6} Z^{2} + 15 X^{2} Y^{6} Z^{3} + X^{2} Y^{5} Z^{4} + 42 X Y^{8} Z^{2} + X Y^{5} Z^{5} + 120 X^{6} Y^{2} Z^{2} + 10 X^{4} Y^{5} Z + 24 X^{4} Y^{4} Z^{2} + 15 X^{4} Y^{2} Z^{4} + 63 X^{2} Y^{6} Z^{2} + X^{2} Y^{5} Z^{3} + 63 X^{2} Y^{4} Z^{4} + X Y^{7} Z^{2} + 6 X Y^{5} Z^{4} + 12 X^{6} Y Z^{2} + 14 X^{4} Y^{4} Z + 12 X^{4} Y^{3} Z^{2} + 60 X^{3} Y^{5} Z + 24 X^{3} Y^{4} Z^{2} + 26 X^{2} Y^{5} Z^{2} + 8 X^{2} Y^{4} Z^{3} + 2 X^{2} Y^{3} Z^{4} + 26 X Y^{6} Z^{2} + 12 X Y^{5} Z^{3} + 8 X^{4} Y^{3} Z + 120 X^{4} Y^{2} Z^{2} + 84 X^{3} Y^{4} Z + 64 X^{2} Y^{5} Z + 109 X^{2} Y^{4} Z^{2} + 12 X^{2} Y^{3} Z^{3} + 13 X^{2} Y^{2} Z^{4} + 2 X Y^{6} Z + 14 X Y^{5} Z^{2} + X Y^{2} Z^{5} + 8 X^{4} Y^{2} Z + 12 X^{4} Y Z^{2} + 48 X^{3} Y^{3} Z + 66 X^{3} Y^{2} Z^{2} + 90 X^{2} Y^{4} Z + 57 X^{2} Y^{3} Z^{2} + 3 X^{2} Y^{2} Z^{3} + X^{2} Y Z^{4} + 57 X Y^{5} Z + 27 X Y^{4} Z^{2} + 2 X Y^{2} Z^{4} + 22 X^{4} Y Z + 48 X^{3} Y^{2} Z + 48 X^{2} Y^{3} Z + 296 X^{2} Y^{2} Z^{2} + 77 X Y^{4} Z + 5 X Y^{3} Z^{2} + 14 X Y^{2} Z^{3} + 4 X Y Z^{4} + 132 X^{3} Y Z + 66 X^{2} Y^{2} Z + 21 X^{2} Y Z^{2} + 54 X Y^{3} Z + 119 X Y^{2} Z^{2} + 5 X Y Z^{3} + 143 X^{2} Y Z + 76 X Y^{2} Z + 29 X Y Z^{2} + 128 X Y Z

Algorithm definition

The algorithm ⟨14×20×21:3453⟩ is serendipitous tensor product (⟨2×5×7:55⟩ - 8) ⊗ ⟨7×4×3:63⟩ +4⟨7×4×6:123⟩.

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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