Description of fast matrix multiplication algorithm: ⟨10×21×30:3716⟩

Algorithm type

4 X^{4} Y^{15} Z^{2} + 6 X^{2} Y^{15} Z^{4} + 4 X^{4} Y^{10} Z^{6} + 8 X^{2} Y^{15} Z^{2} + 4 X^{6} Y^{10} Z^{2} + 4 X^{4} Y^{12} Z^{2} + 36 X^{4} Y^{10} Z^{4} + 4 X^{4} Y^{8} Z^{6} + 10 X^{2} Y^{15} Z + 6 X^{2} Y^{12} Z^{4} + 15 X Y^{15} Z^{2} + 20 X Y^{15} Z + 4 X^{6} Y^{8} Z^{2} + 8 X^{4} Y^{10} Z^{2} + 36 X^{4} Y^{8} Z^{4} + 2 X^{4} Y^{6} Z^{6} + 8 X^{2} Y^{12} Z^{2} + 2 X^{4} Y^{9} Z^{2} + 6 X^{3} Y^{10} Z^{2} + 14 X^{2} Y^{12} Z + 10 X^{2} Y^{10} Z^{3} + 3 X^{2} Y^{9} Z^{4} + 4 X^{2} Y^{5} Z^{8} + 21 X Y^{12} Z^{2} + 2 X^{6} Y^{6} Z^{2} + 18 X^{4} Y^{6} Z^{4} + 20 X^{4} Y^{4} Z^{6} + 10 X^{3} Y^{10} Z + 2 X^{2} Y^{11} Z + 96 X^{2} Y^{10} Z^{2} + 4 X^{2} Y^{4} Z^{8} + 28 X Y^{12} Z + 12 X^{6} Y^{5} Z^{2} + 8 X^{4} Y^{5} Z^{4} + 6 X^{2} Y^{10} Z + 4 X^{2} Y^{9} Z^{2} + 14 X^{2} Y^{8} Z^{3} + 10 X^{2} Y^{5} Z^{6} + 2 X^{2} Y^{3} Z^{8} + 32 X^{6} Y^{4} Z^{2} + 21 X^{4} Y^{6} Z^{2} + 188 X^{4} Y^{4} Z^{4} + 2 X^{4} Y^{2} Z^{6} + 14 X^{3} Y^{8} Z + 8 X^{2} Y^{9} Z + 126 X^{2} Y^{8} Z^{2} + 30 X^{2} Y^{6} Z^{4} + 10 X^{2} Y^{4} Z^{6} + 20 X^{2} Y^{2} Z^{8} + X Y^{10} Z + 12 X Y^{9} Z^{2} + 6 X^{6} Y^{3} Z^{2} + 16 X^{4} Y^{5} Z^{2} + 4 X^{4} Y^{3} Z^{4} + 20 X^{3} Y^{6} Z^{2} + 8 X^{2} Y^{6} Z^{3} + 16 X^{2} Y^{5} Z^{4} + 5 X^{2} Y^{3} Z^{6} + 2 X^{2} Y Z^{8} + 16 X Y^{9} Z + 62 X^{6} Y^{2} Z^{2} + 7 X^{4} Y^{5} Z + 17 X^{4} Y^{4} Z^{2} + 58 X^{4} Y^{2} Z^{4} + 8 X^{3} Y^{6} Z + X^{3} Y^{5} Z^{2} + 119 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{5} Z^{3} + 16 X^{2} Y^{4} Z^{4} + 50 X^{2} Y^{2} Z^{6} + 10 X Y^{5} Z^{4} + 6 X^{6} Y Z^{2} + 16 X^{4} Y^{3} Z^{2} + 4 X^{4} Y Z^{4} + 37 X^{3} Y^{5} Z + 3 X^{3} Y^{4} Z^{2} + 15 X^{2} Y^{6} Z + 32 X^{2} Y^{5} Z^{2} + 8 X^{2} Y^{4} Z^{3} + 11 X^{2} Y^{3} Z^{4} + 5 X^{2} Y Z^{6} + 12 X Y^{6} Z^{2} + 25 X Y^{5} Z^{3} + 14 X Y^{4} Z^{4} + 85 X^{4} Y^{2} Z^{2} + 50 X^{3} Y^{4} Z + 21 X^{3} Y^{3} Z^{2} + 51 X^{2} Y^{5} Z + 146 X^{2} Y^{4} Z^{2} + 80 X^{2} Y^{2} Z^{4} + 21 X Y^{6} Z + 46 X Y^{5} Z^{2} + 35 X Y^{4} Z^{3} + 8 X Y^{3} Z^{4} + 6 X^{4} Y^{2} Z + 9 X^{4} Y Z^{2} + 24 X^{3} Y^{3} Z + 7 X^{3} Y^{2} Z^{2} + 59 X^{2} Y^{4} Z + 64 X^{2} Y^{3} Z^{2} + 22 X^{2} Y^{2} Z^{3} + 8 X^{2} Y Z^{4} + 33 X Y^{5} Z + 57 X Y^{4} Z^{2} + 20 X Y^{3} Z^{3} + 8 X Y^{2} Z^{4} + 5 X^{4} Y Z + 58 X^{3} Y^{2} Z + 61 X^{2} Y^{3} Z + 293 X^{2} Y^{2} Z^{2} + X^{2} Y Z^{3} + 44 X Y^{4} Z + 66 X Y^{3} Z^{2} + 22 X Y^{2} Z^{3} + 22 X Y Z^{4} + 68 X^{3} Y Z + 68 X^{2} Y^{2} Z + 58 X^{2} Y Z^{2} + 76 X Y^{3} Z + 57 X Y^{2} Z^{2} + 58 X Y Z^{3} + 107 X^{2} Y Z + 57 X Y^{2} Z + 103 X Y Z^{2} + 62 X Y Z

Algorithm definition

The algorithm ⟨10×21×30:3716⟩ is serendipitous tensor product (⟨2×7×5:55⟩ - 8) ⊗ ⟨5×3×6:68⟩ +4⟨5×6×6:130⟩.

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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