Description of fast matrix multiplication algorithm: ⟨4×30×32:2391⟩

Algorithm type

X^{4} Y^{26} Z^{4} + 8 X^{4} Y^{24} Z^{4} + 9 X^{2} Y^{26} Z^{2} + X^{2} Y^{25} Z^{2} + 33 X^{4} Y^{20} Z^{4} + 35 X^{2} Y^{24} Z^{2} + 13 X Y^{26} Z + 2 X^{2} Y^{23} Z^{2} + 8 X Y^{25} Z + 3 X^{2} Y^{20} Z^{4} + 25 X Y^{24} Z + 4 X^{2} Y^{21} Z^{2} + X^{2} Y^{20} Z^{3} + 5 X Y^{23} Z + 16 X^{4} Y^{16} Z^{4} + 66 X^{2} Y^{20} Z^{2} + 4 X Y^{22} Z + X^{2} Y^{19} Z^{2} + 9 X Y^{21} Z + 7 X Y^{20} Z^{2} + 2 X^{2} Y^{18} Z^{2} + X^{2} Y^{16} Z^{4} + 40 X Y^{20} Z + X^{2} Y^{17} Z^{2} + X Y^{19} Z + 16 X^{4} Y^{12} Z^{4} + 60 X^{2} Y^{16} Z^{2} + 7 X Y^{18} Z + 2 X^{2} Y^{15} Z^{2} + 3 X Y^{17} Z + 4 X Y^{16} Z^{2} + X^{4} Y^{10} Z^{4} + 52 X Y^{16} Z + 2 X Y^{15} Z^{2} + 17 X Y^{15} Z + 92 X^{4} Y^{8} Z^{4} + 58 X^{2} Y^{12} Z^{2} + X^{2} Y^{11} Z^{3} + 3 X Y^{14} Z + 9 X^{2} Y^{11} Z^{2} + 3 X^{2} Y^{10} Z^{3} + X Y^{12} Z^{2} + 33 X^{2} Y^{10} Z^{2} + 39 X Y^{12} Z + 2 X Y^{11} Z^{2} + 4 X^{2} Y^{9} Z^{2} + X^{2} Y^{8} Z^{3} + 12 X Y^{11} Z + X Y^{10} Z^{2} + 2 X^{4} Y^{4} Z^{4} + 131 X^{2} Y^{8} Z^{2} + X^{2} Y^{7} Z^{3} + 3 X^{2} Y^{6} Z^{4} + 18 X Y^{10} Z + 4 X^{2} Y^{7} Z^{2} + 2 X^{2} Y^{6} Z^{3} + 2 X^{2} Y^{5} Z^{4} + 9 X Y^{9} Z + 6 X Y^{8} Z^{2} + 29 X^{2} Y^{6} Z^{2} + X^{2} Y^{5} Z^{3} + X^{2} Y^{4} Z^{4} + 45 X Y^{8} Z + 2 X Y^{7} Z^{2} + 64 X^{2} Y^{5} Z^{2} + 3 X^{2} Y^{4} Z^{3} + 3 X^{2} Y^{3} Z^{4} + 7 X Y^{7} Z + 8 X Y^{6} Z^{2} + 197 X^{2} Y^{4} Z^{2} + X^{2} Y^{3} Z^{3} + 4 X^{2} Y^{2} Z^{4} + 93 X Y^{6} Z + 12 X Y^{5} Z^{2} + 16 X^{2} Y^{3} Z^{2} + 94 X Y^{5} Z + 8 X Y^{4} Z^{2} + 183 X^{2} Y^{2} Z^{2} + 240 X Y^{4} Z + 6 X Y^{3} Z^{2} + 64 X Y^{3} Z + 8 X Y^{2} Z^{2} + 85 X Y^{2} Z + 11 X Y Z^{2} + 309 X Y Z

Algorithm definition

The algorithm ⟨4×30×32:2391⟩ is serendipitous tensor product (⟨2×6×8:75⟩ - 18) ⊗ ⟨2×5×4:32⟩ +9⟨2×5×8:63⟩.

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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