Description of fast matrix multiplication algorithm: ⟨4×25×32:2006⟩

Algorithm type

8 X^{4} Y^{20} Z^{4} + X^{4} Y^{17} Z^{4} + 2 X^{2} Y^{21} Z^{2} + 20 X^{4} Y^{16} Z^{4} + 40 X^{2} Y^{20} Z^{2} + 14 X Y^{21} Z + 33 X Y^{20} Z + 7 X^{2} Y^{17} Z^{2} + 9 X^{4} Y^{12} Z^{4} + 59 X^{2} Y^{16} Z^{2} + 3 X^{2} Y^{15} Z^{2} + 49 X Y^{16} Z + 5 X^{4} Y^{9} Z^{4} + 9 X^{2} Y^{13} Z^{2} + 16 X Y^{15} Z + 94 X^{4} Y^{8} Z^{4} + 60 X^{2} Y^{12} Z^{2} + X Y^{14} Z + 16 X Y^{13} Z + 24 X^{2} Y^{10} Z^{2} + 52 X Y^{12} Z + 9 X^{2} Y^{9} Z^{2} + 2 X Y^{11} Z + 137 X^{2} Y^{8} Z^{2} + 24 X Y^{10} Z + 10 X^{2} Y^{7} Z^{2} + 14 X Y^{9} Z + 13 X^{2} Y^{6} Z^{2} + 49 X Y^{8} Z + 27 X^{2} Y^{5} Z^{2} + 19 X Y^{7} Z + 161 X^{2} Y^{4} Z^{2} + 20 X Y^{6} Z + 38 X^{2} Y^{3} Z^{2} + 110 X Y^{5} Z + 184 X^{2} Y^{2} Z^{2} + 203 X Y^{4} Z + 131 X Y^{3} Z + 112 X Y^{2} Z + 221 X Y Z

Algorithm definition

The algorithm ⟨4×25×32:2006⟩ is serendipitous tensor product (⟨2×5×8:63⟩ - 19) ⊗ ⟨2×5×4:32⟩ +⟨2×5×12:94⟩ +8⟨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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