Description of fast matrix multiplication algorithm: ⟨4×20×32:1623⟩

Algorithm type

8 X^{4} Y^{16} Z^{4} + X^{2} Y^{18} Z^{2} + X^{4} Y^{13} Z^{4} + 32 X^{2} Y^{16} Z^{2} + 6 X Y^{18} Z + X Y^{17} Z + X^{4} Y^{10} Z^{4} + X^{2} Y^{14} Z^{2} + X^{2} Y^{13} Z^{3} + 2 X^{2} Y^{12} Z^{4} + 24 X Y^{16} Z + 3 X^{4} Y^{9} Z^{4} + 9 X^{2} Y^{13} Z^{2} + 80 X^{4} Y^{8} Z^{4} + 34 X^{2} Y^{12} Z^{2} + 2 X^{2} Y^{11} Z^{3} + X Y^{14} Z + 5 X Y^{13} Z^{2} + 2 X^{2} Y^{11} Z^{2} + X^{2} Y^{10} Z^{3} + 4 X Y^{13} Z + 2 X Y^{12} Z^{2} + X^{4} Y^{6} Z^{4} + X^{2} Y^{10} Z^{2} + 37 X Y^{12} Z + 3 X Y^{11} Z^{2} + 5 X^{4} Y^{5} Z^{4} + 4 X^{2} Y^{9} Z^{2} + 4 X Y^{11} Z + 3 X Y^{10} Z^{2} + 6 X^{4} Y^{4} Z^{4} + 86 X^{2} Y^{8} Z^{2} + 3 X^{2} Y^{7} Z^{3} + 8 X Y^{10} Z + 2 X Y^{9} Z^{2} + 16 X^{2} Y^{7} Z^{2} + 3 X^{2} Y^{6} Z^{3} + 4 X Y^{9} Z + 4 X Y^{8} Z^{2} + 12 X^{2} Y^{6} Z^{2} + 15 X Y^{8} Z + 6 X Y^{7} Z^{2} + 15 X^{2} Y^{5} Z^{2} + 9 X^{2} Y^{4} Z^{3} + 10 X Y^{7} Z + X Y^{6} Z^{2} + 161 X^{2} Y^{4} Z^{2} + 7 X Y^{6} Z + 3 X Y^{5} Z^{2} + 20 X^{2} Y^{3} Z^{2} + X^{2} Y^{2} Z^{3} + 23 X Y^{5} Z + 9 X Y^{4} Z^{2} + 206 X^{2} Y^{2} Z^{2} + 226 X Y^{4} Z + 18 X Y^{3} Z^{2} + 112 X Y^{3} Z + 34 X Y^{2} Z + 5 X Y Z^{2} + 319 X Y Z

Algorithm definition

The algorithm ⟨4×20×32:1623⟩ is serendipitous tensor product (⟨2×4×8:51⟩ - 17) ⊗ ⟨2×5×4:32⟩ +⟨2×5×12:94⟩ +7⟨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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