Description of fast matrix multiplication algorithm: ⟨4×20×24:1221⟩

Algorithm type

X^{2} Y^{19} Z^{2} + X Y^{19} Z + X Y^{16} Z + 12 X^{4} Y^{8} Z^{4} + 4 X^{2} Y^{12} Z^{2} + 2 X Y^{14} Z + X Y^{12} Z^{2} + X^{2} Y^{10} Z^{2} + 2 X^{2} Y^{8} Z^{4} + 5 X Y^{12} Z + X Y^{11} Z^{2} + X Y^{11} Z + 3 X Y^{10} Z^{2} + 66 X^{4} Y^{4} Z^{4} + 33 X^{2} Y^{8} Z^{2} + X^{2} Y^{6} Z^{4} + X Y^{10} Z + 16 X Y^{9} Z + 73 X^{2} Y^{6} Z^{2} + 16 X Y^{8} Z + 132 X^{2} Y^{4} Z^{2} + 72 X Y^{6} Z + 2 X Y^{5} Z^{2} + 6 X Y^{5} Z + 9 X Y^{4} Z^{2} + 218 X^{2} Y^{2} Z^{2} + 59 X Y^{4} Z + 118 X Y^{3} Z + 184 X Y^{2} Z + 180 X Y Z

Algorithm definition

The algorithm ⟨4×20×24:1221⟩ is serendipitous tensor product (⟨2×5×6:47⟩ - 2) ⊗ ⟨2×4×4:26⟩ +⟨2×4×8:51⟩.

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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