Description of fast matrix multiplication algorithm: ⟨4×20×28:1426⟩

Algorithm type

X^{2} Y^{16} Z^{4} + 4 X^{2} Y^{15} Z^{2} + 2 X Y^{16} Z^{2} + 12 X^{4} Y^{10} Z^{4} + 10 X Y^{15} Z + 12 X^{4} Y^{8} Z^{4} + 4 X^{2} Y^{12} Z^{2} + 2 X^{2} Y^{10} Z^{4} + X^{2} Y^{10} Z^{3} + 2 X Y^{12} Z^{2} + 6 X^{4} Y^{6} Z^{4} + 47 X^{2} Y^{10} Z^{2} + 14 X Y^{12} Z + 6 X Y^{11} Z^{2} + 2 X^{2} Y^{9} Z^{2} + X Y^{11} Z + 60 X^{4} Y^{4} Z^{4} + 60 X^{2} Y^{8} Z^{2} + 2 X^{2} Y^{6} Z^{4} + 40 X Y^{10} Z + X^{2} Y^{7} Z^{2} + 5 X^{2} Y^{6} Z^{3} + 8 X Y^{9} Z + 6 X^{4} Y^{2} Z^{4} + 53 X^{2} Y^{6} Z^{2} + 58 X Y^{8} Z + 20 X^{2} Y^{5} Z^{2} + X^{2} Y^{4} Z^{3} + X^{2} Y^{3} Z^{4} + 2 X Y^{7} Z + 128 X^{2} Y^{4} Z^{2} + 3 X^{2} Y^{3} Z^{3} + 3 X^{2} Y^{2} Z^{4} + 43 X Y^{6} Z + 13 X Y^{5} Z^{2} + 17 X^{2} Y^{3} Z^{2} + 2 X^{2} Y^{2} Z^{3} + 63 X Y^{5} Z + 2 X Y^{4} Z^{2} + 191 X^{2} Y^{2} Z^{2} + 110 X Y^{4} Z + 4 X Y^{3} Z^{2} + 10 X^{2} Y Z^{2} + 72 X Y^{3} Z + 8 X Y^{2} Z^{2} + 160 X Y^{2} Z + 17 X Y Z^{2} + 137 X Y Z

Algorithm definition

The algorithm ⟨4×20×28:1426⟩ is serendipitous tensor product (⟨2×5×7:55⟩ - 8) ⊗ ⟨2×4×4:26⟩ +4⟨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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