Description of fast matrix multiplication algorithm: ⟨4×16×28:1166⟩

Algorithm type

X^{2} Y^{16} Z^{2} + X Y^{16} Z + 2 X^{2} Y^{13} Z^{2} + 6 X^{4} Y^{8} Z^{4} + 2 X^{2} Y^{12} Z^{2} + 3 X Y^{13} Z + 6 X^{4} Y^{6} Z^{4} + X^{2} Y^{10} Z^{2} + X^{2} Y^{8} Z^{4} + 6 X Y^{12} Z + 2 X^{2} Y^{9} Z^{2} + 54 X^{4} Y^{4} Z^{4} + 26 X^{2} Y^{8} Z^{2} + X^{2} Y^{6} Z^{4} + 4 X Y^{10} Z + 5 X Y^{9} Z^{2} + X^{2} Y^{7} Z^{2} + 2 X^{2} Y^{5} Z^{4} + 13 X Y^{9} Z + 55 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{4} Z^{4} + 24 X Y^{8} Z + 5 X Y^{7} Z^{2} + 10 X^{2} Y^{5} Z^{2} + 7 X Y^{7} Z + 112 X^{2} Y^{4} Z^{2} + 38 X Y^{6} Z + 10 X^{2} Y^{3} Z^{2} + 6 X Y^{5} Z + 7 X Y^{4} Z^{2} + 200 X^{2} Y^{2} Z^{2} + 73 X Y^{4} Z + 7 X Y^{3} Z^{2} + 101 X Y^{3} Z + 164 X Y^{2} Z + 8 X Y Z^{2} + 200 X Y Z

Algorithm definition

The algorithm ⟨4×16×28:1166⟩ is serendipitous tensor product (⟨2×4×7:45⟩ - 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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