Description of fast matrix multiplication algorithm: ⟨4×25×28:1756⟩

Algorithm type

16 X^{4} Y^{20} Z^{4} + X^{2} Y^{21} Z^{3} + 16 X^{4} Y^{16} Z^{4} + 56 X^{2} Y^{20} Z^{2} + 6 X Y^{21} Z^{2} + X Y^{21} Z + 40 X Y^{20} Z + X^{2} Y^{16} Z^{3} + 8 X^{4} Y^{12} Z^{4} + 72 X^{2} Y^{16} Z^{2} + 57 X Y^{16} Z + X Y^{15} Z^{2} + X Y^{15} Z + 80 X^{4} Y^{8} Z^{4} + 40 X^{2} Y^{12} Z^{2} + 3 X^{2} Y^{10} Z^{3} + 2 X Y^{12} Z^{2} + 2 X^{2} Y^{10} Z^{2} + 5 X^{2} Y^{8} Z^{4} + 33 X Y^{12} Z + 2 X^{2} Y^{8} Z^{3} + 2 X^{2} Y^{7} Z^{4} + 2 X Y^{10} Z^{2} + 8 X^{4} Y^{4} Z^{4} + 117 X^{2} Y^{8} Z^{2} + 3 X^{2} Y^{6} Z^{4} + X^{2} Y^{7} Z^{2} + X^{2} Y^{6} Z^{3} + 8 X Y^{8} Z^{2} + X^{2} Y^{6} Z^{2} + X^{2} Y^{5} Z^{3} + 45 X Y^{8} Z + 11 X Y^{7} Z^{2} + 36 X^{2} Y^{5} Z^{2} + 3 X^{2} Y^{4} Z^{3} + 3 X^{2} Y^{3} Z^{4} + 6 X Y^{7} Z + 8 X Y^{6} Z^{2} + 133 X^{2} Y^{4} Z^{2} + 2 X^{2} Y^{3} Z^{3} + 4 X^{2} Y^{2} Z^{4} + 7 X Y^{6} Z + 12 X Y^{5} Z^{2} + 27 X^{2} Y^{3} Z^{2} + 90 X Y^{5} Z + 3 X Y^{4} Z^{2} + 168 X^{2} Y^{2} Z^{2} + 214 X Y^{4} Z + 5 X Y^{3} Z^{2} + 16 X^{2} Y Z^{2} + 77 X Y^{3} Z + 10 X Y^{2} Z^{2} + 85 X Y^{2} Z + 11 X Y Z^{2} + 193 X Y Z

Algorithm definition

The algorithm ⟨4×25×28:1756⟩ is serendipitous tensor product (⟨2×5×7:55⟩ - 8) ⊗ ⟨2×5×4:32⟩ +4⟨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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