Description of fast matrix multiplication algorithm: ⟨4×20×21:1096⟩

Algorithm type

8 X^{2} Y^{15} Z^{2} + 2 X Y^{16} Z^{2} + 8 X^{4} Y^{10} Z^{4} + 21 X Y^{15} Z + 8 X^{4} Y^{8} Z^{4} + 8 X^{2} Y^{12} Z^{2} + 2 X^{2} Y^{11} Z^{3} + X^{2} Y^{10} Z^{3} + 4 X^{4} Y^{6} Z^{4} + 22 X^{2} Y^{10} Z^{2} + X^{2} Y^{8} Z^{4} + 28 X Y^{12} Z + X Y^{11} Z^{2} + 4 X^{2} Y^{9} Z^{2} + 2 X^{2} Y^{7} Z^{4} + 2 X Y^{11} Z + 2 X Y^{10} Z^{2} + 40 X^{4} Y^{4} Z^{4} + 28 X^{2} Y^{8} Z^{2} + X Y^{10} Z + X^{2} Y^{6} Z^{3} + 16 X Y^{9} Z + 2 X Y^{8} Z^{2} + 4 X^{4} Y^{2} Z^{4} + 58 X^{2} Y^{6} Z^{2} + 4 X Y^{7} Z^{2} + 26 X^{2} Y^{5} Z^{2} + X^{2} Y^{4} Z^{3} + 2 X Y^{6} Z^{2} + 44 X^{2} Y^{4} Z^{2} + 2 X^{2} Y^{3} Z^{3} + 3 X^{2} Y^{2} Z^{4} + 21 X Y^{6} Z + 3 X Y^{5} Z^{2} + 22 X^{2} Y^{3} Z^{2} + 77 X Y^{5} Z + 2 X Y^{4} Z^{2} + 171 X^{2} Y^{2} Z^{2} + 90 X Y^{4} Z + 3 X Y^{3} Z^{2} + 12 X^{2} Y Z^{2} + 107 X Y^{3} Z + 5 X Y^{2} Z^{2} + 63 X Y^{2} Z + 12 X Y Z^{2} + 152 X Y Z

Algorithm definition

The algorithm ⟨4×20×21:1096⟩ is serendipitous tensor product (⟨2×5×7:55⟩ - 8) ⊗ ⟨2×4×3:20⟩ +4⟨2×4×6:39⟩.

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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