Description of fast matrix multiplication algorithm: ⟨4×18×25:1172⟩

Algorithm type

2 X^{3} Y^{14} Z^{2} + 2 X^{2} Y^{15} Z + 2 X^{2} Y^{14} Z + 10 X^{4} Y^{8} Z^{4} + 4 X^{2} Y^{12} Z^{2} + 3 X^{2} Y^{12} Z + 4 X Y^{13} Z + X^{4} Y^{8} Z^{2} + 4 X Y^{12} Z + 3 X^{3} Y^{8} Z^{2} + X^{2} Y^{10} Z + 2 X^{2} Y^{9} Z^{2} + 55 X^{4} Y^{4} Z^{4} + 27 X^{2} Y^{8} Z^{2} + 18 X Y^{9} Z + 62 X^{2} Y^{6} Z^{2} + 14 X Y^{8} Z + 2 X^{2} Y^{5} Z + 110 X^{2} Y^{4} Z^{2} + 56 X Y^{6} Z + 6 X^{2} Y^{4} Z + 4 X Y^{5} Z + 222 X^{2} Y^{2} Z^{2} + 54 X Y^{4} Z + 132 X Y^{3} Z + 156 X Y^{2} Z + 216 X Y Z

Algorithm definition

The algorithm ⟨4×18×25:1172⟩ is serendipitous tensor product (⟨2×6×5:47⟩ - 2) ⊗ ⟨2×3×5:25⟩ +⟨2×6×5:47⟩.

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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