Description of fast matrix multiplication algorithm: ⟨16×18×30:4845⟩

Algorithm type

3 X^{4} Y^{8} Z^{4} + 552 X^{4} Y^{4} Z^{4} + 6 X^{2} Y^{8} Z^{2} + 6 X^{4} Y^{4} Z^{2} + 36 X^{4} Y^{2} Z^{4} + 6 X^{2} Y^{6} Z^{2} + 36 X^{2} Y^{4} Z^{4} + 18 X^{2} Y^{2} Z^{6} + 222 X^{4} Y^{2} Z^{2} + 846 X^{2} Y^{4} Z^{2} + 666 X^{2} Y^{2} Z^{4} + 12 X Y^{6} Z + 18 X Y Z^{6} + 12 X^{2} Y^{4} Z + 36 X^{2} Y Z^{4} + 36 X Y^{4} Z^{2} + 36 X Y^{2} Z^{4} + 324 X^{2} Y^{2} Z^{2} + 300 X Y^{4} Z + 18 X Y^{2} Z^{3} + 126 X Y Z^{4} + 258 X^{2} Y^{2} Z + 198 X^{2} Y Z^{2} + 12 X Y^{3} Z + 378 X Y^{2} Z^{2} + 48 X^{2} Y Z + 342 X Y^{2} Z + 234 X Y Z^{2} + 60 X Y Z

Algorithm definition

The algorithm ⟨16×18×30:4845⟩ is serendipitous tensor product (⟨4×6×5:90⟩ - 10) ⊗ ⟨4×3×6:54⟩ +5⟨4×6×6:105⟩.

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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