Description of fast matrix multiplication algorithm: ⟨16×16×30:4325⟩

Algorithm type

6 X^{3} Y^{5} Z^{5} + 15 X^{3} Y^{4} Z^{6} + 450 X^{4} Y^{4} Z^{4} + 4 X^{3} Y^{4} Z^{5} + 5 X^{3} Y^{4} Z^{4} + 6 X^{2} Y^{5} Z^{4} + 90 X^{6} Y^{2} Z^{2} + 90 X^{4} Y^{4} Z^{2} + 90 X^{4} Y^{2} Z^{4} + 135 X^{2} Y^{6} Z^{2} + 37 X^{2} Y^{4} Z^{4} + 135 X^{2} Y^{2} Z^{6} + 40 X^{2} Y^{4} Z^{3} + 49 X^{2} Y^{3} Z^{4} + 4 X Y^{2} Z^{6} + 495 X^{4} Y^{2} Z^{2} + 275 X^{2} Y^{4} Z^{2} + 41 X^{2} Y^{3} Z^{3} + 266 X^{2} Y^{2} Z^{4} + 60 X Y^{6} Z + 16 X Y^{5} Z^{2} + 71 X Y Z^{6} + 40 X^{2} Y^{4} Z + 29 X^{2} Y^{3} Z^{2} + 17 X^{2} Y^{2} Z^{3} + 40 X^{2} Y Z^{4} + 2 X Y^{5} Z + 10 X Y^{4} Z^{2} + 40 X^{3} Y^{2} Z + 40 X^{3} Y Z^{2} + 230 X^{2} Y^{2} Z^{2} + 31 X Y^{4} Z + 90 X Y^{3} Z^{2} + 60 X Y^{2} Z^{3} + 20 X Y Z^{4} + 220 X^{2} Y^{2} Z + 220 X^{2} Y Z^{2} + 11 X Y^{3} Z + 334 X Y^{2} Z^{2} + 230 X Y^{2} Z + 244 X Y Z^{2} + 37 X Y Z

Algorithm definition

The algorithm ⟨16×16×30:4325⟩ is serendipitous tensor product (⟨4×4×10:115⟩ - 30) ⊗ ⟨4×4×3:38⟩ +15⟨4×4×6:73⟩.

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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