Description of fast matrix multiplication algorithm: ⟨15×20×30:5016⟩

Algorithm type

3 X^{6} Y^{4} Z^{6} + 18 X^{6} Y^{4} Z^{2} + 579 X^{4} Y^{4} Z^{4} + 3 X^{4} Y^{2} Z^{6} + 18 X^{2} Y^{6} Z^{4} + 6 X^{3} Y^{2} Z^{6} + 18 X^{4} Y^{4} Z^{2} + 3 X^{4} Y^{2} Z^{4} + 18 X^{2} Y^{4} Z^{4} + 3 X^{2} Y^{2} Z^{6} + 6 X^{2} Y Z^{6} + 18 X Y^{6} Z^{2} + 210 X^{4} Y^{2} Z^{2} + 18 X^{3} Y^{4} Z + 6 X^{3} Y^{2} Z^{3} + 774 X^{2} Y^{4} Z^{2} + 789 X^{2} Y^{2} Z^{4} + 18 X Y^{3} Z^{4} + 6 X Y Z^{6} + 18 X^{3} Y^{2} Z^{2} + 18 X^{2} Y^{4} Z + 6 X^{2} Y Z^{4} + 18 X Y^{4} Z^{2} + 18 X Y^{2} Z^{4} + 390 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 198 X Y^{4} Z + 216 X Y Z^{4} + 198 X^{2} Y^{2} Z + 228 X^{2} Y Z^{2} + 396 X Y^{2} Z^{2} + 6 X Y Z^{3} + 24 X^{2} Y Z + 360 X Y^{2} Z + 390 X Y Z^{2} + 12 X Y Z

Algorithm definition

The algorithm ⟨15×20×30:5016⟩ is serendipitous tensor product (⟨5×5×5:93⟩ - 5) ⊗ ⟨3×4×6:54⟩ +⟨9×4×6:159⟩ +⟨6×4×6:105⟩.

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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