Description of fast matrix multiplication algorithm: ⟨15×20×22:3858⟩

Algorithm type

4 X^{4} Y^{4} Z^{6} + 4 X^{2} Y^{10} Z^{2} + X^{2} Y^{6} Z^{6} + X^{2} Y^{5} Z^{6} + X^{2} Y^{4} Z^{7} + 2 X Y^{6} Z^{6} + 316 X^{4} Y^{4} Z^{4} + 8 X^{2} Y^{8} Z^{2} + X^{2} Y^{5} Z^{5} + 2 X^{2} Y^{3} Z^{7} + 4 X^{6} Y^{2} Z^{3} + X^{2} Y^{5} Z^{4} + 2 X^{2} Y^{4} Z^{5} + 9 X^{2} Y^{3} Z^{6} + X^{2} Y^{2} Z^{7} + 3 X Y^{6} Z^{4} + 2 X Y^{4} Z^{6} + 316 X^{6} Y^{2} Z^{2} + 4 X^{4} Y^{2} Z^{4} + 5 X^{2} Y^{6} Z^{2} + 4 X^{2} Y^{4} Z^{4} + 3 X^{2} Y^{3} Z^{5} + 5 X^{2} Y^{2} Z^{6} + X Y^{5} Z^{4} + X Y^{4} Z^{5} + 2 X Y^{3} Z^{6} + 5 X Y^{2} Z^{7} + 4 X^{6} Y Z^{2} + 4 X^{3} Y^{5} Z + X^{2} Y^{6} Z + 2 X^{2} Y^{4} Z^{3} + 6 X^{2} Y^{3} Z^{4} + 7 X Y^{2} Z^{6} + 3 X Y Z^{7} + 12 X^{6} Y Z + 13 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{4} Z + 2 X^{3} Y^{3} Z^{2} + 136 X^{2} Y^{4} Z^{2} + 25 X^{2} Y^{3} Z^{3} + 125 X^{2} Y^{2} Z^{4} + 2 X Y^{6} Z + 3 X Y^{4} Z^{3} + X Y^{3} Z^{4} + 9 X Y^{2} Z^{5} + 3 X Y Z^{6} + 4 X^{3} Y^{3} Z + 14 X^{3} Y^{2} Z^{2} + 4 X^{3} Y Z^{3} + 4 X^{2} Y^{4} Z + 8 X^{2} Y^{3} Z^{2} + 16 X^{2} Y^{2} Z^{3} + 12 X Y^{5} Z + 4 X Y^{4} Z^{2} + 3 X Y^{3} Z^{3} + 8 X Y^{2} Z^{4} + X Y Z^{5} + 4 X^{4} Y Z + 126 X^{3} Y^{2} Z + 136 X^{3} Y Z^{2} + 3 X^{2} Y^{3} Z + 1082 X^{2} Y^{2} Z^{2} + 42 X Y^{4} Z + 30 X Y^{3} Z^{2} + 10 X Y^{2} Z^{3} + 16 X Y Z^{4} + 52 X^{3} Y Z + 16 X^{2} Y^{2} Z + 26 X^{2} Y Z^{2} + 43 X Y^{3} Z + 64 X Y^{2} Z^{2} + 45 X Y Z^{3} + 40 X^{2} Y Z + 486 X Y^{2} Z + 370 X Y Z^{2} + 115 X Y Z

Algorithm definition

The algorithm ⟨15×20×22:3858⟩ is serendipitous tensor product (⟨5×5×11:195⟩ - 37) ⊗ ⟨3×4×2:20⟩ +⟨3×4×8:73⟩ +⟨3×4×6:54⟩ +14⟨3×4×4:38⟩ +⟨6×4×2:39⟩.

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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