Description of fast matrix multiplication algorithm: ⟨18×18×20:3648⟩

Algorithm type

3 X^{8} Y^{8} Z^{8} + 3 X^{8} Y^{4} Z^{6} + 3 X^{4} Y^{8} Z^{6} + 3 X^{4} Y^{4} Z^{10} + 6 X^{8} Y^{4} Z^{4} + 3 X^{4} Y^{8} Z^{4} + 3 X^{4} Y^{4} Z^{8} + 3 X^{6} Y^{2} Z^{6} + 48 X^{4} Y^{4} Z^{6} + 6 X^{8} Y^{2} Z^{3} + 36 X^{6} Y^{4} Z^{2} + 42 X^{6} Y^{2} Z^{4} + 36 X^{4} Y^{6} Z^{2} + 306 X^{4} Y^{4} Z^{4} + 36 X^{2} Y^{2} Z^{8} + 6 X^{4} Y^{4} Z^{3} + 6 X^{4} Y^{2} Z^{5} + 75 X^{6} Y^{2} Z^{2} + 6 X^{6} Y Z^{3} + 6 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{2} Z^{4} + 108 X^{2} Y^{6} Z^{2} + 72 X^{2} Y^{4} Z^{4} + 93 X^{2} Y^{2} Z^{6} + 36 X^{6} Y^{2} Z + 48 X^{6} Y Z^{2} + 66 X^{4} Y^{2} Z^{3} + 36 X^{2} Y^{6} Z + 42 X^{2} Y^{4} Z^{3} + 6 X^{2} Y^{2} Z^{5} + 78 X^{6} Y Z + 36 X^{4} Y^{3} Z + 312 X^{4} Y^{2} Z^{2} + 36 X^{3} Y^{4} Z + 402 X^{2} Y^{4} Z^{2} + 114 X^{2} Y^{2} Z^{4} + 108 X Y^{6} Z + 36 X^{3} Y^{2} Z^{2} + 6 X^{3} Y Z^{3} + 24 X^{2} Y^{2} Z^{3} + 36 X^{2} Y Z^{4} + 54 X Y^{4} Z^{2} + 36 X Y^{2} Z^{4} + 72 X^{3} Y^{2} Z + 12 X^{3} Y Z^{2} + 108 X^{2} Y^{3} Z + 135 X^{2} Y^{2} Z^{2} + 132 X^{2} Y Z^{3} + 90 X Y^{4} Z + 54 X Y^{2} Z^{3} + 6 X^{3} Y Z + 126 X^{2} Y^{2} Z + 126 X^{2} Y Z^{2} + 126 X Y^{2} Z^{2} + 78 X Y Z^{3} + 42 X^{2} Y Z + 36 X Y^{2} Z + 36 X Y Z^{2} + 42 X Y Z

Algorithm definition

The algorithm ⟨18×18×20:3648⟩ is serendipitous tensor product (⟨6×3×5:68⟩ - 16) ⊗ ⟨3×6×4:54⟩ +8⟨6×6×4:105⟩.

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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