Description of fast matrix multiplication algorithm: ⟨18×20×21:4259⟩

Algorithm type

2 X^{4} Y^{4} Z^{8} + X^{2} Y^{2} Z^{11} + 36 X^{4} Y^{6} Z^{4} + X^{4} Y^{4} Z^{6} + X^{2} Y^{2} Z^{10} + X^{4} Y^{4} Z^{5} + X^{2} Y^{2} Z^{9} + 432 X^{4} Y^{4} Z^{4} + 36 X^{2} Y^{8} Z^{2} + X^{2} Y^{2} Z^{8} + 3 X Y Z^{9} + 36 X^{6} Y^{2} Z^{2} + 72 X^{2} Y^{6} Z^{2} + 108 X^{2} Y^{4} Z^{4} + 117 X^{2} Y^{2} Z^{6} + 36 X^{4} Y^{3} Z^{2} + 36 X^{2} Y^{3} Z^{4} + 3 X Y^{2} Z^{6} + 8 X Y Z^{7} + 36 X^{6} Y Z + 468 X^{4} Y^{2} Z^{2} + 252 X^{2} Y^{4} Z^{2} + 675 X^{2} Y^{2} Z^{4} + 99 X Y Z^{6} + X^{3} Y Z^{3} + 36 X^{2} Y^{4} Z + 2 X^{2} Y^{2} Z^{3} + 36 X Y^{4} Z^{2} + 108 X Y^{2} Z^{4} + 8 X Y Z^{5} + 36 X^{4} Y Z + 36 X^{3} Y Z^{2} + 72 X^{2} Y^{3} Z + 153 X^{2} Y^{2} Z^{2} + 82 X^{2} Y Z^{3} + 72 X Y^{3} Z^{2} + 12 X Y^{2} Z^{3} + 220 X Y Z^{4} + 252 X^{2} Y^{2} Z + 252 X^{2} Y Z^{2} + 252 X Y^{2} Z^{2} + 59 X Y Z^{3} + 36 X^{2} Y Z + 36 X Y Z^{2} + 37 X Y Z

Algorithm definition

The algorithm ⟨18×20×21:4259⟩ is serendipitous tensor product (⟨3×5×7:79⟩ - 5) ⊗ ⟨6×4×3:54⟩ +⟨6×4×15:263⟩.

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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