Description of fast matrix multiplication algorithm: ⟨6×25×32:2870⟩

Algorithm type

24 X^{4} Y^{12} Z^{4} + X^{2} Y^{10} Z^{5} + 216 X^{4} Y^{8} Z^{4} + 64 X^{2} Y^{12} Z^{2} + 10 X^{2} Y^{8} Z^{6} + X^{2} Y^{8} Z^{5} + 4 X^{6} Y^{2} Z^{6} + 48 X^{2} Y^{8} Z^{4} + 40 X Y^{12} Z + 6 X Y^{10} Z^{3} + X^{6} Y Z^{6} + X^{2} Y^{8} Z^{3} + X Y^{10} Z^{2} + 2 X^{6} Y^{2} Z^{4} + X^{5} Y Z^{6} + 6 X^{4} Y^{2} Z^{6} + 336 X^{2} Y^{8} Z^{2} + X^{2} Y^{6} Z^{4} + 64 X^{2} Y^{4} Z^{6} + 11 X Y^{8} Z^{3} + 4 X^{6} Y^{2} Z^{3} + X^{4} Y Z^{6} + 4 X^{3} Y^{2} Z^{6} + 3 X^{2} Y^{4} Z^{5} + 50 X Y^{8} Z^{2} + 2 X^{6} Y^{2} Z^{2} + 2 X^{6} Y Z^{3} + X^{5} Y Z^{4} + 2 X^{4} Y^{2} Z^{4} + 9 X^{3} Y Z^{6} + 109 X^{2} Y^{4} Z^{4} + 4 X^{2} Y^{2} Z^{6} + 121 X Y^{8} Z + 5 X Y^{6} Z^{3} + 2 X^{6} Y^{2} Z + X^{6} Y Z^{2} + 7 X^{4} Y^{2} Z^{3} + X^{4} Y Z^{4} + X^{3} Y^{3} Z^{3} + 4 X^{3} Y^{2} Z^{4} + 2 X^{2} Y^{4} Z^{3} + 11 X^{2} Y Z^{6} + X Y^{6} Z^{2} + 2 X Y^{2} Z^{6} + 2 X^{4} Y^{2} Z^{2} + 2 X^{4} Y Z^{3} + 10 X^{3} Y^{2} Z^{3} + 2 X^{3} Y Z^{4} + 33 X^{2} Y^{4} Z^{2} + 3 X^{2} Y^{2} Z^{4} + 2 X Y^{6} Z + 70 X Y^{4} Z^{3} + 7 X Y Z^{6} + 3 X^{4} Y^{2} Z + 2 X^{4} Y Z^{2} + X^{3} Y^{3} Z + 2 X^{3} Y^{2} Z^{2} + 4 X^{3} Y Z^{3} + 48 X^{2} Y^{3} Z^{2} + 4 X^{2} Y^{2} Z^{3} + 7 X^{2} Y Z^{4} + 104 X Y^{4} Z^{2} + 2 X Y^{3} Z^{3} + X Y^{2} Z^{4} + 2 X^{3} Y Z^{2} + X^{2} Y^{3} Z + 437 X^{2} Y^{2} Z^{2} + 7 X^{2} Y Z^{3} + 34 X Y^{4} Z + X Y^{3} Z^{2} + 28 X Y^{2} Z^{3} + 7 X Y Z^{4} + 4 X^{3} Y Z + 3 X^{2} Y^{2} Z + 3 X^{2} Y Z^{2} + 80 X Y^{3} Z + 102 X Y^{2} Z^{2} + 141 X Y Z^{3} + 4 X^{2} Y Z + 241 X Y^{2} Z + 214 X Y Z^{2} + 65 X Y Z

Algorithm definition

The algorithm ⟨6×25×32:2870⟩ is serendipitous tensor product (⟨3×5×8:90⟩ - 8) ⊗ ⟨2×5×4:32⟩ +⟨2×5×8:63⟩ +3⟨4×5×4:61⟩.

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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