Description of fast matrix multiplication algorithm: ⟨15×25×25:5370⟩

Algorithm type

2 X Y^{12} Z^{2} + X^{9} Y^{4} Z + X^{2} Y^{2} Z^{9} + X Y^{10} Z^{2} + X Y^{6} Z^{6} + 5 X^{9} Y^{2} Z + 49 X^{6} Y^{4} Z^{2} + 544 X^{4} Y^{4} Z^{4} + 17 X^{4} Y^{2} Z^{6} + 2 X^{3} Y^{8} Z + 64 X^{2} Y^{8} Z^{2} + 17 X^{2} Y^{6} Z^{4} + 32 X^{2} Y^{4} Z^{6} + 5 X^{2} Y Z^{9} + X Y^{9} Z^{2} + 3 X^{6} Y^{4} Z + X^{6} Y^{2} Z^{3} + X^{3} Y^{6} Z^{2} + 2 X^{2} Y^{8} Z + 4 X Y^{8} Z^{2} + 2 X Y^{6} Z^{4} + X Y^{4} Z^{6} + 161 X^{6} Y^{2} Z^{2} + 5 X^{6} Y Z^{3} + 81 X^{4} Y^{4} Z^{2} + 17 X^{4} Y^{2} Z^{4} + X^{3} Y^{6} Z + X^{3} Y^{4} Z^{3} + X^{2} Y^{7} Z + 35 X^{2} Y^{6} Z^{2} + 83 X^{2} Y^{4} Z^{4} + 163 X^{2} Y^{2} Z^{6} + 22 X Y^{8} Z + 5 X Y^{3} Z^{6} + 17 X^{6} Y^{2} Z + 5 X^{6} Y Z^{2} + 2 X^{4} Y^{4} Z + 2 X^{4} Y^{2} Z^{3} + 3 X^{3} Y^{4} Z^{2} + 3 X^{2} Y^{6} Z + 12 X^{2} Y^{5} Z^{2} + 51 X^{2} Y^{4} Z^{3} + 2 X^{2} Y^{2} Z^{5} + 6 X^{2} Y Z^{6} + X Y^{7} Z + 9 X Y^{6} Z^{2} + 2 X Y^{4} Z^{4} + 16 X Y^{2} Z^{6} + 55 X^{6} Y Z + 221 X^{4} Y^{2} Z^{2} + X^{4} Y Z^{3} + 19 X^{3} Y^{4} Z + 5 X^{3} Y^{3} Z^{2} + 5 X^{3} Y^{2} Z^{3} + 571 X^{2} Y^{4} Z^{2} + X^{2} Y^{3} Z^{3} + 223 X^{2} Y^{2} Z^{4} + 18 X Y^{6} Z + 11 X Y^{4} Z^{3} + X Y^{3} Z^{4} + 55 X Y Z^{6} + 23 X^{4} Y^{2} Z + X^{4} Y Z^{2} + 17 X^{3} Y^{2} Z^{2} + 52 X^{2} Y^{4} Z + 16 X^{2} Y^{3} Z^{2} + 27 X^{2} Y^{2} Z^{3} + X^{2} Y Z^{4} + 11 X Y^{5} Z + 82 X Y^{4} Z^{2} + 32 X Y^{2} Z^{4} + 11 X^{4} Y Z + 83 X^{3} Y^{2} Z + 55 X^{3} Y Z^{2} + 13 X^{2} Y^{3} Z + 639 X^{2} Y^{2} Z^{2} + 62 X^{2} Y Z^{3} + 184 X Y^{4} Z + 32 X Y^{3} Z^{2} + 113 X Y^{2} Z^{3} + 11 X Y Z^{4} + 110 X^{3} Y Z + 174 X^{2} Y^{2} Z + 29 X^{2} Y Z^{2} + 34 X Y^{3} Z + 199 X Y^{2} Z^{2} + 110 X Y Z^{3} + 89 X^{2} Y Z + 276 X Y^{2} Z + 100 X Y Z^{2} + 136 X Y Z

Algorithm definition

The algorithm ⟨15×25×25:5370⟩ is serendipitous tensor product (⟨3×5×5:58⟩ - 6) ⊗ ⟨5×5×5:93⟩ +3⟨5×5×10:178⟩.

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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