Description of fast matrix multiplication algorithm: ⟨21×25×25:7366⟩

Algorithm type

2 X^{2} Y^{12} Z^{2} + X^{6} Y^{6} Z^{2} + 17 X^{4} Y^{6} Z^{4} + X^{2} Y^{6} Z^{6} + 6 X Y^{12} Z + X^{2} Y^{9} Z^{2} + 47 X^{6} Y^{4} Z^{2} + 2 X^{4} Y^{6} Z^{2} + 799 X^{4} Y^{4} Z^{4} + 94 X^{2} Y^{8} Z^{2} + 2 X^{2} Y^{6} Z^{4} + 47 X^{2} Y^{4} Z^{6} + X Y^{2} Z^{9} + 5 X^{6} Y^{3} Z^{2} + 5 X^{2} Y^{3} Z^{6} + 3 X Y^{9} Z + 2 X Y^{8} Z^{2} + X Y^{4} Z^{6} + 5 X Y Z^{9} + 235 X^{6} Y^{2} Z^{2} + 94 X^{4} Y^{4} Z^{2} + 3 X^{3} Y^{6} Z + 111 X^{2} Y^{6} Z^{2} + 111 X^{2} Y^{4} Z^{4} + 252 X^{2} Y^{2} Z^{6} + 18 X Y^{8} Z + 3 X Y^{6} Z^{3} + 20 X^{6} Y^{2} Z + X^{4} Y^{3} Z^{2} + X^{3} Y^{4} Z^{2} + 6 X^{2} Y^{6} Z + X^{2} Y^{3} Z^{4} + 7 X Y^{6} Z^{2} + 2 X Y^{4} Z^{4} + 26 X Y^{2} Z^{6} + 100 X^{6} Y Z + 387 X^{4} Y^{2} Z^{2} + 9 X^{3} Y^{4} Z + X^{3} Y^{2} Z^{3} + 766 X^{2} Y^{4} Z^{2} + 370 X^{2} Y^{2} Z^{4} + 48 X Y^{6} Z + 11 X Y^{4} Z^{3} + 96 X Y Z^{6} + 40 X^{4} Y^{2} Z + 15 X^{3} Y^{3} Z + 24 X^{3} Y^{2} Z^{2} + 5 X^{3} Y Z^{3} + 58 X^{2} Y^{4} Z + 7 X^{2} Y^{3} Z^{2} + 22 X^{2} Y^{2} Z^{3} + 69 X Y^{4} Z^{2} + 16 X Y^{3} Z^{3} + 39 X Y^{2} Z^{4} + 20 X^{4} Y Z + 71 X^{3} Y^{2} Z + 95 X^{3} Y Z^{2} + 23 X^{2} Y^{3} Z + 850 X^{2} Y^{2} Z^{2} + 101 X^{2} Y Z^{3} + 169 X Y^{4} Z + 22 X Y^{3} Z^{2} + 84 X Y^{2} Z^{3} + 19 X Y Z^{4} + 130 X^{3} Y Z + 321 X^{2} Y^{2} Z + 39 X^{2} Y Z^{2} + 47 X Y^{3} Z + 315 X Y^{2} Z^{2} + 137 X Y Z^{3} + 166 X^{2} Y Z + 401 X Y^{2} Z + 159 X Y Z^{2} + 182 X Y Z

Algorithm definition

The algorithm ⟨21×25×25:7366⟩ is the (Kronecker) tensor product of ⟨3×5×5:58⟩ with ⟨7×5×5:127⟩.

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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