Description of fast matrix multiplication algorithm: ⟨16×18×32:5145⟩

Algorithm type

3 X^{8} Y^{8} Z^{12} + 7 X^{8} Y^{8} Z^{10} + 35 X^{8} Y^{8} Z^{8} + 2 X^{4} Y^{8} Z^{12} + 3 X^{4} Y^{12} Z^{6} + 2 X^{4} Y^{8} Z^{10} + 12 X^{2} Y^{18} Z^{2} + 13 X^{12} Y^{4} Z^{4} + 39 X^{4} Y^{12} Z^{4} + 14 X^{4} Y^{8} Z^{8} + 16 X^{4} Y^{4} Z^{12} + X^{8} Y^{4} Z^{6} + 28 X^{4} Y^{8} Z^{6} + 16 X^{4} Y^{4} Z^{10} + 6 X^{2} Y^{12} Z^{4} + 4 X^{2} Y^{8} Z^{8} + 7 X^{2} Y^{4} Z^{12} + 2 X^{8} Y^{4} Z^{4} + 46 X^{4} Y^{8} Z^{4} + 29 X^{4} Y^{4} Z^{8} + 19 X^{2} Y^{12} Z^{2} + 8 X^{2} Y^{8} Z^{6} + 5 X^{2} Y^{4} Z^{10} + 12 X^{2} Y^{2} Z^{12} + 12 X^{6} Y^{6} Z^{2} + 3 X^{6} Y^{4} Z^{4} + 35 X^{4} Y^{4} Z^{6} + 19 X^{2} Y^{8} Z^{4} + 5 X^{2} Y^{6} Z^{6} + 20 X^{2} Y^{4} Z^{8} + 6 X^{2} Y^{2} Z^{10} + 42 X^{4} Y^{4} Z^{5} + 16 X^{6} Y^{4} Z^{2} + X^{6} Y^{2} Z^{4} + 272 X^{4} Y^{4} Z^{4} + 9 X^{4} Y^{2} Z^{6} + 10 X^{2} Y^{8} Z^{2} + 13 X^{2} Y^{6} Z^{4} + 49 X^{2} Y^{4} Z^{6} + 2 X^{2} Y^{2} Z^{8} + 18 X^{2} Y^{6} Z^{3} + 12 X^{2} Y^{4} Z^{5} + 72 X Y^{9} Z + 99 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + X^{4} Y^{2} Z^{4} + 256 X^{2} Y^{6} Z^{2} + 131 X^{2} Y^{4} Z^{4} + 125 X^{2} Y^{2} Z^{6} + 6 X^{4} Y^{2} Z^{3} + 168 X^{2} Y^{4} Z^{3} + 96 X^{2} Y^{2} Z^{5} + 36 X Y^{6} Z^{2} + 24 X Y^{4} Z^{4} + 42 X Y^{2} Z^{6} + 13 X^{4} Y^{2} Z^{2} + 290 X^{2} Y^{4} Z^{2} + 206 X^{2} Y^{2} Z^{4} + 114 X Y^{6} Z + 48 X Y^{4} Z^{3} + 30 X Y^{2} Z^{5} + 72 X Y Z^{6} + 72 X^{3} Y^{3} Z + 18 X^{3} Y^{2} Z^{2} + 102 X^{2} Y^{2} Z^{3} + 114 X Y^{4} Z^{2} + 30 X Y^{3} Z^{3} + 120 X Y^{2} Z^{4} + 36 X Y Z^{5} + 96 X^{3} Y^{2} Z + 6 X^{3} Y Z^{2} + 377 X^{2} Y^{2} Z^{2} + 54 X^{2} Y Z^{3} + 60 X Y^{4} Z + 78 X Y^{3} Z^{2} + 222 X Y^{2} Z^{3} + 12 X Y Z^{4} + 126 X^{3} Y Z + 12 X^{2} Y^{2} Z + 6 X^{2} Y Z^{2} + 132 X Y^{3} Z + 282 X Y^{2} Z^{2} + 174 X Y Z^{3} + 6 X^{2} Y Z + 84 X Y^{2} Z + 192 X Y Z^{2} + 30 X Y Z

Algorithm definition

The algorithm ⟨16×18×32:5145⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×9×16:735⟩.

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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