Description of fast matrix multiplication algorithm: ⟨18×24×32:7245⟩

Algorithm type

48 X^{8} Y^{18} Z^{12} + 48 X^{4} Y^{18} Z^{12} + 24 X^{4} Y^{16} Z^{12} + 96 X^{4} Y^{18} Z^{6} + 96 X^{8} Y^{12} Z^{6} + 134 X^{2} Y^{18} Z^{6} + 42 X^{8} Y^{8} Z^{8} + 2 X^{2} Y^{16} Z^{6} + 3 X^{18} Y^{2} Z^{2} + 104 X^{4} Y^{12} Z^{6} + 8 X^{2} Y^{14} Z^{6} + 6 X^{2} Y^{2} Z^{18} + 27 X^{12} Y^{4} Z^{4} + 12 X^{4} Y^{12} Z^{4} + 40 X^{4} Y^{10} Z^{6} + 12 X^{4} Y^{8} Z^{8} + 33 X^{4} Y^{4} Z^{12} + 288 X^{4} Y^{9} Z^{6} + 6 X^{2} Y^{4} Z^{12} + 288 X^{2} Y^{9} Z^{6} + 45 X^{4} Y^{8} Z^{4} + 24 X^{4} Y^{4} Z^{8} + 6 X^{2} Y^{12} Z^{2} + 144 X^{2} Y^{8} Z^{6} + 12 X^{2} Y^{2} Z^{12} + 6 X^{6} Y^{6} Z^{2} + 6 X^{6} Y^{4} Z^{4} + 9 X^{6} Y^{2} Z^{6} + 576 X^{2} Y^{9} Z^{3} + 6 X^{2} Y^{8} Z^{4} + 6 X^{2} Y^{6} Z^{6} + 576 X^{4} Y^{6} Z^{3} + 804 X Y^{9} Z^{3} + 15 X^{6} Y^{4} Z^{2} + 12 X^{6} Y^{2} Z^{4} + 294 X^{4} Y^{4} Z^{4} + 12 X^{2} Y^{8} Z^{2} + 18 X^{2} Y^{4} Z^{6} + 12 X Y^{8} Z^{3} + 18 X^{9} Y Z + 624 X^{2} Y^{6} Z^{3} + 48 X Y^{7} Z^{3} + 36 X Y Z^{9} + 183 X^{6} Y^{2} Z^{2} + 72 X^{2} Y^{6} Z^{2} + 240 X^{2} Y^{5} Z^{3} + 84 X^{2} Y^{4} Z^{4} + 219 X^{2} Y^{2} Z^{6} + 36 X Y^{2} Z^{6} + 291 X^{2} Y^{4} Z^{2} + 144 X^{2} Y^{2} Z^{4} + 36 X Y^{6} Z + 72 X Y Z^{6} + 36 X^{3} Y^{3} Z + 36 X^{3} Y^{2} Z^{2} + 54 X^{3} Y Z^{3} + 36 X Y^{4} Z^{2} + 36 X Y^{3} Z^{3} + 90 X^{3} Y^{2} Z + 72 X^{3} Y Z^{2} + 252 X^{2} Y^{2} Z^{2} + 72 X Y^{4} Z + 108 X Y^{2} Z^{3} + 126 X^{3} Y Z + 72 X Y^{2} Z^{2} + 126 X Y Z^{3} + 126 X Y^{2} Z

Algorithm definition

The algorithm ⟨18×24×32:7245⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×12×16:1035⟩.

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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