Description of fast matrix multiplication algorithm: ⟨12×32×32:6804⟩

Algorithm type

6 X^{8} Y^{16} Z^{8} + 24 X^{8} Y^{12} Z^{8} + X^{4} Y^{16} Z^{8} + 9 X^{12} Y^{8} Z^{4} + 4 X^{8} Y^{12} Z^{4} + 34 X^{8} Y^{8} Z^{8} + 24 X^{4} Y^{16} Z^{4} + 3 X^{4} Y^{8} Z^{12} + 6 X^{4} Y^{14} Z^{4} + 4 X^{2} Y^{18} Z^{2} + 4 X^{2} Y^{16} Z^{4} + 13 X^{12} Y^{4} Z^{4} + 8 X^{8} Y^{8} Z^{4} + 54 X^{4} Y^{12} Z^{4} + 17 X^{4} Y^{8} Z^{8} + 15 X^{4} Y^{4} Z^{12} + 13 X^{2} Y^{16} Z^{2} + 6 X^{4} Y^{12} Z^{2} + 15 X^{4} Y^{10} Z^{4} + 12 X^{2} Y^{14} Z^{2} + 7 X^{2} Y^{12} Z^{4} + 6 X^{8} Y^{4} Z^{4} + 14 X^{6} Y^{8} Z^{2} + 3 X^{4} Y^{10} Z^{2} + 138 X^{4} Y^{8} Z^{4} + 5 X^{4} Y^{4} Z^{8} + 28 X^{2} Y^{12} Z^{2} + X^{2} Y^{10} Z^{4} + 12 X^{2} Y^{8} Z^{6} + 15 X^{6} Y^{6} Z^{2} + 11 X^{4} Y^{8} Z^{2} + 144 X^{4} Y^{6} Z^{4} + 18 X^{2} Y^{10} Z^{2} + 22 X^{2} Y^{8} Z^{4} + 12 X^{2} Y^{6} Z^{6} + 54 X^{6} Y^{4} Z^{2} + 30 X^{4} Y^{6} Z^{2} + 294 X^{4} Y^{4} Z^{4} + 220 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{6} Z^{4} + 18 X^{2} Y^{4} Z^{6} + 36 X^{2} Y^{7} Z^{2} + 24 X Y^{9} Z + 24 X Y^{8} Z^{2} + 111 X^{6} Y^{2} Z^{2} + 65 X^{4} Y^{4} Z^{2} + 353 X^{2} Y^{6} Z^{2} + 128 X^{2} Y^{4} Z^{4} + 120 X^{2} Y^{2} Z^{6} + 78 X Y^{8} Z + 36 X^{2} Y^{6} Z + 90 X^{2} Y^{5} Z^{2} + 72 X Y^{7} Z + 42 X Y^{6} Z^{2} + 47 X^{4} Y^{2} Z^{2} + 84 X^{3} Y^{4} Z + 18 X^{2} Y^{5} Z + 690 X^{2} Y^{4} Z^{2} + 40 X^{2} Y^{2} Z^{4} + 168 X Y^{6} Z + 6 X Y^{5} Z^{2} + 72 X Y^{4} Z^{3} + 90 X^{3} Y^{3} Z + 66 X^{2} Y^{4} Z + 108 X Y^{5} Z + 96 X Y^{4} Z^{2} + 72 X Y^{3} Z^{3} + 36 X^{2} Y^{3} Z + 580 X^{2} Y^{2} Z^{2} + 456 X Y^{4} Z + 24 X Y^{3} Z^{2} + 198 X^{3} Y Z + 102 X^{2} Y^{2} Z + 174 X Y^{3} Z + 156 X Y^{2} Z^{2} + 180 X Y Z^{3} + 66 X^{2} Y Z + 468 X Y^{2} Z + 60 X Y Z^{2} + 240 X Y Z

Algorithm definition

The algorithm ⟨12×32×32:6804⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×16×16:972⟩.

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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