Description of fast matrix multiplication algorithm: ⟨16×22×30:5936⟩

Algorithm type

12 X^{12} Y^{16} Z^{8} + 12 X^{10} Y^{16} Z^{8} + 22 X^{6} Y^{16} Z^{4} + 33 X^{12} Y^{8} Z^{4} + 51 X^{8} Y^{8} Z^{8} + 2 X^{4} Y^{16} Z^{4} + 15 X^{10} Y^{8} Z^{4} + 24 X^{6} Y^{8} Z^{8} + 2 X^{2} Y^{18} Z^{2} + 3 X^{6} Y^{6} Z^{8} + 18 X^{4} Y^{12} Z^{4} + 12 X^{4} Y^{4} Z^{12} + X^{2} Y^{16} Z^{2} + 72 X^{6} Y^{8} Z^{4} + 4 X^{4} Y^{10} Z^{4} + 72 X^{5} Y^{8} Z^{4} + 12 X^{8} Y^{4} Z^{4} + 42 X^{6} Y^{8} Z^{2} + 68 X^{4} Y^{8} Z^{4} + 2 X^{4} Y^{4} Z^{8} + 11 X^{2} Y^{12} Z^{2} + 2 X^{2} Y^{2} Z^{12} + 41 X^{6} Y^{4} Z^{4} + 6 X^{4} Y^{8} Z^{2} + 2 X^{4} Y^{6} Z^{4} + 2 X^{2} Y^{10} Z^{2} + 9 X^{2} Y^{8} Z^{4} + 3 X^{2} Y^{6} Z^{6} + 132 X^{3} Y^{8} Z^{2} + 198 X^{6} Y^{4} Z^{2} + 3 X^{4} Y^{6} Z^{2} + 390 X^{4} Y^{4} Z^{4} + 12 X^{2} Y^{8} Z^{2} + X^{2} Y^{6} Z^{4} + 13 X^{2} Y^{4} Z^{6} + 90 X^{5} Y^{4} Z^{2} + 144 X^{3} Y^{4} Z^{4} + 12 X Y^{9} Z + 88 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{4} Z^{2} + 85 X^{4} Y^{2} Z^{4} + 18 X^{3} Y^{3} Z^{4} + 149 X^{2} Y^{6} Z^{2} + 3 X^{2} Y^{4} Z^{4} + 110 X^{2} Y^{2} Z^{6} + 6 X Y^{8} Z + 24 X^{2} Y^{5} Z^{2} + 121 X^{4} Y^{2} Z^{2} + 252 X^{3} Y^{4} Z + 413 X^{2} Y^{4} Z^{2} + 25 X^{2} Y^{2} Z^{4} + 66 X Y^{6} Z + 12 X Y Z^{6} + 246 X^{3} Y^{2} Z^{2} + 36 X^{2} Y^{4} Z + 12 X^{2} Y^{3} Z^{2} + 12 X Y^{5} Z + 54 X Y^{4} Z^{2} + 18 X Y^{3} Z^{3} + 18 X^{2} Y^{3} Z + 506 X^{2} Y^{2} Z^{2} + 6 X Y^{3} Z^{2} + 78 X Y^{2} Z^{3} + 528 X^{3} Y Z + 72 X^{2} Y^{2} Z + 510 X^{2} Y Z^{2} + 246 X Y^{3} Z + 18 X Y^{2} Z^{2} + 228 X Y Z^{3} + 294 X^{2} Y Z + 30 X Y^{2} Z + 78 X Y Z^{2} + 12 X Y Z

Algorithm definition

The algorithm ⟨16×22×30:5936⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×11×15:848⟩.

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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