Description of fast matrix multiplication algorithm: ⟨18×32×32:9660⟩

Algorithm type

16 X^{8} Y^{12} Z^{8} + 33 X^{8} Y^{10} Z^{8} + 65 X^{8} Y^{8} Z^{8} + 9 X^{18} Y^{2} Z^{2} + 9 X^{2} Y^{2} Z^{18} + 48 X^{12} Y^{4} Z^{4} + 12 X^{8} Y^{8} Z^{4} + 92 X^{4} Y^{12} Z^{4} + 71 X^{4} Y^{8} Z^{8} + 48 X^{4} Y^{4} Z^{12} + 6 X^{12} Y^{4} Z^{2} + 38 X^{8} Y^{6} Z^{4} + 46 X^{4} Y^{10} Z^{4} + 36 X^{4} Y^{6} Z^{8} + 6 X^{2} Y^{4} Z^{12} + 3 X^{12} Y^{2} Z^{2} + 22 X^{8} Y^{4} Z^{4} + 129 X^{4} Y^{8} Z^{4} + 19 X^{4} Y^{4} Z^{8} + 72 X^{2} Y^{12} Z^{2} + 3 X^{2} Y^{2} Z^{12} + 6 X^{6} Y^{6} Z^{2} + 6 X^{6} Y^{4} Z^{4} + 18 X^{6} Y^{2} Z^{6} + 6 X^{4} Y^{8} Z^{2} + 99 X^{4} Y^{6} Z^{4} + 6 X^{4} Y^{4} Z^{6} + 14 X^{2} Y^{10} Z^{2} + 70 X^{2} Y^{8} Z^{4} + 6 X^{2} Y^{6} Z^{6} + 198 X^{4} Y^{5} Z^{4} + 42 X^{6} Y^{4} Z^{2} + 3 X^{6} Y^{2} Z^{4} + 90 X^{4} Y^{6} Z^{2} + 492 X^{4} Y^{4} Z^{4} + 3 X^{4} Y^{2} Z^{6} + 55 X^{2} Y^{8} Z^{2} + 36 X^{2} Y^{6} Z^{4} + 42 X^{2} Y^{4} Z^{6} + 54 X^{9} Y Z + 54 X Y Z^{9} + 297 X^{6} Y^{2} Z^{2} + 81 X^{4} Y^{4} Z^{2} + 24 X^{4} Y^{2} Z^{4} + 558 X^{2} Y^{6} Z^{2} + 437 X^{2} Y^{4} Z^{4} + 297 X^{2} Y^{2} Z^{6} + 36 X^{6} Y^{2} Z + 228 X^{4} Y^{3} Z^{2} + 276 X^{2} Y^{5} Z^{2} + 216 X^{2} Y^{3} Z^{4} + 36 X Y^{2} Z^{6} + 18 X^{6} Y Z + 144 X^{4} Y^{2} Z^{2} + 783 X^{2} Y^{4} Z^{2} + 114 X^{2} Y^{2} Z^{4} + 432 X Y^{6} Z + 18 X Y Z^{6} + 36 X^{3} Y^{3} Z + 36 X^{3} Y^{2} Z^{2} + 108 X^{3} Y Z^{3} + 36 X^{2} Y^{4} Z + 18 X^{2} Y^{3} Z^{2} + 36 X^{2} Y^{2} Z^{3} + 84 X Y^{5} Z + 420 X Y^{4} Z^{2} + 36 X Y^{3} Z^{3} + 252 X^{3} Y^{2} Z + 18 X^{3} Y Z^{2} + 540 X^{2} Y^{3} Z + 612 X^{2} Y^{2} Z^{2} + 18 X^{2} Y Z^{3} + 330 X Y^{4} Z + 216 X Y^{3} Z^{2} + 252 X Y^{2} Z^{3} + 54 X^{3} Y Z + 54 X^{2} Y^{2} Z + 144 X^{2} Y Z^{2} + 36 X Y^{3} Z + 66 X Y^{2} Z^{2} + 54 X Y Z^{3} + 72 X^{2} Y Z + 54 X Y^{2} Z

Algorithm definition

The algorithm ⟨18×32×32:9660⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×16×16:1380⟩.

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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