Description of fast matrix multiplication algorithm: ⟨18×20×32:6412⟩

Algorithm type

64 X^{8} Y^{12} Z^{12} + 44 X^{6} Y^{12} Z^{12} + 48 X^{4} Y^{12} Z^{12} + 4 X^{2} Y^{12} Z^{12} + 6 X^{8} Y^{8} Z^{8} + 2 X^{10} Y^{8} Z^{4} + 32 X^{10} Y^{6} Z^{6} + 6 X^{6} Y^{8} Z^{8} + 4 X^{10} Y^{6} Z^{4} + 6 X^{10} Y^{4} Z^{6} + X^{8} Y^{8} Z^{4} + 64 X^{8} Y^{6} Z^{6} + 15 X^{10} Y^{4} Z^{4} + 3 X^{8} Y^{6} Z^{4} + 6 X^{8} Y^{4} Z^{6} + X^{6} Y^{8} Z^{4} + 176 X^{6} Y^{6} Z^{6} + 27 X^{8} Y^{4} Z^{4} + X^{6} Y^{8} Z^{2} + 2 X^{6} Y^{6} Z^{4} + 477 X^{4} Y^{6} Z^{6} + 264 X^{3} Y^{6} Z^{6} + 10 X^{10} Y^{2} Z^{2} + X^{6} Y^{6} Z^{2} + 26 X^{6} Y^{4} Z^{4} + 21 X^{6} Y^{2} Z^{6} + 2 X^{4} Y^{8} Z^{2} + 3 X^{4} Y^{6} Z^{4} + 2 X^{4} Y^{4} Z^{6} + 325 X^{2} Y^{6} Z^{6} + 24 X Y^{6} Z^{6} + 16 X^{8} Y^{2} Z^{2} + X^{6} Y^{4} Z^{2} + 4 X^{6} Y^{2} Z^{4} + 3 X^{4} Y^{6} Z^{2} + 64 X^{4} Y^{4} Z^{4} + 3 X^{4} Y^{2} Z^{6} + X^{2} Y^{8} Z^{2} + 2 X^{2} Y^{4} Z^{6} + 12 X^{5} Y^{4} Z^{2} + 192 X^{5} Y^{3} Z^{3} + 36 X^{3} Y^{4} Z^{4} + 41 X^{6} Y^{2} Z^{2} + 24 X^{5} Y^{3} Z^{2} + 36 X^{5} Y^{2} Z^{3} + 10 X^{4} Y^{4} Z^{2} + 384 X^{4} Y^{3} Z^{3} + 8 X^{4} Y^{2} Z^{4} + 6 X^{2} Y^{4} Z^{4} + 6 X^{2} Y^{2} Z^{6} + 90 X^{5} Y^{2} Z^{2} + 18 X^{4} Y^{3} Z^{2} + 36 X^{4} Y^{2} Z^{3} + 6 X^{3} Y^{4} Z^{2} + 1056 X^{3} Y^{3} Z^{3} + 222 X^{4} Y^{2} Z^{2} + 6 X^{3} Y^{4} Z + 12 X^{3} Y^{3} Z^{2} + X^{2} Y^{4} Z^{2} + 558 X^{2} Y^{3} Z^{3} + 2 X^{2} Y^{2} Z^{4} + 60 X^{5} Y Z + 6 X^{3} Y^{3} Z + 156 X^{3} Y^{2} Z^{2} + 126 X^{3} Y Z^{3} + 12 X^{2} Y^{4} Z + 18 X^{2} Y^{3} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 222 X Y^{3} Z^{3} + 96 X^{4} Y Z + 6 X^{3} Y^{2} Z + 24 X^{3} Y Z^{2} + 18 X^{2} Y^{3} Z + 191 X^{2} Y^{2} Z^{2} + 18 X^{2} Y Z^{3} + 6 X Y^{4} Z + 12 X Y^{2} Z^{3} + 246 X^{3} Y Z + 24 X^{2} Y^{2} Z + 48 X^{2} Y Z^{2} + 36 X Y^{2} Z^{2} + 36 X Y Z^{3} + 360 X^{2} Y Z + 6 X Y^{2} Z + 12 X Y Z^{2} + 138 X Y Z

Algorithm definition

The algorithm ⟨18×20×32:6412⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨9×10×16:916⟩.

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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