Description of fast matrix multiplication algorithm: ⟨16×20×22:4116⟩

Algorithm type

22 X^{8} Y^{8} Z^{8} + 8 X^{8} Y^{8} Z^{6} + X^{12} Y^{4} Z^{4} + 2 X^{8} Y^{4} Z^{8} + X^{4} Y^{12} Z^{4} + X^{4} Y^{8} Z^{8} + 2 X^{8} Y^{8} Z^{2} + 5 X^{8} Y^{4} Z^{4} + 15 X^{4} Y^{8} Z^{4} + 10 X^{4} Y^{4} Z^{8} + 2 X^{8} Y^{4} Z^{2} + X^{4} Y^{8} Z^{2} + 3 X^{4} Y^{6} Z^{4} + 4 X^{4} Y^{4} Z^{6} + 12 X^{8} Y^{2} Z^{2} + 306 X^{4} Y^{4} Z^{4} + 12 X^{2} Y^{2} Z^{8} + 48 X^{4} Y^{4} Z^{3} + 9 X^{6} Y^{2} Z^{2} + 7 X^{4} Y^{4} Z^{2} + 18 X^{4} Y^{2} Z^{4} + 48 X^{2} Y^{6} Z^{2} + 33 X^{2} Y^{4} Z^{4} + 12 X^{4} Y^{4} Z + 51 X^{4} Y^{2} Z^{2} + 150 X^{2} Y^{4} Z^{2} + 114 X^{2} Y^{2} Z^{4} + 12 X^{4} Y^{2} Z + 6 X^{2} Y^{4} Z + 18 X^{2} Y^{3} Z^{2} + 24 X^{2} Y^{2} Z^{3} + 72 X^{4} Y Z + 1137 X^{2} Y^{2} Z^{2} + 72 X Y Z^{4} + 18 X^{3} Y Z + 42 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 252 X Y^{3} Z + 162 X Y^{2} Z^{2} + 126 X^{2} Y Z + 360 X Y^{2} Z + 324 X Y Z^{2} + 558 X Y Z

Algorithm definition

The algorithm ⟨16×20×22:4116⟩ is the (Kronecker) tensor product of ⟨8×10×11:588⟩ with ⟨2×2×2:7⟩.

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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