Description of fast matrix multiplication algorithm: ⟨16×24×26:5467⟩

Algorithm type

12 X^{8} Y^{12} Z^{8} + 22 X^{8} Y^{10} Z^{8} + 26 X^{8} Y^{8} Z^{8} + 2 X^{8} Y^{6} Z^{8} + 3 X^{6} Y^{12} Z^{4} + 2 X^{8} Y^{4} Z^{8} + X^{6} Y^{12} Z^{2} + 33 X^{4} Y^{12} Z^{4} + X^{2} Y^{10} Z^{8} + 3 X^{6} Y^{8} Z^{4} + 49 X^{4} Y^{10} Z^{4} + 2 X^{2} Y^{14} Z^{2} + X^{2} Y^{12} Z^{4} + X^{2} Y^{10} Z^{6} + X^{6} Y^{8} Z^{2} + 67 X^{4} Y^{8} Z^{4} + 2 X^{4} Y^{6} Z^{6} + 2 X^{2} Y^{10} Z^{4} + 6 X^{6} Y^{6} Z^{2} + 176 X^{4} Y^{6} Z^{4} + X^{2} Y^{10} Z^{2} + 132 X^{4} Y^{5} Z^{4} + 7 X^{4} Y^{6} Z^{2} + 207 X^{4} Y^{4} Z^{4} + X^{4} Y^{2} Z^{6} + X^{2} Y^{8} Z^{2} + X^{2} Y^{6} Z^{4} + 12 X^{4} Y^{3} Z^{4} + 18 X^{3} Y^{6} Z^{2} + 2 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 25 X^{4} Y^{2} Z^{4} + 6 X^{3} Y^{6} Z + 393 X^{2} Y^{6} Z^{2} + 6 X Y^{5} Z^{4} + 18 X^{3} Y^{4} Z^{2} + 294 X^{2} Y^{5} Z^{2} + 12 X Y^{7} Z + 6 X Y^{6} Z^{2} + 6 X Y^{5} Z^{3} + X^{4} Y^{2} Z^{2} + 6 X^{3} Y^{4} Z + 516 X^{2} Y^{4} Z^{2} + 12 X^{2} Y^{3} Z^{3} + 12 X Y^{5} Z^{2} + 36 X^{3} Y^{3} Z + 624 X^{2} Y^{3} Z^{2} + 6 X Y^{5} Z + 42 X^{2} Y^{3} Z + 358 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 6 X Y^{4} Z + 6 X Y^{3} Z^{2} + 12 X^{3} Y Z + 12 X^{2} Y^{2} Z + 78 X^{2} Y Z^{2} + 1170 X Y^{3} Z + 6 X^{2} Y Z + 684 X Y^{2} Z + 312 X Y Z

Algorithm definition

The algorithm ⟨16×24×26:5467⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×12×13:781⟩.

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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