Description of fast matrix multiplication algorithm: ⟨14×22×26:4725⟩

Algorithm type

16 X^{8} Y^{8} Z^{8} + 7 X^{8} Y^{6} Z^{8} + 4 X^{6} Y^{8} Z^{8} + 4 X^{8} Y^{6} Z^{6} + 7 X^{6} Y^{8} Z^{6} + 4 X^{6} Y^{6} Z^{8} + X^{4} Y^{12} Z^{4} + X^{4} Y^{8} Z^{8} + X^{12} Y^{2} Z^{4} + 6 X^{6} Y^{6} Z^{6} + X^{4} Y^{6} Z^{8} + 4 X^{8} Y^{4} Z^{4} + 2 X^{8} Y^{2} Z^{6} + 16 X^{6} Y^{6} Z^{4} + 17 X^{4} Y^{8} Z^{4} + 33 X^{4} Y^{6} Z^{6} + 8 X^{4} Y^{4} Z^{8} + X^{8} Y^{4} Z^{2} + 2 X^{8} Y^{2} Z^{4} + 24 X^{6} Y^{6} Z^{2} + X^{6} Y^{4} Z^{4} + 11 X^{4} Y^{6} Z^{4} + 2 X^{4} Y^{4} Z^{6} + X^{4} Y^{2} Z^{8} + 3 X^{2} Y^{8} Z^{4} + 48 X^{2} Y^{6} Z^{6} + X^{6} Y^{4} Z^{2} + X^{6} Y^{2} Z^{4} + 239 X^{4} Y^{4} Z^{4} + X^{4} Y^{2} Z^{6} + 2 X^{2} Y^{8} Z^{2} + 3 X^{2} Y^{6} Z^{4} + 42 X^{4} Y^{3} Z^{4} + 24 X^{3} Y^{4} Z^{4} + 3 X^{6} Y^{2} Z^{2} + 5 X^{4} Y^{4} Z^{2} + 24 X^{4} Y^{3} Z^{3} + 5 X^{4} Y^{2} Z^{4} + 42 X^{3} Y^{4} Z^{3} + 24 X^{3} Y^{3} Z^{4} + 11 X^{2} Y^{6} Z^{2} + 18 X^{2} Y^{4} Z^{4} + 7 X^{2} Y^{2} Z^{6} + 6 X^{6} Y Z^{2} + 36 X^{3} Y^{3} Z^{3} + 6 X^{2} Y^{3} Z^{4} + 59 X^{4} Y^{2} Z^{2} + 12 X^{4} Y Z^{3} + 96 X^{3} Y^{3} Z^{2} + 208 X^{2} Y^{4} Z^{2} + 198 X^{2} Y^{3} Z^{3} + 91 X^{2} Y^{2} Z^{4} + 6 X^{4} Y^{2} Z + 12 X^{4} Y Z^{2} + 144 X^{3} Y^{3} Z + 6 X^{3} Y^{2} Z^{2} + 66 X^{2} Y^{3} Z^{2} + 12 X^{2} Y^{2} Z^{3} + 6 X^{2} Y Z^{4} + 18 X Y^{4} Z^{2} + 288 X Y^{3} Z^{3} + 6 X^{3} Y^{2} Z + 6 X^{3} Y Z^{2} + 936 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 12 X Y^{4} Z + 18 X Y^{3} Z^{2} + 18 X^{3} Y Z + 30 X^{2} Y^{2} Z + 30 X^{2} Y Z^{2} + 30 X Y^{3} Z + 72 X Y^{2} Z^{2} + 42 X Y Z^{3} + 210 X^{2} Y Z + 636 X Y^{2} Z + 258 X Y Z^{2} + 468 X Y Z

Algorithm definition

The algorithm ⟨14×22×26:4725⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨7×11×13:675⟩.

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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