Description of fast matrix multiplication algorithm: ⟨14×16×20:2695⟩

Algorithm type

2 X^{12} Y^{8} Z^{8} + 2 X^{10} Y^{8} Z^{8} + 2 X^{10} Y^{8} Z^{6} + 4 X^{8} Y^{8} Z^{8} + X^{8} Y^{4} Z^{12} + X^{6} Y^{8} Z^{10} + X^{2} Y^{8} Z^{14} + 2 X^{10} Y^{8} Z^{4} + X^{6} Y^{8} Z^{8} + X^{4} Y^{8} Z^{10} + 2 X^{12} Y^{4} Z^{4} + X^{8} Y^{4} Z^{8} + 4 X^{6} Y^{8} Z^{6} + X^{6} Y^{4} Z^{10} + 2 X^{4} Y^{12} Z^{4} + 3 X^{4} Y^{8} Z^{8} + 4 X^{10} Y^{4} Z^{4} + 2 X^{6} Y^{4} Z^{8} + X^{2} Y^{8} Z^{8} + 2 X^{10} Y^{4} Z^{2} + 4 X^{8} Y^{4} Z^{4} + X^{6} Y^{4} Z^{6} + 2 X^{4} Y^{8} Z^{4} + 36 X^{6} Y^{4} Z^{4} + 3 X^{4} Y^{4} Z^{6} + 3 X^{2} Y^{4} Z^{8} + 12 X^{5} Y^{4} Z^{4} + 6 X^{6} Y^{4} Z^{2} + 12 X^{5} Y^{4} Z^{3} + 97 X^{4} Y^{4} Z^{4} + 12 X^{4} Y^{2} Z^{6} + 6 X^{3} Y^{4} Z^{5} + 3 X^{2} Y^{4} Z^{6} + 6 X Y^{4} Z^{7} + 12 X^{5} Y^{4} Z^{2} + 6 X^{3} Y^{4} Z^{4} + 6 X^{2} Y^{4} Z^{5} + 45 X^{6} Y^{2} Z^{2} + 3 X^{4} Y^{4} Z^{2} + 18 X^{4} Y^{2} Z^{4} + 24 X^{3} Y^{4} Z^{3} + 6 X^{3} Y^{2} Z^{5} + 24 X^{2} Y^{6} Z^{2} + 36 X^{2} Y^{4} Z^{4} + 12 X^{2} Y^{2} Z^{6} + 24 X^{5} Y^{2} Z^{2} + 12 X^{3} Y^{2} Z^{4} + 6 X Y^{4} Z^{4} + 12 X^{5} Y^{2} Z + 63 X^{4} Y^{2} Z^{2} + 6 X^{3} Y^{2} Z^{3} + 44 X^{2} Y^{4} Z^{2} + 18 X^{2} Y^{2} Z^{4} + 144 X^{3} Y^{2} Z^{2} + 18 X^{2} Y^{2} Z^{3} + 18 X Y^{2} Z^{4} + 36 X^{3} Y^{2} Z + 480 X^{2} Y^{2} Z^{2} + 36 X^{2} Y Z^{3} + 18 X Y^{2} Z^{3} + 198 X^{3} Y Z + 18 X^{2} Y^{2} Z + 72 X^{2} Y Z^{2} + 72 X Y^{3} Z + 108 X Y^{2} Z^{2} + 72 X Y Z^{3} + 234 X^{2} Y Z + 192 X Y^{2} Z + 108 X Y Z^{2} + 252 X Y Z

Algorithm definition

The algorithm ⟨14×16×20:2695⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨7×8×10:385⟩.

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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