Description of fast matrix multiplication algorithm: ⟨12×14×16:1673⟩

Algorithm type

5 X^{8} Y^{8} Z^{8} + X^{12} Y^{4} Z^{4} + 2 X^{8} Y^{8} Z^{4} + 5 X^{6} Y^{6} Z^{8} + X^{4} Y^{12} Z^{4} + 2 X^{4} Y^{4} Z^{12} + 2 X^{10} Y^{4} Z^{4} + X^{4} Y^{10} Z^{4} + X^{4} Y^{2} Z^{12} + 4 X^{4} Y^{8} Z^{4} + X^{4} Y^{4} Z^{8} + 2 X^{2} Y^{6} Z^{8} + X^{6} Y^{4} Z^{4} + 5 X^{4} Y^{6} Z^{4} + 82 X^{4} Y^{4} Z^{4} + 2 X^{2} Y^{6} Z^{4} + 18 X^{6} Y^{2} Z^{2} + 18 X^{4} Y^{4} Z^{2} + 2 X^{4} Y^{2} Z^{4} + 30 X^{3} Y^{3} Z^{4} + 18 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{4} Z^{4} + 27 X^{2} Y^{2} Z^{6} + 12 X^{5} Y^{2} Z^{2} + 6 X^{2} Y^{5} Z^{2} + 6 X^{2} Y Z^{6} + 3 X^{4} Y^{2} Z^{2} + 69 X^{2} Y^{4} Z^{2} + 21 X^{2} Y^{2} Z^{4} + 12 X Y^{3} Z^{4} + 6 X^{3} Y^{2} Z^{2} + 30 X^{2} Y^{3} Z^{2} + 342 X^{2} Y^{2} Z^{2} + 12 X Y^{3} Z^{2} + 72 X^{3} Y Z + 36 X^{2} Y^{2} Z + 12 X^{2} Y Z^{2} + 72 X Y^{3} Z + 72 X Y^{2} Z^{2} + 90 X Y Z^{3} + 18 X^{2} Y Z + 270 X Y^{2} Z + 90 X Y Z^{2} + 180 X Y Z

Algorithm definition

The algorithm ⟨12×14×16:1673⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×7×8:239⟩.

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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