Description of fast matrix multiplication algorithm: ⟨12×14×24:2352⟩

Algorithm type

13 X^{8} Y^{8} Z^{8} + 4 X^{6} Y^{8} Z^{8} + X^{6} Y^{6} Z^{8} + 16 X^{4} Y^{8} Z^{4} + 48 X^{4} Y^{6} Z^{6} + 16 X^{4} Y^{4} Z^{8} + 2 X^{2} Y^{8} Z^{4} + 72 X^{2} Y^{6} Z^{6} + 2 X^{2} Y^{4} Z^{8} + 132 X^{4} Y^{4} Z^{4} + 24 X^{3} Y^{4} Z^{4} + 6 X^{3} Y^{3} Z^{4} + 150 X^{2} Y^{4} Z^{2} + 288 X^{2} Y^{3} Z^{3} + 150 X^{2} Y^{2} Z^{4} + 12 X Y^{4} Z^{2} + 432 X Y^{3} Z^{3} + 12 X Y^{2} Z^{4} + 324 X^{2} Y^{2} Z^{2} + 324 X Y^{2} Z + 324 X Y Z^{2}

Algorithm definition

The algorithm ⟨12×14×24:2352⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨6×7×12:336⟩.

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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