Description of fast matrix multiplication algorithm: ⟨10×12×32:2380⟩

Algorithm type

16 X^{8} Y^{12} Z^{10} + 24 X^{4} Y^{12} Z^{10} + X^{8} Y^{8} Z^{8} + 2 X^{6} Y^{8} Z^{6} + 2 X^{8} Y^{4} Z^{4} + 48 X^{4} Y^{6} Z^{6} + 96 X^{4} Y^{6} Z^{5} + 2 X^{6} Y^{4} Z^{4} + 72 X^{2} Y^{6} Z^{6} + 144 X^{2} Y^{6} Z^{5} + 2 X^{6} Y^{4} Z^{2} + 43 X^{4} Y^{4} Z^{4} + 12 X^{3} Y^{4} Z^{3} + 24 X^{2} Y^{6} Z^{2} + 2 X^{2} Y^{4} Z^{4} + 30 X^{4} Y^{2} Z^{2} + 288 X^{2} Y^{3} Z^{3} + 12 X^{3} Y^{2} Z^{2} + 432 X Y^{3} Z^{3} + 12 X^{3} Y^{2} Z + 312 X^{2} Y^{2} Z^{2} + 144 X Y^{3} Z + 12 X Y^{2} Z^{2} + 108 X^{2} Y Z + 540 X Y Z

Algorithm definition

The algorithm ⟨10×12×32:2380⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨5×6×16:340⟩.

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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