Description of fast matrix multiplication algorithm: ⟨10×16×22:2184⟩

Algorithm type

4 X^{8} Y^{8} Z^{8} + X^{8} Y^{8} Z^{6} + X^{8} Y^{6} Z^{6} + 8 X^{6} Y^{8} Z^{6} + 4 X^{6} Y^{6} Z^{6} + 19 X^{4} Y^{8} Z^{4} + 5 X^{4} Y^{4} Z^{8} + 5 X^{4} Y^{8} Z^{2} + 10 X^{4} Y^{6} Z^{4} + 6 X^{4} Y^{4} Z^{6} + 2 X^{4} Y^{6} Z^{2} + 76 X^{4} Y^{4} Z^{4} + X^{4} Y^{2} Z^{6} + 16 X^{2} Y^{8} Z^{2} + 5 X^{2} Y^{4} Z^{6} + 6 X^{4} Y^{4} Z^{3} + 6 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{3} Z^{3} + 48 X^{3} Y^{4} Z^{3} + 20 X^{2} Y^{6} Z^{2} + 4 X^{2} Y^{4} Z^{4} + 9 X^{2} Y^{2} Z^{6} + 24 X^{3} Y^{3} Z^{3} + 6 X^{4} Y^{2} Z^{2} + 160 X^{2} Y^{4} Z^{2} + 60 X^{2} Y^{2} Z^{4} + 30 X^{2} Y^{4} Z + 60 X^{2} Y^{3} Z^{2} + 36 X^{2} Y^{2} Z^{3} + 12 X^{2} Y^{3} Z + 362 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 96 X Y^{4} Z + 30 X Y^{2} Z^{3} + 36 X^{3} Y Z + 12 X^{2} Y^{2} Z + 120 X Y^{3} Z + 24 X Y^{2} Z^{2} + 54 X Y Z^{3} + 36 X^{2} Y Z + 276 X Y^{2} Z + 180 X Y Z^{2} + 300 X Y Z

Algorithm definition

The algorithm ⟨10×16×22:2184⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨5×8×11:312⟩.

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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