Description of fast matrix multiplication algorithm: ⟨10×16×16:1610⟩

Algorithm type

3 X^{8} Y^{8} Z^{8} + X^{8} Y^{8} Z^{4} + 7 X^{6} Y^{8} Z^{6} + X^{4} Y^{12} Z^{4} + X^{4} Y^{8} Z^{8} + 2 X^{10} Y^{4} Z^{4} + 2 X^{4} Y^{4} Z^{10} + X^{2} Y^{12} Z^{4} + X^{10} Y^{4} Z^{2} + X^{6} Y^{8} Z^{2} + 9 X^{4} Y^{8} Z^{4} + X^{2} Y^{8} Z^{6} + X^{2} Y^{4} Z^{10} + X^{4} Y^{8} Z^{2} + X^{4} Y^{4} Z^{6} + X^{6} Y^{4} Z^{2} + 68 X^{4} Y^{4} Z^{4} + X^{2} Y^{8} Z^{2} + 9 X^{6} Y^{2} Z^{2} + 13 X^{4} Y^{4} Z^{2} + 42 X^{3} Y^{4} Z^{3} + 18 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{4} Z^{4} + 9 X^{2} Y^{2} Z^{6} + 12 X^{5} Y^{2} Z^{2} + 12 X^{2} Y^{2} Z^{5} + 6 X Y^{6} Z^{2} + 6 X^{5} Y^{2} Z + 3 X^{4} Y^{2} Z^{2} + 6 X^{3} Y^{4} Z + 111 X^{2} Y^{4} Z^{2} + 3 X^{2} Y^{2} Z^{4} + 6 X Y^{4} Z^{3} + 6 X Y^{2} Z^{5} + 6 X^{2} Y^{4} Z + 6 X^{2} Y^{2} Z^{3} + 6 X^{3} Y^{2} Z + 339 X^{2} Y^{2} Z^{2} + 6 X Y^{4} Z + 54 X^{3} Y Z + 42 X^{2} Y^{2} Z + 72 X Y^{3} Z + 36 X Y^{2} Z^{2} + 54 X Y Z^{3} + 18 X^{2} Y Z + 342 X Y^{2} Z + 18 X Y Z^{2} + 234 X Y Z

Algorithm definition

The algorithm ⟨10×16×16:1610⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨5×8×8:230⟩.

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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