Description of fast matrix multiplication algorithm: ⟨10×20×20:2464⟩

Algorithm type

5 X^{8} Y^{8} Z^{8} + X^{4} Y^{16} Z^{4} + X^{10} Y^{8} Z^{4} + X^{4} Y^{16} Z^{2} + X^{8} Y^{8} Z^{4} + 12 X^{6} Y^{8} Z^{6} + X^{4} Y^{12} Z^{4} + X^{4} Y^{8} Z^{8} + X^{2} Y^{8} Z^{10} + 3 X^{10} Y^{4} Z^{4} + 4 X^{4} Y^{4} Z^{10} + 2 X^{10} Y^{4} Z^{2} + X^{6} Y^{8} Z^{2} + 10 X^{4} Y^{8} Z^{4} + X^{2} Y^{8} Z^{6} + X^{2} Y^{4} Z^{10} + X^{6} Y^{4} Z^{4} + X^{2} Y^{8} Z^{4} + 3 X^{6} Y^{4} Z^{2} + 116 X^{4} Y^{4} Z^{4} + 14 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{4} Z^{6} + 6 X^{5} Y^{4} Z^{2} + 6 X^{2} Y^{8} Z + 15 X^{6} Y^{2} Z^{2} + 13 X^{4} Y^{4} Z^{2} + 72 X^{3} Y^{4} Z^{3} + 21 X^{2} Y^{6} Z^{2} + 13 X^{2} Y^{4} Z^{4} + 15 X^{2} Y^{2} Z^{6} + 6 X Y^{4} Z^{5} + 18 X^{5} Y^{2} Z^{2} + 24 X^{2} Y^{2} Z^{5} + 12 X^{5} Y^{2} Z + 3 X^{4} Y^{2} Z^{2} + 6 X^{3} Y^{4} Z + 129 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^{3} Y^{2} Z^{2} + 6 X Y^{4} Z^{2} + 18 X^{3} Y^{2} Z + 585 X^{2} Y^{2} Z^{2} + 48 X Y^{4} Z + 24 X Y^{2} Z^{3} + 90 X^{3} Y Z + 42 X^{2} Y^{2} Z + 90 X Y^{3} Z + 42 X Y^{2} Z^{2} + 90 X Y Z^{3} + 18 X^{2} Y Z + 414 X Y^{2} Z + 18 X Y Z^{2} + 414 X Y Z

Algorithm definition

The algorithm ⟨10×20×20:2464⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨5×10×10:352⟩.

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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