Description of fast matrix multiplication algorithm: ⟨10×18×25:2726⟩

Algorithm type

2 X^{2} Y^{12} Z^{4} + 34 X^{4} Y^{8} Z^{4} + 10 X^{2} Y^{12} Z^{2} + 4 X Y^{12} Z^{2} + 2 X^{6} Y^{4} Z^{4} + 4 X^{2} Y^{8} Z^{4} + 4 X^{2} Y^{4} Z^{8} + 20 X Y^{12} Z + 10 X^{6} Y^{4} Z^{2} + 11 X^{6} Y^{2} Z^{4} + 191 X^{4} Y^{4} Z^{4} + 70 X^{2} Y^{8} Z^{2} + 11 X^{2} Y^{6} Z^{4} + 2 X^{2} Y^{4} Z^{6} + 22 X^{2} Y^{2} Z^{8} + 8 X Y^{9} Z^{2} + 40 X Y^{9} Z + 8 X Y^{8} Z^{2} + 55 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 22 X^{4} Y^{2} Z^{4} + 191 X^{2} Y^{6} Z^{2} + 48 X^{2} Y^{4} Z^{4} + 11 X^{2} Y^{2} Z^{6} + 4 X Y^{8} Z + 4 X^{3} Y^{4} Z^{2} + 20 X Y^{6} Z^{2} + 8 X Y^{4} Z^{4} + 11 X^{4} Y^{2} Z^{2} + 20 X^{3} Y^{4} Z + 8 X^{3} Y^{3} Z^{2} + 101 X^{2} Y^{4} Z^{2} + 143 X^{2} Y^{2} Z^{4} + 28 X Y^{6} Z + 4 X Y^{4} Z^{3} + 16 X Y^{3} Z^{4} + 40 X^{3} Y^{3} Z + 4 X^{3} Y^{2} Z^{2} + 4 X^{2} Y^{4} Z + 16 X^{2} Y^{3} Z^{2} + 60 X Y^{4} Z^{2} + 8 X Y^{3} Z^{3} + 8 X Y^{2} Z^{4} + 20 X^{3} Y^{2} Z + 18 X^{3} Y Z^{2} + 8 X^{2} Y^{3} Z + 391 X^{2} Y^{2} Z^{2} + 32 X Y^{4} Z + 122 X Y^{3} Z^{2} + 4 X Y^{2} Z^{3} + 36 X Y Z^{4} + 90 X^{3} Y Z + 4 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 146 X Y^{3} Z + 88 X Y^{2} Z^{2} + 18 X Y Z^{3} + 18 X^{2} Y Z + 46 X Y^{2} Z + 234 X Y Z^{2} + 126 X Y Z

Algorithm definition

The algorithm ⟨10×18×25:2726⟩ is the (Kronecker) tensor product of ⟨2×6×5:47⟩ with ⟨5×3×5:58⟩.

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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