Description of fast matrix multiplication algorithm: ⟨10×15×21:2010⟩

Algorithm type

3 X^{6} Y^{4} Z^{4} + 6 X^{8} Y^{2} Z^{2} + 3 X^{4} Y^{6} Z^{2} + 120 X^{4} Y^{4} Z^{4} + 3 X^{4} Y^{2} Z^{6} + 12 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{2} Z^{8} + 42 X^{6} Y^{2} Z^{2} + 6 X^{4} Y^{4} Z^{2} + 30 X^{4} Y^{2} Z^{4} + 15 X^{2} Y^{6} Z^{2} + 15 X^{2} Y^{2} Z^{6} + 24 X Y^{8} Z + 6 X^{3} Y^{4} Z^{2} + 6 X^{2} Y^{6} Z + 51 X^{4} Y^{2} Z^{2} + 243 X^{2} Y^{4} Z^{2} + 15 X^{2} Y^{2} Z^{4} + 30 X Y^{6} Z + 12 X^{4} Y^{2} Z + 6 X^{3} Y^{2} Z^{2} + 12 X^{2} Y^{4} Z + 6 X^{2} Y^{2} Z^{3} + 24 X Y^{2} Z^{4} + 12 X^{4} Y Z + 84 X^{3} Y^{2} Z + 6 X^{2} Y^{3} Z + 366 X^{2} Y^{2} Z^{2} + 6 X^{2} Y Z^{3} + 30 X Y^{4} Z + 30 X Y^{2} Z^{3} + 24 X Y Z^{4} + 84 X^{3} Y Z + 114 X^{2} Y^{2} Z + 60 X^{2} Y Z^{2} + 30 X Y^{3} Z + 30 X Y^{2} Z^{2} + 30 X Y Z^{3} + 102 X^{2} Y Z + 138 X Y^{2} Z + 30 X Y Z^{2} + 132 X Y Z

Algorithm definition

The algorithm ⟨10×15×21:2010⟩ is the (Kronecker) tensor product of ⟨5×5×7:134⟩ with ⟨2×3×3:15⟩.

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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