Description of fast matrix multiplication algorithm: ⟨10×15×16:1520⟩

Algorithm type

4 X^{6} Y^{4} Z^{4} + 16 X Y^{12} Z + 92 X^{4} Y^{4} Z^{4} + 16 X^{2} Y^{8} Z^{2} + 16 X^{2} Y^{2} Z^{8} + 4 X^{3} Y^{6} Z^{2} + 52 X^{6} Y^{2} Z^{2} + 32 X^{4} Y^{2} Z^{4} + 92 X^{2} Y^{6} Z^{2} + 16 X^{4} Y^{2} Z^{2} + 16 X^{2} Y^{2} Z^{4} + 16 X Y^{3} Z^{4} + 52 X^{3} Y^{3} Z + 12 X^{3} Y^{2} Z^{2} + 32 X^{2} Y^{3} Z^{2} + 16 X^{2} Y^{3} Z + 336 X^{2} Y^{2} Z^{2} + 48 X Y^{4} Z + 16 X Y^{3} Z^{2} + 48 X Y Z^{4} + 156 X^{3} Y Z + 96 X^{2} Y Z^{2} + 60 X Y^{3} Z + 48 X^{2} Y Z + 48 X Y Z^{2} + 180 X Y Z

Algorithm definition

The algorithm ⟨10×15×16:1520⟩ is the (Kronecker) tensor product of ⟨2×3×4:20⟩ with ⟨5×5×4:76⟩.

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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