Description of fast matrix multiplication algorithm: ⟨8×10×30:1560⟩

Algorithm type

10 X^{4} Y^{4} Z^{8} + 40 X^{4} Y^{4} Z^{6} + 40 X^{4} Y^{4} Z^{4} + 4 X^{2} Y^{6} Z^{4} + 40 X^{2} Y^{2} Z^{8} + 16 X^{2} Y^{6} Z^{3} + 16 X^{2} Y^{6} Z^{2} + 10 X^{2} Y^{4} Z^{4} + 80 X^{2} Y^{2} Z^{6} + 40 X^{2} Y^{4} Z^{3} + 40 X^{2} Y^{4} Z^{2} + 76 X^{2} Y^{2} Z^{4} + 16 X Y^{3} Z^{4} + 64 X^{2} Y^{2} Z^{3} + 32 X Y^{3} Z^{3} + 40 X Y^{2} Z^{4} + 184 X^{2} Y^{2} Z^{2} + 24 X Y^{3} Z^{2} + 80 X Y^{2} Z^{3} + 64 X Y Z^{4} + 48 X Y^{3} Z + 60 X Y^{2} Z^{2} + 128 X Y Z^{3} + 120 X Y^{2} Z + 96 X Y Z^{2} + 192 X Y Z

Algorithm definition

The algorithm ⟨8×10×30:1560⟩ is the (Kronecker) tensor product of ⟨2×5×5:40⟩ with ⟨4×2×6:39⟩.

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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