Description of fast matrix multiplication algorithm: ⟨9×10×32:1800⟩

Algorithm type

4 X^{6} Y^{2} Z^{6} + 12 X^{4} Y^{6} Z^{4} + 4 X^{3} Y Z^{9} + 108 X^{4} Y^{4} Z^{4} + 4 X^{2} Y^{4} Z^{6} + 4 X Y^{2} Z^{9} + 12 X^{2} Y^{3} Z^{6} + 40 X Y Z^{9} + 4 X^{6} Y^{2} Z^{2} + 20 X^{2} Y^{6} Z^{2} + 28 X^{2} Y^{4} Z^{4} + 148 X^{2} Y^{2} Z^{6} + 28 X Y^{2} Z^{6} + 4 X^{4} Y^{2} Z^{2} + 64 X^{2} Y^{4} Z^{2} + 56 X^{2} Y^{2} Z^{4} + 56 X Y Z^{6} + 16 X^{3} Y Z^{3} + 36 X^{2} Y^{3} Z^{2} + 20 X Y^{3} Z^{3} + 340 X^{2} Y^{2} Z^{2} + 4 X^{2} Y Z^{3} + 76 X Y^{2} Z^{3} + 12 X^{3} Y Z + 60 X Y^{3} Z + 84 X Y^{2} Z^{2} + 136 X Y Z^{3} + 12 X^{2} Y Z + 192 X Y^{2} Z + 168 X Y Z^{2} + 48 X Y Z

Algorithm definition

The algorithm ⟨9×10×32:1800⟩ is the (Kronecker) tensor product of ⟨3×2×4:20⟩ with ⟨3×5×8:90⟩.

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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