Description of fast matrix multiplication algorithm: ⟨10×12×20:1508⟩

Algorithm type

6 X^{6} Y^{2} Z^{4} + 102 X^{4} Y^{4} Z^{4} + 6 X^{2} Y^{6} Z^{4} + 12 X^{2} Y^{2} Z^{8} + 2 X Y^{9} Z^{2} + 10 X Y^{9} Z + 30 X^{6} Y^{2} Z^{2} + 12 X^{4} Y^{2} Z^{4} + 64 X^{2} Y^{6} Z^{2} + 12 X^{2} Y^{4} Z^{4} + 6 X^{2} Y^{2} Z^{6} + 12 X Y^{6} Z^{2} + 6 X^{4} Y^{2} Z^{2} + 2 X^{3} Y^{3} Z^{2} + 142 X^{2} Y^{4} Z^{2} + 78 X^{2} Y^{2} Z^{4} + 42 X Y^{6} Z + 4 X Y^{3} Z^{4} + 10 X^{3} Y^{3} Z + 8 X^{3} Y^{2} Z^{2} + 4 X^{2} Y^{3} Z^{2} + 16 X Y^{4} Z^{2} + 2 X Y^{3} Z^{3} + 16 X Y^{2} Z^{4} + 40 X^{3} Y^{2} Z + 10 X^{3} Y Z^{2} + 2 X^{2} Y^{3} Z + 228 X^{2} Y^{2} Z^{2} + 8 X Y^{4} Z + 36 X Y^{3} Z^{2} + 8 X Y^{2} Z^{3} + 20 X Y Z^{4} + 50 X^{3} Y Z + 8 X^{2} Y^{2} Z + 20 X^{2} Y Z^{2} + 64 X Y^{3} Z + 124 X Y^{2} Z^{2} + 10 X Y Z^{3} + 10 X^{2} Y Z + 66 X Y^{2} Z + 130 X Y Z^{2} + 70 X Y Z

Algorithm definition

The algorithm ⟨10×12×20:1508⟩ is the (Kronecker) tensor product of ⟨2×4×4:26⟩ 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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