Description of fast matrix multiplication algorithm: ⟨10×25×25:3720⟩

Algorithm type

10 X^{6} Y^{4} Z^{2} + 320 X^{4} Y^{4} Z^{4} + 10 X^{4} Y^{2} Z^{6} + 10 X^{2} Y^{6} Z^{4} + 4 X Y^{9} Z^{2} + 10 X^{4} Y^{4} Z^{2} + 10 X^{4} Y^{2} Z^{4} + 4 X^{3} Y^{6} Z + 128 X^{2} Y^{6} Z^{2} + 10 X^{2} Y^{4} Z^{4} + 4 X^{2} Y^{6} Z + 14 X Y^{6} Z^{2} + 110 X^{4} Y^{2} Z^{2} + 10 X^{3} Y^{4} Z + 430 X^{2} Y^{4} Z^{2} + 4 X^{2} Y^{3} Z^{3} + 110 X^{2} Y^{2} Z^{4} + 44 X Y^{6} Z + 10 X^{2} Y^{4} Z + 4 X^{2} Y^{3} Z^{2} + 10 X^{2} Y^{2} Z^{3} + 10 X Y^{4} Z^{2} + 16 X^{3} Y^{2} Z + 44 X^{2} Y^{3} Z + 742 X^{2} Y^{2} Z^{2} + 16 X^{2} Y Z^{3} + 110 X Y^{4} Z + 60 X Y^{3} Z^{2} + 126 X^{2} Y^{2} Z + 16 X^{2} Y Z^{2} + 88 X Y^{3} Z + 126 X Y^{2} Z^{2} + 176 X^{2} Y Z + 396 X Y^{2} Z + 176 X Y Z^{2} + 352 X Y Z

Algorithm definition

The algorithm ⟨10×25×25:3720⟩ is the (Kronecker) tensor product of ⟨2×5×5:40⟩ with ⟨5×5×5:93⟩.

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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