Description of fast matrix multiplication algorithm: ⟨10×12×25:1856⟩

Algorithm type

8 X^{2} Y^{12} Z^{4} + 136 X^{4} Y^{8} Z^{4} + 40 X^{2} Y^{12} Z^{2} + 8 X Y^{12} Z^{2} + 8 X^{6} Y^{4} Z^{4} + 16 X^{2} Y^{8} Z^{4} + 16 X^{2} Y^{4} Z^{8} + 40 X Y^{12} Z + 40 X^{6} Y^{4} Z^{2} + 16 X^{4} Y^{4} Z^{4} + 144 X^{2} Y^{8} Z^{2} + 8 X^{2} Y^{4} Z^{6} + 16 X Y^{8} Z^{2} + 8 X^{4} Y^{4} Z^{2} + 104 X^{2} Y^{4} Z^{4} + 8 X Y^{8} Z + 8 X^{3} Y^{4} Z^{2} + 16 X Y^{4} Z^{4} + 40 X^{3} Y^{4} Z + 72 X^{2} Y^{4} Z^{2} + 8 X Y^{4} Z^{3} + 8 X^{2} Y^{4} Z + 104 X Y^{4} Z^{2} + 16 X^{3} Y Z^{2} + 272 X^{2} Y^{2} Z^{2} + 56 X Y^{4} Z + 16 X Y^{3} Z^{2} + 32 X Y Z^{4} + 80 X^{3} Y Z + 32 X^{2} Y Z^{2} + 80 X Y^{3} Z + 32 X Y^{2} Z^{2} + 16 X Y Z^{3} + 16 X^{2} Y Z + 16 X Y^{2} Z + 208 X Y Z^{2} + 112 X Y Z

Algorithm definition

The algorithm ⟨10×12×25:1856⟩ is the (Kronecker) tensor product of ⟨2×4×5:32⟩ 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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