Description of fast matrix multiplication algorithm: ⟨10×15×24:2176⟩

Algorithm type

16 X^{4} Y^{12} Z^{2} + 16 X^{4} Y^{8} Z^{6} + 24 X^{2} Y^{12} Z^{4} + 16 X^{6} Y^{8} Z^{2} + 144 X^{4} Y^{8} Z^{4} + 32 X^{2} Y^{12} Z^{2} + 16 X^{2} Y^{12} Z + 24 X Y^{12} Z^{2} + 16 X^{2} Y^{4} Z^{8} + 32 X Y^{12} Z + 16 X^{2} Y^{8} Z^{3} + 48 X^{6} Y^{4} Z^{2} + 32 X^{4} Y^{4} Z^{4} + 16 X^{3} Y^{8} Z + 144 X^{2} Y^{8} Z^{2} + 40 X^{2} Y^{4} Z^{6} + 64 X^{4} Y^{4} Z^{2} + 64 X^{2} Y^{4} Z^{4} + 16 X Y^{4} Z^{4} + 48 X^{3} Y^{4} Z + 64 X^{2} Y^{4} Z^{2} + 40 X Y^{4} Z^{3} + 64 X^{2} Y^{4} Z + 32 X^{2} Y^{2} Z^{3} + 64 X Y^{4} Z^{2} + 32 X^{3} Y^{2} Z + 32 X^{2} Y^{3} Z + 288 X^{2} Y^{2} Z^{2} + 32 X Y^{4} Z + 48 X Y^{3} Z^{2} + 32 X Y Z^{4} + 96 X^{3} Y Z + 64 X^{2} Y Z^{2} + 64 X Y^{3} Z + 80 X Y Z^{3} + 128 X^{2} Y Z + 128 X Y Z^{2} + 64 X Y Z

Algorithm definition

The algorithm ⟨10×15×24:2176⟩ is the (Kronecker) tensor product of ⟨2×5×4:32⟩ with ⟨5×3×6:68⟩.

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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