Description of fast matrix multiplication algorithm: ⟨15×24×27:5520⟩

Algorithm type

16 X^{12} Y^{12} Z^{8} + 24 X^{12} Y^{12} Z^{4} + 32 X^{6} Y^{6} Z^{6} + 64 X^{12} Y^{3} Z^{2} + 64 X^{3} Y^{12} Z^{2} + 96 X^{12} Y^{3} Z + 592 X^{6} Y^{6} Z^{4} + 96 X^{3} Y^{12} Z + 48 X^{6} Y^{6} Z^{3} + 16 X^{9} Y^{3} Z^{2} + 920 X^{6} Y^{6} Z^{2} + 24 X^{9} Y^{3} Z + 48 X^{6} Y^{6} Z + 144 X^{3} Y^{6} Z^{4} + 240 X^{3} Y^{3} Z^{6} + 32 X^{6} Y^{3} Z^{2} + 328 X^{3} Y^{6} Z^{2} + 48 X^{6} Y^{3} Z + 168 X^{3} Y^{6} Z + 192 X^{3} Y^{3} Z^{4} + 360 X^{3} Y^{3} Z^{3} + 960 X^{3} Y^{3} Z^{2} + 1008 X^{3} Y^{3} Z

Algorithm definition

The algorithm ⟨15×24×27:5520⟩ is the (Kronecker) tensor product of ⟨3×6×3:40⟩ with ⟨5×4×9:138⟩.

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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