Description of fast matrix multiplication algorithm: ⟨18×21×24:5000⟩

Algorithm type

32 X^{8} Y^{12} Z^{12} + 48 X^{4} Y^{12} Z^{12} + 32 X^{6} Y^{9} Z^{12} + 16 X^{12} Y^{6} Z^{6} + 48 X^{3} Y^{9} Z^{12} + 32 X^{10} Y^{6} Z^{6} + 16 X^{10} Y^{3} Z^{6} + 24 X^{6} Y^{6} Z^{6} + 48 X^{5} Y^{6} Z^{6} + 480 X^{4} Y^{6} Z^{6} + 24 X^{5} Y^{3} Z^{6} + 752 X^{2} Y^{6} Z^{6} + 48 X Y^{6} Z^{6} + 192 X^{6} Y^{3} Z^{3} + 16 X^{2} Y^{3} Z^{6} + 288 X^{4} Y^{3} Z^{3} + 24 X Y^{3} Z^{6} + 288 X^{3} Y^{3} Z^{3} + 1296 X^{2} Y^{3} Z^{3} + 1296 X Y^{3} Z^{3}

Algorithm definition

The algorithm ⟨18×21×24:5000⟩ is the (Kronecker) tensor product of ⟨3×3×6:40⟩ with ⟨6×7×4:125⟩.

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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