Description of fast matrix multiplication algorithm: ⟨12×21×24:3480⟩

Algorithm type

16 X^{8} Y^{12} Z^{12} + 24 X^{4} Y^{12} Z^{12} + 352 X^{4} Y^{6} Z^{6} + 48 X^{2} Y^{9} Z^{3} + 560 X^{2} Y^{6} Z^{6} + 32 X^{2} Y^{3} Z^{9} + 32 X^{4} Y^{3} Z^{6} + 72 X Y^{9} Z^{3} + 48 X Y^{6} Z^{6} + 48 X Y^{3} Z^{9} + 48 X^{6} Y^{3} Z^{3} + 16 X^{2} Y^{6} Z^{3} + 224 X^{2} Y^{3} Z^{6} + 16 X^{4} Y^{3} Z^{3} + 24 X Y^{6} Z^{3} + 264 X Y^{3} Z^{6} + 72 X^{3} Y^{3} Z^{3} + 648 X^{2} Y^{3} Z^{3} + 936 X Y^{3} Z^{3}

Algorithm definition

The algorithm ⟨12×21×24:3480⟩ is the (Kronecker) tensor product of ⟨3×3×6:40⟩ with ⟨4×7×4:87⟩.

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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