Description of fast matrix multiplication algorithm: ⟨15×21×30:5360⟩

Algorithm type

16 X^{4} Y^{6} Z^{9} + 64 X^{2} Y^{12} Z^{3} + 16 X^{2} Y^{9} Z^{6} + 24 X^{2} Y^{6} Z^{9} + 32 X^{2} Y^{3} Z^{12} + 640 X^{4} Y^{6} Z^{6} + 96 X Y^{12} Z^{3} + 24 X Y^{9} Z^{6} + 48 X Y^{3} Z^{12} + 16 X^{6} Y^{3} Z^{6} + 64 X^{8} Y^{3} Z^{3} + 80 X^{2} Y^{9} Z^{3} + 992 X^{2} Y^{6} Z^{6} + 224 X^{2} Y^{3} Z^{9} + 160 X^{4} Y^{3} Z^{6} + 120 X Y^{9} Z^{3} + 48 X Y^{6} Z^{6} + 336 X Y^{3} Z^{9} + 80 X^{6} Y^{3} Z^{3} + 24 X^{3} Y^{3} Z^{6} + 16 X^{2} Y^{6} Z^{3} + 512 X^{2} Y^{3} Z^{6} + 176 X^{4} Y^{3} Z^{3} + 24 X Y^{6} Z^{3} + 408 X Y^{3} Z^{6} + 120 X^{3} Y^{3} Z^{3} + 472 X^{2} Y^{3} Z^{3} + 528 X Y^{3} Z^{3}

Algorithm definition

The algorithm ⟨15×21×30:5360⟩ is the (Kronecker) tensor product of ⟨5×7×5:134⟩ with ⟨3×3×6:40⟩.

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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