Description of fast matrix multiplication algorithm: ⟨16×27×28:6552⟩

Algorithm type

24 X^{6} Y^{8} Z^{9} + 60 X^{6} Y^{8} Z^{6} + 8 X^{3} Y^{4} Z^{12} + 24 X^{6} Y^{8} Z^{3} + 48 X^{3} Y^{4} Z^{9} + 192 X^{4} Y^{4} Z^{6} + 48 X^{3} Y^{4} Z^{6} + 24 X^{2} Y^{8} Z^{3} + 480 X^{4} Y^{4} Z^{4} + 60 X^{2} Y^{8} Z^{2} + 64 X^{2} Y^{2} Z^{8} + 24 X^{2} Y^{8} Z + 192 X^{4} Y^{4} Z^{2} + 40 X^{3} Y^{4} Z^{3} + 384 X^{2} Y^{2} Z^{6} + 8 X Y^{4} Z^{4} + 384 X^{2} Y^{2} Z^{4} + 48 X Y^{4} Z^{3} + 384 X^{2} Y^{2} Z^{3} + 48 X Y^{4} Z^{2} + 1280 X^{2} Y^{2} Z^{2} + 40 X Y^{4} Z + 128 X Y Z^{4} + 384 X^{2} Y^{2} Z + 768 X Y Z^{3} + 768 X Y Z^{2} + 640 X Y Z

Algorithm definition

The algorithm ⟨16×27×28:6552⟩ is the (Kronecker) tensor product of ⟨4×3×7:63⟩ with ⟨4×9×4:104⟩.

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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