Description of fast matrix multiplication algorithm: ⟨16×21×24:4590⟩

Algorithm type

48 X^{8} Y^{8} Z^{8} + 96 X^{4} Y^{8} Z^{4} + 426 X^{4} Y^{4} Z^{4} + 27 X^{6} Y^{2} Z^{2} + 18 X^{4} Y^{2} Z^{4} + 27 X^{2} Y^{6} Z^{2} + 18 X^{2} Y^{4} Z^{4} + 18 X^{2} Y^{2} Z^{6} + 9 X^{4} Y^{2} Z^{2} + 669 X^{2} Y^{4} Z^{2} + 99 X^{2} Y^{2} Z^{4} + 54 X Y^{6} Z + 36 X Y^{4} Z^{2} + 54 X^{3} Y^{2} Z + 1011 X^{2} Y^{2} Z^{2} + 18 X Y^{4} Z + 36 X Y^{2} Z^{3} + 54 X^{3} Y Z + 18 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 54 X Y^{3} Z + 234 X Y^{2} Z^{2} + 36 X Y Z^{3} + 18 X^{2} Y Z + 648 X Y^{2} Z + 198 X Y Z^{2} + 630 X Y Z

Algorithm definition

The algorithm ⟨16×21×24:4590⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨8×7×8:306⟩.

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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