Description of fast matrix multiplication algorithm: ⟨16×27×27:6450⟩

Algorithm type

63 X^{8} Y^{8} Z^{8} + 18 X^{12} Y^{4} Z^{4} + 18 X^{8} Y^{4} Z^{8} + 9 X^{4} Y^{12} Z^{4} + 18 X^{4} Y^{4} Z^{12} + 36 X^{8} Y^{4} Z^{4} + 48 X^{6} Y^{4} Z^{6} + 252 X^{4} Y^{8} Z^{4} + 36 X^{4} Y^{4} Z^{8} + 36 X^{2} Y^{12} Z^{2} + 72 X^{6} Y^{2} Z^{6} + 36 X Y^{12} Z + 72 X^{6} Y^{4} Z^{2} + 360 X^{4} Y^{4} Z^{4} + 252 X^{2} Y^{8} Z^{2} + 72 X^{2} Y^{4} Z^{6} + 72 X^{6} Y^{2} Z^{2} + 144 X^{4} Y^{4} Z^{2} + 72 X^{4} Y^{2} Z^{4} + 96 X^{3} Y^{4} Z^{3} + 36 X^{2} Y^{6} Z^{2} + 144 X^{2} Y^{4} Z^{4} + 72 X^{2} Y^{2} Z^{6} + 144 X^{4} Y^{2} Z^{2} + 72 X^{3} Y^{4} Z + 240 X^{3} Y^{2} Z^{3} + 720 X^{2} Y^{4} Z^{2} + 144 X^{2} Y^{2} Z^{4} + 72 X Y^{6} Z + 72 X Y^{4} Z^{3} + 144 X^{3} Y Z^{3} + 144 X^{2} Y^{4} Z + 144 X Y^{4} Z^{2} + 144 X^{3} Y^{2} Z + 540 X^{2} Y^{2} Z^{2} + 144 X Y^{4} Z + 144 X Y^{2} Z^{3} + 72 X^{3} Y Z + 288 X^{2} Y^{2} Z + 72 X^{2} Y Z^{2} + 36 X Y^{3} Z + 288 X Y^{2} Z^{2} + 72 X Y Z^{3} + 144 X^{2} Y Z + 288 X Y^{2} Z + 144 X Y Z^{2} + 144 X Y Z

Algorithm definition

The algorithm ⟨16×27×27:6450⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨8×9×9:430⟩.

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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