Description of fast matrix multiplication algorithm: ⟨16×18×30:4935⟩

Algorithm type

39 X^{8} Y^{8} Z^{8} + 9 X^{12} Y^{4} Z^{4} + 3 X^{8} Y^{4} Z^{8} + 12 X^{4} Y^{12} Z^{4} + 6 X^{4} Y^{8} Z^{8} + 6 X^{4} Y^{4} Z^{12} + 9 X^{8} Y^{4} Z^{4} + 96 X^{4} Y^{8} Z^{4} + 24 X^{4} Y^{4} Z^{8} + 24 X^{2} Y^{12} Z^{2} + 12 X^{2} Y^{8} Z^{4} + 18 X^{6} Y^{4} Z^{2} + 333 X^{4} Y^{4} Z^{4} + 36 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{4} Z^{6} + 72 X^{6} Y^{2} Z^{2} + 18 X^{4} Y^{4} Z^{2} + 24 X^{4} Y^{2} Z^{4} + 96 X^{2} Y^{6} Z^{2} + 96 X^{2} Y^{4} Z^{4} + 48 X^{2} Y^{2} Z^{6} + 72 X^{4} Y^{2} Z^{2} + 642 X^{2} Y^{4} Z^{2} + 192 X^{2} Y^{2} Z^{4} + 144 X Y^{6} Z + 72 X Y^{4} Z^{2} + 108 X^{3} Y^{2} Z + 624 X^{2} Y^{2} Z^{2} + 216 X Y^{4} Z + 72 X Y^{2} Z^{3} + 108 X^{3} Y Z + 108 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 144 X Y^{3} Z + 360 X Y^{2} Z^{2} + 72 X Y Z^{3} + 108 X^{2} Y Z + 396 X Y^{2} Z + 288 X Y Z^{2} + 180 X Y Z

Algorithm definition

The algorithm ⟨16×18×30:4935⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×9×15:705⟩.

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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