Description of fast matrix multiplication algorithm: ⟨16×21×30:5835⟩

Algorithm type

3 X^{14} Y^{14} Z^{16} + 6 X^{7} Y^{14} Z^{8} + 3 X^{6} Y^{8} Z^{12} + 33 X^{8} Y^{8} Z^{8} + 6 X^{8} Y^{6} Z^{8} + 6 X^{7} Y^{7} Z^{8} + 9 X^{6} Y^{8} Z^{8} + 3 X^{8} Y^{8} Z^{4} + 3 X^{8} Y^{4} Z^{8} + 3 X^{6} Y^{6} Z^{8} + 6 X^{4} Y^{4} Z^{12} + 3 X^{6} Y^{8} Z^{4} + 3 X^{4} Y^{10} Z^{4} + 6 X^{3} Y^{8} Z^{6} + 6 X^{8} Y^{4} Z^{4} + 72 X^{4} Y^{8} Z^{4} + 24 X^{4} Y^{4} Z^{8} + 18 X^{3} Y^{8} Z^{4} + 3 X^{6} Y^{4} Z^{4} + 6 X^{4} Y^{8} Z^{2} + 12 X^{4} Y^{6} Z^{4} + 9 X^{4} Y^{4} Z^{6} + 6 X^{2} Y^{10} Z^{2} + 6 X^{3} Y^{8} Z^{2} + 6 X^{3} Y^{6} Z^{4} + 6 X^{3} Y^{4} Z^{6} + 384 X^{4} Y^{4} Z^{4} + 12 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{4} Z^{6} + 12 X^{4} Y^{3} Z^{4} + 18 X^{3} Y^{4} Z^{4} + 27 X^{6} Y^{2} Z^{2} + 36 X^{4} Y^{4} Z^{2} + 24 X^{4} Y^{2} Z^{4} + 6 X^{3} Y^{3} Z^{4} + 45 X^{2} Y^{6} Z^{2} + 78 X^{2} Y^{4} Z^{4} + 48 X^{2} Y^{2} Z^{6} + 12 X^{3} Y^{4} Z^{2} + 6 X^{2} Y^{5} Z^{2} + 18 X^{2} Y^{4} Z^{3} + 66 X^{4} Y^{2} Z^{2} + 708 X^{2} Y^{4} Z^{2} + 192 X^{2} Y^{2} Z^{4} + 90 X Y^{6} Z + 6 X^{3} Y^{2} Z^{2} + 36 X^{2} Y^{4} Z + 18 X^{2} Y^{2} Z^{3} + 60 X Y^{4} Z^{2} + 54 X^{3} Y^{2} Z + 948 X^{2} Y^{2} Z^{2} + 144 X Y^{4} Z + 72 X Y^{2} Z^{3} + 54 X^{3} Y Z + 144 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 90 X Y^{3} Z + 348 X Y^{2} Z^{2} + 72 X Y Z^{3} + 108 X^{2} Y Z + 720 X Y^{2} Z + 288 X Y Z^{2} + 576 X Y Z

Algorithm definition

The algorithm ⟨16×21×30:5835⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨8×7×10:389⟩.

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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