Description of fast matrix multiplication algorithm: ⟨14×27×30:6585⟩

Algorithm type

27 X^{8} Y^{8} Z^{8} + 3 X^{6} Y^{10} Z^{8} + 9 X^{14} Y^{4} Z^{4} + 3 X^{8} Y^{6} Z^{8} + 6 X^{4} Y^{4} Z^{14} + 3 X^{14} Y^{4} Z^{2} + 27 X^{6} Y^{8} Z^{6} + 9 X^{6} Y^{6} Z^{8} + 18 X^{4} Y^{12} Z^{4} + 3 X^{4} Y^{8} Z^{8} + 3 X^{4} Y^{2} Z^{14} + 3 X^{2} Y^{4} Z^{14} + 9 X^{6} Y^{6} Z^{6} + 6 X^{4} Y^{12} Z^{2} + 3 X^{4} Y^{10} Z^{4} + 6 X^{4} Y^{8} Z^{6} + 6 X^{4} Y^{6} Z^{8} + 6 X^{3} Y^{10} Z^{4} + 3 X^{4} Y^{10} Z^{2} + 60 X^{4} Y^{8} Z^{4} + 3 X^{4} Y^{4} Z^{8} + 36 X^{2} Y^{12} Z^{2} + 9 X^{2} Y^{10} Z^{4} + 3 X^{2} Y^{8} Z^{6} + 3 X^{2} Y^{6} Z^{8} + 12 X^{2} Y^{12} Z + 18 X^{4} Y^{6} Z^{4} + 3 X^{4} Y^{4} Z^{6} + 54 X^{3} Y^{8} Z^{3} + 6 X^{2} Y^{10} Z^{2} + 6 X^{2} Y^{8} Z^{4} + 3 X^{2} Y^{6} Z^{6} + 18 X^{7} Y^{4} Z^{2} + 18 X^{3} Y^{6} Z^{4} + 6 X^{2} Y^{10} Z + 12 X^{2} Y^{8} Z^{3} + 12 X^{2} Y^{4} Z^{7} + 18 X Y^{10} Z^{2} + 12 X^{8} Y^{2} Z^{2} + 6 X^{7} Y^{4} Z + 6 X^{6} Y^{4} Z^{2} + 375 X^{4} Y^{4} Z^{4} + 18 X^{3} Y^{6} Z^{3} + 6 X^{3} Y^{5} Z^{4} + 27 X^{2} Y^{8} Z^{2} + 12 X^{2} Y^{6} Z^{4} + 9 X^{2} Y^{4} Z^{6} + 15 X^{2} Y^{2} Z^{8} + 6 X Y^{8} Z^{3} + 6 X Y^{4} Z^{7} + 18 X^{7} Y^{2} Z^{2} + 6 X^{4} Y^{3} Z^{4} + 18 X^{2} Y^{2} Z^{7} + 6 X Y^{6} Z^{4} + 6 X^{7} Y^{2} Z + 39 X^{6} Y^{2} Z^{2} + 30 X^{4} Y^{4} Z^{2} + 18 X^{4} Y^{2} Z^{4} + 54 X^{3} Y^{4} Z^{3} + 18 X^{3} Y^{3} Z^{4} + 123 X^{2} Y^{6} Z^{2} + 57 X^{2} Y^{4} Z^{4} + 48 X^{2} Y^{2} Z^{6} + 6 X^{2} Y Z^{7} + 30 X Y^{8} Z + 6 X Y^{6} Z^{3} + 6 X Y^{2} Z^{7} + 18 X^{3} Y^{3} Z^{3} + 12 X^{2} Y^{6} Z + 6 X^{2} Y^{5} Z^{2} + 18 X^{2} Y^{4} Z^{3} + 12 X^{2} Y^{3} Z^{4} + 33 X^{4} Y^{2} Z^{2} + 12 X^{3} Y^{4} Z + 6 X^{2} Y^{5} Z + 816 X^{2} Y^{4} Z^{2} + 54 X^{2} Y^{2} Z^{4} + 126 X Y^{6} Z + 18 X Y^{5} Z^{2} + 24 X Y^{4} Z^{3} + 6 X Y^{3} Z^{4} + 24 X^{4} Y^{2} Z + 60 X^{2} Y^{4} Z + 24 X^{2} Y^{3} Z^{2} + 6 X^{2} Y^{2} Z^{3} + 90 X Y^{4} Z^{2} + 6 X Y^{3} Z^{3} + 30 X Y^{2} Z^{4} + 24 X^{4} Y Z + 90 X^{3} Y^{2} Z + 942 X^{2} Y^{2} Z^{2} + 354 X Y^{4} Z + 114 X Y^{2} Z^{3} + 30 X Y Z^{4} + 78 X^{3} Y Z + 126 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 126 X Y^{3} Z + 186 X Y^{2} Z^{2} + 96 X Y Z^{3} + 66 X^{2} Y Z + 852 X Y^{2} Z + 96 X Y Z^{2} + 528 X Y Z

Algorithm definition

The algorithm ⟨14×27×30:6585⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨7×9×10:439⟩.

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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