Description of fast matrix multiplication algorithm: ⟨14×27×32:7000⟩

Algorithm type

8 X^{8} Y^{8} Z^{12} + 8 X^{8} Y^{8} Z^{10} + 4 X^{12} Y^{4} Z^{8} + 4 X^{8} Y^{8} Z^{8} + 8 X^{6} Y^{8} Z^{10} + 4 X^{8} Y^{8} Z^{6} + 4 X^{8} Y^{6} Z^{8} + 4 X^{6} Y^{8} Z^{8} + 8 X^{4} Y^{12} Z^{6} + 8 X^{2} Y^{18} Z^{2} + 8 X^{4} Y^{12} Z^{5} + 4 X^{12} Y^{6} Z^{2} + 4 X^{10} Y^{6} Z^{4} + 4 X^{10} Y^{4} Z^{6} + 12 X^{8} Y^{8} Z^{4} + 4 X^{8} Y^{6} Z^{6} + 4 X^{8} Y^{4} Z^{8} + 8 X^{6} Y^{8} Z^{6} + 4 X^{6} Y^{6} Z^{8} + 12 X^{4} Y^{12} Z^{4} + 8 X^{4} Y^{4} Z^{12} + 8 X^{3} Y^{12} Z^{5} + 8 X^{2} Y^{8} Z^{10} + 4 X^{4} Y^{12} Z^{3} + 4 X^{3} Y^{12} Z^{4} + 4 X^{8} Y^{8} Z^{2} + 12 X^{4} Y^{12} Z^{2} + 4 X^{4} Y^{8} Z^{6} + 16 X^{4} Y^{4} Z^{10} + 8 X^{3} Y^{12} Z^{3} + 8 X Y^{12} Z^{5} + 4 X^{4} Y^{12} Z + 4 X^{4} Y^{9} Z^{4} + 4 X^{2} Y^{12} Z^{3} + 4 X^{6} Y^{9} Z + 4 X^{6} Y^{6} Z^{4} + 8 X^{6} Y^{4} Z^{6} + 4 X^{5} Y^{9} Z^{2} + 4 X^{4} Y^{9} Z^{3} + 4 X^{4} Y^{6} Z^{6} + 16 X^{4} Y^{4} Z^{8} + 4 X^{3} Y^{9} Z^{4} + 8 X^{2} Y^{4} Z^{10} + 4 X Y^{12} Z^{2} + 4 X^{8} Y^{4} Z^{2} + 4 X^{6} Y^{4} Z^{4} + 4 X^{6} Y^{2} Z^{6} + 4 X^{5} Y^{6} Z^{3} + 4 X^{4} Y^{6} Z^{4} + 64 X^{4} Y^{4} Z^{6} + 4 X^{2} Y^{9} Z^{3} + 4 X^{2} Y^{8} Z^{4} + 8 X^{2} Y^{6} Z^{6} + 24 X^{4} Y^{4} Z^{5} + 16 X^{2} Y^{6} Z^{5} + 4 X^{6} Y^{4} Z^{2} + 20 X^{6} Y^{2} Z^{4} + 344 X^{4} Y^{4} Z^{4} + 8 X^{3} Y^{6} Z^{3} + 24 X^{3} Y^{4} Z^{5} + 20 X^{2} Y^{6} Z^{4} + 8 X^{2} Y^{4} Z^{6} + 4 X Y^{9} Z^{2} + 8 X Y^{6} Z^{5} + 4 X^{4} Y^{6} Z + 12 X^{4} Y^{4} Z^{3} + 12 X^{4} Y^{3} Z^{4} + 4 X^{3} Y^{6} Z^{2} + 12 X^{3} Y^{4} Z^{4} + 40 X^{2} Y^{6} Z^{3} + 32 X Y^{9} Z + 12 X^{6} Y^{3} Z + 44 X^{6} Y^{2} Z^{2} + 12 X^{5} Y^{3} Z^{2} + 12 X^{5} Y^{2} Z^{3} + 76 X^{4} Y^{4} Z^{2} + 12 X^{4} Y^{3} Z^{3} + 32 X^{4} Y^{2} Z^{4} + 4 X^{3} Y^{6} Z + 24 X^{3} Y^{4} Z^{3} + 12 X^{3} Y^{3} Z^{4} + 388 X^{2} Y^{6} Z^{2} + 16 X^{2} Y^{4} Z^{4} + 100 X^{2} Y^{2} Z^{6} + 8 X Y^{6} Z^{3} + 24 X Y^{4} Z^{5} + 12 X^{4} Y^{4} Z + 4 X^{3} Y^{3} Z^{3} + 40 X^{2} Y^{6} Z + 12 X^{2} Y^{4} Z^{3} + 48 X^{2} Y^{2} Z^{5} + 16 X Y^{6} Z^{2} + 52 X^{4} Y^{2} Z^{2} + 8 X^{3} Y^{3} Z^{2} + 24 X^{3} Y^{2} Z^{3} + 120 X^{2} Y^{4} Z^{2} + 12 X^{2} Y^{3} Z^{3} + 116 X^{2} Y^{2} Z^{4} + 120 X Y^{6} Z + 24 X Y^{2} Z^{5} + 12 X^{4} Y^{2} Z + 44 X^{3} Y^{3} Z + 12 X^{3} Y^{2} Z^{2} + 12 X^{3} Y Z^{3} + 20 X^{2} Y^{3} Z^{2} + 120 X^{2} Y^{2} Z^{3} + 12 X Y^{4} Z^{2} + 76 X Y^{3} Z^{3} + 12 X^{3} Y^{2} Z + 24 X^{3} Y Z^{2} + 52 X^{2} Y^{3} Z + 1344 X^{2} Y^{2} Z^{2} + 80 X Y^{3} Z^{2} + 24 X Y^{2} Z^{3} + 132 X^{3} Y Z + 120 X^{2} Y^{2} Z + 60 X^{2} Y Z^{2} + 444 X Y^{3} Z + 48 X Y^{2} Z^{2} + 228 X Y Z^{3} + 156 X^{2} Y Z + 360 X Y^{2} Z + 204 X Y Z^{2} + 1044 X Y Z

Algorithm definition

The algorithm ⟨14×27×32:7000⟩ is the (Kronecker) tensor product of ⟨2×3×4:20⟩ with ⟨7×9×8:350⟩.

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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