Description of fast matrix multiplication algorithm: ⟨4×27×30:2100⟩

Algorithm type

6 X^{4} Y^{12} Z^{4} + 3 X^{2} Y^{16} Z^{2} + 18 X^{4} Y^{10} Z^{4} + 24 X^{2} Y^{14} Z^{2} + 6 X Y^{16} Z + 15 X^{4} Y^{8} Z^{4} + 30 X^{2} Y^{12} Z^{2} + 48 X Y^{14} Z + 30 X^{4} Y^{6} Z^{4} + 66 X^{2} Y^{10} Z^{2} + 36 X Y^{12} Z + 51 X^{4} Y^{4} Z^{4} + 48 X^{2} Y^{8} Z^{2} + 60 X Y^{10} Z + 102 X^{2} Y^{6} Z^{2} + 42 X Y^{8} Z + 36 X^{2} Y^{5} Z^{2} + 48 X Y^{7} Z + 168 X^{2} Y^{4} Z^{2} + 96 X Y^{6} Z + 60 X^{2} Y^{3} Z^{2} + 60 X Y^{5} Z + 243 X^{2} Y^{2} Z^{2} + 108 X Y^{4} Z + 60 X Y^{3} Z + 354 X Y^{2} Z + 282 X Y Z

Algorithm definition

The algorithm ⟨4×27×30:2100⟩ is the (Kronecker) tensor product of ⟨2×3×3:15⟩ with ⟨2×9×10:140⟩.

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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