Description of fast matrix multiplication algorithm: ⟨18×18×20:3672⟩

Algorithm type

36 X^{4} Y^{4} Z^{6} + 36 X^{6} Y^{4} Z^{2} + 54 X^{6} Y^{2} Z^{4} + 36 X^{4} Y^{6} Z^{2} + 324 X^{4} Y^{4} Z^{4} + 36 X^{2} Y^{2} Z^{8} + 72 X^{6} Y^{2} Z^{2} + 108 X^{2} Y^{6} Z^{2} + 72 X^{2} Y^{4} Z^{4} + 90 X^{2} Y^{2} Z^{6} + 36 X^{6} Y^{2} Z + 54 X^{6} Y Z^{2} + 36 X^{4} Y^{2} Z^{3} + 36 X^{2} Y^{6} Z + 36 X^{2} Y^{4} Z^{3} + 72 X^{6} Y Z + 36 X^{4} Y^{3} Z + 324 X^{4} Y^{2} Z^{2} + 36 X^{3} Y^{4} Z + 468 X^{2} Y^{4} Z^{2} + 144 X^{2} Y^{2} Z^{4} + 108 X Y^{6} Z + 54 X^{3} Y^{2} Z^{2} + 36 X^{2} Y Z^{4} + 72 X Y^{4} Z^{2} + 36 X Y^{2} Z^{4} + 72 X^{3} Y^{2} Z + 108 X^{2} Y^{3} Z + 144 X^{2} Y^{2} Z^{2} + 90 X^{2} Y Z^{3} + 144 X Y^{4} Z + 90 X Y^{2} Z^{3} + 144 X^{2} Y^{2} Z + 144 X^{2} Y Z^{2} + 144 X Y^{2} Z^{2} + 72 X^{2} Y Z + 72 X Y^{2} Z

Algorithm definition

The algorithm ⟨18×18×20:3672⟩ is the (Kronecker) tensor product of ⟨3×6×4:54⟩ with ⟨6×3×5:68⟩.

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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