Description of fast matrix multiplication algorithm: ⟨18×21×21:4440⟩

Algorithm type

32 X^{6} Y^{8} Z^{6} + 32 X^{6} Y^{6} Z^{6} + 560 X^{6} Y^{4} Z^{6} + 64 X^{3} Y^{10} Z^{3} + 48 X^{6} Y^{3} Z^{6} + 48 X^{3} Y^{6} Z^{6} + 96 X^{9} Y^{2} Z^{3} + 784 X^{6} Y^{2} Z^{6} + 64 X^{3} Y^{8} Z^{3} + 96 X^{3} Y^{2} Z^{9} + 144 X^{9} Y Z^{3} + 24 X^{6} Y Z^{6} + 144 X^{3} Y^{4} Z^{6} + 144 X^{3} Y Z^{9} + 96 X^{3} Y^{6} Z^{3} + 72 X^{3} Y^{3} Z^{6} + 96 X^{3} Y^{5} Z^{3} + 488 X^{3} Y^{2} Z^{6} + 352 X^{3} Y^{4} Z^{3} + 408 X^{3} Y Z^{6} + 144 X^{3} Y^{3} Z^{3} + 432 X^{3} Y^{2} Z^{3} + 72 X^{3} Y Z^{3}

Algorithm definition

The algorithm ⟨18×21×21:4440⟩ is the (Kronecker) tensor product of ⟨3×7×7:111⟩ with ⟨6×3×3:40⟩.

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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