Description of fast matrix multiplication algorithm: ⟨16×22×28:5628⟩

Algorithm type

30 X^{8} Y^{8} Z^{8} + 9 X^{8} Y^{6} Z^{8} + 6 X^{6} Y^{6} Z^{8} + X^{4} Y^{12} Z^{4} + X^{4} Y^{8} Z^{8} + X^{12} Y^{2} Z^{4} + 2 X^{8} Y^{2} Z^{8} + 2 X^{4} Y^{6} Z^{8} + 10 X^{8} Y^{4} Z^{4} + 17 X^{4} Y^{8} Z^{4} + 10 X^{4} Y^{4} Z^{8} + 8 X^{4} Y^{6} Z^{4} + 2 X^{4} Y^{2} Z^{8} + 443 X^{4} Y^{4} Z^{4} + 2 X^{2} Y^{6} Z^{4} + 54 X^{4} Y^{3} Z^{4} + 3 X^{6} Y^{2} Z^{2} + 8 X^{4} Y^{2} Z^{4} + 36 X^{3} Y^{3} Z^{4} + 9 X^{2} Y^{6} Z^{2} + 21 X^{2} Y^{4} Z^{4} + 6 X^{6} Y Z^{2} + 12 X^{4} Y Z^{4} + 12 X^{2} Y^{3} Z^{4} + 114 X^{4} Y^{2} Z^{2} + 243 X^{2} Y^{4} Z^{2} + 144 X^{2} Y^{2} Z^{4} + 48 X^{2} Y^{3} Z^{2} + 12 X^{2} Y Z^{4} + 1710 X^{2} Y^{2} Z^{2} + 12 X Y^{3} Z^{2} + 18 X^{3} Y Z + 48 X^{2} Y Z^{2} + 18 X Y^{3} Z + 90 X Y^{2} Z^{2} + 324 X^{2} Y Z + 846 X Y^{2} Z + 504 X Y Z^{2} + 792 X Y Z

Algorithm definition

The algorithm ⟨16×22×28:5628⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×11×14:804⟩.

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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