Description of fast matrix multiplication algorithm: ⟨14×20×28:4571⟩

Algorithm type

19 X^{8} Y^{8} Z^{8} + X^{8} Y^{8} Z^{6} + 8 X^{6} Y^{8} Z^{8} + 8 X^{6} Y^{8} Z^{6} + 2 X^{4} Y^{8} Z^{8} + 5 X^{8} Y^{4} Z^{4} + 15 X^{4} Y^{8} Z^{4} + 11 X^{4} Y^{4} Z^{8} + X^{8} Y^{4} Z^{2} + 2 X^{6} Y^{4} Z^{4} + 6 X^{4} Y^{6} Z^{4} + 4 X^{4} Y^{4} Z^{6} + 5 X^{2} Y^{8} Z^{4} + X^{2} Y^{4} Z^{8} + 310 X^{4} Y^{4} Z^{4} + 6 X^{2} Y^{8} Z^{2} + 6 X^{4} Y^{4} Z^{3} + 48 X^{3} Y^{4} Z^{4} + 6 X^{6} Y^{2} Z^{2} + 2 X^{4} Y^{4} Z^{2} + 48 X^{3} Y^{4} Z^{3} + 12 X^{2} Y^{6} Z^{2} + 40 X^{2} Y^{4} Z^{4} + 21 X^{2} Y^{2} Z^{6} + 60 X^{4} Y^{2} Z^{2} + 192 X^{2} Y^{4} Z^{2} + 150 X^{2} Y^{2} Z^{4} + 6 X^{4} Y^{2} Z + 12 X^{3} Y^{2} Z^{2} + 36 X^{2} Y^{3} Z^{2} + 24 X^{2} Y^{2} Z^{3} + 30 X Y^{4} Z^{2} + 6 X Y^{2} Z^{4} + 1254 X^{2} Y^{2} Z^{2} + 36 X Y^{4} Z + 36 X^{3} Y Z + 12 X^{2} Y^{2} Z + 72 X Y^{3} Z + 168 X Y^{2} Z^{2} + 126 X Y Z^{3} + 180 X^{2} Y Z + 612 X Y^{2} Z + 504 X Y Z^{2} + 468 X Y Z

Algorithm definition

The algorithm ⟨14×20×28:4571⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨7×10×14:653⟩.

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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