Description of fast matrix multiplication algorithm: ⟨14×15×28:3465⟩

Algorithm type

12 X^{4} Y^{10} Z^{6} + 30 X^{4} Y^{10} Z^{4} + 12 X^{4} Y^{8} Z^{6} + 12 X^{4} Y^{10} Z^{2} + 30 X^{4} Y^{8} Z^{4} + 6 X^{4} Y^{6} Z^{6} + 36 X^{2} Y^{10} Z^{3} + 4 X^{2} Y^{5} Z^{8} + 12 X^{4} Y^{8} Z^{2} + 15 X^{4} Y^{6} Z^{4} + 60 X^{4} Y^{4} Z^{6} + 90 X^{2} Y^{10} Z^{2} + 4 X^{2} Y^{4} Z^{8} + 36 X^{2} Y^{10} Z + 42 X^{2} Y^{8} Z^{3} + 24 X^{2} Y^{5} Z^{6} + 2 X^{2} Y^{3} Z^{8} + 6 X^{4} Y^{6} Z^{2} + 150 X^{4} Y^{4} Z^{4} + 6 X^{4} Y^{2} Z^{6} + 105 X^{2} Y^{8} Z^{2} + 24 X^{2} Y^{4} Z^{6} + 20 X^{2} Y^{2} Z^{8} + 42 X^{2} Y^{8} Z + 24 X^{2} Y^{6} Z^{3} + 24 X^{2} Y^{5} Z^{4} + 12 X^{2} Y^{3} Z^{6} + 2 X^{2} Y Z^{8} + 60 X^{4} Y^{4} Z^{2} + 15 X^{4} Y^{2} Z^{4} + 60 X^{2} Y^{6} Z^{2} + 24 X^{2} Y^{4} Z^{4} + 132 X^{2} Y^{2} Z^{6} + 12 X Y^{5} Z^{4} + 4 X Y Z^{8} + 24 X^{2} Y^{6} Z + 20 X^{2} Y^{5} Z^{2} + 36 X^{2} Y^{4} Z^{3} + 12 X^{2} Y^{3} Z^{4} + 12 X^{2} Y Z^{6} + 72 X Y^{5} Z^{3} + 14 X Y^{4} Z^{4} + 6 X^{4} Y^{2} Z^{2} + 110 X^{2} Y^{4} Z^{2} + 150 X^{2} Y^{2} Z^{4} + 72 X Y^{5} Z^{2} + 84 X Y^{4} Z^{3} + 8 X Y^{3} Z^{4} + 24 X Y Z^{6} + 36 X^{2} Y^{4} Z + 10 X^{2} Y^{3} Z^{2} + 84 X^{2} Y^{2} Z^{3} + 12 X^{2} Y Z^{4} + 60 X Y^{5} Z + 84 X Y^{4} Z^{2} + 48 X Y^{3} Z^{3} + 12 X Y^{2} Z^{4} + 322 X^{2} Y^{2} Z^{2} + 70 X Y^{4} Z + 48 X Y^{3} Z^{2} + 72 X Y^{2} Z^{3} + 52 X Y Z^{4} + 84 X^{2} Y^{2} Z + 10 X^{2} Y Z^{2} + 40 X Y^{3} Z + 72 X Y^{2} Z^{2} + 168 X Y Z^{3} + 60 X Y^{2} Z + 188 X Y Z^{2} + 140 X Y Z

Algorithm definition

The algorithm ⟨14×15×28:3465⟩ is the (Kronecker) tensor product of ⟨2×5×7:55⟩ with ⟨7×3×4:63⟩.

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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