Description of fast matrix multiplication algorithm: ⟨10×22×26:3507⟩

Algorithm type

16 X^{10} Y^{10} Z^{8} + 24 X^{10} Y^{10} Z^{4} + 5 X^{8} Y^{8} Z^{8} + 7 X^{6} Y^{8} Z^{6} + X^{6} Y^{6} Z^{8} + X^{6} Y^{6} Z^{6} + X^{4} Y^{8} Z^{6} + 3 X^{8} Y^{4} Z^{4} + 14 X^{4} Y^{8} Z^{4} + 35 X^{4} Y^{6} Z^{6} + X^{8} Y^{2} Z^{4} + 8 X^{6} Y^{4} Z^{4} + 96 X^{5} Y^{5} Z^{4} + X^{4} Y^{8} Z^{2} + 14 X^{4} Y^{6} Z^{4} + 2 X^{2} Y^{10} Z^{2} + 5 X^{2} Y^{8} Z^{4} + 48 X^{2} Y^{6} Z^{6} + 4 X^{6} Y^{4} Z^{2} + 2 X^{6} Y^{2} Z^{4} + 144 X^{5} Y^{5} Z^{2} + 105 X^{4} Y^{4} Z^{4} + 2 X^{4} Y^{2} Z^{6} + 25 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{6} Z^{4} + 3 X^{2} Y^{4} Z^{6} + 6 X^{6} Y^{2} Z^{2} + 5 X^{4} Y^{4} Z^{2} + 42 X^{3} Y^{4} Z^{3} + 6 X^{3} Y^{3} Z^{4} + 38 X^{2} Y^{6} Z^{2} + 4 X^{2} Y^{4} Z^{4} + 6 X^{2} Y^{2} Z^{6} + 6 X^{3} Y^{3} Z^{3} + 6 X^{2} Y^{4} Z^{3} + 27 X^{4} Y^{2} Z^{2} + 121 X^{2} Y^{4} Z^{2} + 210 X^{2} Y^{3} Z^{3} + 9 X^{2} Y^{2} Z^{4} + 6 X^{4} Y Z^{2} + 48 X^{3} Y^{2} Z^{2} + 6 X^{2} Y^{4} Z + 84 X^{2} Y^{3} Z^{2} + 12 X Y^{5} Z + 30 X Y^{4} Z^{2} + 288 X Y^{3} Z^{3} + 24 X^{3} Y^{2} Z + 12 X^{3} Y Z^{2} + 536 X^{2} Y^{2} Z^{2} + 12 X^{2} Y Z^{3} + 150 X Y^{4} Z + 24 X Y^{3} Z^{2} + 18 X Y^{2} Z^{3} + 36 X^{3} Y Z + 30 X^{2} Y^{2} Z + 228 X Y^{3} Z + 24 X Y^{2} Z^{2} + 36 X Y Z^{3} + 54 X^{2} Y Z + 222 X Y^{2} Z + 54 X Y Z^{2} + 516 X Y Z

Algorithm definition

The algorithm ⟨10×22×26:3507⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨5×11×13:501⟩.

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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