Description of fast matrix multiplication algorithm: ⟨16×20×26:4802⟩

Algorithm type

26 X^{8} Y^{8} Z^{8} + 9 X^{8} Y^{8} Z^{6} + X^{8} Y^{6} Z^{6} + 2 X^{4} Y^{8} Z^{6} + 6 X^{8} Y^{4} Z^{4} + 19 X^{4} Y^{8} Z^{4} + 13 X^{4} Y^{4} Z^{8} + 2 X^{8} Y^{4} Z^{2} + 3 X^{4} Y^{4} Z^{6} + X^{4} Y^{6} Z^{2} + 375 X^{4} Y^{4} Z^{4} + 54 X^{4} Y^{4} Z^{3} + 3 X^{6} Y^{2} Z^{2} + 7 X^{4} Y^{4} Z^{2} + 6 X^{4} Y^{3} Z^{3} + 6 X^{4} Y^{2} Z^{4} + 3 X^{2} Y^{6} Z^{2} + 9 X^{2} Y^{4} Z^{4} + 12 X^{2} Y^{4} Z^{3} + 81 X^{4} Y^{2} Z^{2} + 222 X^{2} Y^{4} Z^{2} + 168 X^{2} Y^{2} Z^{4} + 12 X^{4} Y^{2} Z + 18 X^{2} Y^{2} Z^{3} + 6 X^{2} Y^{3} Z + 1428 X^{2} Y^{2} Z^{2} + 18 X^{3} Y Z + 42 X^{2} Y^{2} Z + 36 X^{2} Y Z^{2} + 18 X Y^{3} Z + 54 X Y^{2} Z^{2} + 270 X^{2} Y Z + 648 X Y^{2} Z + 540 X Y Z^{2} + 684 X Y Z

Algorithm definition

The algorithm ⟨16×20×26:4802⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×10×13:686⟩.

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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