Description of fast matrix multiplication algorithm: ⟨16×26×32:7378⟩

Algorithm type

6 X^{8} Y^{16} Z^{8} + 8 X^{8} Y^{12} Z^{8} + 16 X^{8} Y^{10} Z^{8} + 36 X^{8} Y^{8} Z^{8} + 24 X^{4} Y^{16} Z^{4} + 2 X^{4} Y^{8} Z^{12} + 2 X^{8} Y^{6} Z^{8} + 9 X^{4} Y^{14} Z^{4} + 40 X^{4} Y^{12} Z^{4} + 8 X^{4} Y^{8} Z^{8} + 10 X^{4} Y^{4} Z^{12} + X^{2} Y^{14} Z^{4} + 36 X^{4} Y^{10} Z^{4} + 3 X^{2} Y^{14} Z^{2} + 2 X^{6} Y^{8} Z^{2} + 88 X^{4} Y^{8} Z^{4} + 40 X^{4} Y^{4} Z^{8} + 6 X^{2} Y^{8} Z^{6} + 124 X^{4} Y^{6} Z^{4} + 26 X^{2} Y^{8} Z^{4} + 4 X^{2} Y^{6} Z^{6} + 96 X^{4} Y^{5} Z^{4} + 338 X^{4} Y^{4} Z^{4} + 231 X^{2} Y^{8} Z^{2} + 16 X^{2} Y^{6} Z^{4} + 12 X^{2} Y^{4} Z^{6} + 12 X^{4} Y^{3} Z^{4} + 54 X^{2} Y^{7} Z^{2} + 7 X^{6} Y^{2} Z^{2} + 9 X^{4} Y^{2} Z^{4} + 354 X^{2} Y^{6} Z^{2} + 52 X^{2} Y^{4} Z^{4} + 72 X^{2} Y^{2} Z^{6} + 6 X Y^{7} Z^{2} + 216 X^{2} Y^{5} Z^{2} + 18 X Y^{7} Z + 3 X^{4} Y^{2} Z^{2} + 12 X^{3} Y^{4} Z + 410 X^{2} Y^{4} Z^{2} + 296 X^{2} Y^{2} Z^{4} + 36 X Y^{4} Z^{3} + 456 X^{2} Y^{3} Z^{2} + 156 X Y^{4} Z^{2} + 24 X Y^{3} Z^{3} + 851 X^{2} Y^{2} Z^{2} + 522 X Y^{4} Z + 96 X Y^{3} Z^{2} + 42 X^{3} Y Z + 54 X^{2} Y Z^{2} + 684 X Y^{3} Z + 24 X Y^{2} Z^{2} + 72 X Y Z^{3} + 18 X^{2} Y Z + 588 X Y^{2} Z + 336 X Y Z^{2} + 714 X Y Z

Algorithm definition

The algorithm ⟨16×26×32:7378⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨8×13×16:1054⟩.

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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