Description of fast matrix multiplication algorithm: ⟨10×16×20:1951⟩

Algorithm type

48 X^{4} Y^{12} Z^{4} + 16 X^{4} Y^{12} Z^{2} + 8 X^{4} Y^{8} Z^{6} + 72 X^{4} Y^{8} Z^{4} + 8 X^{4} Y^{4} Z^{8} + 112 X^{2} Y^{12} Z^{2} + 16 X^{2} Y^{8} Z^{6} + 16 X^{2} Y^{12} Z + 8 X^{4} Y^{4} Z^{6} + 32 X^{2} Y^{8} Z^{4} + 64 X Y^{12} Z + 8 X^{2} Y^{8} Z^{3} + 18 X^{6} Y^{4} Z^{2} + X^{5} Y^{5} Z^{2} + 32 X^{4} Y^{4} Z^{4} + 152 X^{2} Y^{8} Z^{2} + 16 X Y^{8} Z^{3} + X^{5} Y^{4} Z^{2} + 32 X Y^{8} Z^{2} + X^{5} Y^{3} Z^{2} + X^{4} Y^{4} Z^{2} + 8 X^{2} Y^{4} Z^{4} + 80 X Y^{8} Z + 7 X^{5} Y^{2} Z^{2} + 6 X^{3} Y^{5} Z + 8 X^{2} Y^{4} Z^{3} + 4 X^{4} Y^{2} Z^{2} + 19 X^{3} Y^{4} Z + X^{2} Y^{5} Z + 104 X^{2} Y^{4} Z^{2} + 5 X^{3} Y^{3} Z + 3 X^{2} Y^{4} Z + 96 X^{2} Y^{3} Z^{2} + 16 X^{2} Y^{2} Z^{3} + 16 X^{2} Y Z^{4} + 6 X^{3} Y^{2} Z + 35 X^{2} Y^{3} Z + 144 X^{2} Y^{2} Z^{2} + 16 X^{2} Y Z^{3} + 72 X Y^{4} Z + 32 X Y^{2} Z^{3} + 44 X^{3} Y Z + 2 X^{2} Y^{2} Z + 64 X^{2} Y Z^{2} + 128 X Y^{3} Z + 64 X Y^{2} Z^{2} + 5 X^{2} Y Z + 160 X Y^{2} Z + 144 X Y Z

Algorithm definition

The algorithm ⟨10×16×20:1951⟩ is serendipitous tensor product (⟨5×4×4:61⟩ - 2) ⊗ ⟨2×4×5:32⟩ +⟨2×8×5:63⟩.

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.

Back to main table