Description of fast matrix multiplication algorithm: ⟨8×16×25:1949⟩

Algorithm type

48 X^{6} Y^{8} Z^{4} + 8 X^{4} Y^{8} Z^{6} + 8 X^{2} Y^{8} Z^{8} + 16 X^{6} Y^{8} Z^{2} + 72 X^{4} Y^{8} Z^{4} + 16 X^{2} Y^{12} Z^{2} + 8 X^{2} Y^{8} Z^{6} + 16 X^{4} Y^{4} Z^{6} + 32 X^{2} Y^{8} Z^{4} + 16 X Y^{12} Z + 48 X^{3} Y^{8} Z^{2} + 8 X^{2} Y^{8} Z^{3} + 8 X Y^{8} Z^{4} + 64 X^{6} Y^{4} Z^{2} + 32 X^{4} Y^{4} Z^{4} + 16 X^{3} Y^{8} Z + 88 X^{2} Y^{8} Z^{2} + 8 X Y^{8} Z^{3} + 32 X Y^{8} Z^{2} + 72 X^{4} Y^{4} Z^{2} + 16 X Y^{8} Z + 16 X^{2} Y^{4} Z^{3} + 5 X^{4} Y^{2} Z^{2} + 64 X^{3} Y^{4} Z + X^{3} Y^{2} Z^{3} + 96 X^{2} Y^{4} Z^{2} + X^{2} Y^{2} Z^{4} + X^{4} Y^{2} Z + X^{4} Y Z^{2} + 100 X^{3} Y^{2} Z^{2} + 72 X^{2} Y^{4} Z + 16 X^{2} Y^{2} Z^{3} + 16 X Y^{2} Z^{4} + 7 X^{4} Y Z + 33 X^{3} Y^{2} Z + 2 X^{3} Y Z^{2} + X^{2} Y^{3} Z + 152 X^{2} Y^{2} Z^{2} + 34 X^{2} Y Z^{3} + 64 X Y^{4} Z + 17 X Y^{2} Z^{3} + 136 X^{3} Y Z + 65 X^{2} Y Z^{2} + 33 X Y^{3} Z + 66 X Y^{2} Z^{2} + 152 X^{2} Y Z + 34 X Y^{2} Z + 132 X Y Z

Algorithm definition

The algorithm ⟨8×16×25:1949⟩ is serendipitous tensor product (⟨4×4×5:61⟩ - 2) ⊗ ⟨2×4×5:32⟩ +⟨4×4×5:61⟩.

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