Description of fast matrix multiplication algorithm: ⟨20×30×32:10640⟩

Algorithm type

4 X^{12} Y^{8} Z^{8} + 16 X^{2} Y^{24} Z^{2} + 92 X^{8} Y^{8} Z^{8} + 16 X^{4} Y^{16} Z^{4} + 16 X^{4} Y^{4} Z^{16} + 4 X^{6} Y^{12} Z^{4} + 52 X^{12} Y^{4} Z^{4} + 32 X^{8} Y^{4} Z^{8} + 92 X^{4} Y^{12} Z^{4} + 16 X^{8} Y^{4} Z^{4} + 16 X^{4} Y^{4} Z^{8} + 16 X^{2} Y^{6} Z^{8} + 52 X^{6} Y^{6} Z^{2} + 36 X^{6} Y^{4} Z^{4} + 32 X^{4} Y^{6} Z^{4} + 96 X Y^{12} Z + 16 X^{4} Y^{6} Z^{2} + 888 X^{4} Y^{4} Z^{4} + 144 X^{2} Y^{8} Z^{2} + 16 X^{2} Y^{6} Z^{4} + 144 X^{2} Y^{2} Z^{8} + 24 X^{3} Y^{6} Z^{2} + 468 X^{6} Y^{2} Z^{2} + 288 X^{4} Y^{2} Z^{4} + 612 X^{2} Y^{6} Z^{2} + 144 X^{4} Y^{2} Z^{2} + 144 X^{2} Y^{2} Z^{4} + 96 X Y^{3} Z^{4} + 312 X^{3} Y^{3} Z + 72 X^{3} Y^{2} Z^{2} + 192 X^{2} Y^{3} Z^{2} + 96 X^{2} Y^{3} Z + 2196 X^{2} Y^{2} Z^{2} + 288 X Y^{4} Z + 96 X Y^{3} Z^{2} + 288 X Y Z^{4} + 936 X^{3} Y Z + 576 X^{2} Y Z^{2} + 360 X Y^{3} Z + 288 X^{2} Y Z + 288 X Y Z^{2} + 1080 X Y Z

Algorithm definition

The algorithm ⟨20×30×32:10640⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨10×15×16:1520⟩.

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